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UBC Theses and Dissertations

The evolutionary ecology of hybridization Thompson, Ken A. 2021

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The evolutionary ecology of hybridizationbyKen A. ThompsonB.Sc., The University of Guelph, 2014M.Sc., The University of Toronto, 2016A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinThe Faculty of Graduate and Postdoctoral Studies(Zoology)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)May 2021© Ken A. Thompson, 2021The following individuals certify that they have read, and recommend to the Faculty of Graduate and Postdoctoral Studies for acceptance, the dissertation entitled:  The evolutionary ecology of hybridization  submitted by Ken A. Thompson  in partial fulfillment of the requirements for the degree of Doctor of Philosphy in Zoology  Examining Committee: Dolph Schluter, Killam Professor, Zoology, UBC Supervisor  Darren Irwin, Professor, Zoology, UBC Supervisory Committee Member  Daniel Matute, Associate Professor, Biology, University of North Carolina at Chapel Hil  External Examiner Judith Mank, Professor, Zoology, UBC University Examiner Jeannette Whitton, Associate Professor, Botany, UBC University Examiner  Additional Supervisory Committee Members: Sarah Otto, Professor, Zoology, UBC Supervisory Committee Member Loren Rieseberg, Professor, Botany, UBC Supervisory Committee Member        ii AbstractHybridization is the process that mediates gene flow between sexually reproducing lineages. As such, thefactors that determine the fitness of hybrids are critically important for speciation. Although hybridiza-tion between natural populations occurs in an explicitly ecological context, where hybrids must competefor resources and attract mates under prevailing ecological conditions, little attention has been paid to themechanisms that mediate the ecological performance of hybrids. In Chapter 2, I expand upon existingmodels of speciation and find that standing variation improves hybrid fitness when parents adapt to similarenvironments, but reduces hybrid fitness when parents adapt to different environments. Chapter 3 system-atically reviews the literature to report that F1 hybrids are often quite mismatched for divergent parentaltraits, and also uses a field experiment with sunflowers to show that this mismatch reduces fitness via seedcount. Chapter 4 also uses data from the literature to demonstrate that divergent adaptation proceeds viapleiotropic alleles. In Chapter 5, I measure morphological traits in the lab to illustrate that the magnitude oftrait ‘mismatch’ in hybrids increases with the phenotypic distance between cross parents. Chapter 6 uses apond experiment hybridizing ’parallel’ ecotypes and reports that hybridization after parallel evolution resultsboth in heterosis and hybrid breakdown. Finally, Chapter 7 uses DNA sequence data to illustrate that thegenetic signature of hybrid incompatibilities - excess heterozygosity - is greater when stickleback hybridsare raised in ponds than when they are raised in aquaria. In sum, my thesis demonstrates that ecologicalselection against hybrids can result from rapid adaptation from standing variation, from mismatched traitcombinations that evolve somewhat predictably, and can have a detectable genetic signature. Hybridizationafter parallel evolution, at least in stickleback, leads to relatively equal measures of hybrid breakdown andheterosis. Ecologically-mediated natural and sexual selection can clearly play a large role in mediating thefitness of hybrids - future work should aim to establish the importance of these processes for speciation morebroadly.iiiLay SummaryHybridization—the generation of viable offspring following mating between different species—is increas-ingly recognized as being common. The fitness of hybrids, that is whether they can successfully survive andreproduce, is key for maintaining the parent species’ distinctness. If hybrids readily survive and interbreed,this can cause the parent species to collapse into a hybrid swarm. In this thesis I generate novel hypotheses,syntheses, and results about how ecology acts to determine hybrid fitness. The first half of my thesis usestheory and synthesizes data to identify generalities about hybridization. The second half of my thesis usesoriginal experiments with threespine stickleback fish to test these predictions. In sum, my thesis advances ourunderstanding of the mechanisms through which ecological processes mediate the fitness of hybrids—what Icall the ‘evolutionary ecology’ of hybridization—and contributes to the larger body of work on mechanismsof speciation.ivPrefaceAlthough the bulk of chapters are written with co-authors, I use the first-person singular pronoun, ‘I’ (and‘my’), throughout this thesis so that the language is consistent throughout. It can probably not be overem-phasized that this thesis is largely the result of collaboration and my use of the first-person singular shouldin no way be interpreted as a dismissal of this fact.A version of Chapter 2 has been published as Thompson, K.A., Osmond, M.M., and Schluter, D. 2019.Parallel genetic evolution and speciation from standing variation. Evolution Letters. 3(2): 129–141. Theproject was conceived by me and I refined the numerical and analytical approaches that were largely imple-mented by M. Osmond. I wrote the manuscript, analyzed, and plotted the data with regular input from M.Osmond. All co-authors contributed to manuscript edits.A version of Chapter 3 has been published as Thompson, K.A., Urquhart-Cronish, M., Whitney, K.D.,Rieseberg, L.H., and Schluter, D. Patterns, predictors, and consequences of dominance in hybrids. TheAmerican Naturalist 197(3) (pagination forthcoming). I conceived of the quantitative review and collecteddata for it with M. Urquhart-Cronish. K. Whitney had the idea to test our hypothesis with the sunflower dataand collected and previously published the dataset. L. Rieseberg and D. Schluter provided input on analysisand study design, and all authors contributed to manuscript edits.A version of Chapter 4 has been published as Thompson, K.A. 2020. Experimental hybridization studiessuggest that pleiotropic alleles commonly underlie adaptive divergence between natural populations. TheAmerican Naturalist 196(1): E16–E22. The paper is sole-authored—I conceived the idea, analyzed the data,and wrote the paper. The data were collected as a part of the literature search in Chapter 3.Chapter 5 is in preparation for submission with co-primary author A. Chhina and senior author D.Schluter. I conceived of the idea with input from D. Schluter, and conducted the fieldwork and most ofthe lab work. A. Chhina and I measured fish, analyzed data, and co-wrote the paper which had later inputfrom D. Schluter.Chapter 6 is in preparation for submission with co-author D. Schluter. The project was conceived by meand developed with input from D. Schluter. I conducted the field and lab work, and collected the data. Ianalyzed the data and wrote the first draft of the paper with input from D. Schluter.Chapter 7 is in preparation for submission with co-authors C.L. Peichel, D. Schluter, D. Rennison, A.Albert, T. Vines, A. Greenwood, A. Wark, and M. Schumer. I conceived of the idea, curated data collec-tion, analyzed the data, and wrote the paper with input from C. Peichel, D. Schluter, and M. Schumer. A.Greenwood, A. Wark and C. Peichel generated genetic data for the Paxton Lake aquaria fish. A. Albert andT. Vines generated genetic data for the Priest Lake aquaria fish. D. Rennison contributed additional data forpond-raised Paxton Lake hybrids.vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv1 General Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Speciation and the role of hybrid fitness . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Evidence and mechanisms of extrinsic post-zygotic isolation . . . . . . . . . . . . . . . . . 21.3 Key areas requiring research and their motivation . . . . . . . . . . . . . . . . . . . . . . . 31.4 Overview of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.4.1 Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.4.2 Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.4.3 Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.4.4 Chapter 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.4.5 Chapter 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.4.6 Chapter 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.5 Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 Parallel genetic evolution and speciation from standing variation . . . . . . . . . . . . . . . 92.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.2.1 Genotype to phenotype . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2.2 Life-cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2.3 Adaptation to a new environment . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.2.4 Quantification of genetic parallelism and hybrid segregation variance & fitness . . . 132.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15vi2.3.1 Genetic parallelism and phenotypic segregation variance . . . . . . . . . . . . . . . 152.3.2 Hybrid fitness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.4.1 Key predictions and possible tests . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.4.2 Alternative sources of standing variation . . . . . . . . . . . . . . . . . . . . . . . 222.4.3 Possible extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.4.4 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 Patterns, predictors, and consequences of dominance in hybrids . . . . . . . . . . . . . . . . 243.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.2 I: Patterns & predictors of dominance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.2.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.2.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.3 II: Fitness consequences of parent-bias and mismatch in recombinant sunflowers . . . . . . 313.3.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343.4.1 Genetic underpinnings of dominance and mismatch . . . . . . . . . . . . . . . . . 343.4.2 Patterns & predictors of dominance . . . . . . . . . . . . . . . . . . . . . . . . . . 353.4.3 Fitness consequences of mismatch . . . . . . . . . . . . . . . . . . . . . . . . . . 363.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374 Experimental hybridization studies suggest that pleiotropic alleles commonly underlie adaptivedivergence between natural populations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425 Adaptive divergence and the evolution of hybrid trait mismatch in threespine stickleback . . 455.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475.2.1 Study system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475.2.2 Fish collection and husbandry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475.2.3 Phenotype measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495.2.4 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535.3.1 Patterns of phenotypic divergence among populations . . . . . . . . . . . . . . . . 535.3.2 Evolution of trait mismatch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535.3.3 Underlying causes of mismatch . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56vii5.3.4 Patterns of dominance in hybrids . . . . . . . . . . . . . . . . . . . . . . . . . . . 585.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 595.4.1 Causes of divergence-mismatch relationship . . . . . . . . . . . . . . . . . . . . . 605.4.2 Causes of recessivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 605.4.3 Evolution of dominance for armour . . . . . . . . . . . . . . . . . . . . . . . . . . 615.4.4 Similarities to patterns of ‘intrinsic’ isolation . . . . . . . . . . . . . . . . . . . . . 625.4.5 Caveats and future directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 626 Fitness consequences of hybridization after parallel evolution in threespine stickleback . . . 646.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 646.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 666.2.1 Experimental crosses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 666.2.2 Pond experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 666.2.3 Lab experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 676.2.4 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 686.2.5 Estimating fitness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 696.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 696.3.1 Patterns of survival and growth in ponds . . . . . . . . . . . . . . . . . . . . . . . 696.3.2 Causes of fitness differences among groups in ponds . . . . . . . . . . . . . . . . . 726.3.3 Patterns of growth and survival in aquaria . . . . . . . . . . . . . . . . . . . . . . . 736.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 746.4.1 Mechanisms underlying fitness differences between parents and hybrid generationsin ponds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 756.4.2 Variation in hybrid fitness among crosses . . . . . . . . . . . . . . . . . . . . . . . 766.4.3 Caveats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 766.4.4 Progress toward speciation via parallel natural selection? . . . . . . . . . . . . . . 777 Genetic evidence for environment-specific hybrid incompatibilities in threespine stickleback 787.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 787.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 807.2.1 Data sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 807.2.2 Marker filtering and estimating heterozygosity . . . . . . . . . . . . . . . . . . . . 827.2.3 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 837.2.4 Heuristic model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 837.3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 857.3.1 Patterns of excess heterozygosity . . . . . . . . . . . . . . . . . . . . . . . . . . . 857.3.2 Heuristic model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 867.3.3 Alternative explanations for excess heterozygosity . . . . . . . . . . . . . . . . . . 867.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89viii8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 918.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 918.2 Areas requiring research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 918.2.1 Mechanisms underlying ecological incompatibilities . . . . . . . . . . . . . . . . . 928.2.2 Theoretical importance of ecological incompatibilities . . . . . . . . . . . . . . . . 938.3 A proposal to slightly refine the language of speciation . . . . . . . . . . . . . . . . . . . . 94Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116A Appendix for Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117A.1 Geometric basis for rapid loss of parallelism . . . . . . . . . . . . . . . . . . . . . . . . . 117A.2 Supplementary figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119B Appendix for Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140B.1 Supplementary methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140B.1.1 Search strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140B.1.2 Evaluation of studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141B.1.3 Data collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141B.1.4 Estimating genetic divergence and divergence time . . . . . . . . . . . . . . . . . . 142B.1.5 Phylogenetic signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142B.1.6 Field experiment with sunflowers . . . . . . . . . . . . . . . . . . . . . . . . . . . 143B.2 Supplementary Tables & Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144C Appendix for Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162C.1 Supplementary figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165D Appendix for Chapter 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171D.1.1 Supplementary methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171D.2 Supplementary Tables & Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173E Appendix for Chapter 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182E.1 Supplementary methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182E.1.1 Experimental animals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182E.1.2 Coded wire tagging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183E.1.3 Estimating fitness via fecundity and overwinter survival . . . . . . . . . . . . . . . 183E.2 Supplementary Tables & Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185F Appendix for Chapter 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192F.1 Supplementary Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192ixList of Tables2.1 Description of parameters and parameter values in parental populations for simulations pre-sented in the main text . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.1 Hypothetical examples of possible F1 trait values, and corresponding values for cross meandunivariate, dparent-bias, and dmismatch (parent phenotypes are scaled to [0, 0] and [1, 1]). . . . . . 267.1 Summary of data sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81B.1 Description of sunflower traits used to quantify parent-bias and mismatch . . . . . . . . . . 145B.2 Mean ± SE (n) for parent species and BC1 hybrids at the common garden site. . . . . . . . . 146C.1 Results with alternative choices for data filtering and binning . . . . . . . . . . . . . . . . . 168E.1 Summary of fish numbers and survival (re-capture numbers) for the 2020 pond experiment . 185E.2 Fitness components and relative fitness estimates for cross types within species . . . . . . . 186xList of Figures1.1 Visual overview of underdominance and hybrid incompatibilities on ‘intrinsic’ fitness land-scapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.1 Visual overview of simulations and concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2 Genetic parallelism and phenotypic segregation variance . . . . . . . . . . . . . . . . . . . 162.3 The relationship between trait dimensionality (m) and genetic parallelism . . . . . . . . . . 172.4 The effect of standing variation on mean hybrid fitness. . . . . . . . . . . . . . . . . . . . . 182.5 The effect of standing variation on the distribution of hybrid phenotypes . . . . . . . . . . . 192.6 Properties of alleles fixed during adaptation . . . . . . . . . . . . . . . . . . . . . . . . . . 213.1 Visual overview of how two-dimensional dominance metrics were calculated . . . . . . . . 273.2 Patterns of dominance in F1 hybrids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.3 Effect of parent-bias and mismatch on fitness in H. annuus× H. debilis BC1 hybrid sunflow-ers growing in the field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334.1 Overview of adaptation with pleiotropic alleles and theoretical prediction. . . . . . . . . . . 414.2 Scatterplot depicting the relationship between phenotypic divergence in parents (statisticallydivergent traits) and segregation variance in hybrids (statistically indistinguishable traits). . . 425.1 Overview of sampling locations and trait measurements . . . . . . . . . . . . . . . . . . . . 485.2 Visual overview of mismatch calculation and observed mismatch results . . . . . . . . . . . 555.3 Dominance is the primary driver of mismatch in F1 hybrids, while variance is the primarydriver of mismatch in F2s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565.4 F2, but not F1, hybrid phenotypic variation increases with the magnitude of phenotypic di-vergence between parents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 575.5 Dominance of the freshwater phenotype in F1 hybrids among traits and populations . . . . . 596.1 Photograph of the study system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 666.2 Survival and growth of pure species and their F1 & F2 hybrids in the experimental ponds . . 706.3 Variation in survival and growth among cross types and crosses in the experimental ponds . . 726.4 Inferring the broad mechanisms underlying patterns of hybrid fitness . . . . . . . . . . . . . 736.5 Growth and survival in aquaria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74xi7.1 Results from simulations illustrating an ecological mechanism underlying the heterozygosity-incompatibility relationship in F2 hybrids . . . . . . . . . . . . . . . . . . . . . . . . . . . 797.2 Patterns of heterozygosity in stickleback hybrids across environments . . . . . . . . . . . . 877.3 Heuristic two-way incompatibility model to illustrate sufficient selection strengths to gener-ate excess heterozygosity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 888.1 A possible ecological incompatibility in monkeyflowers . . . . . . . . . . . . . . . . . . . . 948.2 Fitness effects of incompatibility loci vary across environments and genetic backgrounds . . 96A.1 Genetic parallelism across the continuum of parallel to divergent natural selection (N = 100) 120A.2 Genetic parallelism across the continuum of parallel to divergent natural selection (N = 1000) 121A.3 Genetic parallelism across the continuum of parallel to divergent natural selection (N = 5000) 122A.4 Effect of standing genetic variation on hybrid fitness across the continuum of parallel todivergent natural selection (N = 100) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123A.5 Effect of standing genetic variation on hybrid fitness across the continuum of parallel todivergent natural selection (N = 1000). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124A.6 Effect of standing genetic variation on hybrid fitness across the continuum of parallel todivergent natural selection (N = 5000). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125A.7 Properties of fixed mutations under a variety of parameter combinations (N = 1000). . . . . 126A.8 Simulations under various fitness functions. . . . . . . . . . . . . . . . . . . . . . . . . . . 127A.9 Mutation-selection balance and mutation effect sizes in ancestral populations. . . . . . . . . 128A.10 Mutation-selection balance and mutation effect sizes in ancestral populations under strongerselection (σanc = 1). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129A.11 The effects of standing genetic variation on genetic parallelism and phenotypic segregationvariance in hybrids under parallel and divergent natural selection. . . . . . . . . . . . . . . . 130A.12 Effect of standing variation on the pace of adaptation and attainment of mutation-selection-drift balance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131A.13 Relationship between genetic parallelism and (A) segregation variance and (B) expectedheterozygosity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132A.14 Alternative presentation of simulation results across environments: distance between optima(δ). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133A.15 The effect of population size on the rate of divergence between populations due to drift. . . . 134A.16 Effect of dimensionality on net segregation variance. . . . . . . . . . . . . . . . . . . . . . 135A.17 Fraction of overlap of beneficial mutations with parallel selection (θ = 0°) but unequal dis-tance (d1 6= d2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136A.18 The effect of standing genetic variation (SGV) on relative maximum hybrid fitness acrossenvironments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137A.19 The relationship between segregation variance and θ for different dimensionalities. . . . . . 138A.20 Cartoon illustration of why divergence among populations does not affect whether an alleleis beneficial in both of them. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139xiiB.1 Relationship between SD divergence between parents (SDs in units of smaller parent value)and P-value of t-test evaluating whether parent phenotypes are statistically distinguishable . 144B.2 Example visualisations of four cases of bivariate trait expression . . . . . . . . . . . . . . . 147B.3 Phylogeny of all species used in this study . . . . . . . . . . . . . . . . . . . . . . . . . . . 148B.4 dunivariate across all traits in the datasets (n = 1046 traits) . . . . . . . . . . . . . . . . . . . . 149B.5 Summary of cross median dominance metrics with each cross contributing a single value . . 150B.6 Expected patterns based on sampling error alone (from simulations). . . . . . . . . . . . . . 151B.7 There are no differences (all P > 0.25) in any dominance metrics between intraspecific andinterspecific crosses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152B.8 No association between any dominance metrics and genetic distance between the parents . . 153B.9 No differences in dominance between plants and animals. . . . . . . . . . . . . . . . . . . . 154B.10 Parental phenotypic variation (CV) has significant effects on dominance in hybrids . . . . . 155B.11 The relationship between trait type and univariate dominance (dunivariate . . . . . . . . . . . 156B.12 Relationship between mean pairwise parent-bias and mismatch dominance in systematic re-view and sunflower data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157B.13 Distribution of pairwise trait correlations in the sunflower data (BC1s only) . . . . . . . . . 158B.14 Distribution of partial regression coefficients in multiple regression analyses . . . . . . . . . 159B.15 Phenotype and fitness distribution for a trait pair with substantial mismatch consequences inBC1 hybrid sunflowers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160B.16 Photograph of sunflower experiment at the Lady Bird Johnson Wildflower Center, in Austin,Texas, USA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161C.1 Simulation results to illustrate theoretical prediction . . . . . . . . . . . . . . . . . . . . . . 166C.2 Diagnostics of the linear model testing the main hypothesis . . . . . . . . . . . . . . . . . . 167C.3 Segregation variance in non-divergent traits is not predicted by divergence in those traits . . 169C.4 All available evidence suggests that phenotypic divergence between parents is uncorrelatedwith their divergence time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170D.1 Repeatability data for all measured traits . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173D.2 Summary of pairwise trait correlations in F2 hybrids . . . . . . . . . . . . . . . . . . . . . . 174D.3 Freshwater divergence from the anadromous ancestor . . . . . . . . . . . . . . . . . . . . . 175D.4 Phenotypic divergence between parents is positively associated with the number of traits thatdiffer between them, as well as the number of possible pairwise mismatches . . . . . . . . . 176D.5 Examples of pairwise divergence:mismatch regressions . . . . . . . . . . . . . . . . . . . . 177D.6 Visualization of pairwise mismatch in empirical data . . . . . . . . . . . . . . . . . . . . . 178D.7 Dominance patterns in F2 hybrids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179D.8 Variation in dominance for lateral plate count does not impact the mismatch-divergence re-lationship . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180D.9 The number of mismatched trait pairs ‘snowballs’ with the magnitude of phenotypic diver-gence between parents, but only in F1 hybrids . . . . . . . . . . . . . . . . . . . . . . . . . 181xiiiE.1 Relationship between initial and final mass in the 2020 pond experiment . . . . . . . . . . . 187E.2 Relationship between the number of days in pond and final mass in the 2020 pond experiment 188E.3 Fitness components with the two parent populations plotted separately . . . . . . . . . . . . 189E.4 Relationship between mass and standard length for fish collected from ponds . . . . . . . . 190E.5 Relationship between standard length and fecundity in previously published sticklebackpond experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191F.1 Heterozygosity does not differ between F2 and F3 hybrids . . . . . . . . . . . . . . . . . . . 192F.2 Heterozygosity does not differ between studies involving Paxton Lake benthic × limnetichybrids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193F.3 Estimates of excess heterozygosity for individuals and loci across ‘replicates’. . . . . . . . . 194F.4 Test of main hypothesis using ‘observed’ heterozygosity rather than excess heterozygosity . 195F.5 de Finetti ternary diagrams for genotyped individuals in each of the bi-parental crosses . . . 196F.6 de Finetti ternary diagrams for genotyped loci in each of the bi-parental crosses . . . . . . . 197F.7 No relationship between individual mean heterozygosity and growth (standard length) in theaquarium-raised biparental benthic-limnetic F2 hybrids . . . . . . . . . . . . . . . . . . . . 198F.8 No relationship between estimated directional selection at each locus and its mean excessheterozygosity in ponds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199xivAcknowledgementsThis thesis would not have come together without the friendship and support of many. It has been great beinga part of the Biodiversity Research Centre. There are so many people to thank and although it may proveunwise I will not list names here for fear of leaving someone deserving out. I cherish the friendship of the skitmakers (long live!), the coffee drinkers, the discussion group presenters, the B.E.E.R.S. and retreat goers,the lunch eaters, the KUBB tossers, and the rental accommodation sharers. My supervisory committee—Darren Irwin, Loren Rieseberg, Sally Otto, and Rick Taylor—were incredibly generous with their time andinsightful. Thanks also to my examining committee members, Judith Mank and Jeannette Whitton. Mysupervisor, Dolph Schluter, provided invaluable guidance and support throughout my degree. Most of mythesis chapters were collaborations, and I am grateful to have had the opportunity to work with so manygreat scientists. Members of the Schluter lab, from undergraduates to post-docs, have provided consistentfeedback on my science and support in field and lab. I have had the great pleasure to work with severalcollaborators on my thesis chapters and am immensly grateful to them all. Patrick Tamkee and Eric Lotto,the inSEAS core staff, provided outstanding logistical support without which my ichthyological pursuitswould surely have failed. Thanks to NSERC, UBC, and the Zoology Department for financial support. Myfamily encouraged me to pursue my interests wherever they made lead and gave me unconditional support allthe way through. The companionship of my partner, Mackenzie, has been indescribably valuable throughoutmy time in Vancouver and will no doubt continue to be into the future.xvChapter 1General Introduction1.1 Speciation and the role of hybrid fitnessSpeciation—the evolution of reproductive isolating barriers between diverging lineages (Coyne and Orr,2004)—is the process largely responsible for maintaining the wondrous diversity of life. If not for theseevolved isolating barriers, discontinuities could never persist between lineages. Consider the cedars and firsthat grow on and near the UBC campus. Although plenty of cedar pollen might find its way onto the ovulesof the firs, for various reasons no hybrid seeds are produced from this pollen and the two species remaindistinct. With such extreme barriers it is easy to see how these lineages remain distinct: there is simply nopossible way for cedar genes to introgress into fir, or vice-versa.Clearly, complete gametic incompatibility is sufficient for speciation. Importantly, however, it is not nec-essary because plenty of species stably coexist in sympatry despite complete inter-fertility. For example, thethreespine stickleback (Gasterosteus aculeatus L.) species pairs persist in lakes in coastal British Columbia,Canada, even though they produce perfectly vigorous hybrids in the lab (McPhail, 1984, 1992; Hatfield andSchluter, 1999). Hybrid zones, where hybrids are produced and exist in a continuum from one species toanother (Barton and Hewitt, 1985), form between thousands of populations that nevertheless continue topersist as largely distinct lineages. Sympatric species that produce viable and fertile hybrids in benign (e.g.,laboratory) environments can be maintained if hybrids cannot survive and reproduce under the prevailingecological conditions due to a maladapted phenotype—an isolating barrier referred to as ‘extrinsic postzy-gotic isolation’. Recent theory suggests that postzygotic barriers can be more effective at preventing geneflow than assortative mating in hybrid zones (i.e., pre-mating isolation; Irwin 2020). In many cases wherespecies do not hybridize as a result of assortative mating, this is due to the process of reinforcement, wherebyassortative mating evolves as a direct result of hybrids being unfit (McKinnon and Rundle, 2002; Hopkins,2013). Thus, even when pre-mating isolation is apparent it might be an adaptive product of selection againsthybridization.Ecological (natural or sexual) selection against hybrids can be a sufficiently strong barrier to maintainthe distinctiveness of sympatric reproductively isolated lineages in nature. Yet, we still lack a general un-derstanding of how important extrinsic post-zygotic isolation is for speciation and how it evolves. If hybridstended to perform just as well as parents in the field, how many fewer species would there be? Part ofthe reason for this is that we do not as a field know much about the mechanisms through which extrinsicpost-zygotic isolation operates. The goal of this thesis is to generate hypotheses, document patterns, andtest mechanisms of ecologically-mediated hybrid fitness in the field. In this brief introduction, I summariseprogress to date and key gaps, then conclude with an overview of what follows in the thesis.11.2 Evidence and mechanisms of extrinsic post-zygotic isolationMuch of what is known about post-zygotic isolation, especially its genetic basis, pertains to what are referredto as ‘intrinsic’ post-zygotic isolating barriers. Intrinsic incompatibilities are defined as those that affect theviability and/or fertility of individual hybrids possessing them, and is typically measured in the lab. Thetheory of hybrid incompatibilities, arrived at independently by Bateson (1909), Dobzhansky (1937), andMuller (1942), solved an important problem in speciation research. That is: how do genetic variants thatkill or sterilize intermediate forms evolve? Such ‘underdominant’ alleles cannot readily evolve becauseintermediate steps are inviable. The key intellectual advance was that the authors realized that this processwas much easier when two (or more) loci are involved and when the incompatibility is caused by theirinteraction (Fig. 1.1B). With the theory of hybrid incompatibilities in tow, it was no longer a mystery howevolution could proceed in a manner that rendered some hybrids inviable or sterile.underdominancelandscape aincompatibilitylandscape bbbBbBBaa Aa AAgenotype at locus Agenotype at locus BbbBbBBaa Aa AAgenotype at locus Agenotype at locus BFigure 1.1: Visual overview of underdominance and hybrid incompatibilities on ‘intrinsic’ fitness land-scapes. Both panels are fitness landscapes for loci (yellow is high fitness, purple is intermediate, and blackis low). Panel (a) shows underdominance, wherein heterozygosity is disadvantageous. In this case, fitnesscan be predicted from heterozygosity alone. Panel (b) shows a case of hybrid incompatibilities, where fitnessis affected by the interaction of alleles at two loci. In this case, the (big) B allele is incompatible with the(small) a allele.In the late 1990s and early 2000s, the study of ‘ecological speciation’ came to prominence (Schluter,1996, 2000, 2001; Rundle, 2002; Nosil, 2012; Ostevik et al., 2012). In large part due to this burgeoning field,evolutionary biologists became convinced that adaptation to prevailing ecological conditions could causedivergent lineages to produce hybrids with low fitness due to their poor fit under these conditions (Coyneand Orr, 2004; Langerhans and Riesch, 2013). All throughout this work, substantial progress was being madein generating and testing predictions about the genetic basis of intrinsic post-zygotic isolation (Orr, 1995;Presgraves, 2003, 2010; Matute et al., 2010; Moyle and Nakazato, 2010; Corbett-Detig et al., 2013; Wanget al., 2015), but little in the way of mechanistic connection was made between this work and those studyingecological speciation (also called ‘speciation-by-adaptation’). That is, although hybrid incompatibilities havecome to predominate the theory of intrinsic isolating barriers, they have not historically been consideredimportant for extrinsic isolation.2In recent years, however, researchers have begun to identify how interactions among divergent genes—hybrid incompatibilities—can affect fitness in an ecological context. Typically, this work has been donelooking at the interactions of divergent phenotypes. Vinšálková and Gvoždík (2007) found that newt hy-brids had maternally inherited temperature preferences but were morphologically intermediate, potentiallyrendering them unfit in their preferred thermal niche. Matsubayashi et al. (2010) reviewed the literature andfound that hybrids between several divergent phytophagous insect species often have better performance onone parent species’ native host plant but have a genetic predisposition to be attracted to the other species’,potentially reducing their fitness or that of their offspring. Arnegard et al. (2014) examined the relationshipbetween trait values and fitness in F2 hybrids between divergent stickleback species and found that indi-viduals with mismatched jaw-traits performed worse than fish whose traits were relatively matched. Keagyet al. (2016) made similar crosses to Arnegard et al. (2014) and found that trait interactions governed maleattractiveness to females. Cooper et al. (2018) found that natural Drosophila hybrids were attracted to xerichabitats like one of their parents but had low desiccation tolerance, similar to the other. Other studies havedocumented that more fitness conferred via more ecologically-relevant traits, like the ability to locate food(Turissini et al., 2017), declines with the genetic distance between parents, similar to ‘intrinsic’ postzygoticbarriers in other groups (Coyne and Orr, 1989, 1997). Collectively, these studies imply that interactionsamong divergent loci, acting through trait ‘mismatch’ wherein hybrids express maladaptive combinations oftraits, can be a critical determinant of the fitness of inter-population hybrids in natural environments.Although the same general process—epistasis among alleles of different ancestry—can in principle un-derlie both intrinsic and extrinsic post-zygotic isolation, there are several key differences that might differen-tiate intrinsic and extrinsic incompatibilities. For brevity, I will list only two here. First, the fitness landscapeof individual incompatibility loci likely has much shallower topography when these incompatibilities act viaecological selection (i.e., the fitness of the most fit ancestry combination is not much higher than that of theleast fit). This is because individual extrinsic incompatibilities likely reduce fitness (i.e., survival probabilityand fecundity) by smaller magnitudes than intrinsic incompatibilities and thus, the ‘problem’ of fitness-valley crossing (Dobzhansky, 1937; Osmond and Otto, 2015) might cease to be a problem at all. Second,fitness landscapes of extrinsic incompatibilities are expected to be extremely context-dependent. Whetheror not a pair of alleles is incompatible could readily vary across years, seasons, and community contexts.These differences render it difficult to evaluate the extent to which our theoretical and empirical knowledgeof intrinsic post-zygotic isolating barriers translates to the study of extrinsic isolation. Much work remains toassess the prevalence, phenotypic mechanisms, and effect sizes of ecological hybrid incompatibilities. Thisthesis aims to take several steps forward on these fronts.1.3 Key areas requiring research and their motivationAs discussed above, recent studies have shown that divergent alleles can interact to determine hybrid fit-ness in ecologically-relevant contexts. However, it does not tell us much about the importance of theseprocesses for the larger questions we care about such as their role in speciation. Said another way, if notfor ecologically-mediated hybrid incompatibilities, how much more slowly would lineages diversify? Ulti-3mately, as evolutionary biologists studying speciation, our goal is to arrive at generalities by documentingthe processes that drive speciation and clarifying their relative importance. The limited available evidencemakes ecological hybrid incompatibilities appear as a critically understudied and important determinant ofhybrid fitness. Only by identifying generalities about the evolutionary ecology of post-zygotic isolation canwe truly appraise their role in speciation.Although a thesis structured around the topic of ‘ecologically-mediated hybrid incompatibilities’ mightseem a narrow one at first glance, I hope to convince the reader by the end that it is more than broad enoughto sustain several careers’ worth of exciting research. Many more questions exist than do answers, and thisthesis work just scratches the surface of the work remaining on this topic. We do not know how readilyadaptation gives rise to ecological incompatibilities nor do we understand the processes that might expediteor slow this process. Research is required to clarify how common and severe trait mismatch is in hybrids,and data that directly link individual-level trait mismatch estimates to fitness are entirely lacking. We do notknow if mismatch in hybrids changes deterministically as populations diverge, though theory predicts it will.Theory on hybrid ecological incompatibilities has also seldom been tested, and ample work remains to bedone to see if we can predict the fitness effects of incompatibilities in the field and whether we can detecttheir genetic signature. Addressing these pressing topics will establish a baseline for future work in the area.In the section that follows, I outline how my thesis attempts to accomplish this.1.4 Overview of the thesisThis thesis builds on a range of theoretical and empirical studies to advance the state of knowledge of themechanisms through which adaptation affects the fitness of hybrids. My aim was to generate novel hypothe-ses, establish empirical patterns, and test theoretical predictions. The study of hybridization is wonderfulbecause the problem is amenable to study from multiple perspectives. I use numerical and analytical theory,data synthesis, and original experiments to address my research questions. The chapters are outlined below,and this general introduction closes with similarly general remarks about the thesis document.1.4.1 Chapter 2In Chapter 2, I use theoretical models to evaluate how adaptation from standing genetic variation affectsprogress toward speciation. This area is a topic of pressing interest because it is increasingly clear thatadaptation occurs from both the re-assortment of existing genetic variation and through the use of new(i.e., de novo) mutations. This chapter uses simulations where pairs of populations adapt from either newmutation alone, or new mutation and ancestral standing variation, and asks how this difference affects thephenotypes and fitness of interpopulation hybrids that form after secondary contact. In the process of thisinvestigation, my co-authors and I also derived new analytical and theoretical predictions about how theprobability of parallel genetic evolution changes as the environments to which populations are adaptingbecome increasingly different.The chapter has several key results. First, standing variation slows progress to speciation under parallelselection because populations are more likely to fix the same alleles during adaptation and hybrids have4phenotypes resembling parents and thus high fitness. Second, standing variation makes speciation faster viadivergent selection. This is not because it makes adaptation happen more quickly (though it does do this) noris it because of parallel genetic evolution (populations fix different alleles). Rather, populations tend to fixmore pleiotropic alleles when adapting from standing variation and as a result exhibit maladaptive transgres-sive phenotypes. Another key result of the study was that the probability of parallel genetic evolution rapidlydeclines to zero as the phenotypic optima diverge. Critically, this decline happens more rapidly in morecomplex organisms (i.e., those with more traits or higher ‘dimensionality’). This work generates a numberof novel testable predictions, and provides insight into how major features of the genetics of adaptation affectprogress to speciation via environment-specific selection against hybrids.1.4.2 Chapter 3In Chapter 3, I aimed to address three key questions. First, how are traits generally inherited in F1 hybridsbetween divergent natural populations? Second, can we make predictions about F1 trait values relative toparents from features of a cross, such as its taxon or the genetic divergence that separates parents? And doesindividual-level variation in trait mismatch have a predictable link to fitness in the field? To address the firsttwo questions, I synthesized data from nearly 200 studies that measured the traits of F1 hybrids and bothparents in the same environment. For the third question, I re-analyzed an existing dataset of recombinanthybrid sunflowers transplanted into the field.I found that individual traits, as measured in F1 hybrids, are considerably more dominant than additive(i.e., individual traits are much more similar to one parent than to the other; h = 0.2 or 0.8). I also foundthat dominance is inconsistent among traits, and this causes hybrids to generally resemble one parent a bitmore than the other. In addition, dominance causes F1 hybrids to be rather ‘mismatched’ for divergenttraits, where in the case of two traits F1 hybrids resemble one parent for one of the traits but resemble theother parent for the second trait. I also found that no features of a cross (e.g., taxon, genetic distance betweenparents) reliably predicted any metric of dominance. In the sunflowers, I found that multivariate bias towardsparents (i.e., resembling one parent more than the other or ‘parent-bias’) improved fitness while mismatchbetween traits tended to reduce fitness. Importantly, the effect of mismatch for reducing fitness was largerin magnitude (i.e., steeper slope) than that of parent-bias for improving it. This chapter reveals that traitmismatch in early-generation hybrids is more a rule than an exception and that this mismatch can, in at leastone system, substantially reduce their fitness in the field.1.4.3 Chapter 4Chapter 4 uses data from the literature to test whether adaptive divergence proceeds via the fixation ofalleles with deleterious pleiotropic side-effects. Pleiotropy is a central concept in many evolutionary models,from being the major explanation for aging (Williams, 1957) to being a central assumption of Fisher’s (1930)geometric model. In spite of its central importance, little is known about the degree to which mutations affectfew or many traits—that is, we know little about the ‘universality’ of pleiotropy. Determining the universalityof pleiotropy is difficult because measuring it is typically painstaking—researchers typically must induce asingle mutation and then measure how many traits it affects. Rather than undertaking such an experiment, I5leveraged a prediction of theoretical models that depends on there being universal pleiotropy and is readilytestable using existing data. Specifically, if adaptation uses pleiotropic mutations, compensatory mutationsare expected to fix that counteract the deleterious pleiotropy. Following hybridization, these pleiotropicand compensatory mutations should segregate in recombinant hybrids, resulting in hybrids with substantialtransgressive phenotypic variation in traits for which the parents have the same phenotype. Importantly, theamount of segregation in these non-divergent traits is expected to be positively associated with the magnitudeof phenotypic divergence among populations for divergent traits.I assembled a small dataset of 15 crosses to test this prediction. I found strong support for the theoreticalprediction that was robust to virtually all possible alternative analysis decisions. Tests of alternative expla-nations, such as that the pattern could be caused by drift, were not supported. This project provides positive,albeit strictly correlational, support for a key prediction of models that rely on the assumption of universalpleiotropy. Universal pleiotropy is a key assumption of Chapter 2 and many other models of adaptationand has major implications for the genotype–phenotype map. Thus, models that rely on this assumption areincreasingly supported by empirical evidence, and we can conclude that varying single alleles will typicallyhave off-target effects. Experiments that follow-up on this result to establish its generality would be timely.1.4.4 Chapter 5In Chapter 5, I use threespine stickleback fish (Gasterosteus aculeatus L.) to test the hypothesis that traitmismatch is associated with the amount of divergence between parents of a cross. In the threespine stickle-back, marine populations colonized a range of post-glacial freshwater lakes to which they have adapted overthe previous 10,000+ years. The freshwater lakes vary greatly from one another, with some being massiveand containing both piscivorous species and species that compete for food with stickleback, and others beingsmall and shallow with no other fish species except stickleback. The former, being deep and species-richwaters, resemble the ancestral marine habitat of the open ocean and stickleback in these lakes tend to retainmany of the ancestral characteristics and zooplanktivorous niche. More derived stickleback inhabit lakes inthe latter category—those that are small and species-poor—and are specialized to feed on benthic inverte-brates. Lakes that are intermediate between these extremes abound and are home to relatively intermediatestickleback.Theory predicts that the amount of segregating phenotypic variation in recombinant hybrids should in-crease as populations diverge phenotypically. This should, in turn, lead to hybrids with increasingly novelcombinations of traits. I used a ‘space-for-time’ design to test this prediction in stickleback, because thezooplanktivore–benthivore divergence axis is an effective and meaningful axis of divergence that is pos-itively associated with genomic divergence. I crossed fish from a single marine (anadromous) sticklebackpopulation with twelve derived freshwater populations of increasing divergence from the marine form. I thenmeasured traits of lab-raised parents and hybrids (F1 and F2) and used these data to quantify the magnitudeof hybrid mismatch. I found that, as predicted, hybrid mismatch was greater in ‘wider’ crosses. However, thedetails were surprising. First, although I expected the pattern only to occur in F2 hybrids, mismatch increasedwith divergence in F1s as well because dominance varied considerably among traits. Further analysis clearlyindicates that the cause of mismatch in F1s is dominance and the cause of mismatch in F2s is segregation6variance. Together, this chapter indicates that hybrid mismatch evolves predictably in stickleback, whichmight be an important mechanism linking divergent adaptation with reproductive isolation.1.4.5 Chapter 6In the past three decades, it has become increasingly clear that adaptation in response to divergent naturalselection readily leads to speciation. Much less is known, however, about the efficacy of parallel naturalselection for driving speciation. In Chapter 6, I tested the hypothesis that parallel phenotypic evolution, ifunderpinned by non-parallelism at the genetic level, can lead to the accumulation of hybrid incompatibilities.Such incompatibilities would manifest as novel phenotypes in hybrids that render them poorly adapted to thephenotypic optimum of their (phenotypically similar) parent populations.To test whether parallel evolution leads to hybrid incompatibilities, I used the stickleback benthic-limnetic species pairs, which are among the best models of parallel phenotypic evolution yet discoveredin fishes. I made between-lake within-species crosses between all three of the extant species pairs for bothbenthics and limnetics, and compared growth rates of parents and F1 & F2 hybrids in experimental pondsand in aquaria. I hypothesized that because benthics are more derived, they would have evolved more in-compatibilities than limnetics. I tracked the growth of nearly 4,000 individual fish in ponds and 2,000 fish inaquaria, and found both expected and unexpected results.Surprisingly, patterns for benthics and limnetics were similar in terms of the rank-order fitness of purespecies and hybrid classes. Differences among cross types were also larger in magnitude among limnetics,refuting the hypothesis that patterns would be more exaggerated in benthics. Across both species, I foundevidence for heterosis in the ponds, with F1 hybrids growing faster and surviving more frequently than bothpure species and F2 hybrids. F2 hybrids often performed similarly or worse than parents, however, and asimple toy model demonstrates that this pattern can only be caused by the existence of hybrid incompat-ibilities between divergent alleles at different loci. I found no evidence for hybrid incompatibility in theaquarium-raised fish, whereas heterosis was apparent for limnetics in aquaria. This suggests that hybridincompatibilities are only expressed in the field, whereas heterosis is somewhat intrinsic in limnetics andextrinsic in benthics. Finally, although these main effects were significant, patterns differed meaningfullyacross inter-lake crosses, which confirms a primary role for stochastic processes during speciation by parallelnatural selection. Nevertheless, the fact that the main effects were so similar for both benthics and limnet-ics suggests that general rules governing the fitness of hybrids might become apparent through the noise ifenough comparisons are made.1.4.6 Chapter 7In Chapter 7, the final data chapter, I use the benthic-limnetic stickleback species pairs and allopatricanadromous-freshwater populations to test whether the genetic signature of hybrid incompatibilities is strongerin the field than in the lab. I can expect this prediction to be supported if incompatibilities affect traits likethe ability to find or capture food or avoid predators. In F2 hybrid populations, theory predicts that the netstrength of selection against hybrid incompatibilities can be measured as directional selection for heterozy-gosity. I compared patterns of excess heterozygosity in benthic-limnetic F2 hybrids from both Priest and7Paxton Lakes between populations raised in the lab vs. experimental ponds. I did the same for fish fromCranby Lake crossed with anadromous fish from the Little Campbell River. If incompatibilities are onlyexpressed under ecologically-relevant circumstances, they should only be detected in the ponds.I found that in aquaria, F2s met Hardy-Weinberg expectations and had no significant excess heterozy-gosity. In the ponds, however, surviving fish almost invariably had significant excess heterozygosity whichI hypothesize results from mortality-selection against individuals with many weakly-selected ecological in-compatibilities. This work illustrates that hybrid incompatibilities can be environment dependent and high-lights a simple summary statistic that can be used to test this. Environment-specific heterosis resulting fromdominance might also contribute to this pattern, especially in the allopatric marine-freshwater crosses. Moreimportantly, it implies that ecological hybrid incompatibilities might evolve before ‘intrinsic’ incompatibili-ties and could be the genetic basis of much ecology-based reproductive isolation in nature.1.5 RemarksIn this introduction, I hope to have convinced the reader that the evolutionary ecology of hybridization is arich topic with opportunity for theoretical & empirical generalities waiting to be established and predictionsripe for testing in the field and lab. That is, I hope the work presented herein raises more questions thanit answers. The six chapters that follow comprise the bulk of the thesis, and I conclude the document bysummarizing its findings, discussing what we know now that we didn’t before, and by highlighting key areaswhere progress should be made to solidify our understanding about the general importance and mechanismsof extrinsic post-zygotic isolating barriers for speciation.8Chapter 2Parallel genetic evolution and speciationfrom standing variation12.1 IntroductionIn recent years, two general features of evolution by natural selection have become increasingly established.First, adaptation often proceeds largely via the reassortment of ancestral standing variation rather than viacomplete reliance on de novo mutations (Barrett and Schluter, 2008). And second, variation in the directionof natural selection acting on pairs of populations is best represented by a quantitative continuum rangingfrom parallel selection—favouring identical phenotypes—to divergent selection—favouring distinct pheno-types— rather than falling into discrete ‘parallel’ or ‘divergent’ bins (Bolnick et al. 2018). It is unclear,however, how the extent of parallel genetic evolution—use of the same alleles during adaptation—changeswith the difference in the direction of selection experienced by a pair of populations. It is also unclearwhether adaptation from standing variation has implications for speciation that are distinct from those whenadaptation is from new mutation alone, and whether its effect changes along the continuum from parallelto divergent natural selection. Here, I investigate genetic parallelism and speciation under adaptation fromstanding variation across this selection continuum.Adaptation facilitates progress towards speciation when populations evolve reproductive isolating bar-riers as a by-product. One reason these reproductive isolating barriers might arise is because genetic dif-ferences between populations have maladaptive consequences when combined in hybrids (i.e., postzygoticisolation), thereby reducing gene flow upon secondary contact. When a pair of populations adapts in responseto divergent natural selection, hybrids might have an intermediate phenotype that is unfit in either parentalenvironment (Schluter 2000). When a pair of populations are subject to parallel selection, they may divergegenetically by chance (Mani and Clarke 1990; Schluter 2009) and hybrids might have novel transgressivephenotypes that are poorly suited to the common parental habitat (Barton 1989, 2001). Hybrid unfitness istherefore determined by two factors: (1) additive gene action causing hybrids to ‘fall between the peaks’(Rundle and Whitlock 2001), and (2) cryptic genetic divergence that is released following hybridization andcauses some hybrids to possess maladaptive transgressive phenotypes which vary in directions orthogonalto the axis of parental divergence (Arnegard et al. 2014; Keagy et al. 2016). How adaptation from standingvariation affects progress toward speciation-by-selection (Langerhans and Riesch 2013) is largely unexploredtheoretically.1A version of this chapter has been published as Thompson, K.A., Osmond, M.M., and Schluter, D. 2019. Parallel geneticevolution and speciation from standing variation. Evolution Letters. 3(2): 129–141.9Adaptation from standing variation is common and underlies some of the most spectacular adaptive ra-diations found in nature (Brawand et al. 2015). Genomic studies often implicate standing variation as themajor source of genetic parallelism in replicate populations colonizing similar environments (Jones et al.,2012a,b; Roesti et al., 2014; Lee and Coop, 2017; Haenel et al., 2019) and adapting to novel stressors (Reidet al., 2016; Alves et al., 2019). Previous research has shown that the correlation between selection coeffi-cients of a given allele in each of two populations inhabiting different environments is expected to increasewith the similarity in the direction of selection (equation 6 in Martin and Lenormand 2015). I therefore ex-pected the extent of parallel genetic evolution for two populations to decline from a maximum to a minimumvalue as the angle between the directions of selection between them (θ) increases from completely parallel(θ = 0°) to completely divergent (θ = 180°). My specific goal was to characterize the pattern of decline inparallelism. I also hypothesized that adaptation from standing variation would reduce the evolution of re-productive isolation under parallel selection because parental populations would fix more of the same allelesand therefore evolve fewer incompatibilities (Schluter, 2009). Under divergent selection, I hypothesized thatpopulations would fix alternative alleles regardless of whether they were selected from standing variationor new mutation. Therefore, I expected standing variation to have little effect on speciation by divergentselection compared to adaptation from new mutation alone.I conducted a theoretical investigation into parallel genetic evolution and speciation from standing vari-ation across the continuum from parallel to divergent natural selection. I primarily used individual-basedsimulations and include some simple analytical arguments to gain intuition. I compared results from simu-lations where adaptation proceeds simultaneously via the sorting of ancestral standing genetic variation andde novo mutation to simulations where adaptation proceeds via de novo mutation alone. My results provideinsight into the circumstances under which I should expect high vs. low genetic parallelism and also sug-gest that standing variation has substantial implications for speciation that depend on the difference in thedirection of natural selection between populations.2.2 MethodsI used computer simulations to investigate genetic parallelism and progress toward speciation—via ecologically-dependent postzygotic reproductive isolation—from standing variation across the continuum from parallelto divergent natural selection. My simulations consider pairs of populations and multivariate phenotypesdetermined by multiple additive loci. In each of my simulations, a single ancestral population founds twoidentical populations that each adapt in their respective environments without gene flow (i.e., allopatry; seeFig. 2.1A). After adaptation, populations interbreed to form recombinant hybrids. This general coloniza-tion history—a single population splitting into two populations that independently adapt to their respectivenovel environments—is modelled around the process of adaptation as it can occur in nature, for example inpostglacial fishes (Bell and Foster 1994) and in birds or plants isolated within glacial refugia (e.g., (Weirand Schluter 2004; Pettengill and Moeller 2012). In many such cases, ecologically-dependent postzygoticisolation is thought to be essential for maintaining reproductive isolation (Nosil 2012). See Table 2.1 fordescriptions of all parameters and values used in simulations.10illustration of ‘angleof divergence’ (θ)bangle of divergenceθ ≈ 90°}overview of an individual simulationapop A pop Bt = 0t = Tcommon ancestorhybridssegregation varianceand hybrid fitnesscfit inenv. A fit inenv. BFigure 2.1: Visual overview of simulations and concepts. Panel (a) provides an overview of an individ-ual simulation run. An ancestral population founds two initially-identical parental populations, that evolveindependently for T generations in their respective environments. After T generations of adaptation, theseparental populations interbreed to form hybrids. Panel (b) illustrates the process of adaptation in my simu-lations, wherein two populations (red and blue arrows connect the mean phenotype every 200 generations)independently adapt to specified optima (red and blue stars; behind arrows in [b] but visible in [c]). Concen-tric circles represent fitness contours around the two optima. The ancestor state is indicated by the grey dot,with the angle of divergence, θ, shown between the two axes of selection (red and blue dashed lines; angleshown is approximately 90°). Panel (c) illustrates the segregation variance in a group of hybrids. Individualhybrids (purple points) that are near an optimum have high fitness when measured in that environment. Theblack line is the line connecting parental optima—variance along this line can increase mean hybrid fitnesswhereas variance orthogonal to this line is deleterious.2.2.1 Genotype to phenotypeThe phenotype of a haploid individual is represented by an m-dimensional vector, z = [z1, z2,. . . , zm], with mbeing the number of uncorrelated ‘traits’ or phenotypic ‘dimensions’ (for further discussion of dimension-ality, see Orr 2000 & Tenaillon 2014). Each trait value, zi, is determined by the summed effects of allelesat all underlying loci (i.e., mutations act additively to determine the phenotype), which are initially fixed foralleles with an effect of 0 on all m traits. I primarily present results from simulations with five phenotypicdimensions (m = 5) in the main text. Results for alternative parameter combinations can be found in thesupplementary figures (Figs. A.1–A.7).2.2.2 Life-cycleI model a Wright-Fisher population (Fisher 1930; Wright 1931) with haploid selection. Fitness is a Gaus-sian function that depends on the Euclidean distance between an individual’s phenotype and the phenotypicoptimum, ||z - o||, and the strength of selection, σ (e.g., Lande 1979):W = exp(−σ||z− o||2/2) (2.1)11Table 2.1: Description of parameters and parameter values in parental populations for simulationspresented in the main text.Parameter Valueα, mutation size SD in each dimension 0.1d, distance between ancestral and parental phenotypic optima 1N , number of haploid individuals 1000m, number of traits, or ‘dimensionality’ 5n, initial number of segregating loci 0 (DNM); 100 (DNM & SGV)*µ, probability an individual acquires a new mutation 0.001σ, strength of selection 1θ, angle of divergence (°) 0°≤ θ ≤ 180°*DNM: de novo mutation; SGV: standing genetic variation(My qualitative conclusions are robust to alternative assumptions about fitness functions [see Fig. A.8)].After selection, N haploid parents are randomly sampled with replacement from a multinomial distributionwith probabilities proportional to their fitness, W. Parents then randomly mate and produce two haploidoffspring per pair, with free recombination between all loci. With probability µ, an offspring gains a muta-tion; I assume an effectively infinite number of loci such that all mutations arise at a previously unmutatedlocus (‘infinite-sites’ sensu Kimura 1969). Mutational effects are drawn from a multivariate normal distri-bution (‘continuum-of-alleles’ sensu Kimura 1965), with a mean of 0 and an SD of α in all m traits and nocorrelations among traits (i.e., universal pleiotropy).Generating ancestral standing genetic variationTo generate ancestral standing variation, I conducted burn-in simulations of a large ancestral population(Nanc = 10,000) under stabilizing selection (σanc = 0.01) at the origin (σanc = [0, 0, . . . 0]) for 100,000generations. All other parameters in the ancestor (e.g., mutation rate) were identical to those of parentalpopulations (Table 2.1). This parameter combination facilitates the accumulation of appreciable standingvariation (see Fig. A.9), but my general conclusions hold if the ancestor is under much stronger selection(σanc = 1) that puts it into the multivariate ‘House-of-Cards’ regime (Turelli 1985; see Fig. A.10).Ancestral populations reached mutation-selection-drift balance such that the rate of acquisition of newmutations was balanced by the rate of loss of mutations that arose in earlier generations (Fig. A.9A). Boththe mean frequency of derived alleles and the phenotypic (genotypic) variance were stable (Fig. A.9B), ashas been found in other models of phenotypes under stabilizing selection (e.g., Barton 1989). Segregatingderived alleles were all at unique loci by assumption—that is, each polymorphic locus has exactly two allelesand each derived allele can be traced back to a single mutation event. In addition, segregating derived alleleswere at low frequency in the ancestral population (see Fig. A.9D for the site frequency spectrum). Highderived allele frequencies and fixation are sometimes reached by drift when mutations have nearly-neutralselective coefficients and by positive selection when mutations compensate for deleterious alleles that haverisen to high frequency by drift (Hartl, 2002; Orr, 2005).122.2.3 Adaptation to a new environmentIn simulations with standing genetic variation, a parental population was established by first randomly choos-ing n polymorphic loci in the ancestor (see Fig. A.11 for effect of n on genetic parallelism and segregationvariance). Each parental individual received the mutant (i.e., ‘derived’) allele at each of these n loci witha probability equal to the allele’s frequency in the ancestor. Loci fixed in the ancestral population werealso fixed in the parental population but were not considered when quantifying parallelism. This admittedlyartificial sampling procedure allowed us more control over the amount of standing genetic variation acrosssimulations with different parameter values. Further control was achieved by making the second parentalpopulation initially identical to the first, so that each possessed the exact same collection of genotypes andthere were therefore no founder effects. Populations adapted from only new (i.e., de novo) mutation when n= 0. Within each parameter combination, I began each replicate simulation from a unique realization of theancestor (i.e., distinct burn-in). After initialization, parental populations adapted to their respective pheno-typic optima without inter-population gene flow (Fig. 2.1B), and adaptation proceeded via natural selectionon ancestral standing variation (if n > 0) and new mutation simultaneously.Two properties of the new phenotypic optima are key. The first is the Euclidean distance between eachoptimum and the origin, d (assumed the same for both parental populations for simulations presented inmain text). More distant optima yield a greater amount of genetic and phenotypic change. In the main textI set d = 1, which is equivalent to 10 times the SD of mutation effect size (α). The second key feature ofthe new optima is the angle of divergence, θ, separating vectors that originate at the origin and each passthrough one of the parental optima (dashed lines in Fig. 2.1B). Angle is used to quantify the difference in thedirection of selection from parallel (θ = 0°) to divergent (θ = 180°) and is explicitly invoked in most empiricalmetrics that quantify phenotypic parallelism (Bolnick et al., 2018). The value of θ is what determines themean phenotypic differences that evolve between parental populations in my simulations (because d is heldconstant).I ended the adaptation phase of simulations after T generations (T = 2000 in the main text), at which timeall populations had reached their phenotypic optima (Fig. A.12A) and mutation-selection-drift balance (Fig.A.12B). An unavoidable and important effect of standing variation is that it quickens adaptation becausepopulations do not have to wait for beneficial alleles to arise (Barrett et al., 2008). In my model and otherslike it (e.g., Barton 2001; Chevin et al. 2014), reproductive isolation evolves rapidly during the initial stagesof adaptation. After populations reach their respective phenotypic optima, genetic divergence accumulatesslowly at a rate proportional to the mutation rate (Barton, 1989, 2001; Chevin et al., 2014). Therefore,my results reflect quasi-equilibrium conditions rather than transient states and are unaffected by standingvariation’s influence on the speed of adaptation.2.2.4 Quantification of genetic parallelism and hybrid segregation variance & fitnessAfter the adaptation phase of simulations had ended, I calculated the proportion of alleles that fixed in bothpopulations (i.e., genetic parallelism). To quantify parallel genetic evolution between parental populations, Ifirst determined the number of alleles that fixed in each population (f1 & f2) and the number of alleles that13fixed in both populations (f1,2). I then calculated my metric of ‘genetic parallelism’ as:P g =12(f1f1,2+f2f1,2)(2.2)Values of 1 indicate complete genetic parallelism (i.e., all alleles that fixed were fixed in both populations)and values of 0 indicate complete genetic non-parallelism (i.e., no allele fixed in both populations). I use thismetric because of its ease of interpretation and note that it is highly correlated with other metrics of geneticdivergence between populations (e.g., FST; Fig. A.13). I present some results with this metric scaled to aforced minimum of 0 and a forced maximum of 1 in order to facilitate comparison of simulations conductedwith different parameters.To create inter-population hybrids, I then randomly sampled 100 individuals from each population with-out replacement. Each sampled individual was paired with an individual from the other population to form100 unique inter-population mating pairs. Every inter-population mating pair then produced one recombinanthaploid F1 hybrid for a total of 100 potentially unique hybrids.After forming hybrids I quantified their phenotypic variation—the net segregation variance (Wright,1968; Slatkin and Lande, 1994)—calculated here as the mean phenotypic variance across all m traits. Ipresent analyses of individual axes of variance where relevant. Higher segregation variance results whenparents are differentiated by a greater number of alternative alleles (holding effect size constant) or allelesof individually-larger effect (holding number of alleles constant) (Castle, 1921; Slatkin and Lande, 1994;Chevin et al., 2014). Segregation variance captures the phenotypic consequences of hybridization and hasa direct impact on fitness whereas genetic (non)parallelism is only indirectly related to fitness. Phenotypicvariance in parental populations (i.e., before hybridization) is near zero and does not differ between popula-tions founded with vs. without standing variation nor does it depend on the initial distance to the optimum (d;Fig. A.12C). Such low variance is expected because my simulations have fixed and frequency-independentoptima, no migration, and parameter values corresponding to strong selection and relatively weak mutation(‘house-of-cards’; Turelli 1984, 1985).An individual hybrid’s fitness in a given parental environment was calculated from its phenotype in thesame manner as the fitness of parental populations (Fig. 2.1C). I determined the fitness (Eqn. 2.1) of eachhybrid in both parental environments and recorded its fitness as the larger of the two values. This can beimagined as, for example, giving the hybrid a choice of alternative host-plants (see Drès and Mallet 2002)where it always chooses the host on which it has higher performance. My fitness metric reflects what istraditionally recognized as ‘extrinsic’ postzygotic isolation (Coyne and Orr, 2004), and explicitly considersenvironment-specific epistasis for fitness (Bateson 1909; Dobzhansky 1937; Muller 1942; Chevin et al. 2014;Fraïsse et al. 2016; see also Arnegard et al. 2014; Schumer et al. 2014; Ono et al. 2017 for discussionof environment-specific hybrid incompatibilities). I consider my model to be one of ‘extrinsic’ rather than‘intrinsic’ isolation because I do not consider traits such as gamete viability, which experiences environment-independent selection. Rather, traits in my model are best imagined to be more akin to ecologically-relevanttraits like beak depth, under stabilizing selection with optima that depend on the environment. Becausehybrids are recombinant, hybrid fitness reflects both the effects of displacement of the mean phenotype fromthe optimum (the ‘lag’ load) and what in diploids is known as hybrid breakdown (Burton et al., 2006). I14report hybrid fitness relative to the parents for each individual simulation, calculated as: [mean fitness ofhybrids] / [mean fitness of parents].2.3 Results2.3.1 Genetic parallelism and phenotypic segregation varianceI first investigated how genetic parallelism between two populations—the fraction of alleles that fixed in bothpopulations vs. were unique to a single population—changes with the angle of divergence (θ) when adap-tation is from standing variation. Genetic parallelism is highest under completely parallel natural selection(θ = 0°) and rapidly decreases toward its minimum value as θ increases (dark green line and points in Fig.2.2A; see black line for visual comparison of deviation from linearity). This rapid decrease in genetic paral-lelism also occurs when the phenotypic distance between parental optima is used as the independent variableinstead of θ, although with my parameters non-linearity is only appreciable in higher dimensions (see Fig.A.14). There is considerable variation in genetic parallelism among simulation runs even when populationsadapt to identical environments, which results from stochastic processes in each run. For example, alleles arelost due to drift, populations fix weakly deleterious alleles or different de novo mutations, and populations fixalternative alleles from the standing variation early in the simulations, which affects the selection coefficientsof all other alleles in later generations (Chevin and Hospital, 2008). Genetic parallelism never decreases tozero even under completely divergent selection (θ = 180°), indicating that populations fix some deleteriousalleles. My conclusion that genetic parallelism rapidly decreases with θ is generally robust to variation inpopulation size and selection strength, except for when small populations are under weak selection (Fig.A.1), likely due to an overwhelming effect of drift (see Fig. A.15 for divergence between populations due todrift alone at various population sizes).The changes in segregation variance generally mirror patterns of genetic parallelism (Fig. 2.2B). Withstanding variation, segregation variance is low under parallel selection and rapidly increases with θ. Chevinet al. (2014) found that segregation variance (proportional to their ‘variance load’) does not depend on θ,but in contrast to my model they did not permit genetic parallelism. When there is no standing variation,segregation variance is not affected by the angle of divergence (light green line and points in Fig. 2.2C; linearmodel slope± 1 SE: 4.9×10−7±5.8×10−6, in agreement with the findings of Chevin et al. 2014; their Fig.2). At large angles, segregation variance is greater when populations adapt from standing variation than whenthey adapt from new mutation alone, and the magnitude of this difference increases with dimensionality (seeFig. A.16).Genetic parallelism decreases with θ (and segregation variance increases) because the fraction of allelesthat are beneficial in both parental populations declines as θ increases. For a given population, beneficialalleles bring populations closer to the middle of a hypersphere centred at the phenotypic optimum (the ge-ometric model [Fisher 1930]; see cartoon inset of Fig. 2.3A). Considering two populations, each with itsown hypersphere, a given allele is beneficial in both—and thus could fix in parallel via positive naturalselection—if it brings a population’s mean phenotype into the region where the two hyperspheres overlap(purple region in Fig. 2.3A inset). The size of this region of overlap decreases rapidly with θ (Fig. 2.3A;15genetic parallelism acrossthe selection continuumasegregation variance in hybridsacross the selection continuumb new mutation new mutation & SGV new mutation new mutation & SGV0.000.250.500.751.000 45 90 135 180angle of divergence, θ (°)genetic parallelism0. 45 90 135 180angle of divergence, θ (°)net segregation varianceFigure 2.2: Genetic parallelism and phenotypic segregation variance. Parental populations adapted fromeither new mutation only (light green) or from a combination of new mutation and standing genetic variation(SGV) (dark green). Panel (a) shows the proportion of alleles that fixed in both populations vs. were uniqueto a single population (genetic parallelism; equation 2). The thin black line connects the fit at θ = 0° to thefit at θ = 180° and is shown only to facilitate visualization of the non-linearity. Panel (b) is similar to (a),except with the net segregation variance in hybrids as the dependent variable. Plotted are the results from 10replicate simulations for each of 37 angles of divergence (d = 1). Green lines are loess fits.see Appendix A.1 for mathematical details), and therefore so does the fraction of alleles present as standingvariation that are beneficial in both populations. The rate of decrease of overlap is faster with greater dimen-sionality (compare solid line to dashed lines in Fig. 2.3A) but—perhaps surprisingly—does not depend onthe distance to the optima (d; if d1 = d2 = d) and is not expected to change over the course of an ‘adaptivewalk’ (sensu Orr 1998; see Appendix for detailed explanation). Briefly, this is because adaptation’s effectis to shrink the radii of the hyperspheres (at roughly equivalent rates in the two populations if adaptationproceeds relatively deterministically). Thus, because the fraction of overlap (Eq. A1) does not depend on theradii of the hyperspheres, the fraction of overlap is expected to remain constant throughout adaptation. Sim-ulations conducted for four different dimensionalities (m = 2, 5, 10, 25) qualitatively capture the predictedpattern of decreasing parallelism with increasing dimensionality (Fig. 2.3B), although drift, a limited supplyof standing variation, and run-specific epistasis (etc.) contribute to differences between hypersphere overlapand genetic parallelism.I also modelled an alternative case in which θ is held constant but populations differ in the distanceto their respective optima (i.e., different vector ‘lengths’ rather than ‘angles’ sensu Bolnick et al., [2018]).Even if selection is completely parallel (i.e., θ = 0°), if the distance between the ancestral phenotype and thephenotypic optimum of population 2 is twice that of the ancestor–optimum distance for population 1 (i.e., d216theoretical relationship between (hyper)sphere overlap and θaobserved relationship between genetic parallelism and θb0.000.250.500.751.000 45 90 135 180angle of divergence, θ (°)fraction of overlap0.000.250.500.751.000 45 90 135 180angle of divergence, θ (°)scaled genetic parallelismm  = 2m  = 5m  = 10m  = 25m  = 2m  = 5m  = 10m  = 25Figure 2.3: The relationship between trait dimensionality (m) and genetic parallelism. Panel (a) is an an-alytical result that depicts the relationship between θ and the fraction of overlap between two (hyper)spheresfor four different dimensionalities (see equation A1). In the inset cartoon, mutations that bring the phenotypeinto the red and blue regions are initially beneficial only in the ‘red’ or ‘blue’ environments, while mutationsthat bring the phenotype into the purple region are beneficial in both environments. The horizontal blackline is set at y = 0, where there is no overlap. Panel (b) is a proof-of-concept figure showing loess fits ofsimulation results with 95 % confidence intervals. Within a dimensionality, parallelism is scaled between 0(minimum value of loess fit) and 1 (maximum value of loess fit). Simulations were conducted with strongnatural selection (σ = 10) to minimize the effect of drift. (See Fig. A.19) for a similar result except withsegregation variance on the y-axis.)= 2d1), less than 5 % of the alleles beneficial to population 2 are also beneficial to population 1 (for m = 5;see Fig. A.17). This result indicates that differences in vector lengths are important to consider—in additionto angles—for reducing the extent of genetic parallelism.2.3.2 Hybrid fitnessIn this section, I evaluate the effect of standing variation on hybrid fitness across the continuum from parallelto divergent natural selection. The most readily observable pattern is that the mean relative fitness of hybridsis lower under divergent selection than under parallel selection regardless of whether adaptation proceedswith standing variation (Fig. 2.4A). This pattern occurs because the hybrid mean phenotype is increasinglydistant from either parental optimum as θ increases. In Figure 2.4A, I plot the fitness of the hybrid meanphenotype (representing the ‘lag’ load) as a thin black line.17θ = 0°θ = 60°θ = 180°relative fitness of hybrids withand without standing variationacross the selection continuumaeffect of standing variation on therelative fitness of hybrids across the selection continuumb effect of segregation varianceon relative fitness of hybridscnew mutationnew mutation & SGV‘lag’ load0. 45 90 135 180angle of divergence, θ (°)relative fitness of hybrids0.9550.9801.0051.0301.0551.0800 45 90 135 180angle of divergence, θ (°)0.951. 0.01 0.02 0.03 0.04 0.05net segregation variancefitness with var / fitness without varfitness with SGV / fitness without SGVFigure 2.4: The effect of standing variation on mean hybrid fitness. Panel (a) shows the mean relative fit-ness of hybrids—as compared to parents—across environments in simulations initiated without (light green)and with (dark green) ancestral standing genetic variation. The thin black line represents the mean relativefitness of hybrids due only to the deviation of the observed mean phenotype from an optimum (‘lag’ load)and is close to 1 when the hybrid mean phenotype is on the optimum. Panel (b) shows the effect of standingvariation on mean relative hybrid fitness (the ratio of values for dark / light green lines in panel [a]); thehorizontal line shows where there is no effect of standing variation on relative mean hybrid fitness. Panel (c)is an analytical result that illustrates the relationship between segregation variance and mean hybrid fitnessfor three angles of divergence (black, θ = 0°; brown, θ = 60°; grey, θ = 180°) when the hybrid phenotypeis multivariate normal with a mean exactly in between the two parental optima and equal variance in allphenotypic dimensions (no covariance). Hybrid fitness is plotted for each angle relative to the case of novariance; the horizontal line indicates when segregation variance has no effect on hybrid fitness.Compared to when adaptation is from new mutation, adaptation from standing variation improves meanhybrid fitness when parental populations adapt to similar optima but reduces hybrid fitness when parentsundergo divergent adaptation (Fig. 2.4B). This pattern is caused by environment-specific effects of segre-gation variance on mean hybrid fitness (Fig. 2.4C, Fig. 2.5). When the hybrid phenotype distribution iscentred at the phenotypic optimum—as it is under parallel selection (θ = 0°)—segregation variance is uni-versally deleterious. When parental populations adapt to identical optima from only new mutation, hybridsvary considerably around the parental optimum and thus have relatively low mean fitness. When populationshave access to a common pool of standing variation, parallel genetic evolution leads to lower segregationvariance around the optimum and therefore higher mean fitness under parallel selection compared to whenpopulations adapt from only new mutation (Fig. 2.5A; see Fig. A.18 for similar results but for maximumhybrid fitness instead of mean).18hybrid phenotypes(θ = 135°)ddimensions 1 & 2 3 & 4hybrid phenotypes(θ = 45°)bdimensions 1 & 2 3 & 4hybrid phenotypes(θ = 90°)cdimensions 1 & 2 3 & 4hybrid phenotypes(θ = 180°)edimensions 1 & 2 3 & 4hybrid phenotypes(θ = 0°)adimensions 1 & 2 3 & 4DNM DNM &SGV Figure 2.5: The effect of standing variation on the distribution of hybrid phenotypes. I plot ellipsescontaining 95 % of hybrid phenotypes for five angles of divergence (θ) evenly spaced along the continuum of(a) completely parallel (θ = 0°) to (e) completely divergent (θ = 180°) selection. Separate ellipses are shownfor simulations where populations adapted from only new mutation (light green; DNM) or both new mutationand standing genetic variation (dark green; DNM & SGV). Each ellipse is fit to 1000 hybrids resulting from10 replicate simulations. Parental optima are depicted as stars and the origin (ancestral optimum) is shownas a grey dot. The left side of each panel shows the first two trait dimensions—the only dimensions in whichthe optima might differ. The right side of each panel shows the third and fourth dimensions—both of whichare under stabilizing selection for a phenotype identical to the ancestral phenotype. The axes of selectionconnect the origin and optima (dashed red and blue lines) and I also show the axis connecting parental optimaas a solid black line. Ellipse plotting order is reversed on the right side of panel (e) to facilitate visualization.At large angles of divergence, adaptation from standing variation reduces hybrid fitness compared towhen adaptation is from only new mutation. The reasons for this are twofold. First, since I allow hybridsto ‘choose’ their environment (measuring their fitness in the parental environment they are better adaptedto), at larger angles hybrids increasingly fall into a ‘fitness valley’. In this case some variation along the19axis of divergence can be beneficial (see Fig. 2.4C). Second, since fitness in either environment is a Gaus-sian function, variation becomes beneficial when the mean is far from the optimum (by Jensen’s inequality),even when considering fitness in only a single environment. This result is robust to variation in parametervalues (see Figs. A.4–A.6), except when selection is very weak in small populations. There are appreciabledifferences in patterns of phenotypic variation in hybrids when their parents adapt with standing variationvs. when adaptation is from new mutation alone (Fig. 2.5). Only phenotypic variation along the axisconnecting parental optima (black line connecting stars in Fig. 2.5) is beneficial, whereas variation alongorthogonal axes is deleterious. When θ = 180°, hybrids have reduced variation along the axis connectingparental optima and slightly more variation along all other axes (see Fig. 2.5E). Thus, maladaptive segre-gation variance—resulting from cryptic genetic differences between parental populations revealed only afterhybridization—reduces hybrid fitness under large angles of divergence.Why does adaptation from standing variation alter patterns of phenotypic segregation variance in hy-brids? As discussed above, adaptation from standing genetic variation reduces segregation variance underparallel selection because parents fix the same alleles that therefore do not segregate in hybrids. Popula-tions adapting from standing variation also fix a greater number (Fig. 2.6A) of smaller effect alleles (Fig.2.6B) than populations evolving without standing variation. Fixation of smaller-effect alleles likely occursunder adaptation from standing variation because stabilizing selection in the ancestor effectively removeslarge-effect alleles from the standing variation (Fig. A.9) and because weakly beneficial alleles have a higherprobability of fixation when present in standing variation compared to if they arose de novo (Orr and Betan-court, 2001; Hermisson and Pennings, 2005; Matuszewski et al., 2015). This latter effect seemed to allowalleles with more deleterious pleiotropic effects to fix during adaptation from standing variation than whenadaptation was from new mutation alone (Fig. 2.6C). That is, populations initiated with standing geneticvariation used alleles with proportionally larger pleiotropic side-effects. I quantified pleiotropy by taking theratio of the mean effect size of fixed alleles along the axis of selection in parents (red or blue dashed linesin Fig. 2.5) vs. the mean effect size across all orthogonal axes, termed the ‘efficiency index’. Values of1 (horizontal line in Fig. 2.6C) imply that an allele had an equivalent effect along the axis of selection ason orthogonal axes. Increasingly positive values reflect alleles that take a population to the optimum more‘efficiently’ (i.e., directly along the dashed blue or red line in Fig. 2.5). Together, these results indicate thatadaptive walks from standing variation in my simulations involved more—slightly smaller—steps and aremore ‘meandering’ than adaptive walks from new mutation alone, which use fewer—slightly larger—andmore direct steps (but see Ralph and Coop 2015). These differences in the properties of alleles fixed insimulations initiated with vs. without standing variation contribute to the patterns of phenotypic segregationvariance that ultimately determine the fitness of hybrids.20number of alleles fixed during adaptationa102030DNM DNM &  SGV# alleles fixed0. DNM &  SGVmean effect size12345DNM DNM &  SGVefficiency indexeffect sizeof fixed allelesbpleiotropy of fixed allelescFigure 2.6: Properties of alleles fixed during adaptation. I show results from simulations where parentalpopulations adapted from only de novo mutation (light green; DNM) vs. adaptation from standing variationand new mutation (dark green; DNM & SGV). Each replicate simulation contributed one data point to theplot. Panel (a) shows the average number of alleles fixed during adaptation. Panel (b) shows the averageeffect size (Euclidean length of mutation vector) of alleles fixed during adaptation. Panel (c) shows the allele‘efficiency index’, which plots the ratio of a fixed mutations’ effect size in the direction of selection vs.orthogonal directions. Values of 1 (horizontal line) are equally balanced in these directions, and mutationsare more ‘efficient’ (i.e., they point more directly at the optimum) as this index increases. Statistical testsconfirm all differences as highly significant (not shown).2.4 DiscussionIn this study I investigated parallel genetic evolution and progress toward speciation under adaptation fromstanding variation. I characterized how the extent of genetic parallelism from standing variation changes withthe angle of divergence between parental optima, then illustrated how adaptation from standing variationaffects hybrid fitness under various forms of natural selection. Here, I highlight my key findings, predictionsfor empirical systems, and suggestions for future work.2.4.1 Key predictions and possible testsThe first principal finding of my study is that the degree of genetic parallelism rapidly declines as the angleof divergence increases from parallel toward divergent, especially when a large number of traits affect fit-ness. Practically, this means that the extent of genetic parallelism should decline quickly with phenotypicdivergence. It is possible to test this prediction in natural or experimental populations using techniques suchas ‘Phenotypic Change Vector Analysis’, which estimates important parameters such as the angle between21the vectors and/or the difference in their magnitudes (Bolnick et al., 2018). (Of course, phenotypic mea-surements are imperfect and typically non-comprehensive, and accordingly estimates of inter-populationdivergence are necessarily made with some error.) Natural systems exhibiting repeated instances of easily-quantified phenotypic divergence (Oke et al., 2017; Stuart et al., 2017) are particularly amenable to thisapproach. Given that phenotypic and genetic parallelism are not linearly related (Fig. A.14), I suggest thatanalytical predictions about the extent of genetic parallelism ought to be considered when generating pre-dictions for empirical systems. I also note that studies quantifying genetic parallelism (Jones et al., 2012b)typically do not quantify non-parallel changes. In order to test the predictions about genetic parallelism,it will be necessary for future studies to measure both the number of parallel genetic changes (numerator)and the total number of genetic changes (denominator) in pairs of populations being compared (Alves et al.,2019).My second principal finding is that—relative to when adaptation is from only de novomutation—adaptationfrom standing genetic variation improves the mean fitness of hybrids under parallel natural selection, has lit-tle effect at intermediate angles of divergence, and reduces mean hybrid fitness under completely divergentselection. Practically, this indicates that adaptation from standing variation works against ‘mutation-order’speciation and facilitates ‘ecological’ speciation (Schluter, 2009; Schluter and Conte, 2009). This hypothesiscould be tested most readily in experimental systems where the amount of ancestral standing variation canbe easily manipulated, and where interpopulation hybrids can easily be generated to have their fitness mea-sured in parental environments. It would also be worthwhile to empirically test whether alleles fixed fromstanding variation are indeed more pleiotropic than alleles fixed from de novo mutation, as predicted by mysimulations.I emphasize that the mechanism through which adaptation from standing variation affects hybrid fitness(relative to adaptation from de novo mutation) differs between simulations where populations adapted un-der parallel vs. divergent selection. Under parallel selection, standing variation’s effect on hybrid fitness iscaused largely by parallel genetic evolution and therefore adaptation from standing variation is most likely tohave an effect if populations adapting in parallel are founded with the same standing variation. Under diver-gent selection, standing variation’s effect on hybrid fitness is not caused by genetic parallelism but ratherby cryptic genetic differences—cryptic because they don’t reveal themselves until after hybridization—that evolve between parental populations. Therefore, my predictions about the effect of adaptation fromstanding variation on hybrid fitness under divergent selection should hold regardless of whether populationshave the same or different initial standing variation. A simple prediction—testable theoretically and empir-ically—resulting from my study is that founder effects should have a greater effect on hybrid fitness underparallel selection than under divergent selection.2.4.2 Alternative sources of standing variationMy model addresses the case of adaptation from a pool of standing genetic variation at mutation-selection-drift balance. This framework does not address cases of adaptation where standing variation is generatedfrom other sources. For example, in threespine stickleback, the marine ancestral form maintains standingvariation for freshwater-adapted alleles in a balance between migration of alleles from freshwater populations22and negative selection in the sea (the ‘transporter’ hypothesis; Schluter and Conte 2009; Nelson and Cresko2018. In this case, the pool of standing variation is enriched for alleles that have already swept to highfrequencies in freshwater populations—that is, they are ‘pre-tested’ by selection. Scenarios such as this areespecially likely to lead to genetic parallelism (Schluter and Conte, 2009). The extent to which adaptationfrom standing variation proceeds via the sorting of naïve alleles (as in my model) vs pre-tested alleles (as inthe transporter model) is unresolved.2.4.3 Possible extensionsSome of my conclusions will change under alternative assumptions. Some assumptions—for example a lackof recurrent de novo mutation or gene flow—reduce the extent of genetic parallelism (Nosil and Flaxman,2011; Anderson and Harmon, 2014; Ralph and Coop, 2015; Barghi et al., 2019). I also assumed universalpleiotropy, and future work examining the effect of modularity on my results—especially on changes inparallelism with the angle of divergence—would be valuable. In addition, I considered only haploid selec-tion, had only additive effects of alleles on phenotypes, and assumed that the sole fitness optima availableto hybrids are those to which the two parents are adapted. My analytical results also ignore variation in theprobability that particular mutations arise and fix (or are present as standing variation). Extending my ap-proach to integrate the distribution of fitness effects of new mutations (Eyre-Walker and Keightley, 2007), thecorrelation of selection coefficients across environments (Kassen, 2014; Martin and Lenormand, 2015), andexisting theory on the probability of genetic parallelism from standing variation (MacPherson and Nuismer,2017) will be valuable.I also note that the only reproductive isolating barrier I considered was environment-specific postzygoticisolation. Postzygotic isolation can also be environment-independent, and such ‘intrinsic’ isolating barri-ers are correlated with genetic divergence between populations (Orr 1995; Matute et al. 2010; Moyle andNakazato 2010; Wang et al. 2015). Therefore, my measure of genetic parallelism might be interpreted asbeing inversely proportional to the strength of intrinsic barriers. I also did not consider prezygotic barrierssuch as assortative mating (Gavrilets, 2004). Accordingly, my results might be most relevant for empiricalsystems where ecology-based postzygotic isolation has a primary role in the origin of species.2.4.4 Concluding remarksIn this study I characterized patterns of genetic parallelism and progress toward speciation from standingvariation in pairs of populations with quantitative differences in the direction of selection between them.My findings generate new hypotheses for empirical studies on genetic parallelism and speciation. As evo-lutionary biologists develop increasingly powerful tools for detecting parallel genetic adaptation in nature,it will be important to keep in mind that genetic parallelism could be less common than I might intuit frompatterns of selection and phenotypic similarity. I have also shown that adaptation from standing variationis expected to weaken the strength of isolating barriers that evolve between populations subject to parallelnatural selection. By contrast, adaptation from standing variation can facilitate the process of speciation viadivergent natural selection (i.e., ‘ecological’ speciation), suggesting that adaptation from standing variationmight have a role in adaptive radiation beyond simply increasing the rate of adaptation.23Chapter 3Patterns, predictors, and consequences ofdominance in hybrids23.1 IntroductionWhen divergent populations occur in sympatry, they might mate and form hybrids (Mallet 2005). If thosehybrids are viable and fertile, whether they survive and reproduce depends on their ability to persist underprevailing ecological conditions. Because selection against hybrids limits gene flow between parents (Harri-son 1993), understanding the mechanisms underlying hybrid performance in the field is key to understandingpostzygotic isolation (Barton and Hewitt 1985; Gompert et al. 2017). Quantifying general patterns of pheno-type expression in hybrids would clarify mechanisms of natural and sexual selection that act against hybrids.For example, if hybrids resemble one parent they could thrive in that parent’s niche and readily back-cross(Mallet 1986). Alternatively, if hybrids are phenotypically intermediate for all traits, or possess mismatchedtrait combinations due to dominance in opposing directions (i.e., they resemble parent 1 for trait x, but par-ent 2 for trait y), they might be unable to survive and reproduce in the available niche space (Hatfield andSchluter 1999; Matsubayashi et al. 2010; Arnegard et al. 2014; Cooper et al. 2018). Currently, little is knownabout general patterns of trait expression in hybrids.Previous synthetic studies investigating hybrid phenotypes have conflicting conclusions. Some authorssuggest that hybrid intermediacy is the rule (Hubbs 1940, 1955) whereas others find that hybrids are betterdescribed as mosaics of parental and intermediate characters (Rieseberg and Ellstrand 1993). Such previ-ous studies typically lacked a quantitative framework and/or focused on a single taxon (e.g., fish or plants),limiting our ability to arrive at general conclusions. In addition, previous studies of hybrid phenotype ex-pression tend to use data from domesticated taxa, wherein dominance is often elevated compared to naturalpopulations (Crnokrak and Roff 1995; Fisher 1931). Here, I use a geometric approach to quantify patternsof hybrid phenotypes across a broad range of wild (or recently-wild) plant and animal taxa in a way that iscomparable across studies. By quantifying the ‘parent-bias’ across each pair of traits I determine the extentto which hybrids are intermediate or tend to resemble one parent more than the other. And by quantifyingthe ‘mismatch’ (also termed ‘opposing dominance’ [Matsubayashi et al. 2010; Nosil 2012]) I can determinethe extent to which hybrids have mismatched combinations of divergent parental traits.In this chapter, I systematically document patterns of phenotype expression in hybrids, investigate thepossible predictors of these patterns, and use experimental data to explore the fitness consequences of trait2A version of this chapter has been published as Thompson, K.A., Urquhart-Cronish, M., Whitney, K.D., Rieseberg, L.H., andSchluter, D. Patterns, predictors, and consequences of dominance in hybrids. The American Naturalist 197(3) (awaiting pagination).24interactions in the field. I first summarize the results of 198 studies that compared the phenotypes of hybridsand parents in a common environment and test whether features of a cross—such as the genetic distancebetween, or taxon of, the parents—are associated with dominance (section I). I then use data from an exper-imental planting of recombinant hybrid sunflowers to evaluate whether patterns of pairwise parent-bias andmismatch predict fitness in hypothesized directions (section II). My results provide insight into the mecha-nisms that might commonly underlie selection against hybrids in nature.3.2 I: Patterns & predictors of dominance3.2.1 MethodsIn this section, I provide a brief summary of my methodology for collecting and analysing data on hybridtrait expression from the literature, and then describe the patterns evident in the data. A detailed explanationof all methods is given in the Supplementary Methods.Systematic review of dominance patterns in F1 hybridsI conducted a systematic literature search and identified 198 studies from which I could collect data of atleast one divergent phenotypic trait measured in two parent taxa and their F1 hybrids in a common environ-ment. I included studies that conducted crosses between wild-collected parental populations or laboratorypopulations with ≤ 10 generations of captivity. Crosses in the dataset are both intraspecific (43%) and in-terspecific (57%). Data from wild hybrids (i.e., not from controlled crosses) were only included if hybridswere genotyped to confirm hybrid status and generation. I aimed to include only traits with environment-dependent effects on fitness—traits plausibly under divergent selection between populations (stabilizing se-lection within populations), rather than directional selection in the same direction in both populations. Saidanother way, I attempted only to include traits that could be characterized as ‘non-fitness’ traits [Merilä andSheldon 1999] or ‘ordinary’ traits [Orr and Betancourt 2001]). For example, traits such as ‘embryo viability’are almost certainly under directional selection and were not included in my database. I excluded likelyfitness components because developmental difficulties resulting from hybrid incompatibilities, or heterosisresulting from outbreeding, often affects such traits in hybrids (Coyne and Orr 2004). This choice to excludefitness traits likely renders my analysis on dominance more conservative since hybrid breakdown or heterosiswould manifest as a transgressive phenotype (see Stelkens and Seehausen 2009). By contrast, traits such as‘limb length’ might have particular values best suited to some environments and genetic backgrounds—it isimplausible that such traits would always be selected to a maximum or minimum value. Data from back-cross (BC1 only) and F2 hybrids were collected when available, but were used in a previous publication totest a theoretical prediction about pleiotropy (Thompson 2020). The studies in my analysis spanned a rangeof taxa but included mostly vascular plants (approx. 34 %), vertebrates (approx. 30 %), and arthropods(approx. 30 %), with the few remaining studies using annelids (<1 %), echinoderms (<1 %), red algae(Rhodophyta; <1 %), and molluscs (approx. 2 %).I restricted my dataset to putatively divergently-selected traits. I retained all traits for which the parentswere > 1 phenotypic standard deviation (SD) apart, which was the case for 71.7 % of measured traits (using25Table 3.1: Hypothetical examples of possible F1 trait values, and corresponding values for cross meandunivariate, dparent-bias, and dmismatch (parent phenotypes are scaled to [0, 0] and [1, 1]).F1 phenotype mean dunivariate dparent-bias dmismatch[0.5, 0.5] 0 0 0[0, 1] 1 0 1[1, 1] 1 1 0[0.25, 0.75] 0.5 0 0.5[0.5, 1] 0.5 0.5 0.5[1.25, 1] 1.25 1.25 0.25the smaller of the two parental SDs). I also retained traits for which the parents were < 1 SD apart buthad statistically distinguishable phenotypes (t-test P < 0.05), which accounted for an additional 9.4 % ofmeasured traits. The data for the remaining 18.9 % of traits for which I collected data were discarded (seeFig. B.1). In total, data used for the analysis of dominance patterns comes from 233 unique crosses.After filtering traits, I converted all trait data that were published with a transformation applied (e.g.,ln(x),√x) to their original measurement scale because expectations are not the same on a log or square-rootscale as for raw units. This choice to analyse all traits in their original measurement units influences thedominance patterns because traits that are intermediate on the raw scale might be dominant on a log-scale,or vice-versa, but results greater comparability among traits and studies. I then put all traits in all studieson a common scale where one (arbitrarily determined) parent had a value of 0 for all traits and the otherhad a value of 1 (see Fig. 3.1). Under an expectation of additivity, an F1 hybrid would have a trait valueof 0.5 for all traits. Because I do not make any assumptions about which trait value is ancestral or derived,I cannot distinguish between dominance and recessivity. For example, a trait’s degree of dominance is thesame whether the hybrid trait value is 0.2 or 0.8. Importantly, however, hybrids having two traits with values0.2 and 0.8 have an arithmetic mean phenotype of 0.5 but this hybrid is mismatched rather than intermediate.This failure of simple averaging highlights the need for geometry-based dominance metrics.Quantifying dominance in F1 hybridsI quantified three metrics of dominance. Within a cross, each dominance metric was scaled such that val-ues of 0 indicate no dominance, values of 1 indicate the maximum dominance without transgressing theparental trait range, and values greater than 1 result from transgression (see Table 3.1 for hypothetical hybridphenotypes and corresponding dominance values for all three metrics).The first dominance metric is ‘univariate’ dominance (dunivariate), which considers traits individually.dunivariate measures the deviation of trait values from the additive expectation of 0.5, regardless of direction.For a single trait, this was calculated as:dunivariate = 2(|zi − 0.5|), (3.1)where zi is the scaled mean phenotype of trait i. A dunivariate value of 0 results when a trait is exactly260.000.250.500.751.000.00 0.25 0.50 0.75 1.00trait 1trait 2P1P2{k−1 ∙ dmismatch{visualization of pairwise parent-biasand mismatch in 2D trait spaceF1k−1 ∙ dparent-biasFigure 3.1: Visual overview of how two-dimensional dominance metrics were calculated. When studiescontained two or more divergent traits, I calculated pairwise parent-bias (dparent-bias) and mismatch (dmismatch)of the hybrid phenotype (F1) with respect to the line connecting the two parent phenotypes (P1 & P2 [notethat which parent is called P1 or P2 is arbitrary). This procedure was repeated for every pair of traits. Thescaling factor, k, renders the maximum value observed without transgression (i.e., dmismatch when F1 traitvalues are [0, 1]; or pairwise dparent-bias when F1 trait values are [0, 0]) equal to 1. For two traits, k =√2.Dominance values > 1 can result when traits are transgressive. In this hypothetical example, dparent-bias isapproximately 0.25 and dmismatch is approximately 0.5; see Table 3.1 for other possible F1 two-dimensionalhybrid phenotypes and their corresponding dominance values.intermediate (zi = 0.5; the mean of the parental trait values, 0 and 1); a dunivariate value of 0.5 results whenthe F1’s mean trait value is halfway between intermediate and that of one parent (i.e., zi = 0.25); and adunivariate value of 1 results when the F1 hybrid mean equals that of one of the parents (i.e., zi = 0 or zi = 1).Transgressive traits have dunivariate values > 1. I averaged dunivariate values across traits within each cross toobtain estimates of cross mean dunivariate.The remaining two dominance metrics consider pairs of traits at a time and are calculated in two dimen-sions (see Fig. 3.1 for general overview and Fig. B.2 for examples from the dataset). I consider all pairs oftraits, instead of all traits together, to increase the comparability of dominance values among studies measur-ing different numbers of traits. For crosses where three or more divergent traits were measured, I calculatedtwo-dimensional dominance metrics for each trait pair and then took the mean of all pairwise estimates asthe value for that cross.The second metric of dominance is pairwise parent-bias (dparent-bias), which captures deviation frombivariate intermediacy in the direction of either parent. Imagine a cross between two plant species, oneof which has flowers that are narrow (mean width = z1) and red (colour = z2), representing the bivariatephenotype of [0, 0], and the other species has wide yellow flowers, represented by a bivariate phenotype27of [1, 1]). If their F1 hybrid’s standardized phenotype is [0, 1] (i.e., narrow yellow flowers), then the meandunivariate = 1 but pairwise dparent-bias = 0. A dparent-bias of 0 would also result if the F1 hybrid was exactlyintermediate between the parents (i.e., [0.5, 0.5]). dparent-bias has a minimum value of zero when dominanceis equally strong in the direction of both parents and increases indefinitely as dominance increases in amanner that is biased toward one parent. For each pair of traits, I first determined the scalar projection, b, ofthe hybrid phenotype onto the line connecting parents (solid line in Fig. 3.1). This projection is calculatedas:b =z1 + z2k, (3.2)where z1 and z2 are the hybrid values for trait 1 and 2. I then calculated pairwise parent-bias as:dparent-bias = k ·∣∣∣k2− b∣∣∣, (3.3)where b is the scalar projection from eqn. 3.2, k is a scaling factor (k =√2) used to give a hybrid a phenotypewith parental values for both traits (i.e., [0, 0] or [1, 1]) a dparent-bias value of 1. dparent-bias cannot exceeddunivariate.The third and final metric of dominance is pairwise mismatch (dmismatch), which captures the perpendic-ular distance between the mean hybrid phenotype and the line connecting parental mean phenotypes (Fig.3.1). dmismatch has a minimum value of zero when the hybrid phenotype is on the line connecting parents(i.e., when both hybrid traits in the pair are equally displaced towards the same parent) and increases in-definitely as the variance in dominance among traits increases. Returning to the earlier example of a crossbetween plants with divergent floral traits, dmismatch values of 0 would characterize hybrids with phenotypesthat are varying degrees of intermediate (e.g., [0.5, 0.5] or [0.75, 0.75]) or recover parental phenotypes [0,0] or [1, 1]. A dmismatch value of 1 results when dominance is complete but in opposite directions [0, 1] or[1, 0], which corresponds to narrow yellow flowers or wide red flowers. For each pair of traits, I calculatedmismatch as:dmismatch = k ·√z21 + z22 − b2, (3.4)where, z1 and z2 are as in eqn. 3.1, and b and k are as in eqn. 3.3.Evaluating patterns caused by sampling errorThe above metrics of dominance, applied to data, are a product of both biology—net dominance effects ofgenes—and measurement and/or sampling error. Such error around an intermediate phenotype would appearas dominance because I calculate dominance as the difference between the observed mean phenotype and themid-parent value. In addition, a given amount of error is more likely to result in high (e.g., d> 1) dominanceestimates when the parents involved in a cross are phenotypically similar than when they are more divergent.It is therefore important to quantify the magnitude of dominance observed due to sampling error alone.28To quantify patterns of dominance due to sampling error, I generated 1000 simulated datasets that had anidentical structure to the raw data but where hybrid mean phenotypes were replaced with means calculatedfrom a simulated distribution. Specifically, I generated random normal vectors (using the rnorm function)for each trait measured in F1 hybrids with a length equivalent to the number of hybrids measured by authorsand the original trait SD, but an expected mean that was exactly intermediate between the parents (i.e.,rnorm(n = nF1, mean = µ(P1,P2), sd = SDF1)). I then took the mean of each random vector andreplaced the observed hybrid mean with the simulated mean. The simulated mean can differ from strictintermediacy due only to sampling error. I calculated each of the three dominance metrics for each cross inall simulated datasets and compared the distribution of estimates to what I observed in the original data.Testing possible predictors of dominance in F1 hybridsI explored several possible predictors of dominance motivated by previous results and theoretical predic-tions. For example, previous studies have determined that genetic distance between cross parents affects thefrequency with which hybrid traits transgress the parent range (Stelkens and Seehausen 2009), a pattern thatshould be captured by my dunivariate metric.To determine if genetic distance affects my dominance metrics, I computed genetic distance using genesequence data and tested whether it was associated with any metric of dominance. To maximise the numberof crosses for which I could estimate genetic distance, I used cytochrome b for animals and the internal tran-scribed spacer I and II for plants. Because the species in my dataset can hybridize, it is possible that I mightunderestimate genetic divergence if there is hybridization and introgression in nature—this problem mightbe especially pronounced for the mitochondrial cytochrome b. I could not obtain sufficient nuclear data foranimals, so the genetic distance data should be interpreted with this limitation in mind because mtDNA oftenseems to introgress more readily than nuclear genes (e.g., Bachtrog et al. 2006; Wang et al. 2020). Geneticdistance was calculable for less than one quarter of all crosses, and only 3 intraspecific crosses, so I alsocompared dominance metrics between intraspecific and interspecific crosses—the underlying assumptionbeing that genetic distance between parents is lower in the former compared to the latter.Various taxon-specific reviews have arrived at different conclusions about the extent of dominance ob-served in hybrids. For example, Rieseberg and Ellstrand (1993) considered plants only and concluded thatdominance is common in hybrids whereas Hubbs (1955) worked on fish and concluded that dominance inhybrids is rare. To test whether there might be variation in dominance between taxa, I built a phylogenyencompassing nearly all crosses in my dataset (Fig. B.3) and tested for phylogenetic signal in dominancemetrics. I also tested whether there are differences in dominance between predefined taxonomic groups suchas plants and animals.Finally, I tested for parent-of-origin effects. If parent-of-origin effects are common and have some sys-tematic basis, then hybrid trait values might, for example, tend to resemble the maternal parent more thanthe paternal; this is testable in the present dataset because many crosses (n = 96) were conducted in bothdirections.293.2.2 ResultsPatterns of dominance in F1 hybridsI used data gathered from the literature to generate estimates of dominance in F1 hybrids. I first considereach trait individually, and calculate mean univariate dominance (dunivariate ± 1 SE) for each unique cross inthe dataset. Considering all cross mean dunivariate estimates together, the mean dunivariate for traits measured inF1 hybrids was 0.79 ± 0.078 (Fig. 3.2A [see Fig. B.4 for the same figure with the x-axis extended]; median= 0.55), which suggests that the average trait is not intermediate but rather more than halfway betweenintermediate and parental. In approximately 20 % of crosses (and 20 % of individual traits), the meandunivariate was > 1, indicating transgression.In addition to dunivariate, I calculated two complementary two-dimensional dominance metrics to inves-tigate whether hybrids tend to be biased toward one parent over the other (dparent-bias) or have mismatchedcombinations of divergent traits (dmismatch). These metrics are different from dunivariate because high single-trait dominance could either be in the same direction for both traits (leading to more parent-bias) or inopposite directions (leading to more mismatch). I find that the mean pairwise dparent-bias among crosses was0.68 ± 0.01 (Fig. 3.2B; median = 0.44), implying that, for a given pair of traits, hybrids on average resembleone parent ≥ 68% more than the other. The mean pairwise dmismatch was 0.60 ± 0.10 (Fig. 3.2C; median= 0.31), implying that the average hybrid is about 60% as mismatched as is maximally possible withouttransgression for a given pair of traits. Mismatch did not differ between pairs of traits that were both in thesame category and pairs of traits from different categories (F1,102.47 = 0.0199, P = 0.88).I generated simulated datasets to estimate the magnitude of dominance I would expect from samplingerror alone. I find that the simulation-based estimates of all three dominance metrics were approximatelyone-third as large as what is observed in the real data, with little variation among replicate simulations (seeFig. B.6). These simulation results indicate that the majority of my signal is biological rather than caused bysampling error.Predictors of dominance in F1 hybridsI next investigated whether dominance patterns in F1 hybrids are associated with genetic distance and phy-logeny. I found no significant associations between any metric of dominance and any metric of geneticdistance (see detailed results in Figs. B.7–B.9). In addition, there was no evidence for phylogenetic signal inany dominance metrics (all λ < 1 ×10−5, all P = 1), and no difference in any dominance metrics in compar-isons of major clades (Fig. B.9). I found that dominance is lower when the parental populations have largerdifferences in their phenotype coefficients of variation and greater when parents are more variable, althougheach of these factors explains less than 1 % of the variance in dunivariate (see Fig. B.10). Trait type generallydid not affect dominance, although chemical traits (e.g., pheromones) seemed to have higher dominanceand transgression than all other trait types (Fig. B.11). Some caution is warranted here, however, becausechemical traits were the least well-represented category in the data.Because many crosses were conducted reciprocally (i.e., hybrid crosses were conducted with each parentspecies serving as dam), I could evaluate parent-of-origin effects on trait values. I found that 25.6 % of traits300. 0.5 1.0 1.5density0. 0.5 1.0 1.5density0. 0.5 1.0 1.5densitya distribution of univariate dominance estimates bdistribution of pairwise parent-bias estimates cdistribution of pairwise mismatch estimatescross mean dunivariate cross mean pairwise dparent-bias cross mean pairwise dmismatchFigure 3.2: Patterns of dominance in F1 hybrids. The density plots (y-axis standardized across panels)show the three main dominance metrics contained herein, with each cross contributing at most a single valueper panel. For all three dominance metrics, values of 0 indicate no dominance, values of 1 indicate themaximum without transgression, and values > 1 reflect transgression. The x-axis is truncated at 1.5, but themeans (black arrows) and medians (white arrows; values given in text) are calculated from the whole dataset(see Fig. B.5 for a summary of patterns when each cross contributes a median rather than mean value).Panel a shows univariate dominance (dunivariate; eqn. 3.1), panel b shows parent-bias (pairwise dparent-bias;eqn. 3.3), and panel c shows mismatch (pairwise dmismatch; eqn. 3.4). Panel a contains one value from allcrosses (n = 233) while panels (b) and (c) only contain information from crosses wherein two or more traitswere measured (n = 165).differed significantly (at P = 0.05) between cross directions. The mean magnitude of phenotypic differencebetween cross directions was 0.65 SDs (units of smaller parental SD). Within each cross that was conductedin two directions, I calculated the fraction of traits that exhibited maternal bias and tested whether thisfraction deviated significantly from 0.5. I found that traits of F1 hybrids tend to resemble the maternal parentabout 57 % of the time. (t94 = 2.034, P = 0.0447, 95 % CI = [0.502, 0.657]), suggesting that cytoplasmic ormaternal effects are slightly more common than paternal effects.3.3 II: Fitness consequences of parent-bias and mismatch in recombinantsunflowersThe above analyses were motivated by the hypothesis that, compared to a hybrid that is a perfect intermediate,hybrids resembling parents should fare relatively well and hybrids that exhibit trait mismatches should farerelatively poorly. However, it is not possible to test the fitness consequences of parent-bias and mismatch inthe data synthesized from the literature because no studies in my dataset have both individual-level phenotypeand lifetime fitness data collected in the field. In addition, studies of F1 hybrids would have limited power todetect fitness effects of parent-bias or mismatch because there is little genetically-based phenotypic varianceamong F1s within a cross. Comparisons across systems are undesirable because of methodological andbiological variation among studies and systems. The optimal way to investigate the fitness effects of parent-bias and mismatch is to examine an experimental population of recombinant hybrids—wherein there is31quantitative among-individual variation in the degree of parent-bias, mismatch, and fitness—and then touse these resulting data to test whether dominance metrics are associated with fitness.3.3.1 MethodsStudy system & experimental designTo evaluate the fitness effects of parent-bias and mismatch, I leveraged data from a field experiment in annualsunflowers (Helianthus). The two parent species of the cross were H. annuus ssp. annuus (hereafter simplyH. annuus) and H. debilis ssp. cucumerifolius (hereafter H. debilis). Helianthus annuus is an annual, self-incompatible, diploid that is weedy and widely distributed in its native North America. Helianthus debilis,by contrast, is a small sunflower endemic to central Texas. The two species are highly divergent in manytraits (see Tables B.1 & B.2). Compared to H. debilis, H. annuus is much larger, has a slower life-cycleand greater longevity, has higher water-use efficiency, has thicker leaves and more leaf trichomes, has largerligules and phyllaries, and has a different branching architecture (Whitney et al. 2006, 2010).After four weeks of growth in a glasshouse, 503 H. annuus × H. debilis BC1 hybrid seedlings wereplanted alongside individuals of both parental species in central Texas. Fitness (seed number) as well as 30architectural, floral, ecophysiological, phenological, and herbivore resistance (e.g., trichome density) traitswere measured. Of the 503 BC1 individuals, I retained 475 in the analyses. Fifteen were excluded becauseof labelling mistakes and/or oversights resulting in missing trait data; I expect these exclusions were randomwith respect to trait and fitness values. An additional 13 plants died before some traits could be measuredand were also excluded. Thus, any effects of dominance on fitness detected in my experiment reflect fertilityselection rather than viability selection. Of course, dominance could also affect viability but I could notevaluate this relationship within the current study design. I applied the same trait selection and filteringcriteria as in the systematic review and retained 19 traits (see Table B.1 for trait details). The data from thisexperiment have been previously published (Whitney et al. 2006, 2010).Quantifying dominance metrics in the sunflowersFor each plant, I calculated pairwise dparent-bias and dmismatch (eqns. 3.3 & 3.4) and then took the averageacross all trait pairs. Mean pairwise ln(dparent-bias) and ln(dmismatch) are positively correlated in this dataset(r = 0.81, P < 0.001; Fig. B.12) because the traits of many BC1 individuals are transgressive and highsingle-trait dominance sets the upper limit of both parent-bias and mismatch. Therefore, I investigated theirrespective effects on fitness using multiple linear regressions of the form:ln(Wi) = β0 + β1 · ln(dparent-bias) + β2 · ln(dmismatch), (3.5)where Wi is an individual’s absolute fitness (number of seeds) in this case, and dparent-bias and dmismatchare the mean individual dominance values averaged across each trait pair (residual error term omitted forclarity). I ln-transformed the fitness component and dominance metrics because residuals exhibited severeheteroskedasticity when the raw values were used, although the qualitative conclusions do not change if un-transformed data are analyzed. Diagnostics of the regression model indicated that, in spite of the correlation32101001,00010,0000.5 1.0 3.0mean pairwise dparent−biasseed count1101001,00010,0000.3 0.5 1.0mean pairwise dmismatchseed counta fitness effects ofpairwise parent-biasb fitness effects ofpairwise mismatchFigure 3.3: Effect of parent-bias and mismatch on fitness in H. annuus × H. debilis BC1 hybrid sun-flowers growing in the field. The points are partial residuals extracted from a multiple regression usingvisreg (Breheny and Burchett 2017). Each point represents one individual hybrid plant (n = 475). Bothaxes are log10 transformed. Panel a illustrates the effect of parent-bias and panel b illustrates the effect ofmismatch.between the predictors, my analysis does not suffer from multicollinearity (Variance Inflation Factor = 4.19;maximum Condition Index = 8.19). I also ran the same multiple regression for each trait pair separatelyand asked whether the sign of regression coefficients (β1 and β2) were consistent with those observed in theanalysis of mean pairwise dparent-bias and dmismatch.3.3.2 ResultsIn the BC1 sunflowers, dparent-bias was positively associated with seed count (βˆ1 = 1.75 ± 0.26 [SE], F1,472 =44.68, P = 6.56 × 10−9; Fig. 3.3A) whereas dmismatch had a negative association (βˆ2 = −2.95 ± 0.16, F1,472= 77.26, P < 2.80 × 10−17; Fig. 3.3B). The multiple regression explained 20 % of the variation (i.e., r2) inln(seed count). Both main effects remained significant and in the same direction if an interaction term wasspecified in the model. In this dataset, the fitness consequences of a unit change in dmismatch were larger thanthe fitness consequences of an equivalent unit change in pairwise dparent-bias (|βˆ1| 6= |βˆ2|; F1,472 = 40.86, P =3.94 × 10−10). I note that pairwise trait correlations were typically quite low in these data (mean |ρ| = 0.16;Fig. B.13).I also evaluated dominance-fitness relationships for each pair of traits separately. This analysis is heuris-tic because pairs of traits are not independent, but I present it to complement the above results. Consideringonly statistically significant coefficients, pairwise dparent-bias improved fitness for 67 % of trait pairs anddmismatch reduced fitness for 81 % of trait pairs (Fig. B.14; see also Fig. B.15 for a graphical example ofthe trait pair with the most negative fitness consequences when mismatched). Both of these percentagesare significant departures from 50 %, as determined by exact binomial tests (71 of 106 significant dparent-biascoefficients positive, P = 6.1 × 10−4; 72 of 89 significant dmismatch coefficients negative, P = 3.2 × 10−9).Thus, the fitness consequences of pairwise dparent-bias and dmismatch are consistent between analyses of an33individual’s mean value averaged over all trait pairs and when considering pairs of traits individually.I last evaluated whether the fitness effects of parent-bias and mismatch were driven by individuals withtransgressive dominance values. I first removed all individuals from the dataset with mean pairwise dmismatchvalues > 1 and then conducted the same multiple regression analysis as above. I find that both main effectsremain significant and in the same direction as above (results not shown but included in online R script; n= 430 plants). When conducting the analysis after removing individuals with transgressive mean pairwisedparent-bias values, the main effect terms were in the same direction as above but only mean pairwise dmismatchremained significant (n = 163 plants).3.4 DiscussionIn this chapter, I compiled data from studies that measured phenotypic traits in F1 hybrids to characterisegeneral patterns of hybrid trait expression. I then investigated whether the observed dominance could bepredicted by genetic distance between the parents or phylogeny. Last, I tested whether parent-bias and mis-match were associated with fitness in a field experiment with recombinant hybrid sunflowers. The systematicreview reveals that dominance is common: individual traits in F1 hybrids are typically halfway between theparental midpoint and one parent’s phenotype. This dominance of individual traits causes hybrids to re-semble one parent more than the other and also to be mismatched. Neither genetic distance nor phylogenypredicted any metric of dominance, indicating that it will be difficult to make accurate predictions about thepatterns of dominance for any individual cross. In the sunflower data, pairwise parent-bias improved fitnessand mismatch reduced fitness. I discuss these results in the context of previous research on dominance andtrait expression in hybrids, and highlight the implications for speciation research.3.4.1 Genetic underpinnings of dominance and mismatchAlthough dominance is commonly observed in F1 hybrids, I do not know which trait values are derivedvs. ancestral and therefore cannot relate my data to most theories on the evolution of dominance (e.g.,Haldane’s [1924; 1927] sieve). In any case, inter-population phenotypic divergence in most traits is likelyunderpinned by many quantitative trait loci (QTL) (Otto and Jones 2000) and my results hint at two generalfeatures of such QTL. First, high dominance in F1s implies that, for many alleles underlying adaptation,the heterozygote phenotype is not simply the arithmetic mean of the alternative homozygote phenotypes.Such patterns have been documented in many QTL-mapping studies. For example, Miller et al. (2014)quantified dominance of QTL underlying marine-freshwater phenotypic divergence in threespine stickleback(Gasterosteus aculeatus) and found that the majority of QTL underlying marine-freshwater divergence inthreespine stickleback had partial dominance effects. Second, the QTL underlying different traits seem tohave unequal mean dominance coefficients—dominance for some traits is biased toward one parent anddominance in other traits is more intermediate or biased toward the other.Any specific value of dominance is likely particular to the environment in which study organisms aremeasured. Dominance of individual loci has long been understood to depend on the environment (Hersh1934), and substantial evidence suggests that hybrid phenotypes vary depending on prevailing environmen-34tal conditions (e.g., Demuth and Wade 2007). Although the results of each individual study are likely influ-enced by gene-by-environment interactions (G×Es), I can think of no reason why the overarching patternsdocumented here would change in any particular way if G×Es did not play a role.In F1 hybrids, transgressive trait expression might result from epistasis, although additive gene actionseems more common in reviews of the topic (Rieseberg et al. 1999). Many traits in my dataset transgressedthe parental range, but I caution that this does not necessarily hint at one underlying genetic architectureover another. Dominance values in an F1 are the net effects of dominance at multiple individual loci plusadditive and epistatic effects between loci, with transgressive effects at the tail of the distribution of possibleoutcomes. I therefore see my results in Fig. 3.2 as a documentation of pattern and do not speculate furtherabout underlying causes.3.4.2 Patterns & predictors of dominanceMy results corroborate some previous findings but are inconsistent with others. Hubbs (1940) suggested thatfishes show additive inheritance “as a very general rule" whereas Rieseberg and Ellstrand (1993) suggestedplant hybrids are best characterised as being “a mosaic of both parental and intermediate morphologicalcharacters rather than just intermediate ones”. My quantitative analysis paints a picture more akin to mo-saicism than strict intermediacy. In addition, I find no evidence for any major differences in dominanceamong taxonomic groups, which suggests the choice of study taxon does not bias estimates of dominance.Stelkens and Seehausen (2009) found that the genetic distance between parents was positively correlatedwith transgression frequency—the tendency for traits to fall outside the range of parental values. I used analmost entirely independent dataset and found that genetic distance did not predict transgression or any otheraspect of trait expression in hybrids. Perhaps the most likely cause of this discrepancy is that, in addition to‘ordinary’ traits like those considered herein, Stelkens and Seehausen (2009) also considered more traditional‘fitness’ traits. Transgression in such traits could reflect ‘intrinsic’ hybrid incompatibility (e.g., small bodysize due to poor condition or low seed production due to inviable ovules) and heterosis (e.g., larger bodysize or high seed count due to overcoming inbreeding depression in parents). Incompatibility increases withparental genetic divergence (Orr 1995; Moyle and Nakazato 2010; Matute et al. 2010; Wang et al. 2015),and heterosis seems to as well until inviability becomes substantial (Wei and Zhang 2018). Importantly,such inviability and heterosis would manifest as high dunivariate or transgression using my approach. BecauseI consider traits that are putatively under stabilizing selection within populations, the mechanisms linkinggenetic distance with transgression in earlier studies do not apply to the present dataset.Although I specifically excluded traits that are directly linked to fitness, it remains possible that hybridincompatibilities underlie some patterns documented herein. For example, one study conducted crossesbetween wild Drosophila melanogaster and D. simulans. Male hybrids of this cross are (typically) inviable,and so David et al. (2002) only report data for females in parent species. If there is inviability that isundetected in some studies, this might influence estimates of dominance. A lack of relationship betweengenetic divergence and dominance, however, suggests that incompatibility is not likely the primary drivingforce of the observed patterns.353.4.3 Fitness consequences of mismatchMy results clarify the potential for dominance to have a role in driving progress toward speciation. Thedata collated from the literature challenge the conjecture that reduced F1 fitness is due only to phenotypicintermediacy and hybrids ‘falling between parental niches’ (Coyne and Orr 2004; Nosil 2012). Rather, F1hybrids often possess novel multivariate phenotypes that are mismatched for divergent traits. In nature, thephenotype of an organism is an integrated suite of traits that function together to influence performanceand ultimately fitness (Brodie 1992; Arnold 1983). Because mismatch, caused by dominance in conflictingdirections among traits, breaks up suites of integrated traits, mismatched hybrids might be poorly suited toany environment.In the sunflower data, I found that pairwise parent-bias improved fitness and mismatch reduced fitness.Importantly, mismatch was more detrimental than parent-bias was beneficial. F1 hybrids are likely closer inphenotype to one parent than the other, and yet at the same time have some traits resembling the less-similarparent which might render them unable to survive and reproduce in the similar-parent’s niche or perhapsin any niche at all. At present, it is not clear how general this finding is. It would be valuable to conductmore field experiments with recombinant hybrids to arrive at generalities in the ways that parent-bias andmismatch affect fitness.It is informative to examine the trait pairs that had the highest fitness consequences when mismatched(Fig. B.14). The most negative fitness effects resulted when development duration was mismatched withheight of the uppermost branch (Fig. B.15). Helianthus annuus has a more prolonged phenology than H.debilis, taking about 28 days longer to initiate inflorescence formation in this experiment (Table S2). Inaddition, H. annuus is a tall plant with branches distributed throughout the main stem (uppermost branchheight above ground: mean = 133 cm), whereas H. debilis is a much shorter plant with branches clusteredat the base (uppermost branch: mean = 17 cm). Plants that mature slowly (like H. annuus) but are short andcompact (like H. debilis) have lower fitness than rapid-developing compact plants (Fig. B.15). The parentalphenotypes apparently reflect a trade-off, where the benefits of being a compact plant are compromised by aprolonged development.Due to the segregation of divergent alleles, individual backcross and F2 hybrids might be more mis-matched on average than F1s. Such increased mismatch would result in ecological hybrid breakdown—where recombinant hybrids have lower fitness than F1s due to increased trait mismatches (Arnegard et al.2014). In the present study, I was limited to comparing cross mean data. It would be valuable to compiledata for hybrid crosses raised in a common environment where data for individual hybrids can be analyzed.In particular, quantifying how the magnitude of phenotypic mismatch observed in backcross and F2 hybridscompares to F1s would allow us to infer the likely strength of mismatch-based hybrid breakdown. AlthoughF2s are more variable than F1s (East 1916), if divergent traits are linked in the genome (e.g., Westram et al.2018) or are controlled by the same pleiotropic allele (e.g., Rennison et al. 2015), then segregation might notresult in increased mismatch.363.5 ConclusionIn this study I synthesized data from 198 studies to describe general patterns of phenotype expression inF1 hybrids. Compared to previous studies with a similar goal, the distinguishing features of my analysisare that I used quantitative trait data rather than bins of ‘parental’ vs. ‘intermediate’, looked across severalmajor clades, and examined divergently selected traits in wild organisms. For individual traits, reasonablyhigh dominance is the rule rather than the exception. Previous studies have documented the phenomenonwhere dominance acts in opposite directions for different traits (Matsubayashi et al. 2010). I built on theseprevious studies by quantifying mismatch using simple geometry and demonstrating that mismatch affectsthe average hybrid to a fairly substantial degree.Previous authors have qualitatively drawn a link between trait mismatches and hybrid fitness (e.g., Arne-gard et al. 2014; Cooper et al. 2018), and I add to these earlier results by directly linking individual-levelmismatch metrics to fitness in sunflowers. This result contributes to a growing literature on trait interactionsin hybrids, and I suggest that future studies use my approach (or a complementary approach) to test the fit-ness consequences of mismatch directly. Such trait interactions are similar to Bateson-Dobzhansky-Mullerhybrid incompatibilities (BDMIs) with fitness consequences mediated via ecology. Ecological BDMIs havethe opportunity to affect many F1 hybrids and could be a major mechanism of extrinsic post-zygotic isolation.Only field observations and experiments can provide the data that are necessary to test this hypothesis.37Chapter 4Experimental hybridization studies suggestthat pleiotropic alleles commonly underlieadaptive divergence between naturalpopulations4.1 IntroductionWhen populations adapt to their environment, they increase the frequency of (or fix) alleles that affect thephenotypes of traits under selection. The alleles that underlie adaptation can affect multiple traits at a time,a phenomenon known as pleiotropy (Stearns 2010). In recent years, evidence has accumulated, largely fromevolutionary model systems, which suggests that pleiotropy is common (although it might only affect asmall subset of an organisms’ traits; Wagner et al. 2008; Wang et al. 2010; Wagner and Zhang 2011; Hilland Zhang 2012). If the pleiotropic effects of alleles are deleterious, compensatory mutations that counteractthis deleterious pleiotropy can be favoured by natural selection (Phillips 1996; for empirical examples ofcompensatory mutation, see Adam et al. 1993; Poon and Chao 2005; Howe and Denver 2008; Merker et al.2018). Although this model of adaptation via pleiotropy and compensation emerges in many theoreticalmodels of adaptation (Orr 2000; Barton 2001), it is unclear whether such a process typically characterisesadaptation in natural populations.Predictions from theoretical models of divergent adaptation and hybridization can be tested to inferwhether adaptation in natural populations typically involves pleiotropy and compensation. Barton (2001)conducted simulations of Fisher’s (1930) geometric model of adaptation in a case where two populationswith ten traits experienced divergent selection on a single trait while the other nine were subject to stabiliz-ing selection. Following hybridization of the two populations, there was appreciable segregation variancein the nine traits under stabilizing selection. This segregation variance was caused by the recombinant hy-brids inheriting alternative combinations of compensatory alleles. Importantly, the amount and/or averageeffect size of compensatory alleles should be positively correlated with the amount of phenotypic divergencebetween the parents. Thus, the theoretical prediction under adaptation via pleiotropy and compensation is:as the phenotypic divergence between pairs of populations increases, so should the amount of segregationvariance in non-divergent traits observed in their hybrids. See Fig. 4.1 for a visual overview of this pre-diction and Fig. C.1 for the results of computer simulations illustrating the prediction more quantitatively.In this chapter, I test this theoretical prediction using data collated from experimental hybridization studies.38In doing so, I illustrate that alternative processes such as genetic drift are unlikely to underlie the observedpatterns.4.2 MethodsI conducted a systematic literature search with the goal of identifying studies that measured phenotypic traitsand variances in two parent taxa and their (intra-specific or inter-specific) hybrids in a common environment.Most of the collected data are analyzed in a separate study investigating phenotypic dominance in F1 hybrids(Thompson et al. 2021). To be selected for inclusion in the larger dataset, studies had to measure at least onenon-fitness trait (i.e., ‘ordinary’ trait [Orr 2001]) in two parent taxa (different species or divergent populationsof the same species) and their F1 hybrids. In addition, parent taxa had to be fewer than 10 generationsremoved from the wild (details of the literature search are given in the supplementary methods, and thereasons for excluding each study is included in the main literature search data frame [see Data Accessibility]).In total, I (with help) screened over eleven thousand studies and collected data from 198. Of these 198studies, all that met the following two additional criteria were included in the present analysis: (1) F2 hybridswere measured and (2) the parents had significantly different phenotypes for at least one trait and werestatistically indistinguishable for at least one other trait.After obtaining studies for possible inclusion, I filtered and binned the data to generate summary statisticsfor analysis. Filtering and binning decisions were—by necessity—somewhat subjective, and I present the testof the main hypothesis for summary datasets generated under alternative filtering and binning criteria in TableS2. Since the conclusions are generally robust (highest P = 0.0523) to alternative data processing decisions,it seems unlikely that the study selection criteria bias my conclusions. In addition, further analysis withpotentially low-power studies removed illustrate that the observed patterns are not caused by associationsbetween sample size (number of individuals measured) and any variables (see also Table S1). I also note thatmethods are only briefly detailed here in the main text, but full detail with appropriate citations are givenin the Appendix. All analyses were conducted in R v3.5.1 (R Core Team 2019) and all data underlying thearticle are deposited in the Dryad Digital Repository: the main text, I restrict my analysis to morphological traits—by far the most frequently measuredtrait type in the studies that met the above criteria—to maximize the degree to which traits and units werecomparable. In total, I retained data from 15 crosses (14 studies) for the present analysis (Bradshaw et al.1998; Bratteler et al. 2006; Hermann et al. 2015; Husemann et al. 2017; Jacquemyn et al. 2012; Koellingand Mauricio 2010; MacNair et al. 1989; McPhail 1992; Mione and Anderson 2017; Pritchard et al. 2013;Raeymaekers et al. 2009; Selz et al. 2014; Shore and Barrett 1990; Vallejo-Marín et al. 2017). Of these 14studies, nine crossed vascular plants, four crossed fish (one study contained two crosses), and one crossedcopepods. Eight crosses were inter-specific and seven were intra-specific.For each study I divided traits into two groups: those that differed between the parents — which I assumewas the result of divergent selection — and those that did not and were more likely (though not necessarily)subject to stabilizing selection. I classified traits as divergent if they were significantly different (P < 0.05)in a t-test. My conclusions are unchanged if parent divergence in phenotypic standard deviations is used39[divergent if parents are > 1 SD apart] as a binning criterion. For each trait, I calculated the degree ofphenotypic divergence in units of parental phenotypic SDs using the smaller of the two parental values. Foreach study, I then calculated phenotypic divergence for both groups of traits as the mean of ln-transformeddivergence values.For traits that were statistically indistinguishable between parents, I determined the segregation varianceof each as:var(s) =4var(F2)2var(F1) + var(P1) + var(P2)(4.1)Wright (1968). This quantity normalizes for the standing variation observed in each parent and F1 hybridsand captures the variance due to the segregation of population-specific or species-specific alleles. For eachcross, I took the mean of these values across all non-divergent traits after ln-transformation as an estimate ofsegregation variance.My prediction was that if adaptation commonly proceeds via pleiotropic and compensatory alleles, thereshould be a positive relationship between parental divergence—for divergently selected traits—and segrega-tion variance—for traits that do not differ between the parents. Visualization of linear models and statisticaltests of heteroskedasticity clearly showed that the assumptions of parametric statistical analyses were vio-lated (see Fig. C.2). I therefore tested all predictions using Spearman’s rank-order correlations, which testif more divergent pairs of populations beget hybrids with more (or less) segregation variance as compared tolesser divergent parental taxa.A similar pattern to what is predicted above could be the result of genetic drift and have nothing to dowith divergent natural selection. Specifically, if more phenotypically divergent pairs also diverged longer agothan less phenotypically divergent pairs, they might have fixed a greater number of compensatory mutationsfor all of their traits (if such mutations fix at a steady rate over time). If this was the case, one woulddetect the predicted pattern even if the alleles underlying divergence were not pleiotropic. It is thereforeimportant to rule out this role for time by testing whether phenotypic divergence of parents is correlatedwith their divergence time in the studies analyzed herein. I did this using three main approaches: (1) bycomparing phenotypic divergence of intra-specific cross parents to that of inter-specific cross parents, (2)by evaluating the correlation between neutral gene sequence divergence and phenotypic divergence (unitsof base pairs), and (3) by evaluating the correlation between estimates of divergence time and phenotypicdivergence (similar to [2] but in units of time based on fossil-calibrated phylogenies).4.3 ResultsI observed a positive correlation between the mean parental phenotypic divergence in statistically divergenttraits and the mean segregation variance in statistically indistinguishable traits (Spearman’s ρ = 0.800, P =0.000581, n = 15) (Fig. 4.2). The magnitude of the phenotypic difference between parents for statisticallyindistinguishable traits was not significantly correlated with the segregation variance in those traits (Spear-man’s ρ = 0.446, P = 0.0972, n = 15) (Fig. C.3). The patterns were generally robust to data processingdecisions (see Table S2), only slightly surpassing the significance threshold when I included physiological40(i) little divergence in body size; stabilizing selection on shadebody shadebody size+ (darker)− (lighter)+ (larger)− (smaller)phenotype landscapemutation and adaptationtwo scenarios of adaptation(ii) substantial divergence in body size; stabilizing selection on shadeoverview of mutationwith pleiotropyaoriginalphenotype optimumphenotypemutationderivedphenotypesegregation variance in F2 hybrids(i) little body size divergencebegets little variance in shade (ii) substantial body size divergencebegets substantial variance in shade hypothetical example andtheoretical predictionbFigure 4.1: Overview of adaptation with pleiotropic alleles and theoretical prediction. Panel A showsa general overview of Fisher’s geometric model, which relies on pleiotropic mutation. The upper sectionshows the phenotype landscape under consideration, wherein the x-axis is body size and the y-axis is bodyshade. The lower section illustrates the fixation of a pleiotropic allele during adaptation. The large circledefines the space wherein mutations are beneficial; mutations that point outside the circle are deleterious.The original phenotype is medium in size & shade, whereas the optimal phenotype is larger but the sameshade. A mutation arises that greatly increases size and has a deleterious pleiotropic effect to darken shade.Since the mutation is beneficial (points inside the circle), it has a high probability of fixation in spite of thedeleterious side-effect. Panel B illustrates the theoretical prediction in two diverging populations – red andblue – with the same initial phenotype for size and shade—colour here is just used to visually demarcateparent populations and hybrids (purple) and is not considered a trait. Arrows represent individual mutationsas in panel (a). In each of two scenarios shade is under stabilizing selection in the two populations. Scenario 1is a case where the two populations diverge little in body size and scenario 2 represents substantial divergencein body size. The lower section of the panel illustrates the outcome of hybridization. The key insight is thatthe segregation variance in shade is greater in scenario 2 than scenario 1. Body size segregates as well, but itwould do so in a model without pleiotropy whereas shade would not necessarily. Darker recombinant hybridindividuals inherited mostly compensatory alleles that darken shade (i.e., point ‘up’) and lighter individualsinherited mostly compensatory alleles that darken shade (i.e., point ‘down’).41and chemical traits (P = 0.052) in the analysis. 1.0 1.5 2.0mean ln(phenotypic distance [SDs]of divergent traits) between parentsmean ln(segregation variance) ofnon−divergent traits in hybridsempirical test oftheoretical predictionFigure 4.2: Scatterplot depicting the relationship between phenotypic divergence in parents (statisti-cally divergent traits) and segregation variance in hybrids (statistically indistinguishable traits). Eachpoint (n = 15) represents a unique cross between two populations or species. Points to the right on the x-axisrepresent crosses where the parent taxa exhibit a relatively large magnitude of phenotypic divergence fortraits deemed ‘divergent’. (Spearman’s ρ = 0.800, P = 0.000581). The line is a loess fit.Divergence time could correlate with phenotypic divergence between populations, which would renderit difficult to disentangle the relative roles of time and phenotypic divergence in causing the pattern shownin Fig. 4.2. I found no evidence for a difference between intra-specific and inter-specific crosses in parentalphenotypic divergence (F1,13 = 0.013, P = 0.912; Fig. C.4A & B). Additional analyses found no supportfor associations between any variable and genetic divergence (Fig. C.4C), divergence time (Fig. C.4D), orphylogeny (phylogenetic signal test, all P > 0.5).4.4 DiscussionI leveraged data from experimental hybridization studies to conduct a correlative test of the hypothesis thatdivergent adaptation is associated with transgressive phenotypic variation in recombinant hybrids. Thisprediction holds if the genes underlying divergent adaptation are pleiotropic and does not if they are not (orif they are pleiotropic but have infinitely small individual effects [Barton et al. 2017]) (see Fig. C.1). Giventhe lack of effect of divergence time (or its correlates) on phenotypic divergence in the data, the consistencybetween the results presented here and the theoretical prediction provides indirect and correlative evidencethat the genes used during adaptation are indeed pleiotropic and of appreciably large effect. The results mightalso hint at of the mode of adaptation for the taxa considered herein. For example, adaptation from standingvariation causes greater transgressive segregation variance compared to adaptation from de novo mutation(Thompson et al. 2019), and thus the observed patterns could be a consequence of adaptive divergencefrom standing variation being commonplace (Barrett and Schluter 2008). Even if large-effect pleiotropicmutations arise, models with slowly moving fitness optima predict that only alleles with very-small effects42will be used during adaptation (Matuszewski et al. 2014). The analyses above suggest that optima in naturemove quickly enough for alleles of non-trivial effect sizes to be incorporated.My findings might initially appear to contradict the results of previous studies of transgressive segrega-tion. For example, Stelkens and Seehausen (2009) and Stelkens et al. (2009) found that genetic distance,but not phenotypic distance, predicts transgressive segregation. Although this seems to contradict the pat-tern shown in Fig. 4.2, the predictions are not directly comparable because I binned traits into categoriesof divergent & non-divergent and compared parental divergence in the former to hybrid variance in the lat-ter. By contrast, Stelkens’ studies investigated the degree to which individual hybrids are transgressive fortraits considered on their own or across all traits. Thus, my analyses test separate hypotheses. Rieseberget al. (1999) also predicted that genetic divergence and transgressive segregation will be positively correlatedwhen parents experience stabilizing selection at a common optimum. This prediction arises purely from sub-stitutions fixed by drift and subsequent compensatory mutations. In the present dataset, genetic divergence isnot correlated with transgressive segregation variance (P = 0.801; results not shown but analysis included inarchived R script). It is likely that, in wild and outbred taxa, any effect of drift on transgressive segregationis obscured by the segregation of large-effect pleiotropic alleles and compensatory mutations fixed duringadaptive divergence in other traits.Experiments can be conducted to directly test the prediction considered herein. In an experimental evolu-tion system where individuals and traits are easily measured, parental lines could be selected for divergenceto varying degrees and then hybridized with a common ancestor. The traits that responded to divergent selec-tion should be identified and measured, as should the traits that did not diverge and were putatively subjectto stabilizing selection. The expectation is that—if mutations are universally pleiotropic—the amount ofsegregation variance in non-divergent traits should increase with the phenotypic distance of divergent traits.Because alleles fixed from standing variation are expected to be more pleiotropic than those fixed from denovo mutation (Thompson et al. 2019), the transgressive segregation variance should be greater if the pop-ulation is able to use standing variance for adaptation compared to if it must rely on de novo mutation. Ifdesired, one could attempt to identify the causal alleles directly using QTL mapping.Segregation variance in non-divergent traits is expected to be deleterious and accordingly hybrid fitnessshould decline as the segregation variance increases. If segregation variance is observed for non-divergenttraits, this directly implies that variance in the trait is deleterious—compensatory mutations would not befavoured if not for their ability to counteract deleterious pleiotropy. The problem with relying entirely onphenotypic measurements for empirical tests is that segregation variance could manifest in unmeasured traitsand thus could easily be missed. It will therefore be useful, albeit difficult, to test predictions about fitnessdirectly. If divergent experimental populations are hybridized, the fitness of F1 and F2 hybrids could becompared in a common environment. The clear prediction is that the loss in fitness of F2 hybrids (due tosegregating breakup of co-adapted compensatory alleles) compared to F1s will be greater in more divergentlyselected lines. A difficulty arises when attributing this loss in fitness to segregation variance of non-divergenttraits, because segregation variance in the divergent trait(s) will affect fitness in an environment-dependentmanner (see Fig. 1 of Barton (2001)). For example, in an intermediate environment the F2 would havelower fitness than the F1 even without pleiotropy due to deleterious segregation variance of the selected43trait(s). However, if the F2 has lower fitness than the F1 in both the ancestral and derived environments,this implicates the segregation variance in non-divergent traits as the cause. Perhaps the best test wouldbe to sequence the F2s and look at selection on heterozygosity because the signature of selection againstincompatible compensatory mutations in an F2 is selection for heterozygosity (Simon et al. 2018). Thus, aftermeasuring the fitness of F2s in a particular environment, selection on the divergent trait(s) would manifestas selection favouring particular hybrid index and selection against segregating phenotypic variance in non-divergent traits would manifest as selection for heterozygosity. Such an experiment would be valuable forestablishing a general link between adaptive divergence and reproductive isolation.Although I illustrate a correspondence between theory and data, I did so using a correlational approachand with a small sample size of 15 crosses. I offer no conclusive proof that pleiotropic alleles and com-pensatory mutations are the cause of the observed pattern. There are other plausible mechanisms besidespleiotropy that could underlie segregation variance in non-divergent traits. For example parallel phenotypicevolution (if it has a non-parallel genetic basis [e.g., Ono et al. 2017]) can cause segregation variance in traitsthat do not differ between the parent taxa (Chevin et al. 2014; Thompson et al. 2019). For this mechanismto underlie the pattern shown in Fig. 4.2, there would have to be a correlation between parallel phenotypicevolution in some traits and divergent evolution in others — this seems unlikely. Although results presentedherein are consistent with theory, empirical tests using experimental evolution would be a stronger and moredirect test of the underlying mechanistic hypothesis. The ability of such studies to make a direct link tohybrid fitness is also very powerful. Such studies, paired with my indirect analysis across many taxa, wouldgreatly strengthen my grasp on the generality of pleiotropy’s role in adaptive evolution. At the very least,my analysis should serve to buttress the assessment that models fundamentally based on pleiotropy such asFisher’s (1930) geometric model are robust and useful abstractions of the evolutionary process.44Chapter 5Adaptive divergence and the evolution ofhybrid trait mismatch in threespinestickleback5.1 IntroductionOne of the central tenets of the ‘ecological speciation’ hypothesis is that adaptive phenotypic divergenceleads to the evolution of reproductive isolation (Schluter 2000; Nosil 2012). Synthetic studies have foundsupport for this link by illustrating that gene flow between populations decreases as their environmentsdiverge, controlling for geographic distance (Shafer and Wolf 2013). Such patterns suggest that reproductiveisolation between diverging lineages is indeed, to some extent, a function of phenotypic divergence. Acritical determinant of reproductive isolation is the fitness of hybrids (Coyne and Orr 2004; Irwin 2020).‘Extrinsic postzygotic isolating barriers’, which result from natural and/or sexual selection against otherwiseviable and fertile hybrids, evolve before ‘intrinsic’ hybrid incompatibilities in many systems (Hatfield andSchluter, 1999). In these cases, the performance of hybrids under prevailing ecological conditions is likelyof primary importance for determining gene flow between recently-diverged hybridizing lineages.The phenotype of hybrids is the ultimate determinant of their performance (Arnold, 1983), and recentevidence suggests that hybrids are often ‘mismatched’ for divergent parental traits (Thompson et al., 2021).Mismatch refers to the case where hybrids express trait values in atypical combinations not seen in parentsnor in hypothetical hybrids that are geometrically intermediate. Such mismatch results from two main mech-anisms. First, differences between traits in the degree of dominance can lead to mismatch in hybrids. Forexample, a hybrid that is identical to one parent for some traits and identical to the other parent for othertraits might have difficulty surviving and/or reproducing in nature if the trait combinations function poorly asa consequence (Matsubayashi et al., 2010). Less extreme mismatch can result when dominance is less polar-ized among different traits, for example when the magnitude of dominance is inconsistent among differenttraits that are dominant in the same direction (Thompson et al., 2021). Such dominance-caused mismatchcan affect all hybrids from the first-generation (i.e., F1) and beyond. Mismatch can also result from additivegenetic variation that segregates in hybrids (i.e., segregation variance; Lande 1981; Slatkin and Lande 1994)from the first back-cross and second filial generations (i.e., BC1 and F2; Arnegard et al. 2014). In suchrecombinant hybrids, traits can become uncoupled and individual hybrids can express ‘mismatched’ traitsdue to their unique genetic composition. Importantly, dominance is often expressed in recombinant hybrids,which can mediate the mismatch caused by segregation variance.45Such trait mismatches could limit hybrid fitness in most conceivable environments because many com-binations of trait values are unlikely to ever function well together. Since they cause reduced performanceand fitness, mismatched traits in hybrids represent incompatibilities and are phenotypic analogs of clas-sic Bateson-Dobzhansky-Muller incompatibilities (Bateson, 1909; Dobzhansky, 1937; Muller, 1942), butwhere the fitness effects are only expected to emerge under the appropriate environmental context (Arnegardet al., 2014). Several recent studies have provided evidence of such trait-trait incompatibilities in hybrids.In threespine stickleback fish, (Gasterosteus aculeatus L.), individual F2 hybrids that had mismatched jawtraits tended to have reduced feeding performance compared to relatively intermediate individuals (Arnegardet al. 2014). In sunflowers (Helianthus spp.), individual backcross hybrids with a greater extent of mismatchacross multiple pairs of traits had lower fitness than less mismatched individuals (Thompson et al. 2021).Other studies have drawn fitness inferences indirectly based on mismatched behavioural and morpholog-ical or physiological traits that characterize typical F1 hybrids (e.g., being behaviourally attracted to onehabitat but having a poorly suited physiology for that habitat; Vinšálková and Gvoždík 2007; Matsubayashiet al. 2010; Cooper et al. 2018). If trait mismatch in hybrids evolves in a manner that is predictable basedon the phenotypic divergence between parents, this might represent a mechanism directly linking adaptiveecological divergence to reproductive isolation (Rundle, 2002; Nosil, 2012).There are two main reasons why we might expect trait mismatch to increase with increasing adaptive phe-notypic divergence between populations. The first is due to dominance-caused mismatch. A given amountof dominance relative to parents (e.g., 25 % more similar to parent A for trait 1, and 25 % more similar toparent B for trait 2) will generate a greater magnitude of mismatch as those two traits diverge further. Thesecond mechanism linking mismatch to divergence is related to segregating phenotypic variation in recom-binant (i.e., F≥2 or backcross) hybrids. Theory predicts that the amount of phenotypic variation in the traitsof recombinant hybrids will increase over the course of an adaptive walk (Slatkin and Lande 1994; Barton2001; Chevin et al. 2014). This occurs because the number and/or effect size of QTL for a trait increases aspopulations diverge for that trait, and as a result a greater number of larger QTL are expected to segregate inF2 and BC1 hybrids in ‘wider’ crosses. Because of the number of crosses involved, few studies have explic-itly tested this prediction with phenotype data (but see Thompson 2020; and see Edmands 1999 for a similarstudy with intrinsic fitness components). This increase in variance is expected to cause increased averagemismatch because more extreme combinations of traits will appear in recombinant hybrids as divergenceproceeds. Importantly, the effect of variance on mismatch depends on the underlying dominance patterns. Iftraits are additive and the hybrid mean phenotype is intermediate between parents, variance orthogonal to theaxis of parental divergence will increase mismatch. If traits exhibit opposing dominance, where the hybridmean phenotype is displaced from the axis of parental divergence, such orthogonal variance will have lessof an effect on mismatch because variance will cause some individuals to be less mismatched than the meanand others to be more mismatched than the mean. As a result of these two mechanisms, mismatch in F1s isprimarily expected to be a result of dominance, whereas mismatch in recombinant hybrids might be due toone or both of dominance and segregation variance.In this chapter, I use threespine stickleback fish to test the prediction that mismatch in hybrids increaseswith the magnitude of morphological divergence between parents. I leveraged the unique biology of stick-46leback, where populations have diverged to varying degrees from a common anadromous (i.e., spawning inrivers but otherwise residing in the sea) ancestor. Freshwater stickleback populations primarily differ alonga limnetic (i.e., zooplanktivorous) to benthic (i.e., consuming large macro-invertebrates in vegetation or lakesediments) axis (Bell and Foster 1994). Although all have adapted to the freshwater habitat, the more lim-netic freshwater populations tend to be more phenotypically similar to anadromous populations whereas themore benthic populations are relatively derived. Freshwater populations are recently (approx. 10 kya) andindependently derived from an anadromous ancestor whose descendants remain abundant in the sea todayand are readily crossed with derived forms. Because more benthic populations have undergone more pheno-typic divergence from the anadromous ancestor, I hypothesize that their hybrids (in crosses with an extantanadromous population) will have more mismatch than those produced from less divergent populations. Totest this hypothesis, I measure morphological traits in hybrids of 12 different ancestor-derived crosses, quan-tify mismatch, and investigate its causes. My results hint at a possible general mechanistic basis for thebreakdown of (extrinsic) hybrid fitness during ecological speciation.5.2 Methods5.2.1 Study systemThe threespine stickleback is a teleost fish species distributed throughout the coastal areas of the northernhemisphere (Bell and Foster 1994). Anadromous stickleback colonized an array of post-glacial lakes andhave rapidly adapted to prevailing ecological conditions (Schluter 1996). Stickleback that live in lakes con-taining predators and other competitor fish species (e.g., prickly sculpin) remain similar to the anadromouspopulation for many morphological traits (Ingram et al., 2012; Miller et al., 2019). By contrast, popula-tions that have evolved in small lakes with few or no predators and competitors often have more derivedphenotypes specialized for foraging on large benthic invertebrates.Because adaptive divergence between anadromous and freshwater populations occurred so rapidly, popu-lations can be readily crossed and typically have few if any ‘intrinsic’ incompatibilities (Hatfield and Schluter1999; Rogers et al. 2012; Lackey and Boughman 2017). Extant anadromous populations, within a particulargeographic location, are phenotypically similar to the ancestral populations that founded present-day fresh-water populations (Morris et al. 2018). I leveraged this continuum of phenotypic divergence using crossesto test that hybrid mismatch will be greater when more benthic species are crossed with the anadromousancestor than when the ancestor is crossed with more zooplanktivorous populations.5.2.2 Fish collection and husbandryWild fish were collected in British Columbia, Canada, in April–June of 2017 and 2018. I sampled twelvefreshwater populations from nine lakes (Fig. 5.1A; three lakes [Paxton, Priest, and Little Quarry] containreproductively isolated benthic-limnetic ‘species pairs’ [McPhail 1992] and thus contributed two populationseach). The anadromous population was collected from the Little Campbell River (Fig. 5.1A). Wild fish werecaught using minnow traps or dip nets. I crossed six gravid anadromous females with six males from eachfreshwater population to generate six unique F1 hybrid families per population, and also generated four to six4750 km  longitude (°W)latitude (°N)American SamoaBaBelizeCook Is.Costa RCCaymEcuHonduraMexicoNicaragNiuePitcairn Is.Fr. Polynesiatrait measurementsbsampling locationsa#AFR#DFRFDSSDSSNT #LAPEDHDGRL#GRPFSLBDGWBW PSPGYVR✈YCD✈PCH BULLCRPSTPAXCRNLQUPAQKLNNOR125 124.5 124 123.5 12348.64949.449.649.849.248.8122.5CANADAUSAFigure 5.1: Overview of sampling locations and trait measurements. Panel (a) shows locations wherethe source populations were collected in British Columbia, Canada. Boxes show collection locations of theanadromous population (red box; LCR—Little Campbell River) and freshwater populations (blue boxes;left to right: PCH—Pachena Lake; PAX—Paxton Lake; CRN—Cranby Lake; PST—Priest Lake; LQU—Little Quarry Lake; PAQ—Paq (Lily) Lake; NOR—North Lake; KLN—Klein Lake; BUL—Bullock Lake).Green labels give airport codes for major cities (YCD—Nanaimo; YVR—Vancouver). Panel (b) showsthe measurements of all 16 traits in the dataset and standard length. The upper section of the panel showsthe lateral view (traits left to right: SNT—snout length; ED—eye diameter [the transparent shade of redindicates this trait was measured but not analyzed—see ‘Repeatability’ section of methods]; HD—headlength; FDS—length of first dorsal spine; BD—body depth; SL—standard length; SDS—length of seconddorsal spine; PF—pectoral fin length; #LAP—number of lateral armour plates; #DFR—number of dorsal finrays; #AFR—number of anal fin rays). The bottom left section of the panel shows a zoomed in drawing ofthe upper arm of the outer gill raker arch (#GR—number of gill rakers; GRL—length of longest gill raker).The lower right section shows an anteroventral view of the body (GW—gape width; BW—body width; PG—length of pelvic girdle; PS—length of pelvic spine). The upper drawing was originally published by Belland Foster (1994) and is re-used with permission from M. Bell.48non-hybrid (i.e., ‘pure’) families for each freshwater parental population and the anadromous ancestor. Alloffspring were raised in the lab under common conditions (see Supplementary Methods). Because hybridcrosses were made with the anadromous female, I cannot rule out cross-direction specific patterns. Crosseswere conducted in only one direction to standardize cytoplasm among hybrid crosses and also because ob-taining a sufficient number of wild gravid females for some populations was prohibitively difficult. Whenlab-raised fish reached reproductive maturity, F1 hybrids from unrelated families were crossed to make threeF2 families within each cross population (with the exception of Paxton Lake benthics which, due to aquariumspace constraints in 2018, had only two F2 families from the same two F1 parent families).Fish from each family were lethally sampled when individuals in the tank reached a mean standard lengthof approximately 40 mm. Fish had not reached reproductive maturity at the time of sampling, and I thereforecould not determine their sex. Fish were preserved in formalin, stained with alizarin red, and then storedpermanently in 40% isopropyl alcohol. For F1s, tanks were sub-sampled and remaining individuals wereraised to produce F2s. For F2s, entire tanks were lethally sampled.5.2.3 Phenotype measurementsI measured 16 traits and standard length on stained fish (Fig. 5.1B). For all traits, I measured at least 100 pureanadromous parents, and 30 pure freshwater parents, 30 F1 hybrids, and 60 F2 hybrids from each populationand anadromous-freshwater cross (all lab-raised; see summary dataset [to be archived on Dryad] for traitmeans, standard deviations (SDs), and sample sizes for all populations). I used a dissecting microscope tocount the number of dorsal fin rays, anal fin rays, lateral armour plates, and gill rakers. I also measured thelength of the longest gill raker using an ocular micrometer. I photographed the left and ventral sides of eachfish with a Nikon D300 camera and used ImageJ (Abramoff et al. 2004) to make linear measurements ofbody dimensions and bones (see Fig. 5.1 for more details on measurements). All measurements with theexception of eye diameter were highly repeatable (r ≥ 0.9; see Fig D.1), and as a result all traits except eyediameter were used for subsequent analysis. A few (n = 5) fish had missing second dorsal spines, whichcaused them to be extreme outliers. These were likely broken off during processing, and we excluded thesefish from our analyses.I size-corrected all linear measurements by replacing raw measurements with the residuals from a log-log (ln-transformation) linear regression model on standard length conducted across the entire dataset. Log-transformation of linear measurements renders trait variances comparable across populations with differentmeans. Some measurements are affected if fish are fixed with an expanded buccal cavity, so I further cor-rected for fixation position by assigning all fish a number (0, 1, or 2) depending on the extent to which themouth was open and then performing a further correction as above using residuals for gape width, snoutlength, and head length. Trait measurements for missing spines (first dorsal spine or pelvic spine) or pelvicgirdle were given a raw value of 0.1 mm. Unlike the second dorsal spine, variation in the presence of thesetraits is common and does not result in extreme outliers. Following size-correction, traits were standardizedto a mean of 0 and a standard deviation of 1. I decided a priori to not use an approach of size-standardization(size correction by fitting a separate intercept for each population or group) because I controlled for much ofthe variation among populations by sampling them at a consistent mean size, and small within-group sample49sizes could lead to poorly estimated intercepts and thus less accurate size-corrected trait values.5.2.4 Data analysisI evaluated whether adaptive divergence between parent populations was associated with the phenotype ob-served in hybrids. I investigated quantitative patterns of trait mismatch, and then investigated trait dominanceand variation as possible underlying causes of documented variation in mismatch.SoftwareAll data processing and model-fitting was done using R (R Core Team 2019) using the tidyverse (Wick-ham 2017). Mixed models were fit using lme4 (Bates et al. 2014) and analysed using lmerTest (Kuznetsovaet al. 2014 with the Kenward-Roger approximation for the denominator degrees of freedom (Kenward andRoger 1997). The ‘map’ function in purrr (Henry and Wickham 2019), and associated functions in broom(Robinson et al. 2020), were used to streamline code for iterating models over grouping variables. Theggpubr (Kassambara 2020) and egg (Auguie 2019) packages were used to create, customize, and annotategraphs. Partial residuals were plotted using visreg (Breheny and Burchett 2017). for loop code wasstreamlined with the functions in magicfor Makiyama 2016). I used the emmeans package (Lenth et al.2020) and the ‘cld’ function in multcomp (Hothorn et al. 2008) to assist with post-hoc comparisons. The‘r2beta’ function in r2glmm (Jaeger 2017) was used to calculate the partial r2 coefficient for for the fixedeffects following the method of Nakagawa and Schielzeth (2013). The functions in the ‘correlation’ package(Makowski et al. 2019) produced correlation matrices.Quantifying phenotypic divergenceI quantified the magnitude of phenotypic divergence between pure anadromous and freshwater populationsas my main predictor of mismatch. To do this, I simply calculated the Euclidean distance between each fresh-water population’s mean phenotype for all (mean and variance-standardized) traits and the anadromous meanphenotype for all traits. For pairwise analyses, I computed distances for the pair of traits being considered.Trait ‘mismatch’Trait mismatch is a quantitative metric capturing the extent to which individual hybrids deviate from theline connecting parental mean phenotypes (Thompson et al., 2021). Mismatch is a response variable inmy analyses and is measured for individual hybrids. I used two approaches to compute mismatch: oneconsidering all traits at once in multivariate space and the other considering pairs of traits at a time. Theformer approach captures complexities that are missed when looking at pairs of traits but is less readilyinterpretable because of the high-dimensional data structure. Pairwise mismatch is oversimplified becausemismatch is inherently multidimensional but is more intuitive biologically because patterns can be directlyrelated back to traits and easily visualized. Both analyses include all traits regardless of how divergent theparents are. Genetic correlations between pairs of traits (as measured in F2 hybrids) were low (median|rPearson| = 0.2), and most (87.4 %) were not statistically significant at P = 0.05 (Fig. D.2), and for this reason50I retain original traits and do not use dimensionality-reduction techniques such as principle componentsanalysis.Mismatch is the shortest (i.e., perpendicular) Euclidean distance between a hybrid’s phenotype and theline that connects the two parental mean phenotypes (see Fig. 5.2A & 5.2B for visual overview). Mismatchwas calculated as:dmismatch =∥∥∥∥( ~Fn − ~P0)− ( ~P1 − ~P0)× ( ~Fn − ~P0) • ( ~P1 − ~P0)‖ ~P1 − ~P0‖2∥∥∥∥, (5.1)where ~Fn,~P0, and~P1 are the vectors of individual hybrid (Fn = F1 or F2), pooled mean anadromous, andpooled mean freshwater (of the focal population) scaled trait values, respectively. The magnitude of theresulting vector (||d||) is taken to get the scalar dmismatch.The goal of the mismatch analysis was to test the hypothesis that mismatch is more substantial in hy-brids formed between more divergent parents. Because freshwater populations are phenotypically variable,hybrids might appear ‘mismatched’ if they have similar phenotypic variation to the freshwater parent. Itherefore accounted for this by calculating the distance from the axis of parental divergence for the individu-als of each freshwater parental population (eqn. 5.1). This quantity did not differ significantly among parentpopulations (F11,34.6 = 0.23; P = 0.34), nor did it increase with the magnitude of phenotypic divergence be-tween parents (βˆ = 0.018; F1,43.9 = 0.23; P = 0.64). I therefore do not explicitly account for variation in theparental populations in my analyses. I do subtract the mean estimate of parent ‘mismatch’ from all hybridmismatch values such that hybrids with no ‘excess mismatch’ relative to parents receive a value of 0. Thissimply changes the intercept and has no bearing on the main conclusions which concern slopesI fit mixed models with mismatch (either multivariate or pairwise) as the response, and multivariate Eu-clidean distance between the parental populations, hybrid category (F1 or F2), and their two-way interactionas fixed effects. Family was a random effect. For pairwise mismatch metrics, regressions were repeatedacross all trait pairs. I evaluated the statistical significance of the regression models, as well as the distribu-tion of regression coefficients across models to generated inferences about the relationship between adaptivedivergence between parents and mismatch in hybrids.Estimates of mismatch could be affected by measurement error, but measurement error is low in thisdataset as determined by repeatability scores. Further, measurement error of ln-transformed trait values (i.e.,absolute difference of the two ln-transformed trait measurements) is only correlated with divergence for oneof fifteen traits (body depth), and freshwater population values for body depth are not significantly correlatedwith multivariate parent trait divergence (Spearman’s rank-order correlation P = 0.1474). There is thereforeno reason to think that methodological issues would generate a ‘null’ relationship between mismatch anddivergence.Mechanisms of mismatchI examined how dominance and phenotypic variation contribute to mismatch. To determine how dominanceaffects mismatch, I calculated the mismatch of the mean hybrid phenotype for each population and hybrid51generation as the weighted (by sample size) mean across families. This generates a single estimate of mis-match for each population-generation combination, which is due only to dominance. I used a simple linearmodel to test whether the mismatch of the mean hybrid phenotype—which is not necessarily equivalent tothe mean hybrid mismatch—was associated with the phenotypic distance between parents and whether thisassociation differed between F1 and F2 hybrids.Variance affects mismatch in a manner that depends on dominance, so I tested for the effects of variationon mismatch after accounting for dominance. Specifically, I calculated the mismatch of the mean hybridwithin each family, and then subtracted each individual hybrid’s observed mismatch value from this mean.If variance tends to increase mismatch, these values are expected to be large and positive. If variance causessome hybrids to be more mismatched and some to be less mismatched, these values will be centred aroundzero. After determining the effect of variance on mismatch for each individual hybrid, I tested whether thisquantity was affected by the phenotypic divergence between parents in a mixed model where family was arandom effect. Main effects were parent divergence and category (i.e., F1 or F2), and their interaction.Patterns of phenotypic variation and dominanceMy final series of analyses are meant to document patterns of dominance and trait variation among popula-tions. Because dominance can cause mismatch if it is not consistent among traits (Thompson et al., 2021),I determined whether traits exhibited dominance using linear regressions that accounted for additive anddominant gene action. Throughout, I refer to dominance of the freshwater phenotype, such that traits are‘recessive’ if they resemble the anadromous ancestor. For the additive term, pure anadromous, (F1 and F2)hybrids, and pure freshwater populations were assigned additive values of 0, 0.5, and 1, respectively (i.e.,the proportion of their alleles that are ‘freshwater’). For the dominance term, pure species, F2 hybrids, andF1 hybrids were assigned values of 0, 0.5, and 1, respectively (Lynch and Walsh, 1998) (i.e., the proportionof their genome that was heterozygous for divergent alleles). For these regressions, I only measure domi-nance on traits for which parents had different values (dominance is undefined for traits that don’t differ).Specifically, I retained traits where the freshwater parent populations were either (or both) statistically dif-ferent (t-test P < 0.05) or ≥ 1 SD apart (in units of anadromous standard deviations). I ran models wheretrait values were the response and additivity and dominance were (non-interacting) continuous predictors. Ievaluated the statistical significance of the dominance coefficients as well as the direction of dominance (i.e.,whether the anadromous or freshwater phenotype was dominant).I next evaluated whether dominance differed among traits and populations. For these analyses, I stan-dardized trait values of each individual so that hybrids with non-transgressive trait values fall between 0 and1 (transgressive values are < 0 or > 1). Values of 0 indicate that F1 hybrid trait values are the same as theanadromous parent (P0; i.e., ancestral trait is dominant), values of 1 indicate that trait values are the same asthe freshwater parent (Pfresh; i.e., derived trait is dominant), and values of 0.5 indicate the trait is additive.This scaled trait value, zs, was calculated as:zs =Fn − P0P1 − P0, (5.2)52where Fn is individual hybrid’s (either F1 or F2) trait value, and P0 and P1 represent the trait means ofthe anadromous and freshwater parents, respectively. The pooled means reflect the mean of families withina given cross type. To test whether dominance differed among traits and/or populations, I fit linear mixedmodels with ‘zs’ values (eqn. 5.2) of individual fish as the response variable and family as a random effect. Inmodels testing whether dominance coefficients varied among traits, ‘trait‘ was the fixed effect and in modelstesting whether dominance differed among populations for a given trait, ‘population’ was the fixed effect. AllP-values were Tukey-corrected. Because dominance varied among populations for some traits (see Results),I tested if dominance evolves predictably with the magnitude of phenotypic divergence between each derivedpopulation and their common ancestor for the trait in question (in units of anadromous standard deviations).In these models, family was a random effect.I next examined patterns of phenotypic variation observed in hybrids to test hypotheses about variationbeing the mechanism underlying mismatch. For this analysis, I calculated the variance of each trait withineach F1 and F2 hybrid family. I then took the mean variance across traits, and tested whether within-familymean trait variance evolved as a function of the magnitude of phenotypic divergence between parents. Ifit a linear model with mean family variance as the response and parent divergence and category (and theirinteraction) as predictors.5.3 Results5.3.1 Patterns of phenotypic divergence among populationsI leveraged patterns of phenotypic divergence between anadromous and freshwater stickleback populationsto quantify how mismatch evolves as adaptive ecological divergence proceeds. I found that freshwater pop-ulations differed substantially in their mean phenotypic distance to the mean anadromous phenotype (maineffect of ‘population’: F1,41.8 = 34.1; P = 1.0 ×10−17; Fig. D.3). As expected, the benthic populations fromthe species pairs were among the most divergent from the anadromous ancestor, while two highly zooplank-tivorous populations that co-exist with prickly sculpin were among the least diverged (Pachena Lake andNorth Lake). The least divergent population, Pachena Lake, was closer (in Euclidean phenotype space) tothe anadromous population than it was to the most derived freshwater population, the Paxton Lake benthicspecies. The Paxton benthic population was 3.2× further from the anadromous population than PachenaLake was. Thus, the stickleback populations considered here capture a clear quantitative continuum of phe-notypic divergence from a common ancestral state. Unsurprisingly, the number of traits that differed betweenthe freshwater and anadromous parents was positively correlated with my continuous quantitative predictorof divergence (Fig. D.4).5.3.2 Evolution of trait mismatchI found support for the prediction that hybrid trait mismatch increases with the magnitude of phenotypicdivergence between parents. Considering all traits together, I found that multivariate mismatch in hybridswas positively associated with the magnitude of phenotypic divergence between parents (βˆ = 0.085 ± 0.029[SE], F1,85.9 = 8.62, P = 0.0043) (Fig. 5.2C). A separate model testing for an interaction between category53(i.e., F1 or F2) and parental phenotypic divergence found that it was non-significant (βˆ = 0.035, F1,75.9= 0.31, P = 0.57). This result implies that for every unit of multivariate phenotypic divergence betweenparents, mismatch in hybrids increases by slightly less than one-tenth that amount. The lack of a significantinteraction term implies that this result holds for both F1 and F2 hybrids.54−0.15 0.00 0.15 0.30036912036912mismatch:divergence slopefrequency4 6 8 10−2024−2024phenotypic distance between parentsexcess hybrid multivariate mismatchPFPAphenotypes of hypotheticalparents in 2D trait spaceline connectingparental phenotypesparentalmidpointarelationships between hybridpairwise trait mismatch and parent phenotypic divergenceF1PFPAphenotypes of hypotheticalhybrids in 2D trait spacelow mismatchbF2F2high mismatchdcrelationship between hybrid multivariate trait mismatch andparent phenotypic divergenceF1F2* n.s.F2* n.s.Figure 5.2: Visual overview of mismatch calculation and observed mismatch results. Panel (a) shows hy-pothetical parent phenotypes for the number of lateral armour plates and gill raker number in 2D trait space,and highlights the parental midpoint and the line connecting parents. Panel (b) shows two hypothetical hy-brids in the same trait space with low or high values of mismatch (calculated as the length of the dashed greylines). One hybrid is particularly mismatched because it has few gill rakers (a benthic freshwater-like value)and many lateral armour plates (an anadromous-like phenotype). The other hybrid has somewhat interme-diate values for both traits and is, as a result, less mismatched. Panel (c) shows the statistically significantrelationship between hybrid multivariate trait mismatch and parent phenotypic divergence in multivariatetrait space for both F1 and F2 hybrids. Points are partial residuals from the model (after accounting for ran-dom effect of ‘family’) and are slightly jittered horizontally to aid visualization. The effect of phenotypicvariation in parents (mean ‘mismatch’ across all parent populations) is subtracted from raw mismatch val-ues to show the ‘excess’ mismatch in hybrids. This changes the height of the regression line (i.e., reducesthe intercept) but does not affect the slope. Panel (d) is a histogram depicting the distribution of slopes forthe pairwise mismatch analyses in F1 (pink; upper) and F2 (purple; lower) hybrids. These slopes are thehow mismatch for a pair of traits changes with the magnitude of phenotypic divergence between parents forthose two traits. All slopes are shown, with significant slopes (*) being shown in a darker shade than non-significant (n.s.) slopes. Bi-modality in the F2s is caused by the segregation of genes with large phenotypiceffect underlying lateral armour plates and the presence and size of the pelvic girdle.55I next examined the relationship between phenotypic divergence and hybrid mismatch for pairs of traits ata time. For these analyses, the predictor variable is the Euclidean distance between parent mean phenotypesfor the pair of traits under consideration. I found that pairwise trait mismatch was significantly associatedwith parent trait divergence for 35 of 105 trait pairs in F1s (33 %), of which 34 associations (i.e., slopes) werepositive (97 %). In F2 hybrids, 39 of 105 trait pairs (37 %) had significant mismatch-divergence associationsand 38 were positive (97 %) (Fig. 5.2D). The mean absolute slope of significant relationships was approx-imately 0.14 in F1 hybrids and 0.13 in F2 hybrids, indicating that for every unit of divergence in phenotypespace for a given pair of traits, mismatch between those two traits increases by a bit less than one-sevenththat amount—slightly larger than the multivariate observation because this considers only significant traitpairs whereas the multivariate analysis considers all traits. Across all trait pairs, including non-significantmismatch-divergence relationships, pairwise slopes were comparable in magnitude to multivariate slopes(mean |βˆ| ≈ 0.075). See examples of these pairwise regressions in Fig. D.5. For a depiction of pairwisemismatch for individual hybrids in 2D trait space with real data, see Fig. D.6.− 6 8 10phenotypic distance between parentsindividual mismatch − mismatch of mean hybrid1.01.52.04 6 8 10phenotypic distance between parentsmismatch of mean hybridphenotypeeffect of varianceon mismatchbeffect of dominanceon mismatchaF1 F2 F1 F2Figure 5.3: Dominance is the primary driver of mismatch in F1 hybrids, while variance is the primarydriver of mismatch in F2s. Panel (A) depicts the mismatch of the mean hybrid phenotype, which is onlycaused by dominance. One point is shown per population and category (i.e., F1 or F2). The relationshipis significant and positive in F1s and non-significant in F2s. Panel (B) depicts the effect of variance onmismatch, which is calculated as an individual’s observed mismatch minus the mismatch of the mean hybrid.The relationship is significant and positive in F2s and non-significant in F1s.5.3.3 Underlying causes of mismatchMismatch is caused by dominance and/or segregating genetic variation displacing the mean hybrid pheno-type from multivariate intermediacy. In F2 hybrids, mismatch can result from both segregation variance anddominance, whereas only dominance is expected to cause mismatch in F1s. Because the effect of variance isdependent on underlying dominance patterns, I consider dominance first. I investigated the effects of domi-nance on mismatch by calculating the mismatch of the mean trait value for all traits within each populationand hybrid generation, and testing whether this effect of dominance changed with the magnitude of pheno-56typic divergence between parents. I found that this relationship differed between F1 and F2 hybrids (parentdivergence × category interaction term: F1,20 = 11.47; P = 0.003). This interaction was caused by the factthat mismatch of the mean hybrid increased with the magnitude of phenotypic divergence between parentsin F1 hybrids (βˆ = 0.16; t20 = 5.09;P = 0.0001) but not in F2s (βˆ = 0.0096; t20 = 0.3;P = 0.76). Patternswere qualitatively similar for pairwise trait analyses of dominance-effects (not shown). Thus, dominance is amajor cause of mismatch in F1 hybrids but not in F2s (see results section ‘Patterns of dominance in hybrids’for an analysis of dominance patterns).Theory predicts that the phenotypic variation observed in hybrids will increase as their traits divergeand that this relationship will hold in F2 hybrids but not in F1s. The results of phenotypic variance supportthis prediction (Fig. 5.4). Across traits, mean variance increased with parent trait divergence in F2 hybrids(βˆ = 0.088± 0.01 [SE], t88 = 8.68; P < 0.0001) but not in F1s (βˆ = 0.0077± 0.0077, t88 = 1.0; P = 0.31).I tested whether variance causes mismatch by subtracting each individual’s observed mismatch value fromthe mismatch of the mean hybrid of its family. I then regressed this variance-effect on mismatch against themagnitude of phenotypic divergence between parents. Similar to the dominance results, I found that thisrelationship differed between F1 and F2 hybrids (parent divergence × category interaction term: F1,102.54= 14.0; P = 0.0003; type-III SS). This interaction was caused by the fact that variance had an increasinglypositive effect on mismatch in F2 hybrids (βˆ = 0.12; t38.3 = 4.93; P < 0.0001) but had no effect in F1s(βˆ = −0.013; t155.4 = −0.48; P = 0.63). Patterns were qualitatively similar for pairwise trait analyses ofvariance-effects (not shown). Thus, variance is a major cause of mismatch in F2 hybrids but not in F1s.0.250.500.751.004 6 8 10phenotypic distance between parentsmean variance across traitsrelationship between hybrid multivariate trait variance andparent phenotypic divergenceF1 F2Figure 5.4: F2, but not F1, hybrid phenotypic variation increases with the magnitude of phenotypicdivergence between parents. Points represent the mean of variances across all 15 traits within each inde-pendent family (minimum n = 5). F1 and F2 hybrids are distinguished by colour. Linear measurements areln-transformed, so this result is not simply due to scaling means and variances (count data are raw but valuesare lower in more derived crosses for all meristic traits). Points are horizontally jittered to ease visualization.575.3.4 Patterns of dominance in hybridsPatterns of dominance differed among traits. Across all divergent traits in all populations, I found that 49 %of trait× population combinations (63 / 129) had significant dominance coefficients (i.e., approximately halfof traits were not inherited additively). Of these traits with significant deviation from additivity, only 15.9 %were dominant (i.e., more similar to the freshwater parent than the anadromous parent; Fig. 5.5A; see Fig.D.7), while the remaining 84.1 % were recessive. As a result, dominance coefficients varied significantlyamong traits (‘trait’ main effect; F14,106 = 2.37, P = 0.0066), which is what results in the observed dominance-caused mismatch. For example, most F1 hybrids have pectoral fins that are larger than the parental-midpoint,which is similar to the anadromous phenotype (Fig. 5.5A). Most F1 hybrids also have heads that are longerthan the parental-midpoint, however this is similar to the freshwater phenotype (note that this is on a log-scale). Importantly, as the magnitude of divergence between parents for two traits increases, so too willmismatch if the dominance coefficients of traits are held constant.Dominance patterns were consistent among populations for most traits. For individual traits, dominancewas typically statistically indistinguishable among all populations for a given hybrid class (e.g., mean 5.6%of pairwise differences significant among F1 hybrids) and did not exhibit any association with phenotypicdivergence. There was one notable exception, however: dominance of the lateral plate phenotype was pre-dicted by parental phenotypic divergence. Specifically, hybrids whose freshwater parent had a relatively highnumber of plates (e.g., 7–8) often expressed the ancestral anadromous high-plated phenotype (i.e., trait wasrecessive) whereas hybrids whose freshwater parent was more derived (i.e., lower plate count [0–3 plates])expressed an increasingly intermediate or derived freshwater phenotype (i.e., trait was dominant; Fig 5.5B).Although unexpected and biologically interesting, the evolution of dominance for lateral plate count doesnot affect the divergence-mismatch relationship (Fig. D.8).5801020304012 13 14divergence in plate # (anadromous SDs)F 1 hybrid plate #variation of mean (standardized) F1 hybrid values across traitsa evolution of dominance oflateral plate phenotypebanadromous−likefreshwater−like0.00.40.8BW PG #LAP PF GW #AFR PSLSDSGRL#DFR FDS BD SNT#GR HDtraitmean trait value ± 0.5 SDmid parentvalueFigure 5.5: Dominance of the freshwater phenotype in F1 hybrids among traits and populations. Inboth panels, phenotypes ([a] scaled and [b] raw), rather than dominance coefficients, are shown for easeof interpretation. Panel (a) depicts the estimated mean (±12 SD) scaled trait value—calculated across allpopulations—for all measured traits (N = 862 fish including F1 hybrids and parents). The dashed lines at 0and 1 represent the ancestral anadromous parent and derived freshwater parent trait values, respectively, andthe red dashed line at 0.5 represents the expected value with no dominance. Panel (b) depicts the relationshipbetween adaptive divergence in lateral plate number (in units of anadromous SDs for plate count) and F1phenotype (raw values) for lateral plate count. North Lake, which is fully plated, is not shown. Low valueson the horizontal axis indicate that the parent population is less derived and larger values indicate that it ismore derived. Black and grey dots delimit adjacent populations (as in chromosomes on a Manhattan plot).The red line is a loess-smooth fit to the data, and the blue line shows the parental midpoint. For a similarfigure with F2 hybrids, see Fig. D.7.5.4 DiscussionIn this chapter, I used experimental hybridization to investigate how hybrid phenotypes evolve as populationsdiverge to different extents. I was motivated by the fact that, although studies have documented a seeminglygeneral relationship between ecological divergence and barriers to gene flow (Shafer and Wolf 2013), the-oretical predictions of mechanisms that could link adaptive divergence to maladaptive hybrid phenotypesare untested. My results suggest that, at least in stickleback, more divergent parental populations tend tohave hybrids with increasingly mismatched (multivariate and pairwise) phenotypes. Such a pattern mightlink adaptive ecological divergence with reduced gene flow via extrinsic hybrid fitness alongside other well-documented processes such as assortative mating (Rundle, 2002; Coyne and Orr, 2004; Jiang et al., 2013).This pattern manifested in both F1 and F2 hybrids, but for different reasons—it was caused by dominance inthe F1 and by phenotypic variation in the F2. Below, I describe the possible mechanisms underlying thesepatterns, discuss their implications for speciation, and highlight critical next steps.595.4.1 Causes of divergence-mismatch relationshipThe key result of this study is that, as the magnitude of phenotypic divergence between ancestral anadromousand derived freshwater populations increases, so too does the magnitude of phenotypic mismatch observedin their hybrids. This was true when examining all traits together, and for approximately 40 % of all traitpairs. I specifically found that for every unit of divergence between parents, hybrid mismatch increases byapproximately 111 that amount in multivariate trait space. For trait pairs that showed a significant divergence-mismatch relationship, every unit divergence between the parents increased mismatch by approximately 17that amount. Although patterns were qualitatively similar among hybrid generations, further analyses revealsthat they have different causes.I found that mismatch was primarily caused by dominance in F1 hybrids, and primarily caused by seg-regation variance in F2s. In F1s, traits exhibited substantial variation in dominance and had significantdominance more often than not. Although traits were dominant in F2s, variation was more consistent amongtraits than in F1s. In addition, traits tended to be more dominant in F1s than F2s. Because dominance typi-cally did not change with the magnitude of divergence between parents (though see below for a discussionof lateral armour plates), increasing mismatch is therefore a natural consequence of phenotypic divergence.By contrast, phenotypic variation was the primary cause of mismatch in F2 hybrids and had little ef-fect on mismatch in F1s. Theory predicts that, if traits are inherited additively (such that F1s were strictlyintermediate), segregation variance in the F2 variance would lead directly to mismatch and that this wouldincrease with divergence. In support of theory (Slatkin and Lande, 1994; Barton, 2001; Chevin et al., 2014),I did find that total phenotypic variance increased with the magnitude of divergence between cross parentsin F2 hybrids. As a result, I observed the expected pattern of increasing mismatch with parent phenotypicdivergence in F2 hybrids. In F1s, variance did not have an effect on mismatch, likely because F1s weresomewhat mismatched already due to dominance and some individuals became less mismatched as a resultof variance while other individuals became more mismatched. Thus, my data support the theoretical predic-tion that segregation variance in recombinant hybrids causes trait mismatch, and that the size of this effectincreases with the magnitude of divergence between cross parents.5.4.2 Causes of recessivityI found that most F1 traits measured in the present study tended to be recessive (Fig. 5.5). The predominanceof recessive alleles could be explained by processes that remove dominant alleles from the standing variation.In stickleback, alleles that allow populations to adapt to freshwater are maintained in the sea during the inter-glacial periods and are ‘transported’ back to freshwater when new post-glacial lakes are colonized (Schluterand Conte 2009). Alleles are thought to be maintained by migration-selection balance, but are likely underdivergent selection between environments (Nelson et al., 2019). The alleles that freshwater populations useto adapt are therefore likely deleterious in the sea and must be maintained in the face of selection until theycan be re-introduced into freshwater (Nelson et al., 2019). Theory and empirical studies indicate that, in agiven environment, deleterious alleles that are recessive are maintained at higher frequencies than those thatare relatively additive (Simmons and Crow, 1977; Charlesworth and Hughes, 1998; Willis, 1999; Robinsonet al., 2018). Thus, a sort of ‘transporter sieve’ might act to reduce the frequency of dominant alleles in the60sea during inter-glacial periods, and hence influence the distribution of dominance coefficients of alleles inthe standing variation. In stickleback, much of the (parallel) adaptation to freshwater habitats proceeds viathe sorting of ancient standing variation (Jones et al., 2012b; Nelson and Cresko, 2018). Because the fix-ation probability of alleles in the standing variation increases with their initial frequency (MacPherson andNuismer, 2017), if recessive alleles rise to higher frequency in the sea than additive or dominant ones, thismight lead to their over-representation during adaptation. An alternative hypothesis is simply that most ben-eficial mutations are inherently recessive and their contributions to adaptation simply reflect the distributionof dominance among beneficial mutations.5.4.3 Evolution of dominance for armourUnlike most other traits, where dominance differed little among populations or was idiosyncratic with respectto parental divergence, dominance of the lateral armour plate phenotype exhibited predictable evolution. Al-though all freshwater populations (North Lake excepted) are low-plated (i.e., they have 0–9 plates whereasanadromous populations have around 30), populations on the higher-end of this distribution (e.g., PachenaLake) gave rise to F1 hybrids that largely expressed the marine phenotype. By contrast, the most derivedpopulations (e.g., the Paxton Lake Benthic species) had values that were more similar to the freshwater par-ent. Plate reduction is known to be largely caused by a single large-effect variant at the Eda locus (Colosimoet al. 2005; Archambeault et al. 2020), which is fixed for the freshwater allele in all of the freshwater popula-tions considered here (except for North Lake which is unusual in that it is fully plated). In addition, previousstudies have shown that dominance modifiers influence plate number within populations (Colosimo et al.,2004) and that dominance for fitness at Eda can differ among natural populations (Schluter et al. 2021).My findings build on these earlier results by showing that the net effect of alleles that modify dominanceof lateral armour plates is predictable based on the armour phenotype of the freshwater parent. It is unclearwhether the alleles that modify the low-plated phenotype (i.e., reduce plate count from 7–9 plates to 0–2plates) are themselves dominance modifiers or whether dominance modifiers are being selected for directlyin the more derived populations.Resolving the genetic basis of dominance and armour variation in these populations would shed light onwhether the pattern—the predictable evolution of dominance—is incidental or adaptive. The former ‘inci-dental’ hypothesis reflects the view of Sewall Wright (Wright, 1934), who believed that dominance is largelya physiological process determined by the underlying biochemistry of adaptive substitutions. By contrast,Ronald Fisher (1931) held a differing view that observed dominance was not a product of biochemistry butrather the result of selection acting to modify the expression of a deleterious phenotypes in heterozygotes.Both phenomena are common (Mayo and Bürger, 1997), but it is unclear which is at work here. Becauseheterozygotes for Eda have likely been rare or absent for millennia in many of the freshwater populations,this suggests a physiological explanation rather than selection to reduce expression of armour plates in Edaheterozygotes (Otto and Bourguet, 1999). One promising way to move forward would be to identify the QTLthat affect plate number differences among freshwater populations (e.g., by crossing Pachena Lake fish withPaxton Lake Benthics). In crosses with anadromous populations, it could be determined if these QTL modifydominance of Eda heterozygotes. Such a study would contribute novel data to a longstanding problem in61genetics.5.4.4 Similarities to patterns of ‘intrinsic’ isolationTrait mismatch represents an interaction between traits inherited from different parent lineages and affectsthe performance and fitness of hybrids. This is analogous to epistasis between genes that underlie tradi-tional BDM incompatibilities. An important model in speciation genetics with some analogy to the resultspresented herein is the ‘snowball’ model of the accumulation of hybrid incompatibilities. This model, firstput forward by Orr (1995), suggests that the number of hybrid incompatibilities should increase at leastas quickly as the square of the number of substitutions separating species. This is because, for each ad-ditional substitution, the number of pairwise interactions—and thus pairwise incompatibilities—increasesfaster-than-linearly. Empirical work has found support for this snowball model (Moyle and Nakazato, 2010;Matute et al., 2010; Wang et al., 2013). My study can draw parallels to the snowball model. I determinedthe number of trait pairs that are significantly mismatched in hybrids (by testing whether it exceeds the ‘mis-match’ expected based on phenotypic variation in non-hybrid freshwater populations) and tested whetherthis number is correlated with the magnitude of phenotypic divergence between parents. In this analysis,I find evidence of a snowball (Fig. D.9). In F1 hybrids, a quadratic model (with parent divergence as thedependent variable) is a substantially better predictor of the number of mismatched traits (AICquad = 54.4)than a linear model (AIClin = 69.1). For F2s, the two models fit equally well (AIClin = 83.9; AICquad = 85.2).Because trait pairs are not independent this analysis should probably be viewed as heuristic. Nevertheless,trait mismatches could snowball in a similar manner to more ‘intrinsic’ BDMIs and this possibility warrantsfurther investigation.Because mismatch increases with parental divergence, this implies that extrinsic post-zygotic isolationevolves in a similar ‘clock-like’ manner to intrinsic post-zygotic isolation. Coyne and Orr (1989, 1997) werethe first to demonstrate that reproductive isolation between populations evolves as a function of divergencetime. In their case, they found that both pre-mating and intrinsic post-zygotic isolation increased with neutralgenetic distance in Drosophila. This work spawned a small industry (Coughlan and Matute, 2020; Matuteand Cooper, 2021) that found similar patterns in groups as diverse as orchids and fishes (Bolnick and Near,2005; Scopece et al., 2013). The present chapter asks whether a component of extrinsic post-zygotic isolationevolves as divergence proceeds. In stickleback, genomic and phenotypic divergence are largely coincident(Miller et al., 2019; Wang, 2018), so my conclusions would likely be the same if I used genetic divergenceas the predictor variable. To establish the generality of this pattern, it would be useful for other studies todetermine if mismatch evolves predictably with genetic and/or phenotypic divergence in other systems.5.4.5 Caveats and future directionsThe biggest limitation of my study is its lack of a direct link between mismatch and fitness. In sticklebackspecifically, extrinsic selection against hybrids is well-known to occur in anadromous-freshwater sticklebackhybrid zones (Jones et al. 2006; Vines et al. 2016), including the Little Campbell River (Hagen 1967) stud-ied here. Clearly, we must begin to conduct comparative studies where mismatch can be linked to fitnessdirectly. In hybrid zones, biologists can estimate the strength of selection against hybrids by, among other62methods, measuring cline width and back-crossing rates (Barton and Hewitt, 1985; Harrison, 1993). Naturalstickleback hybrid zones abound in the present study region, and these areas of ongoing hybridization couldbe used to evaluate whether phenotypes measured in crosses (or gene expression) predicts the strength ofselection against natural hybrids. Similar studies could be undertaken in other systems, and experimentalarrays could be used to relate mismatch to back-crossing rates. Experimental evolution studies could alsobe used to robustly estimate the generality of the divergence-mismatch relationship and its effect on hybridfitness. More work is necessary to solidify our general understanding of the fitness effects of mismatch.Ultimately, the causes of speciation are multifarious and trait mismatch will be one of many causes ofreproductive isolation. Empirical estimates of the relationship between ecological divergence and hybridfitness (Edmands 1999; Funk et al. 2006; Shafer and Wolf 2013), or neutral divergence and hybrid fitness(Coughlan and Matute, 2020; Matute and Cooper, 2021), invariably find that these relationships are noisy.Because F1 hybrid mismatch is prevalent in many systems (Thompson et al., 2021), increases in magnitudewith divergence, and is expressed in all hybrids (i.e., mismatch is not expected to be highly asymmetric likelethal/sterilizing incompatibilities; Coyne and Orr 2004), it could be an immediate and powerful barrier togene flow between many diverging lineages. As shown above, it might even ‘snowball’. Nevertheless, solittle is known about the extent, evolution, and fitness effects of trait mismatch that it is difficult at this stageto say whether it is a major or bit player in speciation generally. Future studies clarifying the importance ofmismatch for speciation are sorely needed.63Chapter 6Fitness consequences of hybridization afterparallel evolution in threespine stickleback6.1 IntroductionEcological speciation occurs when reproductive isolation evolves between lineages as a consequence of theiradaptation to divergent environments (Schluter, 2000; Nosil, 2012). This process is well-documented innature and a substantial amount of evidence has accumulated over the past two decades to suggest that diver-gent natural selection has played an important role in many speciation events (Schluter, 2001; Langerhansand Riesch, 2013; Zhang et al., 2021). The alternative form of speciation by natural selection has come tobe known as ‘mutation-order’ speciation, wherein parallel or uniform natural selection—favouring the samephenotypes in both lineages—drives the evolution of reproductive isolation (Schluter, 2009). Compared tospeciation by divergent natural selection, speciation via parallel selection is relatively difficult to study dueto the few cases of truly parallel evolution in nature (Ostevik et al., 2012), though recent work in Australianwildflowers has provided compelling support (Melo et al., 2019). As originally defined by Schluter (2009),mutation-order speciation results from the fixation of alternative alleles that would be advantageous in bothpopulations but, due to chance processes, fix (or rise to high frequency) in only one of the two populations.When combined in hybrids, these alleles interact negatively and reduce the fitness of hybrids possessing bothof them (Kvitek and Sherlock, 2011; Ono et al., 2017). Although originally proposed as a mechanism driving‘intrinsic’ post-zygotic isolation, such as sterility or lethality, mutation-order processes can have importantconsequences for the fitness of otherwise viable and fertile hybrids. In many systems, strong ‘extrinsic’ bar-riers to gene flow can evolve before any intrinsic barriers, and my focus is on the evolution of such extrinsicpost-zygotic isolation arising via mutation-order processes.Theoretical models predict that parallel phenotypic evolution in allopatry, if underpinned by non-parallelevolution at the genetic level, can result in one or both of heterosis and hybrid breakdown (Barton, 2001;Johansen-Morris and Latta, 2006). One of the most valuable models in evolutionary genetics, Fisher’s (1930)geometric model (Orr, 2005; Tenaillon, 2014), often finds heterosis in the F1 and breakdown in the F2 (Bar-ton, 2001; Fraïsse et al., 2016; Simon et al., 2018; Yamaguchi and Otto, 2020). This heterosis results fromthe fact that F1 hybrids are intermediate between parents for most traits, and therefore are typically closerto an optimum than one or both parents. Breakdown results from the segregation of divergent alleles duringadaptation that greatly displace hybrids from the optimum (Chevin et al., 2014). Although the availability ofa common pool of standing variation can reduce the degree of segregation variance, theoretical studies sug-gest that it typically does not fully preclude the evolution of some reproductive isolation (Thompson et al.,642019). The relative magnitude of heterosis and breakdown vary widely depending on model parameters(Simon et al., 2018), with some parameters predicting breakdown even in the F1 (Fraïsse et al., 2016). Withrespect to progress toward speciation via parallel selection, heterosis is expected to impede such progresswhile breakdown is expected to facilitate it. Given the range of possibilities, data from natural systems areneeded to evaluate the fitness consequences of hybridization after parallel evolution in allopatry.I examined the fitness consequences of hybridization after parallel evolution using the sympatric benthicand limnetic stickleback (Gasterosteus aculeatus L.) species pairs (Fig. 6.1A), which are native to threewatersheds along the south coast of British Columbia, Canada (two additional species pairs, in Hadley Lakeand Enos Lake, have recently become extinct—Hadley via complete removal of stickelback from the lakeand Enos via collapse into a hybrid swarm). The benthic species is large-bodied and uses high suction to feedon large invertebrates in the substrate, while the limnetic species is relatively small-bodied and uses rapidjaw protrusion to feed on zooplankton in the open water (McPhail, 1984, 1992; Schluter and McPhail, 1992;Schluter, 1993; McGee et al., 2013, 2015). The species formed within the last 15,000 years after anadromousstickleback colonized newly-formed post-glacial lakes (Schluter, 1996), and genetic data indicate that each ofthe three extant species pairs is thought to have arisen independently (Taylor, 1999; Wang, 2018). Althoughsympatric, the species are thought to have arisen through a process of ‘double invasion’, wherein the originalanadromous colonists became the benthic species and a second anadromous immigrant population eventuallybecame the limnetic species. The benthic form is highly derived and is more genomically divergent from theanadromous ancestor than the limnetic species, which retains the ancestral zooplanktivorous niche (Joneset al., 2012a; Wang, 2018). Among fishes, the benthic-limnetic species pairs represent one of the clearestexamples of parallel evolution when measured using approaches that geometrically quantify parallelism (i.e.,phenotypic change vector analysis; Oke et al. 2017). Although evolution at the phenotypic level is highlyparallel, QTL-mapping indicates that the benthic and limnetic forms in both Paxton and Priest lakes haveonly 40 % of QTL effects in common—suggesting that the majority of alleles used for adaptation are uniqueto one lake (no similar data are available for the Little Quarry Lake species pair). Given this phenotypicparallelism and genetic non-parallelism, conditions are right for heterosis and/or breakdown.I made crosses among allopatric benthic populations and among allopatric limnetic populations (i.e.,between-lake within-‘species’ crosses) and tracked the growth and survival of nearly 4,000 individually-tagged fish in semi-natural experimental ponds and over 2,000 fish in aquaria. I examine the fitness ofparents, F1 hybrids, and F2 hybrids to evaluate patterns of heterosis and breakdown. Because benthics aremore derived and theoretical models predict a positive association between the magnitude of phenotypicdivergence (in this case between the benthic and anadromous) and hybrid breakdown (Barton, 2001; Fraïsseet al., 2016), I expected fitness differences among cross types to be more exagerated in benthics than inlimnetics. My results provide insight into the efficacy of parallel natural selection for driving progresstoward speciation.656.2 MethodsHere I provide the methodological details necessary to fully understand the results. More detailed explana-tions regarding experimental procedures are given in Appendix E.6.2.1 Experimental crossesFor simplicity of notation I refer to allopatric populations of the same form (i.e., benthic or limnetic) asthe same ‘species’ even though they originated independently (Taylor and McPhail, 2000; Wang, 2018). Imade all possible between-lake within-species crosses using the extant species pairs—Paxton, Priest, andLittle Quarry Lakes. I generated pure (i.e., within-lake and within-species) individuals for each speciesand lake, and also made between-lake F1 and F2 hybrids. All crosses were between unrelated families, butsome families and individuals were used in separate crosses—family structure was not accounted for in theanalysis (see below for rationale). Parents of all crosses were born in the lab and were either one or twogenerations removed from the wild (i.e., all experimental fish were at minimum from the second laboratorygeneration). Crosses were made in March 2020, and fish were raised in 100L aquaria until mid-June 2020when I began the pond experiment.photographs of the three exant threespine stickleback species pairsLittle Quarry Lake Priest LakePaxton LakeFigure 6.1: Photograph of the study system. The figure contains photographs of all three extant threespinestickleback species pairs. Each photograph was taken in 2017 and shows females of the benthic (top) andlimnetic (bottom) species.6.2.2 Pond experimentThe pond experiment took place in three experimental ponds on the University of British Columbia campus.The ponds were established between 2008 and 2010 and are 15 × 25 m in surface area. The 25 m lengthof the pond is made up of a 12.5 m gradually sloping shallow littoral zone with macroalgae and a 6 m deepopen-water zone (see extended data Fig. 1 from Arnegard et al. 2014 for a detailed description and diagram).The diet of benthics and limnetics in the ponds closely matches their diet in natural lakes (Arnegard et al.,2014). Except for their use in previous experiments, the ponds are unmanipulated environments. Each pondcontained fish (pure [i.e., non-hybrid] species, and F1 & F2 hybrids) with ancestry from two lakes (pond4—Paxton & Little Quarry; pond 9—Priest & Little Quarry; pond 19—Priest & Paxton). For each pond,66tagging and release took place over the course of approximately two weeks (release windows—Pond 4: June14–28; Pond 9: June 29–July 10; Pond 19: July 11–24).Power analyses conducted in advance of the experiment were used to determine a sample size that wouldbe necessary to detect a 2 % difference in standard length between treatment groups, parameterized on thestandard length data of Arnegard et al. 2014. I determined that a comparison of approximately 100 fish intwo treatment groups was sufficient for this purpose. I estimated that approximately 50 % of fish wouldperish during the experiment and so, for both benthics and limnetics, I aimed to introduce approximately100 individuals of each pure species (i.e., 100 of both benthic parents and 100 of both limnetic parents), 200F1 hybrids (i.e., 200 benthic F1s and 200 limnetic F1s), and 200 F2 hybrids into each pond. Total numbers ofintroduced fish are given in Table E.1.Before introduction, each fish was weighed to the nearest 0.01 g and implanted with a sequential codedwire tag (CWT; Northwest Marine Technology, Anacortes, WA, USA) in the dorsal musculature on the rightside of the body. CWTs can be recovered from surviving fish at the end of an experiment to identify anindividual via dissection and the use of a microscope. Detailed methodology is given in Appendix E. Themean initial body mass (± SD) was 0.56 ± 0.16 g for introduced benthics and 0.44 ± 0.112 g for limnetics,which corresponds to approx. 30–40 mm standard length for both species. After tagging, fish were returnedto their original tank for a 48 hr recovery period, then moved to the ponds in coolers where their original tankwater was diluted 50:50 with pond water. Fish were kept in these coolers overnight—with two aerating airstones, several plastic plants, and sections of PVC pipe—and released into the ponds the following morning.The few fish that perished before introduction had their tags extracted and read so they could be excludedfrom the analysis.I retrieved surviving fish from each pond using minnow traps and by dip-netting beginning on 14 Septem-ber 2020, after the experiment had run for approximately three months. Minnow traps were baited using oldcheddar cheese wrapped in several layers of lightly perforated aluminum foil that fish could sense but notconsume. After several days of trapping and netting, when fish returns slowed to fewer than five per eveningof trapping, I added 2 L of 5 % rotenone to each pond. The rotenone caused remaining fish to swim to thesurface of the pond, where they were easily collected with a dip net. After collection, fish were euthanizedwith an overdose of MS-222. I recorded the fresh mass of each fish, took a photograph, and then immedi-ately stored the fish at −20◦ C in 15 mL centrifuge tubes containing unique paper labels. Coded wire tagswere dissected out of frozen fish after lightly thawing them, then read under a microscope (Magniviewer,Northwest Marine Technology). Tags were matched with the original data to identify each fish. From this, Icould calculate the survival and total growth of each individual released into ponds.6.2.3 Lab experimentAt the same time as the pond experiment was ongoing, I conducted a similar experiment in the lab usingsiblings or relatives of fish released into ponds. The goal of this experiment was to provide a baselineestimate of ‘intrinsic’ survival and growth for fish of around the same age and starting size.The laboratory growth rate experiment was conducted using 60× 110 L aquaria in a common recirculat-ing system. Most tanks contained both benthic and limnetic individuals, and all individuals within a species67were from the same family (benthics and limnetics are easily distinguished by eye). 20 g of fish were addedto each tank to standardize initial mass. I recorded the mass of each fish at the experiment onset, but dueto logistical constraints individual fish were not tagged. Immediately after I ended the pond experiment, Ieuthanized all surviving fish in aquaria with an overdose of MS-222 and recorded their mass (mean n daysin aquaria = 74). I assume that the largest fish at introduction was the same individual as the largest fish atthe end of the experiment (I do not know the day that a given fish died). I measured survival by comparingthe number of fish of each species in tanks between the experiment’s start and end. I estimate growth onlyin tanks where all fish survived to the end of the experiment.6.2.4 Data analysisAnalyses proceeded via linear or generalized linear models depending on the fitness component and thehypothesis being tested. Response variables were either survival (binary; generalized linear model) or finalmass (continuous; linear model). For experiment-wide differences between species and cross types withinspecies, I fit models with pond as a random effect and initial mass as a fixed effect. For models of growth,I also included a ‘duration’ fixed effect which was the number of days between the introduction into pondsor aquaria and the final mass measurement. For survival models this ‘duration’ term was the minimumobservation period, calculated as the difference between the day a fish was introduced into the pond and thefirst day of trapping for that pond at the end of the experiment. For models examining differences amongponds, I included pond as a fixed effect in the models and included a cross type × pond interaction term.I did not include family (i.e., unique fertilized clutch) as a random effect, so I assume each fish constitutesa unique experimental unit (as in similar experiments, e.g., Martin and Wainwright 2013). Although familiesdiffer in survival and growth, family is completely confounded with species and cross type (by necessity) andtherefore this fact alone is not useful for evaluating whether intrinsic differences among families, irrespectiveof their cross type, might underlie any of the main effects documented herein. To evaluate the causes ofvariation among families, I analyzed the initial mass data of 56 families that were split into 124 differenttanks early in life. This analysis indicates that family—a biological variable—does not explain any additionalvariation in initial mass after accounting for ‘tank’—a methodological variable (model comparison ANOVA;P = 0.24). Adding ‘tank’ into a model that contains only ‘family’ substantially improves the fit (P< 0.0001).This indicates that the specific tank a family was raised in underlies the ‘family’ effect. Such differencesmight result from many technical artifacts, such as there being slightly different densities, personalities,temperatures, and so on. I therefore conclude that the ‘family’ effect is noise rather than signal and feel thechoice to exclude family is justified. During the pond experiment, fish across families were raised in thesame broad environment (pond), which I do account for in my analysis. Accounting for initial mass in themain analysis remains useful, however, because it reduces the noise introduced by the existence of variationamong rearing tanks.Most models pool the two ‘pure’ (i.e., non-hybrid) species parents of a given cross for analysis. This wasdone because the point of comparison most relevant to heterosis and breakdown compares hybrids to the themid-parent value. I note that important differences did exist between pure (i.e., non-hybrid) parental crosses,which are presented in the results.68All analysis was done in R version 4.0.3. Mixed models were fit with the lme4 package (Bates et al.,2014) and analyzed with the sequential SS modifications to ‘anova’ in lmerTest (Kuznetsova et al., 2014).Main effects were evaluated using the Kenward-Roger approximation for the denominator degrees of free-dom (Kenward and Roger, 1997). Post-hoc analyses were done using the ‘emmeans’ and ‘pairs’ functions inemmeans (Lenth et al., 2020), with Tukey HSD–corrected P-values. Regression model fits were visualizedwith visreg (Breheny and Burchett, 2017). Data processing used functions in the tidyverse (Wickham,2017).6.2.5 Estimating fitnessI wished to generate an estimate of fitness that considered variation in both survival and growth among crosstypes within a species. Estimates were made for each species (limnetic or benthic) and cross type (pure,F1, or F2) as measured across ponds. This is important because survival and growth cumulatively affectfitness—if one cross type had 1⁄2 the survival and 1⁄2 the fecundity of another, its fitness would be 1⁄4. Forsimplicity, I simply multiply estimates of relative survival by estimates of relative size (which is proportionalto overwinter survival and fecundity) to generate a single estimate of relative fitness. A more complicatedanalysis estimating fecundity and overwinter survival generates less conservative estimates of relative fitness(i.e., larger differences among classes) and is presented in Appendix E.6.3 Results6.3.1 Patterns of survival and growth in pondsBroad differences between benthics and limneticsI recovered and read CWTs from 59.6 % of fish that were introduced into ponds (n recaptured = 2213; nreleased = 3713). Across both benthics and limnetics, the initial size of the fish and the number of days a fishspent in the ponds predicted its final mass (Fig. E.1 & E.2). Recapture rates, which are assumed to reflectdifferences in survival, differed markedly between benthics and limnetics. I recaptured 78.2 % of benthicsbut only 40.9 % of limnetics (‘species’ main effect: χ2 = 552.3;P < 0.0001). Benthics grew in ponds morethan limnetics, accumulating on average 0.98± 0.018 g [SE] more mass than individual limnetics (F1,2191.1 =2808.4; P < 0.0001). Recaptured benthics were on average 3.8× their initial mass and recaptured limneticswere 2.4× their initial mass.691234pure F1 F2cross typefinal mass (g; partial residual)2.052.10pureF1 F2cross typemean final mass ± comp. lim. 0.400.420.44pure F1 F2cross typemean survival ± comp. components in limnetic crosses (ponds)ai survival ii growth0.51.01.5pure F1 F2cross typefinal mass (g; partial residual)0.9751.0001.0251.0501.075pureF1 F2cross typemean final mass ± comp. lim. fitness components in benthic crosses (ponds)bi survival ii growth0.8000.8050.8100.815pure F1 F2cross typemean survival ± comp. lim.Figure 6.2: Survival and growth of pure species and their F1 & F2 hybrids in the experimental ponds.Data for limnetics are presented in panel (A), and data for benthics are shown in panel (B). All data areeither estimated marginal means or partial residuals from models that included ‘pond’ as a random effect(see Methods). Mean survival (‘i’ panels) was estimated from generalized linear mixed models. Growthpanels (‘ii’ panels) show individual-level variation (left) and estimated marginal means from linear mixedmodels. Arrows are comparison limits, with arrowheads indicating the direction of the comparison. Non-overlapping bars indicate a significant difference at P = 0.05 (Tukey’s HSD).70Survival and growth differences among cross types in the experimental pondsSurvival and growth rates differed among cross types within species in the experimental ponds (Fig. 6.2).I first consider main effects across the three different inter-lake crosses—differences among crosses withinspecies (including differences between the two pure parents) are considered below.In limnetics, survival was higher in F1s than non-hybrids (i.e., ‘pure’; Tukey’s HSD: odds ratio = 1.33 ±0.155 [SE]; z = 2.46; P = 0.038) and F2 hybrids (odds ratio = 1.33 ± 0.155; z = 2.45; P = 0.037), which didnot differ from each other (odds ratio = 1.00 ± 0.12; z = 0.013; P = 0.99). A similar pattern was evident inthe limnetic growth data, where F1 hybrids grew more than both non-hybrids (β = 0.084 ± 0.020 [SE]; t745= 4.107; P = 0.0001) and F2 hybrids (β = 1.06 ± 0.029; t743 = ; P < 0.0001), which did not differ from eachother (β = 0.027 ± 0.024; t710 = 0.95; P = 0.61).Qualitative patterns for fitness components were similar for benthics as in limnetics, though the differ-ences among cross types were smaller in magnitude. Survival in benthics was not significantly differentbetween any cross types (all P > 0.65). Benthic F1 hybrids grew more than both non-hybrids (β = 0.076 ±0.028 [SE]; t1437 = 2.68; P = 0.0204) and F2 hybrids (β = 0.13 ± 0.028; t1437 = 4.43; P < 0.0001), whichdid not differ from each other (β = 0.05 ± 0.028; t1437 = 1.80; P = 0.17).As a result of the alignment between survival and growth, overall fitness differences among cross typesmatched expectations from the two fitness components and were more substantial in limnetics than in ben-thics. For simplicity, I simply estimate fitness as relative survival× relative growth, though less conservativeestimates estimating overwinter survival and fecundity are presented in the Appendix. For both species, theF1s had the highest fitness, followed by non-hybrids then by F2 hybrids. For limnetics, the estimates ofrelative fitness were 1, 0.78, and 0.76, respectively. For benthics, these values were 1, 0.92, and 0.9. Thus,relative fitness of limnetic pure species and F2 hybrids was less than 4⁄5 that of F1 hybrids, whereas pure andF2 hybrid benthics had approximately 9⁄10 the fitness of F1s.Although there were strong main effects of cross type across the different ponds, patterns differed mean-ingfully among ponds (i.e., lake-of-origin pair). Because of the number of tests, I show the results of contrastsin Fig. 6.3 and refrain from extensive summary in text. Generally speaking, two of the three limnetic crossesbroadly recapitulated the main effects, whereas there was no effect of cross type in the Little Quarry× PriestLake cross. There were few differences among benthic cross types, except for the Paxton× Priest Lake crosswhere F1s had much higher growth than both pure species and F2 hybrids. In many of the crosses, there weresubstantial differences between cross parents which are shown in Fig. E.3. In most cases where heterosis isevident from a comparison of cross means, the F1 mean exceeds both parents or is equivalent to the more fitparent.710. F 1 F 2mean survival ± comp. lim. F 1 F 2mean final mass (g) ± comp. lim. F 1 F 2mean survival ± comp. lim. F 1 F 2mean final mass (g) ± comp. lim. F 1 F 2mean survival ± comp. lim. F 1 F 2mean final mass (g) ± comp. lim. 0.350.400.450.50pure F 1 F 2mean survival ± comp. lim. 0.850.951.051.151.25pure F 1 F 2mean final mass (g) ± comp. lim. 0.350.400.450.50pure F 1 F 2mean survival ± comp. lim. 0.850.951.051.151.25pure F 1 F 2mean final mass (g) ± comp. lim. 0.350.400.450.50pure F 1 F 2mean survival ± comp. lim. 0.850.951.051.151.25pure F 1 F 2mean final mass (g) ± comp. lim. ai little quarry × paxtonfitness components in limnetic crosses (within each pond)ii little quarry × priest iii paxton × priestbi little quarry × paxtonfitness components in benthic crosses (within each pond)ii little quarry × priest iii paxton × priestFigure 6.3: Variation in survival and growth among cross types and crosses in the experimental ponds.The upper panels show patterns in limnetics and the lower panels show benthics. All data are estimatedmarginal means ± comparison interval limits—non-overlapping intervals are significantly different at aTukey-HSD P < 0.05. Arrows denote the direction of a contrast. Vertical axis limits for a given fitnesscomponent are fixed across panels for each species.6.3.2 Causes of fitness differences among groups in pondsAnalysis of a toy model indicates that both heterosis and hybrid incompatibility underlie the rank-order ofmain effects observed in the pond experiment, which I qualitatively summarise as F1 > pure ≥ F2. Forsimplicity, the toy model assumes there is no dominance and that genotypic fitness landscapes are symmet-rical. Heterosis is evident because F1 hybrids exceed the fitness of pure species, and breakdown is evidentbecause the F2 comparison limits do not include the mid-point between pure species and F1 hybrids. This iseasily seen via toy models of simple two-locus fitness landscapes. Under a model of heterosis, fitness is a72positive function of heterozygosity (Fig. 6.4A, left) and as a result the rank order fitness is F1 > F2 > pure.Under a model of Bateson-Dobzhansky-Muller incompatibilities (Fig. 6.4B), individuals that have alterna-tive homozygous genotypes (i.e., AA at locus 1 and BB at locus 2) have the lowest fitness which results inrank-order fitness of F1 = pure > F2. Models combining features from both heterosis and BDMI modelsbetter match the empirical data. Models where the benefit of heterozygosity exceeds the cost of opposinghomozygosity (i.e., heterosis > incompatibility; Fig. 6.4C) result in F1 > F2 ≥ pure, and models with theopposite precedence (i.e., incompatibility > heterosis) typically find F1 > pure ≥ F2. Thus, I conclude thatBDMIs act at least as strongly on F2s as heterosis in this system.AAABBBAA AB BBgenotype at locus 1genotype at locus 2pure F1 F2fitnessAAABBBAA AB BBgenotype at locus 1genotype at locus 2pure F1 F2fitnessAAABBBAA AB BBgenotype at locus 1genotype at locus 2pure F1 F2fitnessAAABBBAA AB BBgenotype at locus 1genotype at locus 2pure F1 F2fitnesspossible mechanisms underlying patterns of hybrid fitness (toy model)a heterosis only b incompatibility only c het. > incomp. d incomp. > het.low fitness high fitnessFigure 6.4: Inferring the broad mechanisms underlying patterns of hybrid fitness. Panel (A) illustratesfour possible two-locus fitness landscapes (upper) and associated expected fitness values for parents and bothF1 and F2 hybrids (lower). A legend for fitness is included at the bottom of the plot, with brighter coloursindicating higher fitness. The final two landscapes consider cases with both heterosis and incompatibilities,but where either heterosis (iii) or incompatibilities (iv) are stronger. The lower panels show the expectedfitness values (F2s are mean ± 1SD) for each landscape.6.3.3 Patterns of growth and survival in aquariaAs a point of comparison to the growth in ponds, I generate inferences about ‘intrinsic’ survival and growthof cross types using a separate set of fish reared in aquaria while the pond experiment was ongoing. Theaquarium experiment ran for an approximately equal duration as the pond experiment and used fish fromthe same crosses (either siblings or relatives). As in the pond data, there were significant differences amonglimnetics for both survival and growth, and for benthics differences only manifested through growth.In aquarium-raised limnetics, patterns were generally consistent for both fitness components where bothhybrid classes were equally fit and both were more fit than non-hybrids. F1 and F2 hybrids had equivalentsurvival (odds ratio = 0.71 ± 0.18 [SE]; z = 1.40; P = 0.35) and growth (β = 0.013 ± 0.0215; t258 = 0.62;73P = 0.81). Non-hybrid individuals had lower survival than both F1 (odds ratio = 1.86 ± 0.38; z = 3.06; P =0.0062) and F2 (odds ratio = 2.64 ± 0.64; z = 3.98; P = 0.0002) hybrids. Similar differences were observedfor growth—F1 hybrid limnetics grew significantly larger than parents (β = 0.052 ± 0.020; t258 = 2.63; P =0.024) and F2s were similar though the difference was only marginally significant (β = 0.066 ± 0.028; t258= 2.35; P = 0.051). Note that the sample size is subtantially smaller for the growth analysis (n = 264 fish)than the survival analysis (n = 1024 fish) because the growth dataset was restricted to tanks where all fishsurvived. Thus, there is evidence for heterosis but not F2 hybrid breakdown in the limnetic aquarium crosses.In aquarium-raised benthics, I found general hybrid inferiority and no evidence for heterosis nor F2breakdown. Survival did not differ among cross types (all P > 0.27). For growth, however, I found thatnon-hybrids grew larger than both F1 hybrids (β = 0.22 ± 0.029; t432 = 7.62; P < 0.0001) and F2 hybrids (β= 0.18 ± 0.030; t432 = 5.92; P < 0.0001). F1 and F2 hybrids did not differ in growth (β = 0.039 ± 0.028;t432 = 1.39; P = 0.34). The aquarium data thus provide no evidence for heterosis nor hybrid breakdown inbenthics.0.930.940.95pure F1 F2cross typemean survival ± comp. lim.1.551.601.651.701.75pure F1 F2cross typemean final mass (g) ± comp. lim.0.800.840.88pure F1 F2cross typemean survival ± comp. lim.0.820.840.86pure F1 F2cross typemean final mass (g) ± comp. components inlimnetic crosses (aquaria)afitness components inbenthic crosses (aquaria)bFigure 6.5: Growth and survival in aquaria. Panels show means and comparison interval limits for (A)limnetics and (B) benthics raised in recirculating aquaria. Survival data is from all fish, whereas growth dataonly uses data from tanks for which all individuals of a given species survived.6.4 DiscussionIn this study, I experimentally quantified the fitness consequences of hybridization after parallel phenotypicevolution in threespine stickleback. I considered hybridization between allopatric populations of the lim-netic ‘species’ as well as between allopatric populations of the benthic ‘species’. Fitness differences amongthe three cross types—pure species, F1 hybrid, and F2 hybrid—were qualitatively similar for both species,with the F1 being superior to both pure species and F2s, and the F2 being less than or equal to parents. Ihypothesized that fitness differences would be greater among benthic cross types than among limnetics, butfound the opposite was true. The data suggest that both heterosis and hybrid incompatibilities govern thefitness of hybrids between these parallel species. Hybrid breakdown seems to be specific to the pond envi-74ronment because it did not occur in aquaria, whereas heterosis was apparent in aquarium-raised limneticsbut not benthics. Although these main effects were significant, there were meaningful differences amongunique crosses, which is consistent with the hypothesis that stochastic processes have a substantial and de-terminative role in governing the fitness outcomes of hybridization after parallel evolution. Nevertheless,the agreement among main effects for both species suggests that in spite of the stochastic processes operat-ing for individual populations, there might still be general rules that become apparent when looking acrosspairs of populations. Below, I discuss the mechanisms that might underlie these patterns and highlight theirimplications more broadly for speciation via parallel natural selection.6.4.1 Mechanisms underlying fitness differences between parents and hybrid generationsin pondsAlthough similar in rank-order, the differences between cross types were greater in magnitude among lim-netics than among benthics. Because benthics are more derived than limnetics, and the two species havea quantitatively similar fraction of genomic non-parallelism for QTL (about 50 % of QTL unique to onelake; Conte et al. 2015), I predicted that patterns would be more pronounced in benthics. Greater groupdifferences among limnetics might best be explained by differences in the selective regimes experienced bythe two species. In the experimental ponds, limnetics were clearly under stronger selection than benthics,which is inferred through survival. If benthics experience relatively relaxed selection compared to limnetics,their fitness landscape might be viewed more as a plateau whereas that of the limnetics would be a relativelysharp peak. Thus, selection scrutinizing the phenotypic variation among limnetic crosses more closely thanbenthics might explain why predictions from patterns of genomic divergence were unmet.Heterosis is the only mechanism that can readily explain the high relative fitness of F1 hybrids comparedto parents. Heterosis is often observed via extrinsic fitness in theoretical models where high dimensionalorganisms (i.e., having many traits) adapt to a common phenotypic optimum (Barton, 2001; Rosas et al.,2010; Fraïsse et al., 2016; Wei and Zhang, 2018; Fiévet et al., 2018; Dagilis et al., 2019; Vasseur et al.,2019). One possible cause of heterosis is inbreeding depression. Relative to limnetics, benthics have lowercensus population sizes (Schluter et al., 2017), heterozygosity (Jones et al., 2012a), and effective populationsizes resulting from substantial recent bottlenecks (Wang, 2018). If benthics are inbred and/or cannot readilyaccess beneficial alleles, they might benefit more from outbreeding than limnetics. The fact that hetero-sis was greater in limnetics, where inbreeding is likely relatively reduced, suggests that inbreeding is notthe main cause of heterosis. Because morphological and niche-use divergence seem largely additive in thissystem (Miller et al., 2014; Arnegard et al., 2014), phenotypic dominance of advantageous traits is also anunlikely explanation for heterosis. Associative or pseudo-overdominance, wherein deleterious alleles hitch-hike to high frequencies during adaptation (Ohta, 1971; Owens et al., 2019), might be the best explanationfor the observed patterns of heterosis. In benthics, heterosis seems to be environment-specific, which is aphenomenon that has been noted before (Dominigues and Albornoz, 1987) and is well-known from cases ofhybrid speciation (Rieseberg et al., 2007).Because F2 hybrids had equivalent or lower fitness than parents, this implicates Bateson-Dobzhansky-Muller incompatibilities. Quantification of hybrid breakdown can only occur after accounting for heterosis75(Barton, 2001), and a null expectation for F2s is that their fitness will lie between the that of the parentmid-point and the heterotic F1. The pond data clearly show that the F2 hybrids of both species have lowerfitness than this null expectation (i.e., their comparison limits do not include the pure–F1 midpoint). In theaquarium-raised crosses, F2 hybrids had equivalent fitness to F1s in both species. This suggests that thehybrid incompatibilities are primarily subject to ecologically-mediated natural selection, rather than someform of endogenous conflict between parental genomes.6.4.2 Variation in hybrid fitness among crossesAlthough I focus my general inferences on the main effects, patterns of heterosis and hybrid breakdownvaried considerably among populations. One unanticipated finding is that growth (but not survival) of the twonon-hybrid (i.e., pure) crosses of a given species often differed within a pond. This implies that although thespecies are highly parallel with respect to some measured morphological characters, parallelism is imperfectwith respect to other traits.Qualitative patterns of cross type fitness were somewhat inconsistent among unique crosses for a givenspecies. For limnetics, two of the three crosses recapitulated the main effect (i.e., F1 > pure ≥ F2), whereasthis was only true for one of the three benthic crosses. The cross with the greatest among-cross differenceswas the benthic cross between Paxton and Priest lake, which were studied by Conte et al. (2015) and found tohave approximately 40% of parallel QTL underlying adaptation. The variation among ponds is in agreementwith the notion that stochastic processes play a major role in speciation by parallel natural selection (Maniand Clarke, 1990; Schluter, 2009). As a result, it might be difficult to predict the outcome of hybridizationafter parallel phenotypic evolution in any one population. Importantly, the main effects were largely consis-tent across benthics and limnetics, which might suggest that generalities can be found when looking acrosspopulations (Melo et al., 2019).6.4.3 CaveatsThe experiment makes a number of assumptions that should be acknowledged. First, an implicit assumptionis that the experimental ponds are reasonable stand-ins for the lakes. This assumption is common to allstudies taking place outside of species’ source habitat. Unfortunately, introducing inter-lake hybrids intostudy lakes, even into enclosures, carries an unacceptable risk of escape and thus will never be attempted.Previous studies have found that the diet of benthic and limnetic stickleback in these same ponds closelymatch that of the natural habitat (Arnegard et al., 2014), which could alleviate this concern. My crosses alsoonly capture natural selection, and important differences in sexual selection might have been overlooked(Keagy et al., 2016). I also assume that selection was parallel, when in reality there are probably some traitsthat are divergently selected between allopatric benthics and between allopatric limnetics. Finally, selectionagainst larval fish can be extremely strong (China and Holzman, 2014) but could not be accounted for herebecause my experimental design required me to tag fish, which could not be done until fish were large enoughto survive such handling.766.4.4 Progress toward speciation via parallel natural selection?In this chapter I have shown that parallel evolution can result in (some) ecological hybrid breakdown andalso (some) heterosis. It remains unclear how this breakdown would affect progress toward speciation. Inthe sympatric benthic-limnetic species pairs, the species seem reproductively isolated because the genes thatunderlie adaptation also underlie mate choice (Bay et al., 2017). The species differ in body size, which actsas a reliable signal of species recognition (Conte and Schluter, 2013), and this selection has been honedthrough reinforcement (McKinnon and Rundle, 2002). Thus, although the allopatric benthic and limneticspecies’ genomes are weakly incompatible, it seems unlikely that the incompatibility is so strong that theallopatric ‘parallel’ species would remain distinct if brought together in sympatry. The observed heterosismight render a collapse even quicker. Thus, I conclude that there has been little progress toward speciationvia parallel natural selection in this system. If this is general, it would imply that parallel natural selectionis unlikely to generate substantial reproductive isolation via extrinsic post-zygotic isolation. Chance fixationof alleles with substantial ‘intrinsic’ effects (Melo et al., 2019) might be the primary pathway through whichmutation-order speciation can be expected to act.77Chapter 7Genetic evidence for environment-specifichybrid incompatibilities in threespinestickleback7.1 IntroductionHybrid incompatibilities—interactions among divergent genetic loci that reduce the fitness of hybrids—area key component of reproductive isolation between diverging lineages (Coyne and Orr 2004). Incompati-bilities have been studied most intensively in the context of sterility and embryo mortality, because thesetraits are conducive to reliable phenotyping in the laboratory and often seem to be underpinned by few loci(Maheshwari and Barbash 2011; Fishman and Sweigart 2018). These sorts of barriers have come to becalled ‘intrinsic’ hybrid incompatibilities due to the fact that there are conflicts within the hybrid genomethat are expected to severely impact hybrids in most environmental contexts (though note that the strength ofselection against some intrinsic incompatibilities can vary across environments [Demuth and Wade 2007]).Studies have shown that the number of intrinsic incompatibilities increases deterministically with geneticdivergence between parents (Matute et al. 2010; Moyle and Nakazato 2010; Wang et al. 2013) and thatincompatibilities are common throughout the genomes of isolated populations of a given species (Corbett-Detig et al., 2013). Collectively, these studies have made substantial progress toward identifying generalitiesabout the evolutionary genetics of intrinsic hybrid incompatibilities.Incompatibilities can also be caused by exogenous ecological selection if particular allele combinationsrender hybrids unable to perform ecological functions such as predator avoidance or prey capture. Severalrecent studies have shown patterns to this effect, wherein hybrids have ‘mismatched’ trait combinations andreduced fitness as a result (Arnegard et al., 2014; Thompson et al., 2021). Such studies have successfullydemonstrated incompatibilities via interactions among traits, but links to the underlying genetics have notbeen made. Perhaps the most significant barrier to progress in measuring ‘ecological’ hybrid incompatibil-ities is that they are likely difficult to detect because of their small individual effect sizes (Rockman 2012).For example, Arnegard et al. (2014) found that combining divergent jaw bone traits together in an F2 stickle-back (Gasterosteus aculeatus L.) hybrid reduced their fitness because these traits interacted in a manner thatrendered hybrids unable to effectively generate suction for feeding. The underlying interacting jaw boneseach map to several QTL that individually explain a small fraction of the phenotypic variance, thus renderingit difficult to study their individual fitness effects.Recent theoretical advances, however, suggest ways to test for and measure the net effect of hybrid in-780.000.250.500.751.000.00 0.25 0.50 0.75 1.00trait 1 valuetrait 2 value0. 0.4 0.6 0.8heterozygositytrait mismatcheffect of heterozygosity ontrait mismatchbdistribution of simulated hybrid phenotypesaFigure 7.1: Results from simulations illustrating an ecological mechanism underlying theheterozygosity-incompatibility relationship in F2 hybrids. Both panels depict results from a represen-tative simulation run of adaptive divergence and hybridization between two populations. I consider an or-ganism with two traits that have both diverged as a result of selection. Panel (A) depicts the distributionof 1,000 F2 hybrid phenotypes in two-dimensional trait space. Large black points are the two parent phe-notypes, which are connected by a black line indicating the ‘axis of divergence’. Points are coloured byheterozygosity, as in (B). Panel (B) depicts the relationship between heterozygosity and trait ‘mismatch’ ofindividual hybrids. Mismatch is calculated as the shortest (i.e., perpendicular) distance between a hybrid’sphenotype and the black line connecting parents. The plot shows that mismatch is lower in more heterozy-gous F2s. Heterozygosity values are discrete because a small number of loci underlie adaptation in the plottedsimulation run.compatibilities using experimental crosses. Specifically, selection against hybrid incompatibilities in an F2hybrid cross manifests as directional selection for increased heterozygosity (Barton and Gale, 1993; Simonet al., 2018). This is expected because F2 hybrids have a hybrid index of approximately 0.5—having halfof their alleles from one parental species and half from the other. Given this, individuals with high het-erozygosity have fewer pairs of homozygous loci with opposite ancestry than more homozygous individuals.Having many loci with opposite homozygous ancestry can result in hybrids with maladaptive ‘mismatched’phenotypes, whereas highly heterozygous individuals are expected to be relatively intermediate (Fig. 7.1).Whether ‘mismatch’ affects fitness, however, ultimately depends on the ecology of the system and the under-lying fitness landscape. Such ‘coarse’ approaches—coarse because they use summary statistics rather thanfine mapping—are a promising means to identify the net strength of small-effect hybrid incompatibilitiesusing field experiments.In this study, I compare patterns of directional selection on heterozygosity between F2 hybrid familiesraised in the lab to those from the same cross types raised in field enclosures. If ecological selection on‘trait mismatch’ (i.e., selection favouring ‘matched’ trait values whether parental or somewhat intermediate)is operating in the field but not in the lab, selection for heterozygosity should be specific to the field (or at79least stronger than in the lab). I focus on hybrids between two types of ecologically divergent threespinestickleback populations. First, I consider hybridization between sympatric benthic and limnetic popula-tions. These populations, which are in effect reproductively isolated species due to strong assortative mating(McKinnon et al. 2004) and reduced hybrid fitness due to extrinsic selection pressures (Hatfield and Schluter1999), comprise sympatric species pairs that have evolved independently in at least five watersheds in BritishColumbia, Canada (McKinnon and Rundle 2002; McPhail 1992). Although reproductively isolated in prac-tice, the species pairs have no known intrinsic barriers that reduce fitness in the lab (Hatfield and Schluter1999). Second, I consider hybridization between allopatric populations of anadromous and solitary freshwa-ter stickleback. Similarly to the benthic-limnetic species pairs, these populations are recently diverged andcan readily hybridize. I pair an analysis of genetic data with a heuristic model to infer the strength of selectionthat is necessary to cause the observed patterns. My results provide compelling support for the hypothesisthat environment-specific hybrid incompatibilities separate recently diverged stickleback populations.7.2 Methods7.2.1 Data sourcesI used both previously published and unpublished data in my analyses. Summary information about eachdata source is listed in Table 7.1. I base my main inference on a comparison of heterozygosity in hybridsraised in aquaria to hybrids from the same crosses raised in experimental ponds. Besides their use in previousexperiments, ponds are natural contained ecosystems. See Extended Data in Arnegard et al. (2014) for addi-tional information about ponds. Pond-raised crosses capture both ‘intrinsic’ and ‘extrinsic’ incompatibilities,whereas aquarium-raised crosses are expected to capture ‘intrinsic’ incompatibilities that kill hybrids fromthe embryo to adult stage.Studies raising fish from the same cross type (benthic × limnetic or marine × freshwater) in the sameenvironment (aquaria or pond) were pooled for analysis. Two studies (Rennison et al., 2019; Schluter et al.,2021) genotyped both F2 and F3 hybrids, which I analyze together because mean heterozygosity did notdiffer between generations within a study (Fig. F.1). Similarly, data were analyzed together for four studiesof benthic × limnetic hybrids from Paxton Lake raised in experimental ponds because heterozygosity wasstatistically indistinguishable among them (Fig. F.2). This grouping of studies was done only to simplifythe presentation of results—patterns are highly repeatable across replicates and analyses showing results foreach pond and/or study separately are shown in Fig. F.3. Relevant details of each data source are outlinedbelow.Studies genotyped fish using either microsatellites, SNPs, or Genotyping-by-Sequencing (GBS). Allthree lab studies used microsatellites, whereas the pond studies all used SNPs or GBS. I have no reason tobelieve that differences in methodology among studies influence the results presented herein. First, I onlyconsider loci where parents have no alleles in common and thus can accurately assign ancestry. Second, Ionly use loci that were heterozygous for ancestry in F1s, so loci with ‘null’ microsatellites or any difficultiesin distinguishing alleles would be filtered out. In the largest microsatellite dataset (Rogers et al., 2012), 100% of loci that were different in parents were accurately called as heterozygous across eight F1s (288 of 28880loci across all eight F1 fish). SNP genotypes of the same cross type similarly had 100 % heterozygosity in F1s(Schluter et al., 2021). I also have no reason to suspect any systematic differences in the genetic constitutionof wild fish (i.e., F0s) used to found field vs. lab studies. In light of the above, it seems most likely that theresults presented herein reflect biology rather than methodology.Table 7.1: Summary of data sources.species design study population method gen env. n fish n loci ± [1SD]ben × lim biparental present Paxton microsatellites F2 lab 89 99.4 ± 6.2ben × lim biparental Conte et al. (2015) Paxton SNP array F2 pond 636 64.0 ± 0.0ben × lim biparental present Priest microsatellites F2 lab 92 22.8 ± 1.3ben × lim biparental Conte et al. (2015) Priest SNP array F2 pond 412 90.0 ± 0.0ben × lim 8 × F0 Arnegard et al. (2014) Paxton SNP array F2 pond 615 62.5 ± 17.9ben × lim 4 × biparental Rennison et al. (2019) Paxton GBS (RAD) F2 & F3 pond 649 85.1 ± 34.0marine × fresh biparental Schluter et al. (2021) LCR × Cranby SNP array F2 & F3 pond 723 120.3 ± 5.6marine × fresh biparental Rogers et al. (2012) LCR × Cranby microsatellites F2 lab 374 58.2 ± 4.2Benthic × limnetic crossesI obtained data from three sources for the pond-raised benthic × limnetic hybrids.Conte et al. (2015) generated a single F1 family from each of the Priest and Paxton Lake species pairs.Both were founded by a single wild benthic female and a limnetic male that were collected and crossed in2009. 35 adult F1 Paxton Lake hybrids and 25 adult F1 Priest Lake hybrids were released into separate pondswhere they bred naturally to produce F2 hybrids. F2 adults were collected over one year later. 407 F2s weregenotyped from the Paxton Lake pond, and 324 F2s were genotyped from the Priest Lake pond. Genotypingused a SNP microarray (Jones et al., 2012a), and 246 SNPs were found in the Paxton cross, and 318 werefound in the Priest cross.Arnegard et al. (2014) conducted a pond experiment with eight F0 grandparents from Paxton Lake. Twocrosses used a limnetic female and two crosses used a benthic female. Five F1 males and five F1 femalesfrom each family were added to the ponds in March 2008 where they bred naturally. 633 juvenile F2s werecollected in October of that same year and genotyped at 408 SNPs.Bay et al. (2017) genotyped 383 F2 hybrid females between Paxton Lake benthics and limnetics at 494SNPs. Fish are from several crosses and study designs. One used a cross with four unique F0s that wereused to produce two F1—one with a limnetic as dam and the other with a benthic as dam. A second hadeight unique F0s, where two F1 crosses were in each direction. These two crosses used wild fish collectedin 2007. A third set of crosses was done in 2009, one in each direction. The two F1 families were releasedinto separate ponds. Since the goal of the authors’ study was to examine the genetics of mate choice, a largenumber of F2 females were genotyped at a small number of microsatellite markers to determine whether agenotyped egg or fry was their offspring. 383 F2 females were identified in this parentage analysis and werethen genotyped at SNP markers. A total of 302 females were assigned to families with 10 or more full-sibs(which was necessary for linkage mapping), and these 302 females comprise my dataset.Finally, Rennison et al. (2019) conducted a study with four unique Paxton Lake benthic × limneticF1 hybrid families that were each split between two ponds. One pond in each pair contained a cutthroat81trout predator (heterozygosity did not differ across pond types and data are pooled across all pairs and pondtypes). Wild fish were caught in 2011 and F1s were released in 2012. Fish bred naturally and juvenileF2s were sampled in September of that same year. F3 hybrids were collected in September 2013. 50 fishfrom each pond and hybrid generation were genotyped at 2243 SNPs using restriction-site associated DNAsequencing (genotyping-by-sequencing).The Paxton and Priest Lake laboratory cross data are original to this study. Crosses used a single wild-caught benthic female fish and a single wild-caught limnetic male fish as F0 progenitors. Wild fish werecrossed in 2003. Sibling mating of F1 hybrids was used to produce a single F2 hybrid family for analysis, andfish were raised in glass aquaria and fed ad libitum. 92 Priest Lake F2s were genotyped at 85 microsatellitemarkers, and 86 Paxton Lake F2s were genotyped at 216 microsatellite markers.Marine × freshwater crossesSchluter et al. (2021) conducted a pond experiment with anadromous (hereafter simply ‘marine’)× freshwa-ter hybrids. This study crossed a marine female from the Little Campbell River, BC, with a freshwater malefrom Cranby Lake, BC. Over 600 juvenile F2 hybrids were introduced into the ponds directly in August 2006.F2s overwintered with an estimated over-winter survival rate of approximately 86 % (from mark-recapture).(Simulations designed to capture the experimental design, mortality, and sub-sampling procedures indicatethat 86 % survivorship, if caused by viability selection on hybrid incompatibilities, leads to a mean heterozy-gosity value of 51.8 % ± 0.5 [SD]; not shown.) In spring 2007, surviving F2s bred and were genotypedat 1,294 biallelic SNP markers. 500 of their F3 hybrid offspring were collected in October 2007 and weregenotyped with the same methodology.The data for the laboratory comparison to the Schluter et al. (2021) data were originally published byRogers et al. (2012). The population used a single Little Campbell River female as the F0 dam and a singleCranby Lake male as the F0 sire. Wild adult fish were captured in 2001 to generate a single F1 hybrid family.Four F2 crosses were made from individuals from this F1 family (eight F1 parents total) for a total of 374genotyped F2s. Fish were genotyped at 96 microsatellite markers.7.2.2 Marker filtering and estimating heterozygosityFor each dataset, I restricted my analysis to loci where the F0 progenitors of a given F2 family had noalleles in common (e.g., all BB in benthic F0s and all LL in limnetic F0s) and where all F1 hybrids wereheterozygous for ancestry. GBS data were filtered to 20× coverage. Final sample sizes of fish and markersare given in Table 7.1. In all cases, the sex chromosome (chromosome 19) was not analyzed.Because some studies have more individuals than loci, and others have more loci than individuals, Ianalyze heterozygosity both in individuals (averaged across loci) and at loci (averaged across individuals).I retained individuals for which at least 20 loci were genotyped, and retained loci for which at least 20individuals were genotyped.Ancestry proportion, directional selection, and segregation distortion reduce the expected heterozygositybelow 50 %. I account for this and base my main inference on estimates of excess heterozygosity. Excess het-erozygosity was calculated as observed heterozygosity (pAB) minus expected heterozygosity (2pApB, where82pA and pB are the frequencies of both ancestries at the locus or in the individual’s genome). My conclusionsare unchanged, however, if an uncorrected ‘observed’ heterozygosity is used as the response variable (Fig.F.4) or if the expected heterozygosity is adjusted for sample size (i.e., multiplying by 2N2N−1 following Irwinet al. 2018).7.2.3 Data analysisI evaluated whether excess heterozygosity differed between crosses using linear models. I first used simple t-tests to evaluate whether heterozygosity differed from the Hardy-Weinberg expectation (i.e., whether excessheterozygosity was significantly different from 0). This was done because studies are separate experimentsand this is a useful way to evaluate patterns of heterozygosity. To avoid basing conclusions on such indirectcomparisons, I also compared aquarium and pond studies directly in common linear models. Linear modelshad excess heterozygosity—of individuals or loci—as the response variable and environment (lab or pond) asa categorical predictor. For the benthic× limnetic data, ‘lake’ was included as a second categorical predictor.A lake× environment interaction term was non-significant and was omitted from the final model. Thus, twomodels were run: one for the benthic × limnetic cross type, and another for the marine × freshwater crosstype.7.2.4 Heuristic modelI used a simple heuristic model to infer the strength of selection on incompatibilities that is sufficient to causethe observed excess heterozygosity. I assume that incompatibilities only act between pairs of loci and thatfitness is based only on the genotype of individual F2 hybrids. There is no directional selection and fitnessis not frequency- or density-dependent. I also assume that all possible pairs of incompatible loci reducean individual’s fitness. By assumption, I ignore higher-order interactions among loci (i.e., incompatibilitiesbetween three or more loci).I consider two broad incompatibility architectures, recessive (Fig. 7.3A, left) and additive (7.3A, right).The recessive model assumes that only loci with opposite homozygous ancestry (i.e., homozygous at onelocus for BB and at the other locus for LL) interact, whereas the additive model allows heterozygous loci tobe involved in incompatibilities. The additive model is symmetric for simplicity and because it is plausiblethat populations could easily cross shallow fitness valleys such as those that typically underlie individualecological incompatibilities.The models simply sum the count of each incompatibility type, and penalize the individual’s fitness ac-cording to a linear function where the penalty is determined by s—the selection coefficient acting againstincompatibilities of opposite homozygous ancestries (i.e., BB-LL or FF-MM incompatibilities). For simplic-ity I use notation of benthic (‘B’) and limnetic (‘L’) ancestries, but this is arbitrary and one could substitutemarine or freshwater. I assume the strength of incompatibilities involving heterozygous loci is half of thatinvolving only homozygous loci (see below). The selection coefficient, s, can be interpreted as the reductionin fitness caused by individual incompatibilities. For example, an s value of 0.002 implies that each BB-LLor FF-MM incompatibility reduces an individual’s fitness by 0.2 %.83For a case where all incompatibilities are assumed to be recessive, the fitness of an individual hybrid iscalculated as:Wi = 1− n2 · pBB · pLL · s, (7.1)where Wi is the fitness of the ith individual F2 hybrid, n is the number of unlinked loci, pBB & pLL are thefrequencies of homozygous ancestries among genotyped loci (here benthic or limnetic, but could also bemarine and freshwater), and s is the selection coefficient acting against each BB-LL or FF-MM incompat-ibility. If an individual has 4 loci where ancestry is 1 × BB, 1 × LL, and 2 × BL, this individual has onepossible pairwise incompatibility—the lone BB locus with the lone LL locus. If the individual has 5 lociwith ancestries 2 × BB, 1 × LL, and 2 × BL, this individual has 2 pairwise incompatibilities—each BBwith the lone LL. The fitness of a given individual is reduced by a given amount, s, for each incompatibility,so fitness in the first former case is 1− s and fitness in the latter case is 1− 2s. I assume fitness is linear forsimplicity, but note that this causes the model to return negative fitness values and thus fail under extendedparameter combinations.I next consider an additive model where heterozygous loci interact with homozygous loci to influencehybrid fitness. For systems where niche divergence is additive, as it likely is in threespine stickleback (Arne-gard et al., 2014), an additive model might be more realistic than a recessive one. Under the additive model,an individual’s fitness is calculated as:Wi = 1− n2 · pBB · pLL · s− (n2 · pBB · pBL + n2 · pLL · pBL) · s2, (7.2)where terms are as in Eqn. 7.1, and pBL is the frequency of loci with heterozygous ancestry. The first termin the equation quantifies homozygote-homozygote incompatibilities (i.e., those between BB and LL), andthe second term quantifies homozygote-heterozygote incompatibilities (i.e., those between BB and BL & LLand BL). This model assumes that the strength of selection on homozygous-heterozygous incompatibilitiesis half that acting on incompatibilities between loci of opposite homozygous ancestry. Consider again anindividual with four loci, with 1:2:1 BB:BL:LL frequencies. The individual has 1 homozygote-homozygoteincompatibility (BB-LL) and four heterozygote incompatibilities (BB-BL1, LL-BL2, LL-BL1, and LL-BL2).I used this heuristic model as the basis of simple simulations to evaluate the connection between theabove fitness functions and observed patterns of excess heterozygosity. These simulations interpret fitnessfrom Eqns. 7.1 & 7.2 as survival probability. In simulations, I assumed that F1 hybrid stickleback typicallyhave between 1 and 1.5 recombination events per chromosome (2n chromosomes = 42; Roesti et al. 2013),and therefore assume that F2 hybrids inherit 50 unlinked haplotype blocks (hereafter referred to as the 50genotyped ‘loci’; approximately 1.2 recombination events per chromosome). I generated individuals with50 loci where each locus had a 25 % probability of having ancestry ‘BB’, a 25 % probability of having‘LL’, and a 50 % probability of being heterozygous, ‘BL’. I calculated each individual’s fitness under bothEqns. 7.1 and 7.2 then implemented probabilistic selective mortality according to an individual’s predictedfitness (using random numbers). Finally, I recorded the mean excess heterozygosity of survivors. I repeatthese simulations for various values of s to determine the strength of selection against incompatibilities that84returns estimates of excess heterozygosity that match those in the empirical data. As noted above, I assumeincompatibilities only act between pairs of loci (i.e. they are digenic rather than trigenic, etc.) even thoughtrigenic interactions are likely to be much more common than digenic ones (Kuzmin et al. 2018). Therefore,the resulting estimates of the minimum s required to observe a given amount of heterozygosity are veryconservative and likely overestimated by one or more orders of magnitude.7.3 Results and discussion7.3.1 Patterns of excess heterozygosityI begin this section by evaluating patterns of excess heterozygosity in aquaria and ponds separately for bothbenthic × limnetic and marine × freshwater crosses. These comparisons are indirect but are justified bythe fact that the data are from separate studies measured in different years. I then make a direct comparisonbetween these two environments in using linear models. Conclusions are consistent between approaches.Aquarium-raised crossesMean individual excess heterozygosity was not significantly different from zero in any aquarium-raisedstickleback cross (see left side [red] of panels in Fig. 7.2). Specifically, t-tests evaluating whether excessheterozygosity was significantly different from zero failed to reject the null hypothesis for both benthic ×limnetic crosses (mean & 95 % CI Paxton Lake—β = 0.014 [−0.010, 0.037], t88 = 1.16, P = 0.25; PriestLake—β = 0.0098 [−0.014, 0.034], t89 = 0.81, P = 0.42). The aquarium-raised marine × freshwater crosswas similar (β = −0.0047 [−0.013, 0.00396], t373 = 0.28, P = 0.28).The lack of excess heterozygosity in aquaria is not surprising given what is known about ‘intrinsic’ hy-brid incompatibilities in stickleback. Previous studies of benthic × limnetic hybrids have found no evidencefor intrinsic inviability in F2 benthic× limnetic stickleback crosses, either in embryo development and hatch-ing success McPhail (1984, 1992); Hatfield and Schluter (1999) or lifetime fitness (Hatfield and Schluter,1999). In a recent review summarising the literature on reproductive isolation in threepsine stickleback,Lackey and Boughman (2017) report that ‘intrinsic’ barriers are typically weak to nonexistent. Both marine(i.e., anadromous) × freshwater and benthic × limnetic crosses had no evidence for intrinsic inviability inthis review (Lackey and Boughman, 2017). By contrast, the authors found evidence for hybrid ecologicalinviability in both systems (Lackey and Boughman, 2017).Pond-raised crossesMean individual excess heterozygosity exceeded zero in each pond-raised cross (see right side [blue] ofpanels in Fig. 7.2). This was the case for both Paxton and Priest Lake hybrids for the benthic × limneticcrosses (mean & 95 % CI Paxton Lake—β = 0.029 [−0.024, 0.033], t2222 = 13.16, P < 0.0001; PriestLake—β = 0.039 [0.029, 0.048], t411, P < 0.0001), as well as the marine × freshwater cross (β = 0.034[0.027, 0.041], t722 = 9.33, P < 0.0001). Thus, there is support for the hypothesis that ponds select forheterozygosity.85Direct comparison between aquarium- and pond-raised crossesI evaluated the difference between aquarium- and pond-raised crosses using simple linear models. For thebenthic × limnetic crosses, I used a linear model where lake (Paxton or Priest), environment (aquaria orpond), and their interaction, were predictors. The interaction term was non-significant and was droppedleaving the two main effects. I found that individual mean excess heterozygosity was 2.2 % higher in pond-raised benthic × limnetic hybrids than in aquarium-raised hybrids (βˆ = 0.022 ± 0.0083 [SE; units are het-erozygote frequency], F1,2509 = 6.89, P = 0.0087) (Fig. 7.2A; also see Fig F.5 for plots of individual hybridindex and heterozygosity). The ‘lake’ term was non-significant (P = 0.11). For the marine × freshwatercrosses, I found that individual mean excess heterozygosity was 3.9 % higher in pond-raised fish than inaquarium-raised fish (βˆ = 0.039 ± 0.0059 [SE], F1,1095 = 41.88, P = 1.46 ×10−10) (Fig. 7.2B). I repeatedthese analyses using loci as the unit of replication, rather than individuals, and found virtually identical pat-terns to the analysis of individuals (Fig. 7.2C&D; Fig F.6). These results are consistent with the hypothesisthat hybrid incompatibilities act more strongly in the wild than in the lab and implies that individuals with agreater number of incompatibilities are more likely to die than those with fewer.7.3.2 Heuristic modelAnalysis of the heuristic model revealed that, as expected, fitness (W) is lower when incompatibilities actadditively rather than recessively (compare black and grey lines in Fig. 7.3B) and when F2 individuals aremore homozygous (compare dashed to solid lines in Fig. 7.3B). I used simulations of selective mortalityto estimate the per-incompatibility s value that is sufficient to generate 3 % excess heterozygosity, whichis the mean lab-pond difference of the two crosses. For the recessive model, I found that I observed amean of 3 % excess heterozygosity when s ≥ 0.0036. Under the additive model, I found that mean 3 %excess heterozygosity resulted when s ≥ 0.0017. These results imply that if each two-way incompatibilityreduces survival probability only by 0.0036 (i.e., 0.36 %) under a recessive model, or 0.0017 (i.e., 0.17%)under an additive incompatibility model, this would be sufficient to cause the observed patterns of excessheterozygosity. As noted above, it is possible that these values are substantial over-estimates because theyonly account for two-way incompatibilities.7.3.3 Alternative explanations for excess heterozygosityAlthough I framed my predictions on the hypothesis of hybrid incompatibilities, several other mechanismscould possibly underlie the observed pattern of excess heterozygosity. These alternative mechanisms—heterosis and dominance—involve processes operating at single loci rather than interactions among loci.Ultimately, the data cannot directly distinguish between single-locus processes like heterosis and multi-locus processes like incompatibilities, so indirect inference is required to evaluate the plausibility of causalprocesses.Heterosis refers to the case where heterozygosity at a given locus is favoured per se, rather than as ameans to escape incompatibilities caused by interactions involving homozygous alleles. Typically, heterosisis caused by the dominance of a fit allele over a less fit one. If individual loci were overdominant only86− pondenvironmentexcess heterozygosity−0.4− pondenvironmentexcess heterozygosity− pondenvironmentexcess heterozygosityheterozygosity in benthic × limenticcrosses (individuals)a− pondenvironmentexcess heterozygosityheterozygosity in marine × freshwatercrosses (individuals)bexcess heterozygosity in benthic × limenticcrosses (loci)c excess heterozygosity in marine × freshwatercrosses (loci)dFigure 7.2: Patterns of heterozygosity in stickleback hybrids across environments. Panels (A) and (B)show excess heterozygosity for individual hybrids (averaged across loci), while panels (C) and (D) showexcess heterozygosity for individual loci (averaged across individuals). Points represent the residual mean± 95 % CI (from visreg). Violin overlays show the full distribution of the data. Paxton Lake pond dataare from several different studies considered together (see Methods and Table 7.1).870. 0.002 0.004 0.006incompatibility selection coefficient (s)excess heterozygosity0. 0.0005 0.0010 0.0015incompatibility selection coefficient (s)fitness (W)BBBLLLBB BL LLgenotype at 'B' locusrecessive (wrec)BB BL LLadditive (wadd)two-locus incompatibilityfitness landscapesagenotype at 'A' locuseffect of heterozygosity andincompatibility type on fitnessbp12 = 0.4; waddp12 = 0.6; wrecp12 = 0.6; waddp12 = 0.4; wrecheterozygosity in simulations of viability selectioncw = 1w = 1 −  w = 1 − ss2Figure 7.3: Heuristic two-way incompatibility model to illustrate sufficient selection strengths to gen-erate excess heterozygosity. Panel (A) is an illustration of two two-locus incompatibility fitness landscapemodels where colour represents fitness. Panel (B) shows fitness values (W) calculated using Eqn. 7.1 (re-cessive incompatibility; black) and Eqn. 7.2 (additive incompatibility; grey) for different values of s. Foreach model, I show fitness for two values of heterozygote ancestry frequency (p12). Panel (C) shows excessheterozygosity in simulations of F2 hybrids experiencing different selection strengths (using Eqns. 7.1 and7.2) (see Methods). The horizontal red line indicates average difference in excess heterozygosity betweenthe lab and pond studies (p12 = 0.03).88under field conditions, then excess heterozygosity could result without any interactions among loci. In thebenthic× limnetic crosses, this possibility can be disregarded based on prior knowledge about hybrid fitnessin this system. If heterosis were common, then hybrids should have higher fitness than parents. However,F1 and reciprocal backcross hybrids—which are highly heterozygous—have lower growth and/or survivalthan parent taxa in field experiments (Hatfield and Schluter 1999; Vamosi et al. 2000; Rundle 2002). In thelab, F1 hybrid growth rate matches the additive expectation of parents (Hatfield, 1997; Hatfield and Schluter,1999). These patterns simply would not occur if heterosis was a general feature of benthic-limnetic crosses.Less is known about heterosis in marine × freshwater crosses. Further evidence against heterosis comesfrom the fact that there is no relationship between body size and heterozygosity in the lab in any cross (Fig.F.7; family sizes are too small for a robust analysis in ponds). Thus, heterosis seems an unlikely explanationunderlying selection for heterozygosity in stickleback hybrids.Patterns of excess heterozygosity could also be caused by directional selection and dominance. If het-erozygotes were just as likely to survive as the favoured homozygote, this would lead to a higher observedheterozygosity than expected (i.e., >2pApB) for loci that are under directional selection. I quantified thestrength of directional selection on each locus as |pAA − pBB|, the absolute difference between the frequen-cies of both homozygotes. Loci under strong directional selection should have larger values. If dominancewas common, then excess heterozygosity should be greater at loci that are under stronger directional selec-tion. I find that the excess heterozygosity of loci is not correlated with this metric of directional selection ineither pond-raised benthic × limnetic hybrids nor marine × freshwater hybrids (both P > 0.15; Fig. F.8).Thus, because directional selection is not a strong predictor of heterozygosity, it is unlikely that dominanceof beneficial alleles alone can explain the observed patterns of excess heterozygosity.7.4 ConclusionThe main result of this study is that heterozygosity was elevated in F2 stickleback hybrids raised in the fieldcompared to those raised in aquaria. Because single-locus processes such as heterosis and dominance areunlikely to explain this pattern, I suggest that hybrid incompatibilities are the most likely causal mechanism.Selection on a per-incompatibility basis need not be terribly strong to cause levels of excess heterozygositysimilar to what I observed. This finding has implications for our understanding of the genetic basis ofextrinsic reproductive isolation. At least for the benthic × limnetic crosses, it is well-established that thespecies are reproductively isolated and hybrids perform worse than parents under field conditions. Thus,hybrid incompatibilities might underlie extrinsic post-zygotic isolation in this classic case of ‘ecologicalspeciation’ (McKinnon and Rundle, 2002). Moreover, the analysis gives insight into the number of genesthat might underlie speciation. The data presented here suggests that many genes of small effect (i.e., wheretheir interactions reduce fitness by considerably less than 1 %), located throughout the genome, underliereproductive isolation between ecologically divergent populations of threespine stickleback.This study used crosses with different F0 progenitors, genotyped with different methodologies, for itsmain comparison. Although this is less than ideal, there is no obvious mechanism that would cause thelab-raised fish to exhibit significant excess heterozygosity. In light of this, a valid though less conservative89approach would simply have tested if pond-raised crosses exhibit excess heterozygosity, which they almostinvariably do. The fact that this pattern—excess heterozygosity in pond-raised hybrids—repeats across somany pond experiments from different years, might be seen as an even stronger conclusion than one basedon a single comparison in a single year.The evidence presented herein is consistent with the hypothesis that extrinsic hybrid incompatibilities,which operate between parental alleles at different loci, underlie extrinsic post-zygotic isolation in this sys-tem. To the extent that this study documents the existence of environment-specific hybrid incompatibilities,it cannot identify their underlying mechanisms. Experiments that directly manipulate individual phenotypes,or their interactions with the environment, are needed to establish such causality. Such studies represent anexciting new frontier for empirical research into the mechanisms of ecological speciation.90Chapter 8Conclusion8.1 OverviewMy thesis used theory, data synthesis, and experiments to generate hypotheses, establish patterns, and testpredictions about the evolutionary ecology of hybridization. The narrative thread throughout this thesissurrounded hybrid incompatibilities that affect the ecological performance of hybrids. I have tried to explorethis topic using a variety of techniques and data types.The first three data chapters of my thesis used theoretical approaches and previously published data.Chapter 2 used simulations to clarify how adaptation from standing variation affects progress toward specia-tion and used analytical models to arrive at generalities about when we should expect populations to use thesame vs. different alleles for adaptation. Chapter 3 synthesized data from the literature to illustrate that diver-gent quantitative traits are often dominant and ‘mismatched’ in F1 hybrids, and used data from a large-scalefield experiment to illustrate that this mismatch has negative fitness consequences. Chapter 4 used data fromthe literature to provide support for a key assumption of models of hybrid fitness—that mutations used foradaptation are typically pleiotropic. These three chapters established a theoretical and empirical frameworkfor studying the causes and consequences of ecological hybrid incompatibilities. I leveraged this frameworkin the final three data chapters which test theoretical predictions in the lab and field.The final three data chapters of my thesis use threespine stickleback fish (Gasterosteus aculeatus) totest key predictions about ecological hybrid incompatibilities. Chapter 5 found support for the theoreticalprediction that hybrid trait mismatch evolves in a manner that is positively associated with the magnitudeof phenotypic divergence between parent populations. Chapter 6 used a pond experiment to illustrate thatparallel phenotypic evolution can lead to the evolution of hybrid breakdown due to ‘mutation-order’ pro-cesses in both benthics and limnetics, but also found a surprising amount of heterosis. Finally, Chapter 7found that the genetic signature of hybrid incompatibilities—excess heterozygosity—is reliably observed inpond-raised F2 stickleback hybrids but is not observed in the lab. These three chapters collectively indicatethat ecological hybrid incompatibilities might be an important form of post-zygotic reproductive isolationseparating natural stickleback populations.8.2 Areas requiring researchBy illustrating that traits are often mismatched in hybrids and that hybrid incompatibilities can have an im-portant ecological dimension, my thesis work has illuminated several research directions worth addressing.As I expressed at the outset, I hoped that this thesis would raise more questions than it answered. Though I91will leave it to the reader to decide whether this was accomplished, below I highlight several of the key areasthat I see as high-priority for future research.8.2.1 Mechanisms underlying ecological incompatibilitiesBefore my thesis, scientists had been making rapid progress in identifying (putative) mechanisms underlyingecological incompatibilities (Vinšálková and Gvoždík, 2007; Matsubayashi et al., 2010; Cooper et al., 2018;Martin and Wainwright, 2013; Keagy et al., 2016; Arnegard et al., 2014). These pioneering studies generatedcompelling and testable hypotheses about the mechanisms through which trait interactions affect fitness, butit was beyond their scope to quantify ‘mismatch’ more directly and directly link it to fitness. My thesisbuilt on this strong foundation in several ways. First, in Chapter 3 I quantified individual-level mismatch insunflowers and related it directly to fitness via seed count. Second, in Chapter 7 I showed that individualswith high ‘genetic mismatch’ (i.e., high homozygosity for a given hybrid index) were selected against undersemi-natural conditions but not in the lab. While I think the above two conclusions are valuable and novelcontributions to the literature, it is important to acknowledge their main limitation. Specifically, the linkbetween mismatch and fitness is correlational because I cannot decouple environment-specific endogenousselection—intrinsic conflicts preventing development or gametogenesis—from environment-specific exoge-nous selection—selection imposed by the biotic or abiotic environment. Nor can I conclusively identify anyagents of selection that link mismatch to fitness.Future work on ecological incompatibilities should strive to identify the mechanisms of ecological se-lection underlying them. To accomplish this, I envision two main approaches. First, one can use population-level manipulations to change how groups of hybrids experience selection. For example, Rennison et al.(2019) split hybrid families into some ponds that contained trout and other ponds that didn’t—such an ap-proach could test for trout-mediated selection on incompatibilities if one hypothesized that it might exist.Rundle et al. (2003) conducted a similar experiment also removing predatory insects. Such approaches havethe advantage that treatments are relatively easy to apply, but the disadvantage that they reduce sample sizeto the number of replicate enclosures (e.g., ponds, mesocosms, tanks) across which organisms are divided.For some groups of organisms, like fish, this is likely the only feasible approach because individuals cannotbe reliably recaptured and manipulated during their lifetimes.A second approach to studying mechanisms of ecological incompatibilities involves individual-levelmanipulations to randomize the selection regimes of individual organisms in a common garden. For example,one can provide supplemental resources or exclude mutualists (e.g., pollinators) to confirm a role for anyparticular selective agent that is hypothesized to underlie incompatibility. In my planned post-doctoral work,I plan to experimentally manipulate hand-pollination across flowers in individual F2 hybrids between bird-pollinated Penstemon centranthifolius and wasp-pollinated P. spectabilis. Individual plants that are unableto attract and/or interact with pollinators (i.e., receive or deposit pollen) will have low seed production in theopen-pollination treatment compared to those who are relatively well-suited to interacting with pollinators.Hand pollinations can confirm that low-fitness individuals have low fitness because of their interactionswith pollinators, rather than some ‘intrinsic’ unfitness. Thus, a prediction is that the fitness effect of hand-pollination will be correlated with mismatch. If possible, one might also manipulate phenotypes directly to92decouple them from the genetic basis (Sinervo and Svensson, 2002). In these approaches using natural orexperimental hybrids, hypotheses can be robustly tested by examining whether the manipulations affectedselection on excess heterozygosity, the mismatch-fitness relationship, and/or patterns of hybrid breakdown.8.2.2 Theoretical importance of ecological incompatibilitiesThe work in this thesis generally concerns early generation—F1, F2, or BC1—hybrids, but future work mustextend the findings herein to later generations. Models of hybrid zones or sympatric populations that considerhow various genetic architectures influence the probability of collapse into a swarm are needed to resolvethe efficacy of both intrinsic and extrinsic incompatibilities for maintaining reproductive isolation. One keydifference between intrinsic incompatibilities and ecological incompatibilities is that extrinsic fitness land-scapes are likely more dynamic and subject to a greater magnitude of negative frequency-dependent anddensity-dependent selection—more intrinsic incompatibilities are more likely subject to positive frequency-dependence. A truly intrinsic incompatibility, where selection is consistent across all plausible environments,could theoretically be removed (i.e., one set of compatible alleles reaches fixation) from a region of hybridza-tion (e.g., a hybrid zone) by selection rather easily if it involves only a small number of loci (Xiong andMallet, 2021). If these incompatibilities are all that keep species apart, reproductive isolation could breakdown following the loss of one set of alleles. If the alleles underlying an ecological incompatibility reachlow frequency, however, the lower frequency type might be increasingly favoured by selection. (Testingwhether selection on ecological incompatibilities is frequency- or density-dependent is an exciting empiricalopportunity). If selection is frequency-dependent, incompatibilities acted on by ecologically-mediated selec-tion might be more robust in the face of potentially homogenizing gene flow. Future theory on this subject,perhaps integrating approaches from adaptive dynamics (wherein frequency-dependent selection is central[Dieckmann and Doebeli 1999]), will be valuable.To better understand the role of ecological incompatibilities in speciation, we must also expand ourphenotypic models of selection against hybrids. A given reduction in F1 fitness could result from two generalphenotypic mechanisms: relative intermediacy—where intermediate phenotypes are selected against due totheir being no intermediate niche—or mismatch—where particular combinations of traits render hybrids unfitin any niche including a possible intermediate one. For a given reduction of F1 fitness, is the maintenanceof species more likely when one or the other mechanism is responsible? Selection against the F1 is what itis, regardless of the underlying phenotypes or genetics. But patterns of selection against second generationhybrids and beyond (e.g., backcrosses and F≥2s) will differ depending on whether traits are additive ordominant. Conducting simulations wherein population divergence is underpinned by additive vs. dominantloci—and where dominance differs in the same or different directions among traits—is likely the best way todetermine how trait mismatch affects the persistence of reproductively isolated populations, and to ascertainthe importance of trait mismatch for speciation.93shapecolour (YUP allele)shape – colourcombinationsA051015bumblebees (10−3  visits flower−1 hr−1)effects of shape and colouron bumblebee visitationB050100150hummingbirds (10−3  visits flower−1 hr−1)effects of shape and colouron hummingbird visitationCFigure 8.1: A possible ecological incompatibility in monkeyflowers. Mimulus (syn. Erythranthe) lewisiihas pink petals and is pollinated by bumblebees, whereas M. cardinalis has red-coloured petals and is polli-nated by hummingbirds. The species differ in a QTL at the YUP locus that confers flower colour differences.When the cardinalis YUP allele is introgressed into the M. lewisii background pollination by bumblebeesdecreases bee visitation by 83 % (arrow in B). By contrast introgressing the lewisii YUP allele into cardi-nalis only decreases hummingbird visitation by 10 % (arrow in panel C). This could represent an asymmetricincompatibility that is only identifiable in the field. Images digitized from Schemske and Bradshaw (1999)and data taken from Bradshaw and Schemske (2003).8.3 A proposal to slightly refine the language of speciationIncreasing evidence, including that presented in this thesis, indicates that we must change the way we use theterm ‘hybrid incompatibility’. In this brief section, I argue two main points. First, the Bateson-Dobzhansky-Muller mechanism should be seen as a general mechanism of post-zygotic isolation, rather than only resultingfrom endogenous conflicts in hybrid genomes. Second, the general intrinsic vs. extrinsic classification haslargely outlived its usefulness and its continued use is more harmful than productive.As literature on speciation has accumulated in the past decades, the language we use to describe its un-derlying processes and mechanisms has grown. Noting this, Harrison (2012) cautioned against introducingnew terms and re-configuring old definitions because often new language can reflect the idiosyncrasies ofthe systems we are most familiar with and many new terms are invented for describing long-understoodprocesses. In their book, Coyne and Orr (2004) describe the mechanism of Bateson-Dobzhansky-Muller(Bateson, 1909; Dobzhansky, 1937; Muller, 1942) hybrid incompatibilities only when discussing embryoinviability and hybrid sterility. The BDMI mechanism is specifically included as a subsection of their dis-cussion of ‘intrinsic’ postzygotic isolation. Even in books dedicated to the study of ecological speciation,incompatibilities are seldom if ever raised as the genetic basis of extrinsic postzygotic isolating barriers(Nosil, 2012). The sorts of mismatch-based incompatibilities described in this thesis act via an identicalgenetic mechanism to the more traditional ‘intrinsic’ BDM incompatibilities in that they involve epistasisbetween two or more loci. The fact that they might differ in their average fitness effects only implies thatthey differ in degree and not kind.94Although incompatibilities subject to ecologically-mediated selection are likely weak generally, thisshould not be seen as a bright line differentiating them from ‘intrinsic’ incompatibilities. Indeed, as sci-entists study ecological incompatibilities further, we are likely to discover many ‘intrinsic’ incompatibilitiesthat have weak fitness-effects and many ‘ecological’ incompatibilities where the fitness consequences aresubstantial. Some in the latter category likely have already been discovered; for example, introgressing theallele for ‘red’ flowers from Mimulus cardinalis into bee-pollinated M. lewisii almost completely reducesvisitation from bee pollinators from whom the flowers are adapted to receive pollen and on whose backsthey are adapted to deposit it (Fig. 8.1). This substitution does not substantially affect visitation from hum-mingbirds. Although the fitness consequences of this substitution in terms of seed set were unmeasured, itis reasonable to conclude that a complete lack of pollination likely had a substantial effect on seed set thatrivals many ovule- or pollen-sterilizing incompatibilities and thus would have a fitness effect rivalling manysterilizing incompatibilities.Importantly, many incompatibilities that are called ‘intrinsic’ are sensitive both to the environmentalcontext and the genetic background (Fig. 8.2). For example, using an experimental approach that mimicshybridization, Ono et al. 2017 used yeast to examine the fitness consequences of combining two alleles thatevolved in an experimental evolution experiment and individually confer resistance to a fungicide. In theenvironment under which the alleles evolved, combining both in a common genetic background caused areduction in fitness compared to each type examined alone (compare purple to red and blue in Fig. 8.2A.However, in a different environment with a higher concentration of the fungicide, combining these allelesimproved fitness rather than reduced it. Thus, even incompatibilities that might appear ‘intrinsic’ becausethey reduce growth rate in the lab can have an important environmental context.The word ‘intrinsic’ can literally mean ‘essential’, and incompatibilities described as such are oftenthought to be permanent or irreversible. However, recent evidence indicates that incompatibilities can alsointeract in a manner that refutes the hypothesis that they are in fact ‘intrinsic’. For example, Guerrero et al.(2017) investigated interactions among different incompatibility-causing alleles in tomato (Solanum spp.).The authors compared plants where one region of the genome had hybrid ancestry (i.e., single-introgressionlines) to those with two regions of hybrid ancestry (double-introgression lines). The goal was to determineif incompatibilities typically act additively (e.g., if same phenotypic effect, then double-introgression linesare twice as bad as single-introgression lines), synergistically (double-introgression more than twice as bad),or antagonistically (double-introgression less than twice as bad). The authors found that antagonistic inter-actions were pervasive, and occasionally even found that double mutants had higher fitness than both singlemutants. If two incompatibility-causing alleles improve hybrid fitness in the presence of one another, thensubstituting an ‘incompatibility’ allele into some genetic backgrounds is beneficial. Calling such incompati-bilities ‘intrinsic’ might mislead us into thinking they are invariably deleterious. In fact, whether or not an in-compatibility is ‘intrinsic’ is fundamentally unfalsifiable because there could always be a genetic backgroundor environment that impacts its fitness effect. We can avoid this pitfall by simply referring to the phenotypiceffect of incompatibilities. By calling them ‘sterility-causing’ or ‘lethality-causing’ incompatibilities ratherthan intrinsic, we get our point across while remaining agnostic to any environment-dependence.Coyne and Orr (2004) acknowledge the somewhat fuzzy distinction between intrinsic and extrinsic iso-95genotypesagenotypesaFitnesswild-type erg3erg7erg3 +erg7 growth in 2 µMNystatinaFitnessgrowth in 16 µMNystatinwild-typeLA3915 LA3947LA3950 +LA3995pollen fertilityaseed fertilityFitnessFitnessieffect of incompatibilities indifferent environmentsAieffect of incompatibilities indifferent genetic backgroundsBiiiiiiiiiiFigure 8.2: Fitness effects of incompatibility loci vary across environments and genetic backgrounds. (A)Adapted from Ono et al. (2017). In their experiment, an ancestral strain is divided into (i) different populations ofbrewer’s yeast (Saccharomyces cerevisiae) that fixed independent mutations in the ergosterol biosynthesis pathway(ERG3 and ERG5) in response to treatment with the fungicide Nystatin. Nystatin binds ergosterol embedded in thecell membrane, forming channels that cause cells to leach their contents; mutations reduce the quantity of ergosterol inthe membrane. (ii) In the presence of 2 μM nystatin, these mutations are individually beneficial because they reducethe target size of nystatin, at the cost of making a less permeable membrane. However, individuals with both mutationshave reduced fitness because their membranes are too impermeable, acting as a BDMI. (iii) In higher concentrations ofNystatin, the single mutants are unfit whereas double-mutants have high fitness, illustrating that the incompatibility isenvironment-specific. (B) Adapted from Guerrero et al. (2017). (i) In this experiment, short chromosomal regions fromSolanum habrochaites (here LA3947 and LA3915) reduced fitness when introgressed onto the genetic background ofS. lycopersicum. When combined in a single genetic background (purple tomato), these alleles often restored fitnessfor at least one fitness component (restored in [ii], further reduced in [iii]).96lating barriers. In light of the emerging evidence, some of which I have briefly touched on above, I ad-vocate for a slight modification to the way we use the term ‘hybrid incompatibility’. Namely, we needto recognize that ‘incompatibility’ need not mean sterility or embryo inviability. Rather, all interactionsamong alleles of divergent ancestry that interact epistatically to reduce hybrid fitness fully deserve the titleof incompatibility—regardless of the reason why they reduce fitness. We should stop adding the prefaceof ‘intrinsic’ or ‘extrinsic’ when describing incompatibilities and be more agnostic unless we are confidentin having identified a particular mechanism. 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Evolution 75:476–489.115Appendices116Appendix AAppendix for Chapter 2A.1 Geometric basis for rapid loss of parallelismHere, I outline an explanation for why genetic parallelism decreases rapidly with the angle of divergence, θ(Fig. 2.2A) and distance between optima (Fig. A.15B). My explanation focuses on the extent of phenotypicspace wherein mutations improve the fitness of both adapting populations in their respective environments.At the time of founding both adapting populations have the same mean phenotype, which is the mean an-cestral phenotype. Mutations that move this ancestral mean phenotype into the region that leads to higherfitness in both parental environments are thus beneficial in both populations. The region of phenotypic spacethat has higher fitness than the mean phenotype in one environment is a hypersphere (of dimensionality, m),centred on the optimum with a radius equal to the distance between the mean phenotype and the optimum,d. A similar hypersphere characterizes the phenotypic space that has higher fitness than the mean pheno-type in the other parental environment. The region that is mutually beneficial is then the intersection of twohyperspheres, which is the union of two hyperspherical caps.Fortunately, the volume of a hyperspherical cap is known for any dimension, m (Li, 2011). It dependson the dimensionality (m), the radii of the two hyperspheres (D), and the distance between their centers (δ).In my case the distance between the two centres is δ = 2d × sin(θ/2). The amount of phenotypic space thatis beneficial in a given environment is simply the volume of one of the hyperspheres. Thus, dividing thevolume of the mutually-beneficial space (the union of the hyperspherical caps) by the volume of the spacebeneficial in a given environment (one of the hyperspheres) gives the fraction of beneficial mutations whichare mutually beneficial. Using the formula given by Li (2011; their eqn 3) for the volume of a hypersphericalcap created by the intersection of two m-dimensional hyperspheres with radii d whose centres are distance δapart, the fraction of beneficial mutations that are expected to be beneficial in both, O, is:O = Ix[1 +m/2, 1/2] (A.1)where Ix[a, b] is the regularized incomplete beta function (Equation 6.6.2 in Abramowitz and Stegun 1972)and here x = cos(θ/2)2. Eqn. A.1 depends on only m and θ, that is the solution is independent of the distancefrom the ancestor to the new optima, d. I refer to Eqn. A.1 as the fraction of overlap in the main text, butnote that this is only true when d1 = d2 (the formula is more complex when d1 6= d2, but can easily be used,e.g., Fig. A.16B). The incomplete regularized beta function arises from integrating sinm(θ) over θ (Li, 2011).The solution of Eqn. A.1 exhibits a rapid decrease with θ for all values of m > 0, and the decreaseis faster for greater values of m (Fig. 2.2B). Thus, if standing genetic variation was uniformly distributedthroughout the beneficial hyperspheres, the percent of segregating beneficial mutations that were beneficial117in both parental populations, and thus expected to potentially fix in both, would decrease rapidly with theangle of divergence.The above analysis considers only the very onset of adaptation, when the two parental populations havethe same mean phenotypes, such that the fraction of phenotypic space that is beneficial in one populationthat is also beneficial in the other population (call this X) is equivalent to the fraction of possible beneficialmutations (if uniformly distributed across the hyperspheres) that are beneficial in both populations (call thisY). As adaptation proceeds the mean phenotypes of the parental populations depart from one another andX therefore no longer equals Y. This is because mutations are vectors that move a phenotype in a particulardirection, and thus a mutually beneficial point in phenotypic space is only guaranteed to be a mutuallybeneficial mutation if both populations have the same mean phenotype.To account for the inequality between phenotypic space (X) and mutational vectors (Y) during adaptationwe must shift the mean phenotypes so that they are at the same point in phenotypic space and move theiroptima by an identical translation (see Fig. A.20). We then have X = Y . One way to imagine this is tokeep the mean phenotypes in place at the mean ancestral phenotype (the origin) and consider adaptation asthe movement of the optima closer to the mean phenotypes. From this perspective, adaptation’s effect is ashrinking of the radii of the hyperspheres (at roughly equivalent rates in the two populations if adaptationproceeds relatively deterministically). Thus, because the fraction of overlap (Eq. A.1) does not depend onthe radii of the hyperspheres, the fraction of overlap is expected to remain relatively constant throughoutadaptation.In reality and in my simulations, standing genetic variation is not uniformly distributed, the probabilityof fixation varies across the region of overlap, and adaptation uses up some of the standing variation so thatthe distribution of standing variation changes with time. Taking the first two complications into accountwould require weighted averages across the space contained in the hyperspherical caps, which is beyondthe scope of my study. The third complication is yet more involved and would require an analysis of howstanding genetic variation is used as adaptation proceeds (i.e., how the distribution of segregating effects andallele frequencies shift as alleles fix). Such a calculation is also beyond the scope of this chapter. Despitethese complications, it seems as though the simple analysis above qualitatively captures the essence of whygenetic parallelism decreases rapidly with the angle of divergence.118A.2 Supplementary figures1190.000.250.500.751.000 45 90 135 180angle of divergence, θ (°)genetic parallelismA; σ = 0.1, m = 45 90 135 180angle of divergence, θ (°)genetic parallelismB; σ = 0.1, m = 45 90 135 180angle of divergence, θ (°)genetic parallelismC; σ = 0.1, m = 45 90 135 180angle of divergence, θ (°)genetic parallelismD; σ = 1, m = 45 90 135 180angle of divergence, θ (°)genetic parallelismE; σ = 1, m = 45 90 135 180angle of divergence, θ (°)genetic parallelismF; σ = 1, m = 45 90 135 180angle of divergence, θ (°)genetic parallelismG; σ = 10, m = 45 90 135 180angle of divergence, θ (°)genetic parallelismH; σ = 10, m = 45 90 135 180angle of divergence, θ (°)genetic parallelismI; σ = 10, m = 10Figure A.1: Genetic parallelism across the continuum of parallel to divergent natural selection (N =100). This figure presents simulations similar to Fig. 2.2A in the main text but with varying parameter values(selection [σ] and dimensionality [m]). I ran these particular simulations for T = 5000 generations. All otherparameters as in main text.1200.000.250.500.751.000 45 90 135 180angle of divergence, θ (°)genetic parallelismA; σ = 0.1, m = 45 90 135 180angle of divergence, θ (°)genetic parallelismB; σ = 0.1, m = 45 90 135 180angle of divergence, θ (°)genetic parallelismC; σ = 0.1, m = 45 90 135 180angle of divergence, θ (°)genetic parallelismD; σ = 1, m = 45 90 135 180angle of divergence, θ (°)genetic parallelismE; σ = 1, m = 45 90 135 180angle of divergence, θ (°)genetic parallelismF; σ = 1, m = 45 90 135 180angle of divergence, θ (°)genetic parallelismG; σ = 10, m = 45 90 135 180angle of divergence, θ (°)genetic parallelismH; σ = 10, m = 45 90 135 180angle of divergence, θ (°)genetic parallelismI; σ = 10, m = 10Figure A.2: Genetic parallelism across the continuum of parallel to divergent natural selection (N =1000). This figure presents simulations similar to Fig. 2.2A in the main text but with varying parametervalues (selection [σ] and dimensionality [m]). I ran these particular simulations for T = 2000 generations.All other parameters as in main text.1210.000.250.500.751.000 45 90 135 180angle of divergence, θ (°)genetic parallelismA; σ = 0.1, m = 45 90 135 180angle of divergence, θ (°)genetic parallelismB; σ = 0.1, m = 45 90 135 180angle of divergence, θ (°)genetic parallelismC; σ = 0.1, m = 45 90 135 180angle of divergence, θ (°)genetic parallelismD; σ = 1, m = 45 90 135 180angle of divergence, θ (°)genetic parallelismE; σ = 1, m = 45 90 135 180angle of divergence, θ (°)genetic parallelismF; σ = 1, m = 45 90 135 180angle of divergence, θ (°)genetic parallelismG; σ = 10, m = 45 90 135 180angle of divergence, θ (°)genetic parallelismH; σ = 10, m = 45 90 135 180angle of divergence, θ (°)genetic parallelismI; σ = 10, m = 10Figure A.3: Genetic parallelism across the continuum of parallel to divergent natural selection (N =5000). This figure presents simulations similar to Fig. 2.2A in the main text but with varying parametervalues (selection [σ] and dimensionality [m]). I ran these particular simulations for T = 1000 generations.All other parameters as in main text. These simulations are computationally intensive and were therefore notrun for as many replicates as those plotted in Fig. A.1 or A.2.1220.980.991.001.011.020 45 90 135 180angle of divergence, θ (°)fitness with SGV / fitness without SGVA; σ = 0.1, m = 20.980.991.001.011.020 45 90 135 180angle of divergence, θ (°)fitness with SGV / fitness without SGVB; σ = 0.1, m = 50.980.991.001.011.020 45 90 135 180angle of divergence, θ (°)fitness with SGV / fitness without SGVC; σ = 0.1, m = 100.900.951.001.051.100 45 90 135 180angle of divergence, θ (°)fitness with SGV / fitness without SGVD; σ = 1, m = 20.900.951.001.051.100 45 90 135 180angle of divergence, θ (°)fitness with SGV / fitness without SGVE; σ = 1, m = 50.900.951.001.051.100 45 90 135 180angle of divergence, θ (°)fitness with SGV / fitness without SGVF; σ = 1, m = 45 90 135 180angle of divergence, θ (°)fitness with SGV / fitness without SGVG; σ = 10, m = 45 90 135 180angle of divergence, θ (°)fitness with SGV / fitness without SGVHσ = 10, m = 45 90 135 180angle of divergence, θ (°)fitness with SGV / fitness without SGVI; σ = 10, m = 10Figure A.4: Effect of standing genetic variation on hybrid fitness across the continuum of parallel todivergent natural selection (N = 100). This figure presents simulations similar to Fig. 2.4B in the main textbut with varying parameter values (selection [σ] and dimensionality [m]). I ran these particular simulationsfor T = 5000 generations. All other parameters are as in the main text. Note different y-axis scales acrossrows.1230.991.001.010 45 90 135 180angle of divergence, θ (°)fitness with SGV / fitness without SGVA; σ = 0.1, m = 20.991.001.010 45 90 135 180angle of divergence, θ (°)fitness with SGV / fitness without SGVB; σ = 0.1, m = 50.991.001.010 45 90 135 180angle of divergence, θ (°)fitness with SGV / fitness without SGVC; σ = 0.1, m = 100.900.951.001.051.100 45 90 135 180angle of divergence, θ (°)fitness with SGV / fitness without SGVD; σ = 1, m = 20.900.951.001.051.100 45 90 135 180angle of divergence, θ (°)fitness with SGV / fitness without SGVE; σ = 1, m = 50.900.951.001.051.100 45 90 135 180angle of divergence, θ (°)fitness with SGV / fitness without SGVF; σ = 1, m = 10120 45 90 135 180angle of divergence, θ (°)fitness with SGV / fitness without SGVG; σ = 10, m = 2120 45 90 135 180angle of divergence, θ (°)fitness with SGV / fitness without SGVHσ = 10, m = 5120 45 90 135 180angle of divergence, θ (°)fitness with SGV / fitness without SGVI; σ = 10, m = 10Figure A.5: Effect of standing genetic variation on hybrid fitness across the continuum of parallelto divergent natural selection (N = 1000). This figure presents simulations similar to Fig. 2.4B in themain text but with varying parameter values (selection [σ] and dimensionality [m]). I ran these particularsimulations for T = 2000 generations. All other parameters as in main text. Note different y-axis scalesacross rows.1240.991.001.010 45 90 135 180angle of divergence, θ (°)fitness with SGV / fitness without SGVA; σ = 0.1, m = 20.991.001.010 45 90 135 180angle of divergence, θ (°)fitness with SGV / fitness without SGVB; σ = 0.1, m = 50.991.001.010 45 90 135 180angle of divergence, θ (°)fitness with SGV / fitness without SGVC; σ = 0.1, m = 100.900.951.001.051.100 45 90 135 180angle of divergence, θ (°)fitness with SGV / fitness without SGVD; σ = 1, m = 20.900.951.001.051.100 45 90 135 180angle of divergence, θ (°)fitness with SGV / fitness without SGVE; σ = 1, m = 50.900.951.001.051.100 45 90 135 180angle of divergence, θ (°)fitness with SGV / fitness without SGVF; σ = 1, m = 45 90 135 180angle of divergence, θ (°)fitness with SGV / fitness without SGVG; σ = 10, m = 45 90 135 180angle of divergence, θ (°)fitness with SGV / fitness without SGVHσ = 10, m = 45 90 135 180angle of divergence, θ (°)fitness with SGV / fitness without SGVI; σ = 10, m = 10Figure A.6: Effect of standing genetic variation on hybrid fitness across the continuum of parallelto divergent natural selection (N = 5000). This figure presents simulations similar to Fig. 2.4B in themain text but with varying parameter values (selection [σ] and dimensionality [m]). I ran these particularsimulations for T = 1000 generations. All other parameters as in main text. Note different y-axis scalesacross rows.125A; σ = 0.1, m = 201020304050DNM DNM &  SGV# alleles fixed0. DNM &  SGVmean effect size0. DNM &  SGVefficiency indexB; σ = 0.1, m = 501020304050DNM DNM &  SGV# alleles fixed0. DNM &  SGVmean effect size0. DNM &  SGVefficiency indexC; σ = 0.1, m = 1001020304050DNM DNM &  SGV# alleles fixed0. DNM &  SGVmean effect size0. DNM &  SGVefficiency indexD; σ = 1, m = 201020304050DNM DNM &  SGV# alleles fixed0. DNM &  SGVmean effect size0. DNM &  SGVefficiency indexE; σ = 1, m = 501020304050DNM DNM &  SGV# alleles fixed0. DNM &  SGVmean effect size0. DNM &  SGVefficiency indexF; σ = 1, m = 1001020304050DNM DNM &  SGV# alleles fixed0. DNM &  SGVmean effect size0. DNM &  SGVefficiency indexG; σ = 10, m = 201020304050DNM DNM &  SGV# alleles fixed0. DNM &  SGVmean effect size0. DNM &  SGVefficiency indexH; σ = 10, m = 501020304050DNM DNM &  SGV# alleles fixed0. DNM &  SGVmean effect size0. DNM &  SGVefficiency indexI; σ = 10, m = 1001020304050DNM DNM &  SGV# alleles fixed0. DNM &  SGVmean effect size0. DNM &  SGVefficiency indexFigure A.7: Properties of fixed mutations under a variety of parameter combinations (N = 1000). Thisfigure presents simulations similar to Fig. 2.6 in the main text but with varying parameter values (selection[σ] and dimensionality [m]). See main text and panel description of Fig. 2.6 for more detail. Patterns weresimilar for other population sizes.1260.000.250.500.751.000 45 90 135 180angle of divergence, θ (°)genetic parallelismA; Gaussian0.9500.9751.0001.0251.0501.0750 45 90 135 180angle of divergence, θ (°)fitness with SGV / fitness without SGVB; Gaussian0.000.250.500.751.000 45 90 135 180angle of divergence, θ (°)genetic parallelismC; linear0.9500.9751.0001.0251.0501.0750 45 90 135 180angle of divergence, θ (°)fitness with SGV / fitness without SGVD; linear0.000.250.500.751.000 45 90 135 180angle of divergence, θ (°)genetic parallelismE; quadratic0.9500.9751.0001.0251.0501.0750 45 90 135 180angle of divergence, θ (°)fitness with SGV / fitness without SGVF; quadraticFigure A.8: Simulations under various fitness functions. Here I plot simulations across environments for(A & B) Gaussian (W = exp(σ ||z – o||2/2)), (C & D) linear (W = 1 – σ ||z – o||), and (E & F) quadratic (W= 1 – σ ||z – o||2/2) fitness functions. I show results for both genetic parallelism and the effect of standingvariation on hybrid fitness. I ran these simulations with a nearer optimum and weaker selection (d = 0.5, σ =0.5, N = 1000, m = 5) because populations otherwise became extinct with linear/quadratic fitness functions.Under these conditions, the non-linear decrease in parallelism is less substantial for all parameter values.Nevertheless, the patterns are qualitatively similar among the three sets of simulations (note differences iny-axis scales).1270501001502000 25000 50000 75000 100000generationnumber of segregating allelesA0.0000.0250.0500.0750.1000 25000 50000 75000 100000generationmean frequency of segregating allelesB02460.0 0.1 0.2 0.3 0.4mutation effect sizedensityC0510150.0 0.2 0.4 0.6 0.8frequency of derived alleledensityD0.0000.0250.0500.0750 25000 50000 75000 100000generationphenotypic varianceEFigure A.9: Mutation-selection balance and mutation effect sizes in ancestral populations. In panel(A) I am showing the number of segregating sites in each of 10 ancestral populations and (B) the meanfrequency of the derived alleles at each of these sites in the ancestral populations. The black line is plottedthrough the mean of all populations at each generation, and all ten burn-ins used to generate my main textresults are shown. Panel (C) illustrates the distribution of mutation effect sizes—the Euclidean distanceof a mutational vector in phenotypic space—at the end of a single representative burn-in simulation (darkgreen), as compared to the distribution of mutations that arise de novo (light green). The vertical linesrepresent the median mutation effect size for each group. Panel (D) represents the site-frequency spectrumfor segregating sites (excluding sites that have fixed). And panel (E) shows the phenotypic variance in theancestral population over time. (σ = 0.01; m = 5 for all simulations shown; for rest of parameters see Table2.1).1280501000 25000 50000 75000 100000generationnumber of segregating allelesA0. 25000 50000 75000 100000generationmean frequency of segregating allelesB051015200.0 0.1 0.2 0.3 0.4 0.5mutation effect sizedensityC01002003004005000.00 0.05 0.10 0.15frequency of derived alleledensityD0.000.250.500.751.000 45 90 135 180angle of divergence, θ (°)genetic parallelismE0.991.001.011.020 45 90 135 180angle of divergence, θ (°)fitness with SGV / fitness without SGVFFigure A.10: Mutation-selection balance and mutation effect sizes in ancestral populations understronger selection (σanc = 1). These parameter values imply µ « α2 σ, as in the House-of-Cards regime(Turelli, 1984, 1985) from a Gaussian regime under an alternative set of parameters. (A) The number ofsegregating sites in each of 10 ancestral populations and (B) the mean frequency of derived alleles at eachof these sites in the ancestral populations. The black line is plotted through the mean of all populations ateach generation, and all ten burn-ins used to generate the results ([e] and [f]) are shown. Panel (C) illustratesthe distribution of mutation effect sizes—the absolute value of a mutation’s effect on the phenotype—at theend of a single burn-in simulation (dark green), as compared to the distribution of mutations that arise denovo (light green). The vertical lines represent the median mutation effect size for each group. Panel (D)represents the site-frequency spectrum histogram for segregating sites. (Compare these to Fig. A.9). Panels(E) and (F) are as in Fig. 2.2A and 2.4B in the main text. For unspecified parameters see Table 2.1 in themain text.1290.000.250.500.751.000 50 100 150number of ancestral mutations (n)genetic parallelismA0. 50 100 150number of ancestral mutations (n)segregation varianceB203040500.00 0.25 0.50 0.75 1.00initial distance to optimum (d )(n) at max genetic parallelismC0. 50 100number of ancestral mutations (n)initial phenotypic varianceDFigure A.11: The effects of standing genetic variation on genetic parallelism and phenotypic segrega-tion variance in hybrids under parallel and divergent natural selection. I show (A) genetic parallelism(main text equation 2.1) and (B) net segregation variance for populations founded with varying quantities ofancestral standing variation (n: number of ancestral mutations). Populations were subject to either parallel(θ = 0°; black) and divergent (θ = 180°; grey) selection, with d = 1, and there were 10 replicate simulationsper parameter combination. Genetic parallelism values of 0 indicate no parallelism and values of 1 indicatecomplete parallelism (main text Eq. 2.2). The curves are loess fits. Panel (C) shows that the quantity ofancestral standing variation that maximizes genetic parallelism under parallel selection (θ = 0°) increaseswhen populations adapt to more distant optima. A value of d = 1 is 10 mutational SDs. The line is a lin-ear regression. Panel (D) shows the relationship between the genetic (phenotypic) variation in a parentalpopulation as a function of n.1300.000.250.500.751.000 500 1000 1500 2000generationremaining distance to optimumA02550750 500 1000 1500 2000generationnumber of segregating lociB0. 500 1000 1500 2000generationsegregation variance (in parent)DNMDNM & SGVCFigure A.12: Effect of standing variation on the pace of adaptation and attainment of mutation-selection-drift balance. (A) Populations that adapt with standing variation in addition to new mutation(DNM & SGV; n = 100 segregating alleles; dark green) reach the phenotypic optimum more quickly thanpopulations that adapt from new mutation only (DNM; n = 0 segregating alleles; light green). (B) Althoughpopulations equipped with standing variation adapt more quickly than populations adapting from new mu-tation only, they both reach mutation-selection-drift balance by generation 2000. (C) The phenotypic (andgenotypic) variance in parental populations, calculated as it is in hybrids (see main text), is stable and nearzero by the end of each simulation. The initial distance to the optima, d, is d = 1 for all simulations. I plot10 replicate simulations, and lines connect the mean values at each sampled generation. For unspecifiedparameters see Table 2.1 in the main text.1310. 0.25 0.50 0.75 1.00genetic parallelismsegregation varianceA0. 0.25 0.50 0.75 1.00genetic parallelismgenome−wide expected heterozygosityBFigure A.13: Relationship between genetic parallelism and (A) segregation variance and (B) expectedheterozygosity. Our metric of genetic parallelism (main text equation 2) is on the x-axis. This is the dataplotted in Fig. 2.2A 2.2C of the main text. I show the correlation between genetic parallelism and (A)segregation variance (r2 = 0.56) and (B) genome-wide expected heterozygosity (2p[1−p)], averaged acrossall loci (r2 = 0.63). Patterns were similar for FST (Hudson et al., 1992) and net pi (Nei and Li, 1979) (notshown).132A0.000.250.500.751.000.0 0.5 1.0 1.5 2.0distance between parental optima (δ)scaled genetic parallelismB0.000.250.500.750.0 0.5 1.0 1.5 2.0distance between parental optima (δ)genetic parallelismB120.0 0.5 1.0 1.5 2.0distance between parental optima (δ)fitness with SGV / fitness without SGVC0.000.250.500.751.000 45 90 135 180angle of divergence, θ (°)distance between parental optima (δ) of overlapm  = 2m  = 5m  = 10m  = 25m  = 2m  = 5m  = 10m  = 25δFigure A.14: Alternative presentation of simulation results across environments: distance betweenoptima (δ). Panel (A) plots the relationship between the angle of divergence, θ, and the Euclidean distancebetween parental optima, δ (thick black line; note reversal of left y-axis; scaled between 0 and 1 by dividingby 2d). I also plot the fraction of non-overlap (right [green] y-axis) as in the main text Fig. 2.3A for fourdifferent dimensionalities (m; coloured lines). Panel (B) shows observed (scaled) genetic parallelism vs. δfor the same dimensionalities as plotted in (A). For a given value of θ, δ is invariant with dimensionality (i.e.,the distance between optima does not change as dimensionality increases). Accordingly, the non-linearityemerges even when considering δ, but only appreciably when considering higher dimensions (m > 5). Inboth panels, the thin and straight black line connects the fit at 0° with 180° for visual reference. In panels(C) and (D) I show the raw data for genetic parallelism and relative hybrid fitness in simulations conductedfor simulations conducted 10 dimensions (m = 10, σ = 1, N = 1000).1330. 1000 2000 3000 4000 5000generation (t)segregation varianceA0.000.250.500.751.000 1000 2000 3000 4000 5000generation (t)expected heterozygosityBPopulation size1001000500010000Figure A.15: The effect of population size on the rate of divergence between populations due to drift.I show populations held at a common optimum with no standing variation (i.e. d = 0, N = 0) and plot(A) segregation variance and (B) expected heterozygosity in hybrids over time for 5,000 generations. Theevolution of segregation variance is proportional to the rate of evolution of reproductive isolation underparallel natural selection. Greater drift in smaller populations leads to greater segregation variance andheterozygosity. The lines are drawn as the average of 10 replicate simulations (m = 5, σ = 1).1340.0000.0250.0500.0750 45 90 135 180angle of divergence, θ (°)net segregation varianceA; .. = 1, m = 20.0000.0250.0500.0750 45 90 135 180angle of divergence, θ (°)net segregation varianceB; .. = 1, m = 50.0000.0250.0500.0750 45 90 135 180angle of divergence, θ (°)net segregation varianceC; .. = 1, m = 10Figure A.16: Effect of dimensionality on net segregation variance. These plots are similar to Fig. 2.2Cin the main text except I show results for three different dimensionalities. Under divergent natural selec-tion, simulations where populations adapted from standing variation (dark green) had higher segregationvariance—relative to simulations where populations adapted only from de novo mutation (light green)—in higher dimensions. Note the overall trend of a decrease in net segregation variance as dimensionalityincreases.1350.000.250.500.751.001 3 5 7 9d2 / d1fraction of overlapA; P(s > 0 in 2 | s > 0 in 1) 3 5 7 9d2 / d1fraction of overlapB; P(s > 0 in 1 | s > 0 in 2) C{ {d1 d2Figure A.17: Fraction of overlap of beneficial mutations with parallel selection (θ = 0°) but unequaldistance (d1 6= d2). The main text explores how the fraction of overlap changes with theta while holdingd1 = d2 = d constant. Here I explore how the fraction of overlap changes with the ratio d2/d1 when holdingθ = 0° constant. Unlike the metric presented in the main text this metric is asymmetrical because onepopulation is completely contained within the other. Panel (A) plots the fraction of overlap for population 1(the fraction of alleles that are beneficial in population 1 are also beneficial in population 2) as a function ofd2⁄d1. With d1 < d2 the value is 1 for any ratio d2/d1 because population 1’s hypersphere is contained withinpopulation 2’s. Panel (B) plots the fraction of alleles that are beneficial in population 2 that are also beneficialin population 1. This latter result mirrors what is seen in the main text Fig. 2.3A: as the locations of theoptima depart from one another the fraction of overlap rapidly approaches zero and does so most rapidly atthe onset of departure. Panel (C) shows a cartoon example of a case in 2-dimensions where d2 = 2d1.1360.800.850.900.951.000 45 90 135 180angle of divergence, θ (°)relative maximum fitness of hybridsDNMSGV & DNMA0.9550.9801.0050 45 90 135 180angle of divergence, fitness with SGV / fitness without SGVBθ (°)Figure A.18: The effect of standing genetic variation (SGV) on relative maximum hybrid fitness acrossenvironments. Data are from simulations plotted in the main text, but instead of mean fitness of all hybridsI depict the mean fitness of the top 5 % of hybrids relative to the mean fitness of parents. I plot both the (A)raw values of relative maximum fitness and (B) the effect of standing variation on maximum hybrid fitness(dark green divided by light green).1370.000.250.500.751.000 45 90 135 180angle of divergence, .. (°)scaled segregation variance251025Figure A.19: The relationship between segregation variance and θ for different dimensionalities. I plotthe loess fits of proof-of-concept simulation results with 95 % confidence intervals conducted in four differentdimensionalities (colours), each scaled between 0 (at 0°) and 1 (at 180°). Simulations were conducted withstrong natural selection (σ = 10) to minimize the effect of drift.138possible mutations &selective effectsiibody size body shadephenotype andselection landscapei−ve in1 & 2+ve in 1 & 2+ve in  2−ve in 1+ve in  1−ve in 21212Figure A.20: Cartoon illustration of why divergence among populations does not affect whether anallele is beneficial in both of them. Panel (i) depicts the phenotype landscape and selection landscape.Variation in the horizontal dimension reflects phenotypic variation in body size, and the vertical dimensionreflects variation in body shade. I depict two ‘populations’ with differences in body size and shade (smalllight; big dark). The stars reflect local optima after a hypothetical environmental shift—selection favoursadaptation toward a larger body size in population 1 and selection for darker body shade in population 2. IfI illustrate the circle of beneficial mutational space (dashed circles) with respect to the current phenotypicposition they do not overlap. Panel (ii) illustrates the selection landscape as it is ‘experienced’ by eachpopulation. An allele that slightly increases body size and darkens the body shade from the current phenotype(the position of the fish cartoons) is beneficial (blue) in both of populations. Some alleles are beneficial inonly one population, and others are deleterious in both (red). Thus, even though the spheres do not overlapin (i) it is not the case that they populations will undergo non-parallel genetic evolution.139Appendix BAppendix for Chapter 3B.1 Supplementary methodsB.1.1 Search strategyI searched the literature for studies that made measurements of traits in F1 hybrids and their parents. Toidentify studies for possible inclusion, I conducted a systematic literature search using Web of Science. Iincluded all papers that resulted from a general topic search of “Castle-Wright”, and from a topic search of“F1 OR hybrid OR inherit*” in articles published (from any year) in Evolution, Proceedings of the RoyalSociety B, Journal of Evolutionary Biology, Heredity, or Journal of Heredity. These journals were selectedbecause a preliminary search indicated that they contained nearly half of all suitable studies. These searchesreturned 82 of the 198 studies deemed suitable after screening. The literature search included all studiespublished until 31 December 2017.To be more comprehensive, I then examined journals outside of the original group of 5 focal journals. Iperformed a forward search for articles that both cited key references (Dobzhansky 1937; Hubbs 1955; Mayr1963; Grant 1981; Lande 1981; Tave 1986; Churchill and Doerge 1994; Bradshaw et al. 1998; Lynch andWalsh 1998; Hatfield and Schluter 1999; Schluter 2000; Coyne and Orr 2004) and contained the keywordsdescribed above. After screening, this search identified the remaining 116 studies of the 198 analyzed inmy study. These searches collectively returned 14,048 studies and after removing duplicates this left 11,287studies to be screened for possible inclusion. The full literature search results are available in the archiveddata.Comments on systematic nature of reviewI attempted to follow PRISMA (Moher et al. 2009) guidelines to the best of my ability. Most of the criteriahave been addressed in the main text but a few other comments are warranted. In particular, I have noreason to suspect that any bias was introduced about dominance. This is because no studies seemed to havea priori hypotheses about such patterns. Accordingly, I do not believe that my estimates suffer from a filedrawer problem. I emphasise that a formal meta-analytic framework—wherein data from multiple studiesare aggregated with various weights—is not appropriate because I am not comparing studies that had anyexperimental treatment. Because the studies in my dataset do not have anything resembling an ‘effect size’,a simple summary across all of them is most appropriate.140B.1.2 Evaluation of studiesI required studies to meet several criteria to merit inclusion in the database. Most of these criteria aresummarised in the main text, but additional details are given here. I excluded all domesticated speciesand most laboratory populations (or ‘strains’) because dominance patterns differ considerably followingdomestication (Crnokrak and Roff 1995). However, laboratory populations were included if founders were10 or fewer generations removed from the wild. If populations were maintained in a lab for more than 10generations but were found by comparison to still strongly resemble the source population, I included thestudy (n = 2 studies). I also excluded studies where the origin of the study populations was ambiguous.Hybrids had to be formed via the union of gametes from parental taxa, so I excluded studies that usedtechniques like somatic fusion. If authors had genotyped wild hybrids, I typically included hybrids wherethe probability of correct category assignment was > 95%; in some cases the authors themselves used adifferent cut-off in which case I went with their cut-offs.I only included traits that I thought were not directly linked to fitness. The majority of cases werenot difficult to assess, but I have included reasons for excluding particular studies or traits in the databasescreening notes (see Data accessibility in main text).Traits had to be measured in a quantitative manner to be included in the dataset. For example, if a trait wasreported as being in categories related to parents or intermediacy (‘parent-like’ or ‘intermediate’), I did notinclude it. Some traits such as mate choice must often be scored discretely (in the absence of multiple trialsper individual), even though the trait can vary on independent trials. Accordingly, I included discretely scoredtraits—like mate choice—when it was possible in principle to obtain a different outcome on independenttrials. Such traits are recorded as 0s and 1s, but hybrids can be intermediate if both outcomes occurred withequal frequencies. I included traits where authors devised their own discrete scale for quantification. Whensuitable data were collected by the authors but not obtainable from the article, I wrote to the authors andrequested the data. If the author cited a dissertation as containing the data, I attempted to locate the datatherein because dissertations are not indexed by Web Of Science. I included multivariate trait summaries(e.g., PC axis scores) when reported. If traits reported both the raw trait values and the PC axis scores for asummary of those same traits, I collected both sets of data but omitted the PCs in my main analyses.Using the above criteria, I screened each article for suitability. As a first pass, I quickly assessed eacharticle for suitability by reading the title and abstract and, if necessary, consulting the main text. After thisinitial search, I retained 407 studies. Since the previous steps were done by a team of five, the primaryauthor conducted an in-depth evaluation of each study flagged for possible inclusion. If deemed suitable,I next evaluated whether the necessary data could be obtained. After this second assessment, 198 studiesremained. The reasons for exclusion of each study are documented the archived data (see Data accessibilityin main text).B.1.3 Data collectionFor each study, I recorded several types of data. First, I recorded the mean, sample size, and an estimateof uncertainty (if available; e.g., SD or variance) for each measured trait for each parental taxon and hybridcategory (cross generation and/or direction). In most cases, these data were included in tables or could be141extracted from figures. For figure data extraction, I used ‘WebPlotDigitizer’ (Rohatgi 2019). In some cases,I contacted authors for the raw data or summary data.Each study contributed a minimum of three records to the larger database: one trait measured in eachparent and the F1 generation. If the same traits were measured over ontogeny, I used only the final datapoint. When data were reported from multiple ‘trials’ or ‘sites’ I pooled them within and then across sites.If data were reported for different cross directions and/or sexes I recorded data for each cross direction/sexcombination separately. I recorded whether each variable was a linear measurement (1D), area measurement(2D), volume measurement (3D; e.g., mass), categorical, or discrete. I did not find meaningful differences indominance among trait types (ANOVA, P = 0.998) and so these data do not factor in to the present analyses.Data processing was greatly aided by the functions implemented in the tidyverse (Wickham 2017).Occasionally, different studies analysed different traits of individuals from the same crosses. In thesecases, I simply grouped them as being the same cross before analysis.B.1.4 Estimating genetic divergence and divergence timeI estimated genetic distance for crosses where sequence data were available for both parents. I downloadedsequences in R using the rentrez package (Winter 2017), and retained up to 40 sequences per species.Sequences were then aligned with the profile hidden Markov models implemented in the align functionin the package, aphid (Wilkinson 2018). After aligning sequences I calculated genetic distance by simplycounting the number of sites that differed between two aligned sequences, implemented using the rawmodeloption in the dist.dna function within ape (Paradis and Schliep 2018). I made this computation for eachpair of sequences and then calculated the average over all pairs for one summary estimate of parental geneticdivergence per cross.I also used timetree (Kumar et al. 2017) to obtain estimates of divergence time for each species pair intheir database in years. After obtaining estimates of divergence time I regressed divergence time against theresponse and predictor variables used in the main analysis. The conclusions from the timetree data do notdiffer from those using genetic distance and I do not discuss them further (see archived analysis code forthese analyses).B.1.5 Phylogenetic signalIn the data from the systematic review, I was interested in evaluating whether there was phylogenetic signalin dominance. I retrieved NCBI taxonomy IDs for my species using the taxize R package (Chamberlainand Szöcs 2013), and used these IDs (one arbitrarily chosen per cross) to generate a phylogeny using phy-loT ( Because branch lengths negligibly affect estimates of phylogenetic signal(Münkemüller et al. 2012), I assigned all branches equal lengths and used the phylosig function imple-mented in phytools (Revell 2012) to test for phylogenetic signal via Pagel’s λ. Assigning random branchlengths never affected my conclusions. Because I am not testing a causal model, and also because there wasno evidence of phylogenetic signal, I do not use the phylogeny in my main text analyses.142B.1.6 Field experiment with sunflowersWhitney et al. (2010, 2006) generated artificial hybrids to resemble the presumed early ancestors of anexisting natural hybrid sunflower, Helianthus annuus ssp. texanus, which grows in Texas, USA. For furtherdetails on the cross, experimental setup and trait measurements, see Whitney et al. (2010, 2006). The BC1generation was obtained by first mating H. debilis ssp. cucumerifolius from Texas to wild H. annuus ssp.annuus from Oklahoma to produce F1 progeny in the greenhouse. In order to produce enough BC1 seed forreplicate field populations, a single progeny from the F1 generation was propagated vegetatively to produce14 F1 clones. A single H. a. annuus pollen donor was mated to the F1 clones to produce 3,758 BC1 seeds.To obtain seedlings for the field experiment, seeds were germinated on damp filter paper in late February2003. Approximately six-day old seedlings were transplanted into peat pots containing field soil and grownin a greenhouse for four weeks before transplanting to the field at the Lady Bird Johnson Wildflower Center,Austin, Texas (hereafter LBJ; 30°10.886’ N, 97°52.58’ W). Prior to planting, plots were tilled to removestanding vegetation. All plants were planted at 90 cm spacing. Plots were fenced with plastic deer fencingto reduce disturbance by deer and rabbits. After planting, local vegetation was allowed to colonise theplots unhindered. BC1 individuals were planted in the ‘selection plot’ of Whitney et al. (2006)), and parentindividuals were planted into a second common garden plot approximately 500 m away from the BC1 plantsbut within the same site (see Table S2 for sample sizes of parents and of BC1s grown at that same secondcommon garden.). A photograph of the experiment is included as Fig. B.16. A parallel experiment at asecond site, the Brackenridge Field Laboratory, Texas, was analyzed and showed similar patterns as LBJ, butresults are not reported here for brevity.Plant traits and fitness were measured from March–September 2003. Viable seed production was cho-sen as the measure of fitness in these annual plants. Bags made from plastic mesh (DelStar Technologies,Delaware, USA) were secured onto flowerheads with twist-ties to prevent seed loss in the field. Flowerheadswere bagged throughout the season (June to September) to obtain a representative sample. Seed productionwas estimated by multiplying the total number of heads (bagged & unbagged) by the average number ofviable seeds per head in a pooled sample of the bagged heads. In addition to fitness, 30 traits comprisingarchitectural, floral, ecophysiological, phenological, and herbivore resistance traits were measured on eachplant, and those traits included herein after filtering are described in Table S1. Further details on trait mea-surement protocols and the relevance of individual traits to plant performance are given by Whitney et al.(2006, 2010).143B.2 Supplementary Tables & Figures18.9% 3.0%68.7%9.4% 10 20 30SDs difference between parentsP−value of differencebetween parentsFigure B.1: Relationship between SD divergence between parents (SDs in units of smaller parent value)and P-value of t-test evaluating whether parent phenotypes are statistically distinguishable. The hor-izontal line is at P = 0.05 and the vertical line is at SD = 1. All traits except for those in the upper-leftquadrant—with < 1 SD difference and P > 0.05— were used to measure dominance. The percentage oftraits in each quadrant is shown in the inset. Few traits with> 1 SD divergence have non-significant P-values(upper-right quadrant).144Table B.1: Description of sunflower traits used to quantify parent-bias and mismatchTrait Name Trait Description and units Trait CategoryHeight of uppermost branch cm ArchitecturalHeight of lowest branch cm ArchitecturalRelative branch diameter Mean primary branch basal diameter / stem diameter ArchitecturalPlant volume Volume of the main stem (cm3) ArchitecturalSeed weight Avg mass of individual seed ArchitecturalSpecific leaf area ratio of leaf area to mass, cm2 ·g−1 EcophysiologicalWater-use efficiency δ13C EcophysiologicalLeaf Carbon:Nitrogen ratio Ecophys. & palat.Disk diameter Diameter of the inflorescence disk (mm) FloralLigule number FloralLigule length cm FloralLigule width cm FloralPhyllary length mm FloralPhyllary width mm FloralBud initiation time Time between planting and initiation of first inflorescence bud (days) PhenologicalLongevity Time between planting and death PhenologicalSeed maturation time Period between pollination and seed maturity (days) PhenologicalGlandular trichome density On bottom surface of leaf; these contain sesquiterpene lactones (mm2) PalatabilityNonglandular trichome density On bottom surface of leaf; physical rather than chemical defenses (mm2) Palatability145Table B.2: Mean ± SE (n) for parent species and BC1 hybrids at the common garden site.Trait* H. annuus** BC1 H. debilisBud initiation time 71.429 ± 2.886 (14) 70.378 ± 1.315 (45) 43.297 ± 1.803 (37)Disk diameter 39.887 ± 1.498 (13) 32.649 ± 0.694 (45) 17.629 ± 0.35 (36)Glandular trichome density 22.974 ± 2.143 (14) 15.752 ± 1.1 (45) 2.423 ± 0.585 (37)Height of uppermost branch 132.786 ± 7.683 (14) 94.844 ± 3.496 (45) 17.183 ± 0.849 (36)Height of lowest branch 44.429 ± 6.946 (14) 25.111 ± 2.584 (45) 8.417 ± 0.733 (36)Leaf Carbon:Nitrogen ratio 10.213 ± 0.52 (7) 9.907 ± 0.202 (18) 9.487 ± 0.476 (18)Ligule length 39.435 ± 1.072 (14) 37.222 ± 0.641 (45) 23.523 ± 0.629 (37)Ligule number 22.571 ± 0.824 (14) 20.156 ± 0.218 (45) 14.568 ± 0.314 (37)Ligule width 11.265 ± 0.412 (14) 12.511 ± 0.288 (45) 9.537 ± 0.204 (37)Longevity 169.357 ± 4.435 (14) 183.111 ± 1.729 (45) 188.515 ± 6.051 (33)Nonglandular trichome density 15.965 ± 1.117 (14) 17.369 ± 0.647 (45) 12.722 ± 0.774 (37)Phyllary length 21.234 ± 0.619 (14) 20.31 ± 0.524 (45) 11.857 ± 0.264 (37)Phyllary width 9.254 ± 0.47 (14) 7.673 ± 0.191 (45) 2.045 ± 0.047 (37)Plant volume 636.321 ± 89.82 (14) 378.758 ± 24.027 (45) 39.886 ± 6.162 (37)Relative branch diameter 0.28 ± 0.011 (14) 0.305 ± 0.007 (45) 0.538 ± 0.017 (37)Seed maturation time 29.923 ± 0.836 (13) 23.8 ± 0.349 (45) 19.25 ± 0.42 (36)Seed weight 9.842 ± 0.268 (14) 7.401 ± 0.177 (45) 2.146 ± 0.076 (37)Specific leaf area 140.693 ± 5.923 (14) 137.769 ± 2.939 (45) 164.722 ± 3.866 (37)Water-use efficiency −28.704 ± 0.299 (7) −28.638 ± 0.058 (18) −29.317 ± 0.188 (18)*For trait descriptions, see Table S1. I include only a subset of BC1 individuals here, which represent those grown in the exact same location as parents. The 475BC1s analyzed for fitness were grown nearby.**Values differ from those reported for three H. a. annuus populations in Whitney et al. (2006, 2010) because the values here refer to the single population,RAR59, which served as a cross parent to the BC1 hybrids.146llldmismatch = 0dparent−bias = 0.25 0.50 0.75 1.00Standard length (scaled)Body depth (scaled)Allldmismatch = 0.2dparent−bias = 0.670.000.250.500.751.000.00 0.25 0.50 0.75 1.00Calyx length (scaled)Corolla width (scaled)Bllldmismatch = 0.63dparent−bias = 0.25 0.50 0.75 1.00Tibio−fibula length (scaled)Parasphenoid width (scaled)Cllldmismatch = 0.94dparent−bias = 0.940.000.250.500.751.00−0.5 0.0 0.5 1.0Aperture height (scaled)Lateral petal flex (scaled)DFigure B.2: Example visualisations of four cases of bivariate trait expression. Here I show scaled traitvalues of parents and hybrids. Panel (A) shows a case where hybrids are intermediate for both traits (Hatfieldand Schluter 1999). Panel (B) shows a case where hybrids are similar to one parent for both traits (Fishmanet al. 2015). Panel (C) shows a case where hybrids are similar to one parent for one trait and to the otherfor the second trait (Lamb and Avise 1987). Panel (D) shows a case where the hybrids are transgressive forone trait and intermediate for the other (Bradshaw et al. 1998; ‘LC’ cross). I show values for mismatch andparent-bias in each case.147Ophrys x arachnitiformisErythranthe cardinalisOphraella notulataDelphinium recurvatumPopulus deltoidesLabeotropheus fuelleborniThamnophis elegansHaplochromis tweddleiPlatichthys stellatusTriturus dobrogicusPenstemon centranthifoliusStreblospio benedictiCarabus iwawakianusAltica viridicyaneaSilene dioicaCyprinodon beltraniLeptinotarsa decemlineataNeochlamisus bebbianaeSaguinus fuscicollisPhymata americanaPetunia exsertaGeospiza scandensMagicicada septendecimHeliconius timaretaErythranthe laciniataPirata piraticusGambusia holbrookiAnigozanthos humilisMitoura muiriPhoenicurus ochrurosTriticum dicoccoidesLaupala cerasinaDrosophila gouveaiAmphilophus labiatusOphrys lupercalisMitoura nelsoniChamaenerion angustifoliumColias philodiceYponomeuta cagnagellusOncorhynchus gorbuschaDrosophila melanogasterSenecio vulgarisOphraella slobodkiniPetunia axillarisPotamogeton wrightiiChrysoperla carneaMus musculusNeodiprion leconteiPenstemon barbatusSilene latifolia Vaccinium myrtillusIpomopsis tenuifoliaDryophytes gratiosusTigriopus californicusDrosophila antonietaePhoenicurus phoenicurusNeodiprion pinetumPlethodon electromorphusPhymata pennsylvanicaMaylandia benetosErythranthe lewisiiSida fallaxViviparus aterCoregonus palaeaLaupala eukoleaCyprinodon desquamatorChorthippus oscheiErythranthe arvensisEublepharis maculariusAmphilophus citrinellusLeucopsarion petersiiLaupala kohalensisArabidopsis lyrataPlethodon cinereusChrysoperla plorabundaOrchis militarisChorthippus biguttulusCarduus acanthoidesCarduus nutansNicotiana alataPrimula elatiorLittorina saxatilisAnas platyrhynchosEuphydryas edithaPseudacris feriarumMimulus peregrinusMeridiastra calcarAnacamptis papilionaceaErythranthe guttataGeospiza fortisPlantago asiaticaGeum urbanumChrysoperla agilisGeospiza fuliginosaLaupala paranigraRhinichthys atratulusColias eurythemeChorthippus brunneusMagicicada cassiniDiplacus aurantiacusDryophytes cinereusIpomopsis guttataCoregonus suidteriCarabus maiyasanusDraba nivalisGambusia affinisHeliconius pachinusFundulus diaphanusZea maysFundulus heteroclitusKareius bicoloratusPitcairnia flammeaLepomis microlophusAstyanax mexicanusEucalyptus globulusAcyrthosiphon pisumVestiaria coccineaPetunia integrifoliaDrosophila simulansChrysomela lapponicaFicedula hypoleucaOrchis purpureaTurnera ulmifoliaGeum rivaleChorthippus jacobsiDactylorhiza maculataSilene vulgarisHeliconius cydnoGerris costaeSpea multiplicataCostus villosissimusTrifolium pratenseDanaus chrysippusMelanoplus sanguinipesSaxicola torquataPoecilia mexicanaBembicium vittatumViviparus contectusPundamilia nyerereiDalechampia scandensGasterosteus aculeatusCrepis tectorumPrimula vulgarisDrosophila athabascaCarabus blaptoidesEucalyptus nitensDianthus carthusianorumPungitius pungitiusChrysoperla johnsoniIpomopsis aggregataAnolis distichusYponomeuta malinellusSepsis neocynipseaMuscidifurax raptorellusEurosta solidaginisDactylorhiza fuchsiiHaplochromis burtoniDelphinium hesperiumMelanoplus devastatorNicotiana forgetianaDanaus gilippusCampostoma anomalumHeliconius melpomeneCarabus dehaaniiRana temporariaLeavenworthia crassaPseudopleuronectes americanusSpodoptera latifasciaAstyanax hubbsiGryllus texensis Astatotilapia callipteraProtomelas taeniolatusFicedula albicollisClinostomus elongatusCostus alleniiCyprinodon simusPenstemon davidsoniiIpomopsis tenuitubaPseudacris nigritaPlantago hakusanensisYponomeuta padellusPopulus angustifoliaPotamogeton perfoliatusDiatraea grandiosellaLepomis cyanellusAnacamptis morioChorthippus albomarginatusPundamilia pundamiliaVaccinium vitis-idaeaIris fulvaDianthus arenariusMetrosideros polymorphaHenosepilachna vigintioctomaculataHimatione sanguineaSenecio vernalisLeavenworthia alabamicaOncorhynchus nerkaSpodoptera descoinsiSepsis cynipseaHeliosperma pusillumPenstemon newberryiGryllus rubensPoecilia veliferaErythranthe pardalisEogammarus confervicolusCyprinodon variegatusCoregonus clupeaformisSalmo salarErythranthe microphyllaLochmaea capreaeSalvelinus fontinalisOstrinia nubilalisLeonardoxa africanaMaylandia mbenjiiChorthippus mollisPenstemon spectabilisPopulus fremontiiZea diploperennisPopulus trichocarpaNocomis biguttatusTropheops sp. 'red'Iris hexagonaLongitarsus jacobaeaeIris brevicaulisHeliosperma veselskyiPiriqueta cistoidesSpea bombifronsTriturus carnifexOncopeltus fasciatusHenosepilachna pustulosaCoregonus zugensisCyprinodon brontotheroidesErythranthe nasutaAnigozanthos manglesiiLymantria disparJaltomata procumbensMeridiastra gunniiPenstemon neomexicanusMyzopsetta ferrugineaAltica fragariaePolygonia c-albumSemotilus atromaculatusChamaecrista fasciculataWyeomyia smithiiMaylandia zebraRana arvalisErythranthe parishiiFigure B.3: Phylogeny of all species used in this study. For phylogenetic signal analyses, I arbitrarily choseone of the parent species from each pair.1480. 1 2 3 4 5univariate dominancedensityFigure B.4: dunivariate across all traits in the datasets (n = 1046 traits). The x-axis is truncated at dunivariate= 5.1490. 0.5 1.0 1.5cross median univariate dominancedensityA0. 0.5 1.0 1.5cross median pairwise parent−biasdensityB0. 0.5 1.0 1.5cross median pairwise mismatchdensityCFigure B.5: Summary of cross median dominance metrics with each cross contributing a single value.Everything is the same as Fig. 2.2 of the main text, except here each cross contributed the median valueinstead of the mean for each dominance metric. The density plots (y-axis standardized across panels) showthe three main dominance metrics contained herein, with each cross contributing a single value per panel.Values of 0 indicate no dominance, values of 1 indicate the maximum without transgression, and values >1 indicate transgression. The x-axis is truncated at 1.5, but the mean of cross medians (black arrows) andmedian of cross medians (white arrows) are calculated from the whole dataset. Panel a shows the univariatedominance (dunivariate; eqn. 1), panel b shows parent-bias (pairwise dparent-bias; eqn. 3), and panel c showsmismatch (pairwise dmismatch; eqn. 4). Panel a contains one value from all crosses (n = 233) while panels band c only contain information from crosses wherein two or more traits were measured (n = 165).150010200.0 0.2 0.4 0.6median univariate dominance (duni)densityA0102030400.0 0.1 0.2 0.3 0.4 0.5median parent−bias (dparent−bias)densityB0102030400.0 0.2 0.4median mismatch (dmismatch)densityCFigure B.6: Expected patterns based on sampling error alone (from simulations). The vertical linesare the median values observed in the main text. Density plots are the distribution of median values (n =1000 simulations) of each metric in simulations where the true (scaled) mean was 0.5 for each trait andindividual phenotypes were simulated with an identical SD and identical sample sizes to the real data. Thesesimulations reveal the extent of ‘dominance’ caused by sampling error alone.151l l051015inter intracross categorymean univariate dominanceAl l051015inter intracross categorymean pairwise parent−biasBl l051015inter intracross categorymean pairwise mismatchCFigure B.7: There are no differences (all P > 0.25) in any dominance metrics between intraspecificand interspecific crosses. Each point is the cross mean dominance metric for dunivariate (panel a), pairwisedparent-bias (panel b), and pairwise dmismatch (panel c). All P > 0.5. Note that the y-axis is ln-transformed.152llllll lllllllllll llllll lll lllllllllllllllllllllll0.−6 −4 −2ln(genetic distance)mean univariate dominanceAlllllllllllllll lllll lll llllllllllllllllllllll0.−6 −4 −2ln(genetic distance)mean pairwise parent−biasBllllllllllllllllllll ll llllllllllllll lllllllll0.000.250.500.751.00−6 −4 −2ln(genetic distance)mean pairwise mismatchCFigure B.8: No association between any dominance metrics and genetic distance between the parents.Divergence time was calculated from nucleotide sequences (see methods). Each point is the dominancemetric for a cross (calculated following eqns 1–4 in the main text). Grey points are plants, and black pointsare animals. All P > 0.5.1530. 0.5 1.0 1.5 2.0mean univariate dominancedensityA0. 0.5 1.0 1.5 2.0mean pairwise parent−biasdensityB0. 0.5 1.0 1.5 2.0mean pairwise mismatchdensityCFigure B.9: No differences in dominance between plants and animals. Each point is the dominance metricfor a cross (calculated following eqns 1–4 in the main text). All P > 0.08. Light grey density plot representsplants, and dark grey represents animals.1540. 25 50 75 100|difference in parental CVs|ln(univariate dominance + 1)A0. 25 50 75 100mean |parental CVs|ln(univariate dominance + 1)BFigure B.10: Parental phenotypic variation (CV) has significant effects on dominance in hybrids. Panel(A) shows the relationship between the absolute difference in parent CVs (i.e., |CV1 − CV2|) and univariatedominance (P = 0.035). Panel (B) shows the relationship between the mean of parental CVs and univariatedominance (P = 0.0092). These analyses are simple linear models; only the pattern shown in (B) remainsstatistically significant after accounting for study as a random effect.155lll l l l051015BehaviourChemicalLife_historyMorphologyPhysiologyPigmenttrait typecross mean univariate dominanceFigure B.11: The relationship between trait type and univariate dominance (dunivariate). Chemical traitshave a significantly higher mean dunivariate than all other trait categories (all P < 0.05) traits, which do notdiffer from one another (P > 0.9). This pattern is entirely caused by a substantial outlier.1560. 1.0 10.0mean pairwise (dparent−bias)mean pairwise (dmismatch)A0. 1.0 3.0mean pairwise (dparent−bias)mean pairwise (dmismatch)BFigure B.12: Relationship between mean pairwise parent-bias and mismatch dominance in systematicreview and sunflower data. Panel a shows the distribution of pairwise dparent-bias and dmismatch in the sys-tematic review data (F1s). Panel b shows the same metrics calculated at the individual level in the sunflowerfield experiment data (BC1s). Both relationships are statistically significant. Note the log10-scale.157012340.00 0.25 0.50 0.75 1.00abs(rho)densityFigure B.13: Distribution of pairwise trait correlations in the sunflower data (BC1s only). Since mostcorrelations are weak, I conclude that it is unlikely issues caused by trait correlations undermine any of myconclusions.1580123−0.5 0.0 0.5regression coefficient (dparent−bias)densityA0123−0.4 −0.2 0.0 0.2regression coefficient (dmismatch)densityBFigure B.14: Distribution of partial regression coefficients in multiple regression analyses (see eqn. 5).The thin vertical line demarcates a slope of zero. The black arrows show the mean of pairwise regressioncoefficients (plotted in the density plot). All coefficients are shown, not just those that are significant (n traitpairs =(192)= 171).159AD5010015040 60 80 100Bud initiation time (days)Height of uppermost branch (cm)Figure B.15: Phenotype and fitness distribution for a trait pair with substantial mismatch consequencesin BC1 hybrid sunflowers. Darker values indicate lower log10(seed count). Large circles labelled D and Arepresent mean bivariate phenotypes of the parent species, Helianthus debilis and H. annuus, respectively.Individual plants that resemble the H. debilis parent in stature (i.e., are compact with branches clusteredat the base of the plant) but resemble the H. annuus parent in phenology (i.e. are slow-developing) haveparticularly low fitness.160Figure B.16: Photograph of sunflower experiment at the Lady Bird Johnson Wildflower Center, inAustin, Texas, USA.161Appendix CAppendix for Chapter 4Please note that some of the information contained herein is redundant with that in Appendix B. However, Ihave elected to reproduce their supplementary materials in a format so that they can be consulted indepen-dently and so that each appendix contains all information that is relevant to each paper.Search strategyI searched the literature for studies that made measurements of traits in F1 hybrids and their parents. Toidentify studies for possible inclusion, I conducted a systematic literature search using Web of Science( I included all papers that resulted from a general topic search of“Castle-Wright”, and from a topic search of “F1 OR hybrid OR inherit*” in articles published in Evolu-tion, Proceedings of the Royal Society B, Journal of Evolutionary Biology, Heredity, or Journal of Heredity.These journals were selected because a preliminary search indicated that they contained nearly half of allsuitable studies. These searches returned 106 studies deemed suitable after screening. To be more com-prehensive, I conducted additional systematic searches by conducting similar topic searches among articlesciting influential and highly-cited publications (Dobzhansky 1937; Hubbs 1955; Mayr 1963; Grant 1981;Lande 1981; Tave 1986; Churchill and Doerge 1994; Bradshaw et al. 1998; Lynch and Walsh 1998; Hatfieldand Schluter 1999; Schluter 2000; Coyne and Orr 2004). The full literature search results are available in thearchived data. My initial search returned 14048 studies, and after removing duplicates this left 11287 stud-ies to be screened for possible inclusion. This literature search was primarily done for another unpublishedstudy with the goal of understanding phenotype expression in F1 hybrids.Evaluation of studiesI required studies to meet several criteria to merit inclusion in my database. First, the study organisms hadto originate recently from a natural (i.e., ‘wild’) population. This is because dominance patterns in domesticspecies differ substantially from non-domesticated species (Crnokrak and Roff 1995) and because I amexplicitly interested in patterns as they occur in nature. I excluded studies using crops, domestic animals,laboratory populations that were > 10 (sexual) generations removed from the wild, or where populationswere subject to artificial selection in the lab. If populations were maintained in a lab for more than 10generations but were found by comparison to still strongly resemble the source population, I included thestudy (n = 2). I also excluded studies where the origin of the study populations was ambiguous. Hybridshad to be formed via the union of gametes from parental taxa, so I excluded studies using techniques likesomatic fusion. Second, the ancestry of hybrids had to be clear. Many studies reported phenotypes of naturalhybrids, for example in hybrid zones. I did not include these studies unless the hybrid category (i.e., F1, F2,162backcross) was confidently determined with molecular markers (typically over 95 % probability, unless theauthors themselves used a different cut-off in which case I went with their cut-off) or knowledge that hybridswere sterile and thus could not be beyond the F1).Third, because I was interested in the inheritance of traits that are proximally related to organismalperformance (McGee et al., 2015), I required studies to report measurements of at least one ‘non-fitness’trait (’ordinary’ traits [Orr 2001]) . Non-fitness traits (hereafter simply ‘traits’) are those that are likelyunder stabilizing selection at their optimum, whereas ‘fitness’ traits are those that are likely under directionalselection and have no optimum (Merilä and Sheldon 1999; Schluter et al. 1991). In most cases it waspossible to evaluate this distinction objectively because authors specifically referred to traits as componentsof fitness, reproductive isolating barriers, or as being affected by non-ecological hybrid incompatibilities. Insome cases, however, I made the distinction myself. If particular trait values could be interpreted as resultingin universally low fitness, for example resistance to herbivores or pathogens, this trait was not included. Themajority of cases were not difficult to assess, but I have included reasons for excluding particular studies ortraits in the database screening notes (see Data accessibility).Traits had to be measured in a quantitative manner to be included in the dataset. For example, if a traitwas reported categorically (e.g., ‘parent-like; or ‘intermediate’), I did not include it. Some traits such as matechoice must often be scored discretely (in the absence of multiple trials per individual), even though the traitcan vary on independent trials. Accordingly, I included discretely scored traits — like mate choice — whenit was possible in principle to obtain a different outcome on independent trials. Such traits are recorded as0s and 1s, but hybrids can be intermediate if both outcomes occurred with equal frequencies. I includedtraits where authors devised their own discrete scale for quantification. When suitable data were collectedby the authors but not obtainable from the article, I wrote to the authors and requested the data. If the authorcited a dissertation as containing the data, I attempted to locate the data therein because dissertations are notindexed by Web Of Science. I included multivariate trait summaries (e.g., PC axis scores) when reported. Iftraits reported both the raw trait values and the PC axis scores for a summary of those same traits, I collectedboth sets of data but omitted the PCs in my main analyses.Using these criteria, I screened each article for suitability. As a first pass, I quickly assessed each articlefor suitability by reading the title and abstract and, if necessary, consulting the main text. After this initialsearch, I retained 407 studies. Since the previous steps were done by a team of five, I personally conductedan in-depth evaluation of each study flagged for possible inclusion. If deemed suitable, I next evaluatedwhether the necessary data could be obtained. After this second assessment, 198 studies remained. Thereasons for exclusion of each study are documented the archived data (see Data accessibility).Data collectionFor each study, I recorded several types of data. First, I recorded the mean, sample size, and an estimate ofuncertainty (if available) for each measured trait for each parental crosses and hybrid category. In most cases,these data were included in tables or could be extracted from figures. In some cases, I contacted authors forthe raw data or summary data. Each study conducted a minimum of three records to the larger database: onetrait measured in each parent and the F1 generation. Traits were categorized as one of: behaviour, chemical,163life history, morphological, physiological, or pigmentation. If the same traits were measured over ontogeny,I used only the final data point. When data were measured in multiple ‘trials’ or ‘sites’ I pooled them withinand then across sites. If data were reported for different cross directions and/or sexes I recorded data foreach cross direction / sex combination separately. Data processing was immeasurably aided by the functionsimplemented in the tidyverse (Wickham 2017).For each paper I recorded whether the phenotypes were measured in the lab or field, if in the lab thenumber of generations of captivity, and whether a correlation matrix (preferably in recombinant – F2 orBC – hybrids; see below) was available or calculable from the raw data or figures. For the present study,specifically, each study would have had to contribute 8 or more datapoints – two traits from each of P1, P2,F1, and F2. Occasionally, different studies analysed different traits from individuals from the same crosses.In these cases, I simply grouped them as being the same study before analysis.Comments on systematic nature of reviewI attempted to follow PRISMA (Moher et al. 2009) guidelines to the best of my ability. Most of the criteriahave been addressed above but a few other comments are warranted. I have no reason to suspect that any biaswas introduced about estimates of parental divergence or segregation variance. This is because no studiesseemed to have a priori hypotheses about such patterns. Accordingly, I do not believe that my estimatessuffer from a file drawer problem, since detecting segregation variance in non-divergent traits was not thestated goal of any contributing studies. In addition, a formal meta-analytic framework here is not appropriatebecause I am not comparing studies that had any experimental treatment.Estimating genetic divergence and divergence timeI estimated genetic distance for pairs of species where data were available for both parents. A preliminaryscreening revealed that the internal transcribed spacer (ITS I and II) was the most commonly availablegene for plants and cytochrome b was the most available gene for animals in my dataset. I downloadedsequences in R using the rentrez package (Winter 2017), and retained up to 40 sequences per species.Sequences were then aligned with the profile hidden Markov models implemented in the align functionin the package, aphid (Wilkinson 2018). After aligning sequences I calculated genetic distance by simplycounting the number of sites that differed between two aligned sequences, implemented using the rawmodeloption in the dist.dna function within ape (Paradis and Schliep 2018).I also used timetree (; Kumar et al. 2017) to obtain estimates of divergence time foreach species pair in their database in years. After obtaining estimates of divergence time I regressed diver-gence time against the response and predictor variables used in the main analysis.Phylogenetic signalTo determine whether patterns might be spurious and caused by differences among taxa, I wished to seeif there was phylogenetic signal in the data. If either my response or predictor variables co-varied with164phylogeny this might indicate that phylogenetic independent contrasts or similar is necessary for anal-ysis. I retrieved NCBI taxonomy IDs for my species using the taxize R package (Chamberlain andSzöcs 2013), and used these IDs (one arbitrarily chosen per cross) to generate a phylogeny using phy-loT ( Because branch lengths negligibly affect estimates of phylogenetic signal(Münkemüller et al. 2012), I assigned all branches equal lengths and used the phylosig function imple-mented in phytools (Revell 2012) to test for phylogenetic signal via Pagel’s λ.C.1 Supplementary figuresAlthough the analysis presented in the main text is, in my view, the most justifiable, there were severalsubjective decisions that I made when going from raw data to summary statistics. Accordingly, I wishedto investigate the extent to which my findings were robust to making alternative choices. In this sectionI present supplementary figures that illustrate results described in the main text. In addition, I present asimple table showing the Spearman’s ρ coefficient and P-value for the correlation between phenotypic di-vergence in divergent traits and segregation variance in non-divergent traits under many alternative datafiltering/binning/transformation decisions. In all but one case, the pattern remains statistically significant.Accordingly, I conclude that the qualitative patterns observed are quite robust.There were correlations between sample size and some of my response variables, including estimates ofparental divergence. To determine if my results were robust to the exclusion of potentially low-power studies,I generated two new datasets with studies measuring fewer than (i) 20 or (ii) 70 parental individuals excluded.Sample size did not predict parental divergence for these datasets. These results are presented below in TableS1 and indicate that sample size is not responsible for the pattern. I also note that a multiple regression withparental divergence and sample size as predictors — flawed because of potential heteroskedasticity and lowdata - predictor ratio — indicated that only parental divergence was a significant predictor of segregationvariance (divergence P = 0.0195; sample size P = 0.755).1651.00e−061.25e−061.50e−061.75e−062.00e−060.3 0.6 0.9distance to optimumsegregation variance(non−divergent trait)pleiotropy; "infinitesimal"A0.0000.0020.0040.0060.0080.3 0.6 0.9distance to optimumsegregation variance(non−divergent trait)no pleiotropy; finiteB0. 0.6 0.9distance to optimumsegregation variance(non−divergent trait)pleiotropy; finiteC9.0e−071.2e−061.5e−061.8e−062.1e−060.3 0.6 0.9distance to optimumsegregation variance(divergent trait)pleiotropy; "infinitesimal"D0. 0.6 0.9distance to optimumsegregation variance(divergent trait)no pleiotropy; finiteE0. 0.6 0.9distance to optimumsegregation variance(divergent trait)pleiotropy; finiteFFigure C.1: Simulation results to illustrate theoretical prediction. I conducted individual based simulations usingmethods similar to those described fully in Thompson et al. (2019), which is open access. Briefly, two initially iden-tical populations diverged without gene flow between them for 1000 generations. All mutations were unique to eachpopulation (no parallelism). Individuals had two traits and only trait 1 was under selection. Optima were defined as[d, 0] for population 1 and [-d, 0] for population 2, where d is the distance to the optimum from the origin. I varyd along the horizontal axis in all figures. After 1000 generations I made interpopulation hybrids and measured thevariance in traits 1 (y-axis, top row) and 2 (y-axis, bottom row). Panels A and D show simulations where populationsadapt from pleiotropic but very small alleles. Panels B and E show the case where mutations are appreciably large butnot pleiotropic—only affecting trait 1 or trait 2 but never both. Panels C and F show the case where mutations areappreciably large-effect and can affect both traits simultaneously. Simulation code is archived online. Simulations arehaploid and so the F1 variance is the segregation variance. Here is what I would like you to get from the figure:(1)When mutations are small, there is no relationship between d and segregation variance in any trait, even with universalpleiotropy. (2) When mutations are large but there is no pleiotropy, a relationship between d and and segregation vari-ance is observed only for the divergently-selected trait. And (3), with pleiotropic mutations of reasonably large effect,I see a relationship between d and and segregation variance for both traits. The only parameter that varies (other thanthe presence of pleiotropy) is mutation effect size; set to 10-6 in panels A and D and and 0.1 in the others.1669113− 0.8 1.0 1.2Fitted valuesResidualsResiduals vs Fitted9113−10123−2 −1 0 1 2Theoretical QuantilesStandardized residuals Normal Q−Q91130. 0.8 1.0 1.2Fitted valuesStandardized residuals Scale−Location9114−101230. Residuals Residuals vs LeverageFigure C.2: Diagnostics of the linear model testing the main hypothesis. The figure was produced withthe autoplot function in the ggfortify R package. Although the linear regression is significant (F1,12= 10.03, r2 = 0.455, P = 0.00812), the diagnostic plots reveal significant heteroskedasticity (Breusch-Pagantest P = 0.00182). This plot is meant to convince the reader that a non-parametric approach is better-suitedto test the hypothesis at hand.167Table C.1: Results with alternative choices for data filtering and binning.Difference Description Spearman’s ρ PMain text analysis For reference 0.8 0.0005809Less strict binningTraits with ≥ 1 SD differencebetween parents deemed ‘divergent’0.714 0.00543Same segvar fomula; difference Eqn. 1 used but difference not ratio 0.729 0.00286Alternative segvar fomula; ratio segvar = var(F2) / var(F1) 0.607 0.0186Alternative segvar fomula; difference segvar = var(F2) − var(F1) 0.607 0.0186All traits included No longer restricted to morphology 0.518 0.0523Most traits includedAll traits except for physiology & chemical(morphology, behaviour, pigment, life history)0.451 0.0364No transformation No log transformation of variables 0.746 0.00202Sample size filter #1 No studies with fewer than 20 parent individuals 0.736 0.00557Sample size filter #2 No studies with fewer than 70 parent individuals 0.762 0.0368Note: All analyses with morphological traits only and binning based on statistical tests except where noted.1681. 0.5 1.0 1.5 2.0mean ln(phenotypic distance [SDs]of non−divergent traits) between parentsmean ln(segregation variance) ofnon−divergent traits in hybridsFigure C.3: Segregation variance in non-divergent traits is not predicted by divergence in those traits.This analysis complements the analysis in the main text. A Spearman’s rank-order correlation is non signif-icant (ρ = 0.446; P = 0.0972).169− intracross typeln(phenotypic distance [SDs]of divergent traits)A01234inter intracross typeln(phenotypic distance [SDs]of divergent traits)B01234−6 −4 −2ln(phenotypic distance [SDs]of divergent traits)log(genetic divergence)C0240 10 20 30 40divergence time (MYA)ln(phenotypic distance [SDs]of divergent traits)DFigure C.4: All available evidence suggests that phenotypic divergence between parents is uncorrelated withtheir divergence time. Panels A and B use intra- vs interspecific crosses as a proxy for divergence time. Panel Acompares the taxa analyzed in the main text (P > 0.9) and panel B uses a larger dataset of 198 studies (P = 0.268).Panel C uses continuous genetic distance between each pair of parents for which I could obtain DNA sequences in thelarger database of 198 studies (green points = plants, brown points = animals); sequence divergence does not predictparental phenotypic divergence (P = 0.746). Panel D uses estimates of divergence time from timetree for all pairs ofspecies for which data were available; there is no relationship (P = 0.93). I calculated a unique value for each uniquepair of species—if two studies crossed the same two species (regardless of subspecies or population status) the speciespair only provides a single datum. For example, a study not included in the subset analyzed in the main text crossedDrosophila simulans to multiple D. melanogaster populations, but only provided a single datapoint for panels B - D.170Appendix DAppendix for Chapter 5D.1.1 Supplementary methodsDetails of crossing protocol and fish husbandryFemale stickleback were selected for spawning when their abdomens were sharply angled at the cloaca andthe first egg was visible. I gently squeezed the sides of the female fish’s body to release the eggs into aPetri dish containing water from her source habitat (tank, lake, or river water). Mature male sticklebackwere identified by their bright blue colouration and red throat. Males were euthanized with an overdose ofMS-222, and then testes were extracted from the body cavity using fine forceps after making a small incisionbeginning at the cloaca. I used a small paintbrush to release sperm from testes and to ensure that spermcontacted all eggs. The live fish and fertilized clutches were transported to the InSEAS aquatic facility at theUniversity of British Columbia, Vancouver, British Columbia, Canada.All fish were hatched in 100 L aquaria with room temperature between 17 and 19 °C and a photoperiodthat followed local dawn and dusk times. Instant Ocean® Sea Salt was added to maintain a salinity of 5ppt in all tanks. Fry were fed live brine shrimp nauplii. Chopped frozen bloodworms were added to thediet when fish were large enough, and then finally adult-sized fish were fed full size frozen bloodworms andfrozen mysis shrimp ad libitum (Hikari Bio-Pure®).I sampled fish for phenotype measurements typically when the mean standard length of a family wasapproximately 40 mm. Sticklebacks have adult morphology at this stage and are not sexually reproducing.Due to occasional logistical constraints, some tanks were sampled at earlier or later mean standard lengthsizes. Also, due to logistical constraint, all populations except for Paxton benthic and Paxton limnetic werecollected from lakes and rivers in 2017 (see Fig. 5.1).RepeatabilityI evaluated the repeatability of my measurements to determine the fraction of variance that could be at-tributable to measurement error. Repeat measurements were made on at least 25 fish. For linear measure-ments (including pectoral fin length), I took two separate photographs of each fish (or fin) and made therepeated measurements on these separate photographs. Second photographs were made after returning andthen removing the fish (or fin) from its storage vial. Count and gill raker measurements were made on theoriginal specimens. In all cases except pectoral fin length, first and second measurements were made morethan one year apart.171Data diagnosticsI checked for outliers in the raw data and evaluated outlier individuals to ensure they were not caused bymeasurement or transcription error. If fish were inadvertently measured twice, I averaged trait values acrossmeasurements. Fish with broken second dorsal spines were removed from the dataset. One fish was removedbecause it had an unusual body shape—qualitatively appearing as if it had failed to inflate its swim bladder—and it was an extreme outlier in Normal Q-Q plots and in standardized residuals vs. leverage plots. Suchphenotypes seem to be caused by environmental factors (e.g., a too-powerful air stone) rather than biologicalfactors (e.g., hybrid incompatibilities).172D.2 Supplementary Tables & FiguresSL SNTHD PF PG PSL SDSBW ED FDS GRL GW#AFR #DFR #GR #LAP BD35 40 45 2.5 3.0 3.5 4.0 4.511 12 13 14 15 4 5 6 7 8 0 3 6 9 12 0.0 2.5 5.0 7.5 10.0 2 3 4 5 65 6 7 8 2.50 2.75 3.00 3.25 3.50 0 2 4 6 30 40 50 60 2.1 2.4 2.7 3.0 3.37 8 9 10 9 10 11 12 13 13 14 15 16 17 18 0 10 20 30 8 9 10 118910112.02.53.0024601020302030405060700. measurementsecond measurementFigure D.1: Repeatability data for all measured traits. All plots show the first and second measurementsmade on all traits. Black lines are 1:1 lines, and blue lines are linear regressions. Trait codes are as in Fig.5.1. The fish with a value of ‘0’ for second dorsal spine (SDS) likely had its spine broken off during thetime-frame between first and second measurements. All rPearson > 0.9, except for eye diameter (ED), whichwas dropped from the analysis.17301002003000.00 0.25 0.50 0.75 1.00rcountA01002000.00 0.25 0.50 0.75 1.00P−value of rcountBFigure D.2: Summary of pairwise trait correlations in F2 hybrids. Correlations were run within each F2family where at least 10 individuals were measured. Panel (A) shows the distribution of Pearson’s correlationcoefficients (i.e. r) across the dataset, and panel (B) shows the distributions of P-values with blue indicatingvalues of P < 0.05.1740369LCRPCHNORKLNPAQPXLLQLPLLCRNPLBBULLQBPXBpopulationfamily mean distance tomean marine phenotypeFigure D.3: Freshwater divergence from the anadromous ancestor. Boxplots show the distribution of par-tial residuals of individual phenotypic distance from the anadromous ancestor after accounting for the effectof ‘family’. Population codes: PCH—Pachena Lake; PAX—Paxton Lake; CRN—Cranby Lake; PST—Priest Lake; LQU—Little Quarry Lake; PAQ—Paq (Lily) Lake; NOR—North Lake; KLN—Klein Lake;BUL—Bullock Lake.17581012144 6 8 10phenotypic distance between parents# divergent traits (stats or SD)A3694 6 8 10phenotypic distance between parents# divergent traits (stats)BFigure D.4: Phenotypic divergence between parents is positively associated with the number of traitsthat differ between them, as well as the number of possible pairwise mismatches. There is one datumper freshwater population. Panels (A) and (B) show the number of traits that differ between the populationsusing both statistical and variance-based filtering ([A]; see Methods), or only statistics (B).176#AFR:BW #LAP:BD HD:PG0.5 1.0 1.5 2.0 2.0 2.5 3.0 3.5 1 2 3 4 distance between parents (focal trait pair)pairwise mismatchFigure D.5: Examples of pairwise divergence:mismatch regressions. The three plots show different re-gressions that generated coefficients in Fig. 5.2D. Trait labels are as in Fig. 5.1 (#AFR—number of analfin rays; BW—body width; #LAP—number of lateral armour plates; BD—body depth; HD—head length;PG—pelvic girdle length). In the head length:pelvic girdle length regression, patterns are largely driven bythe two girdle-less populations expressing a largely-marine phenotype for this trait but a largely freshwaterhead length.177−2−101−4−3−2−10length of pelvic girdle# lateral platesPachena Lake x Marine Hybrids−2−101−4−3−2−10length of pelvic girdle# lateral platesPaxton Lake Benthic x Marine HybridsFigure D.6: Visualization of pairwise mismatch in empirical data. Each plot shows the scaled phenotypedata used in all analyses. The red points indicate the freshwater parent, and the blue points indicate theanadromous parent. Black points are individual F1 hybrids. Each hybrid’s phenotype is connected to theline connecting parents by a perpendicular line—the length of this line is mismatch. For Pachena Lake F1hybrids, mean mismatch is 0.087. For Paxton Benthic F1 hybrids, mean mismatch is 1.54. In this case,the high mismatch of the Paxton Benthics is due to the fact that the pelvic girdle phenotype resemblesthe anadromous ancestor whereas the plate number of biased toward the freshwater parent. The Pachenapopulation is among the least divergent from the anadromous ancestor overall, whereas the Paxton Benthicpopulation is the most.178anadromous−likefreshwater−like0.000.250.500.751.00PG PSL BW SDS HD #LAP#AFR FDSGRL#GR PF GW #DFR SNT BDtraitmean trait value ± 0.5 SDA10203012 13 14divergence in lateral plate # (anadromous SDs)F 2 hybrid lateral plate #BFigure D.7: Dominance patterns in F2 hybrids. Patterns are largely similar to F1s with a few notableexceptions. First, pelvic traits tend to be smaller than parents. Otherwise, trait values tend to be moreintermediate among populations and dominance tends to be more consistent among populations. For thenumber of lateral plates, the general trend of increasing freshwater-dominance with divergence is apparentin F2s, though they are much more variable than F1s. Low values on the horizontal axis indicate that theparent population is less derived and larger values indicate that it is more derived. The red line is a loess-smooth fit to the data, and the blue line shows the parental midpoint.179F1 F24 6 8 10 4 6 8 10−0.4− D.8: Variation in dominance for lateral plate count does not impact the mismatch-divergencerelationship. Both plots show the difference between mismatch if dominance were intermediate betweenparents minus the mismatch of the median hybrid—on this scale positive values indicate that dominance ofthis trait increases mismatch. Regressions for the F1 and F2 are both non-significant.180F1 F20.0 2.5 5.0 7.5 10.0 0.0 2.5 5.0 7.5 10.005101520phenotypic distance from anadromous# mismatched trait pairsFigure D.9: The number of mismatched trait pairs ‘snowballs’ with the magnitude of phenotypic diver-gence between parents, but only in F1 hybrids. The y-axis shows the number of trait pairs with significantmismatch, determined using t-tests which tested the null hypothesis that the difference between hybrid mis-match (with weighted pooling by families) and the pooled ‘mismatch’ across pure freshwater populationswas 0. P-values were Bonferroni-corrected. The plot and regression lines are modelled after the ‘snowball’studies of Moyle and Nakazato (2010) and Matute et al. (2010). The blue lines are linear regressions and thered lines are quadratics. Results hold if the intercept is not forced through zero, and if the ‘origin’ datum isomitted.181Appendix EAppendix for Chapter 6E.1 Supplementary methodsE.1.1 Experimental animalsWild fish were collected from Priest and Paxton Lakes (Texada Island, BC, Canada) and Little Quarry Lake(Nelson Island, BC) from 2017–2019. Two Paxton benthic males were collected from a pond populationon UBC campus founded with wild Paxton Lake benthic fish in 2016. All fish in the experiment weretherefore 2–5 generations removed from the wild. All benthics were captured using minnow traps as weremost limnetic males. Gravid limnetic females were caught almost invariably by dip-netting. One Paxtonlimnetic family and one Little Quarry limnetic family was raised from a nest-collected clutch. In these casesI closely examined resulting fish to ensure none were benthic × limnetic hybrids.Wild fish were crossed either at the lakeside or at the lab by gently squeezing the eggs from a gravidfemale fish into a small Petri dish filled with lake or aquarium water. Male parents were euthanized with anoverdose of MS-222, and their testes were removed and placed in the Petri dish. A fine paintbrush was thenused to release sperm from the testes and ensure it was well mixed among the eggs in the clutch. Crossesfor the present experiment were all made in the lab in much the same way. Males were occasionally used tofertilize multiple clutches. Due to logistical constraints, I made crosses as females became gravid—this ledfish from different treatments to have different mean ages. In total, fish from 124 crosses were used in thisstudy.Crosses were made from 4 March to 9 April, 2020, and raised in 5 ppt saltwater (Instant Ocean) 110 Laquaria with a small amount of methylene blue added as a fungicide. These two additions reduce the loss ofclutches to fungus and also reduce labour required to raise healthy fish (because Artemia nauplii can live fora couple of days in 5 ppt saltwater). Fish were fed Artemia nauplii daily. Due to logistical constraints I couldnot monitor hatching success but I note that I observed very little mortality. In general, there is very limitedevidence that F1 or F2 hybrid stickleback exhibit ‘intrinsic’ deficiencies (Lackey and Boughman, 2017).After fish were large enough to handle without risk of mortality (approx. 3–4 weeks), I split large familiesinto multiple tanks and culled excess fish. At this time I began feeding fish chopped frozen bloodworms andconducting weekly 50 % water changes with fresh dechlorinated water. After splitting and culling I kept thedensity of fish to fewer than 30 individuals per aquarium. When fish were large enough, I added unchoppedbloodworms, spirulina adult brine shrimp, and chopped mysis shrimp to their diets. Eventually, the mysisshrimp were fed whole.182E.1.2 Coded wire taggingHere I fully document my methodology for using sequential coded wire tags (CWTs). I ordered sufficientquantities of CWTs from Northwest Marine Technology (NMT,; Anacortes, WA, USA).The CWTs come on sheets with two columns—one ‘fish’ column and one ‘reference’ column. AlthoughCWTs appear in sequential order, the numbers do not increase in perfect 1:1 association with tag position.Because of this, the unique sequences on CWTs cannot be inferred without some possibility of error. It istherefore neccessary to pre-read some tags. I never used adjacent (i.e., on the same row) tags for fish boundfor the same pond. This allowed me to pre-read fewer tags without risking error. Specifically, I pre-readevery third tag in the ‘reference’ column using a Magniviewer (NMT) and could reliably infer other tagsbecause I know which pond each fish was retrieved from.Before tagging, fish were anaesthetised with MS-222. I then used a single-shot CWT injector (NorthwestMarine Technology) to inject CWTs beneath the skin on the fish’s dorsal musculature. Fish were injectedwhile laying on their side atop a large sponge, and their head was covered with a paper towel soaked in waterfrom their original tank. Light pressure was applied to the head and caudal peduncle to stabilize the fishduring injection. Injection was easiest if the lateral plates were used as a leverage point to implant the headof the needle beneath the skin. (Limnetics, with their denser musculature and invariable presence of lateralplates, were easier to inject). I found maximal success when the push rod was not pushed to be maximallyextended—in fact this can cause the CWT to emerge from the fish, rather an extension of about 3⁄4 workedbest. When injecting, I took care that the pectoral fin was either oriented toward the head or down toward theventral area, so as to not be pierced by the tagging needle. Fish were kept temporarily in aerated water fromtheir original tank for recovery and then moved back to their original tank before introduction into the pondsthree days later. Methylene blue was added to their original tank to prevent infection of the tagging wound.I estimate that each fish took approximately 30 seconds to anaesthetize, weigh, and tag, and it took about 10minutes to pre-read a page of CWTs.At the end of the experiment I retrieved and read tags from each fish. I located tags under a dissectingmicroscope. Tags were always handled delicately because metal forceps can easily damage them. Mostoften, a scalpel was used to cut away skin and visually identify the tag. After cutting away muscle, themagnetic tag is attracted to the scalpel, where it can be gently placed onto a magnetic pencil. Removed tagswere read with a MagniViewer (NMT) and then stored for later reference if necessary.Ambiguities and possible transcription errors were identified by ensuring a match between species (ben-thic or limnetic) and pond, checking for duplicates and implausible values, and ensuring each recovered tagwas assigned to a fish.E.1.3 Estimating fitness via fecundity and overwinter survivalIn the main text I use a conservative fitness estimate that incorporates only survival and growth. A morecomplicated and possibly more accurate estimate of fitness would account for overwinter survival and fecun-dity. This estimate of relative fitness considers three components. The first, survival during the experiment(i.e., ‘summer survival), was directly measured. The next two fitness components consider the fitness effectsof body size (directly measured) on overwinter survival and fecundity (both estimated). Absolute fitness was183calculated as summer survival × (estimated) winter survival × (estimated) fecundity. Relative fitness wascalculated as the absolute fitness of each cross type divided by the cross type with the highest absolute fitness(within species).I estimated relative overwinter survival and fecundity using previously published data. These previousstudies used standard length to predict fitness components, and I measured approximately 50 individuals ofboth species to estimate the mass–length relationship for both. Quadratic models had a high explanatorypattern for both species (r2limnetic = 0.88; r2benthic = 0.79) (Fig. E.4).To estimate relative overwinter survival, I conservatively interpret the analysis of Carlson et al. (2010),who found that standard length was positively associated with overwinter survival in Alaskan stickleback.The specific relationship between length and survival was either quadratic (concave) or linear, depending onthe year (Carlson et al., 2010). I conservatively assume that relative overwinter survival is a linear function ofstandard length. I estimated fecundity using two previously published datasets from stickleback experimentsin the UBC Experimental Ponds (Fig. E.5). Schluter et al. (2021) estimated fecundity in F2 marine ×freshwater stickleback hybrids. Specifically, the fitness of over 200 F2 hybrid females was quantified as thetally of her surviving F3 offspring (from a sample of 500 F3s). Male fitness was not estimated by Schluteret al. (2021), but the authors speculate that selection acted similarly on males and females because theevolutionary response observed was highly similar to what was expected from estimates of female fitness.Bay et al. (2017) estimated the number of mating events for Paxton Lake F2 benthic × limnetic hybridfemales, and pure (i.e., non-hybrid) benthic and limentic males. Analysis of the data suggested that length–mating relationships were the same across groups (i.e., no significant interaction) so all data were grouped foranalysis. Data were analyzed using simple linear models from which intercepts and slopes were extracted.Relationships were significant (in a Poisson generalized linear model) and positive in both datasets, but Ichose to base fecundity estimates on the estimates from Schluter et al. (2021) because differences in relativefitness among groups were smaller (i.e., it is more conservative).184E.2 Supplementary Tables & FiguresTable E.1: Summary of fish numbers and survival rates for the 2020 pond experimentpond origin species type n released n recaptured survival proportion4 Little Quarry b Parent 102 46 0.454 Paxton b Parent 107 70 0.654 hybrid b F1 206 123 0.604 hybrid b F2 210 130 0.624 Little Quarry l Parent 106 31 0.294 Paxton l Parent 107 39 0.364 hybrid l F1 207 101 0.494 hybrid l F2 208 62 0.309 Little Quarry b Parent 104 84 0.819 Priest b Parent 106 93 0.889 hybrid b F1 203 185 0.919 hybrid b F2 205 169 0.829 Little Quarry l Parent 105 36 0.349 Priest l Parent 105 57 0.549 hybrid l F1 204 86 0.429 hybrid l F2 205 100 0.4919 Priest b Parent 103 95 0.9219 Paxton b Parent 103 87 0.8419 hybrid b F1 204 174 0.8519 hybrid b F2 205 161 0.7919 Priest l Parent 105 32 0.3019 Paxton l Parent 105 42 0.4019 hybrid l F1 206 88 0.4319 hybrid l F2 205 72 0.35185Table E.2: Fitness components and relative fitness estimates for cross types within species.species cross type summer surv. mass (g) std. lgth. (cm)* rel. winter surv.* fecundity* rel. fit.†limneticF1 0.454 1.09 4.59 1.000 1.74 1.000F2 0.386 0.98 4.40 0.959 1.45 0.678pure 0.387 1.01 4.46 0.971 1.54 0.731benthicF1 0.818 2.14 5.91 1.000 3.80 1.000F2 0.797 2.01 5.73 0.970 3.53 0.877pure 0.799 2.06 5.81 0.982 3.64 0.918*estimate; †w = summer surv × rel. winter surv. × fecundity186b l0.4 0.8 1.2 0.2 0.4 0.6 mass (g)final mass (g, residual)Figure E.1: Relationship between initial and final mass in the 2020 pond experiment. The left plotshows benthics and the right shows limnetics. Points are partial residuals from a mixed model with pond asa random effect.187b l70 80 90 100 80 90 1000. days in pondfinal mass (g, residual)Figure E.2: Relationship between the number of days in pond and final mass in the 2020 pond experi-ment. Both relationships are significant and positive.188(a); paxton × little quarry limnetic−0.75−0.50−0.250.00lq.l.ppx.l.ppx.lq.l.f1px.lq.l.f2mean survival ± comp. lim. final mass (g) ± comp. lim. (b); priest × little quarry limnetic−0.4− survival ± comp. lim. final mass (g) ± comp. lim. (c); paxton × priest limnetic−0.8−0.6−0.4− survival ± comp. lim. final mass (g) ± comp. lim. (d); paxton × little quarry benthic0.20.40.6lq.b.ppx.b.ppx.lq.b.f1px.lq.b.f2mean survival ± comp. lim. final mass (g) ± comp. lim. (e); priest × little quarry benthic1.501.752.002.252.50lq.b.ppr.b.ppr.lq.b.f1pr.lq.b.f2mean survival ± comp. lim. final mass (g) ± comp. lim. (f); paxton × priest survival ± comp. lim. final mass (g) ± comp. lim. Figure E.3: Fitness components with the two parent populations plotted separately. Points are estimatedmarginal means and arrows are comparison limits. Note the differences in scale among all plots.189benthic limnetic1 2 3 4 5 1 2 3 4 (g)standard length (mm)Figure E.4: Relationship between mass and standard length for fish collected from ponds. Relationshipsare shown separately for benthics and limnetics. Both are highly significant and positive. These data wereused to estimate standard length across the dataset.19002468103.5 4.0 4.5 5.0 5.5standard length (mm)# surviving offspring(a); Schluter et al. 202102468104 5 6 7 8standard length (mm)# times mated(b); Bay et al. 2017Figure E.5: Relationship between standard length and fecundity in previously published sticklebackpond experiments. Schluter et al. (2021) considered F2 marine-freshwater hybrid females and measured thenumber of F3 hybrids to which they could be confidently assigned parentage. Bay et al. (2017) considered F2benthic-limnetic (Paxton) hybrid females and non-hybrid males of both species and recorded the number ofsuccessful mating events (inferred from genotyped eggs and offspring). A generalized linear model did notreject the hypothesis that the slope differed by group (F2 female, pure benthic male, or pure limnetic male),so I plot them together. Both relationships are significant and positive as evaluated with a generalized linearmodel.191Appendix FAppendix for Chapter 7F.1 Supplementary FiguresRennison SchluterF2 F3 F2 F3− excess heterozygosityFigure F.1: Heterozygosity does not differ between F2 and F3 hybrids. The plots show individual excessheterozygosity from the two studies that genotyped both the F2 and F3 generations (Schluter et al., 2021;Rennison et al., 2019). The means do not differ between generations in either study.192− Bay Conte Rennisonsourceindividual mean heterozygosityFigure F.2: Heterozygosity does not differ between studies involving Paxton Lake benthic × limnetichybrids. The means of all three studies are statistically indistinguishable.193lociindividualslab LCRxCRN MxF Rogers 1lab Paxton BxL unpub. 1lab Priest BxL unpub. 2pond LCRxCRN MxF Schluter 1pond Paxton BxL Arnegard 1pond Paxton BxL Bay 1pond Paxton BxL Bay 2pond Paxton BxL Bay 3pond Paxton BxL Conte 1pond Paxton BxL Rennison 1pond Paxton BxL Rennison 2pond Paxton BxL Rennison 3pond Paxton BxL Rennison 4pond Paxton BxL Rennison 5pond Paxton BxL Rennison 6pond Paxton BxL Rennison 7pond Paxton BxL Rennison 8pond Priest BxL Conte 2−0.0250.0000.0250.0500.075−0.0250.0000.0250.0500.075unique study and replicatemean excess heterozygosity ± 95% CIFigure F.3: Estimates of excess heterozygosity for individuals and loci across ‘replicates’. We considera replicate to be a unique bi-parental cross for aquarium studies, and a unique pond for pond studies. Meanexcess heterozygosity is shown for each such replicate for both individuals (upper) and loci (lower). In eachpanel the horizontal line indicates no excess heterozygosity. Red points are ‘lab’ replicates, and blue pointsare ‘pond’ replicates.1940.250.500.75lab pondenvironmentobserved ancestryheterozygosity0.250.500.75lab pondenvironmentobserved ancestryheterozygosityFigure F.4: Test of main hypothesis using ‘observed’ heterozygosity rather than excess heterozygosity.Plots are as in Fig. 7.2, and quantitative conclusions are unchanged from those gained from an analysis ofexcess heterozygosity.195lab pondBxLMxF0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 indexheterozygosityFigure F.5: de Finetti ternary diagrams for genotyped individuals in each of the bi-parental crosses.Each point represents an individual F2 hybrid shows each individual’s hybrid index (frequency of benthicalleles in its genome) and its mean heterozygosity. Loci with significant deviations from Hardy-Weinbergequilibrium (χ2-test) are shown in blue.196lab pondBxLMxF0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 of 'A' ancestry'AB' frequencyFigure F.6: de Finetti ternary diagrams for genotyped loci in each of the bi-parental crosses. Each plotshows relative frequency of benthic and limnetic alleles along the x-axis and of heterozygotes on the y-axis.Loci with significant deviations from Hardy-Weinberg equilibrium (χ2-test) are shown in blue.197450.2 0.4 0.6 0.8individual mean heterozygositystandard length (mm, residual)Figure F.7: No relationship between individual mean heterozygosity and growth (standard length)in the aquarium-raised biparental benthic-limnetic F2 hybrids. Results are residuals from visreg(Breheny and Burchett, 2017). Each point is an individual F2 hybrid. The interaction between lake-of-originmean heterozygosity was non-significant so I plot the main effect across both lakes-of-origin (Paxton andPriest). Mean heterozygosity was not significantly associated with standard length (β = 0.46 ± 2.75 [SE],F1,175 = 0.028, P = 0.86).198Benthic x Limnetic Marine x Freshwater0.0 0.1 0.2 0.3 0.4 0.0 0.1 0.2 0.3 0.4−0.4− selection (|p2 − q2|)excess heterozygosityFigure F.8: No relationship between estimated directional selection at each locus and its mean excessheterozygosity in ponds. Results are residuals from visreg (Breheny and Burchett, 2017). Each point isan individual locus genotyped in F2 hybrids in ponds. The left panel shows benthic-limnetic hybrids and theright panel shows marine-freshwater hybrids. Directional selection was calculated as the absolute differencein the frequency of both homozygotes. Both relationships are non-significant.199


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