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Trophic metacommunities : lessons from studying bromeliad and teaching programming in biostatistics Guzman Uribe, Laura Melissa 2019

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Trophic metacommunities:Lessons from studying BromeliadsAndTeaching programming inbiostatisticsbyLaura Melissa Guzman UribeB.Sc. (Hons), McGill University, 2012M.Res. (Distinction), Imperial College London, 2013A 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)April 2019© Laura Melissa Guzman Uribe, 2019The following individuals certify that they have read, and recommend to theFaculty of Graduate and Postdoctoral Studies for acceptance, a dissertationentitled:Trophic metacommunities: Lessons from studying BromeliadsAnd Teaching programming in biostatisticssubmitted Laura Melissa Guzman Uribe in partial fulfillmentby of the requirements forthe degree Doctor of Philosophyofin ZoologyExamining Committee:Diane Srivastava, ZoologySupervisorMary O’Connor, ZoologySupervisory committee memberLeticia Aviles, ZoologyUniversity ExaminerJeannette Whitton, BotanyUniversity ExaminerAdditional Supervisory Committee Members:Sarah Otto, ZoologySupervisory committee memberLoren Rieseberg, BotanySupervisory committee memberVinicius Farjalla, UFRJCo - SupervisoriiAbstractTrophic metacommunity ecology brings together the spatial thinking of meta-community ecology and the complexity of food web ecology. While theoret-ical development in this field has been bountiful, empirical development hasbeen slower. Using a diverse methodology, I bring together three differentempirical approaches to understand trophic metacommunities as exemplifiedby bromeliads macro-invertebrates. First, I used Markov network analysisto study the effect of regional environmental gradients on community com-position and trophic interactions. I found that a gradient in precipitationunderlies the spatial turnover of some species and that the interactions ofcertain predators differed due to differences in bromeliad water volume. Sec-ond, I combined experimental feeding trials and a food web model to studythe effect of body size diversity at the local scale on food web dynamics.I found that predator persistence was maximized when the minimum preysize in the community was intermediate, but as prey diversity increased theminimum body size could take a broader range of values due to Jensen’sinequality. Third, I used population genetics to estimate dispersal kernelsof a predator and a prey. I then used these empirical estimates of dispersalkernels and feeding rates to parameterize a trophic metacommunity model,to study the effect of differences in dispersal between a predator and a preyon persistence. From the empirical dispersal kernel estimates, I found thatthe prey dispersed up to 25 km whereas the predator dispersed up to 200 m.From the trophic metacommunity model, I found that differences in dispersalrates were sufficient to generate differences in occupancy of our modelledlandscape, without requiring variation in the abiotic niche. None of thisiiiwork would have been possible without strong programming skills and agood understanding of statistics. In my final chapter, I studied the effectof using cognitive load theory to design R programming assignments forundergraduate biostatistics courses. I found that students that learned Rthrough our assignments rated their programming ability higher and weremore likely to put the usage of R as a skill in their CVs than control students.ivLay SummaryFood webs show which species eat each other. For my Ph.D., I investigatedhow food webs change when: (i) the environment changes, (ii) species havedifferent body sizes, (iii) or species move different distances between genera-tions. I studied a food web of aquatic invertebrates that live inside bromeliadplants. First, I found that a predatory crane fly interacted negatively withother species when the water volume in the plant was low. Second, I foundthat the damselfly predator needed mid-sized prey to survive. Third, I foundthat the crane fly moved up to 23 km(!), while the damselfly moved only 200m.Finally, I wanted to teach undergraduate students in biology how to programand do statistics at the same time. I designed homework assignments usingeducational theories about how to teach two concepts simultaneously. Thesewere successful: students felt motivated and confident in their skills.vPrefaceChapter 2 has been previously published as:Guzman, L. M., Vanschoenwinkel, B., Farjalla, V. F., Poon, A., andSrivastava, D. S. (2018). A precipitation gradient drives change inmacroinvertebrate composition and interactions within bromeliads.PloS one, 13(11), e0200179.I conceived of the idea, alongside Vinicius Farjalla and Diane Srivastava. Icollected and processed the data. Anita Poon assisted in processing the data.I analyzed the data and Bram Vanschoenwinkel and Diane Srivastava su-pervised the analysis. I wrote the manuscript with comments from DianeSrivastava, Anita Poon and Bram Vanschoenwinkel. Permit number 47164-1 was provided by Ministério do Meio Ambiente (MMA), Instituto ChicoMendes de Conservação da Biodiversidade (ICMBio) and Sistema de Autoriza-ção e Informação em Biodiversidade (SISBIO). This field study did not involveendangered or protected species.Chapter 3 has been submitted to the Proceedings of the Royal Society Band it is under review.I conceived the idea, ran the experiments, collected the data, analyzed thedata, wrote the model and wrote the manuscript under the supervision ofDiane Srivastava.Chapter 4I conceived the idea alongside Vinicius Farjalla and Diane Srivastava. Icollected the invertebrates and extracted the DNA. Extracted DNA of theviodonate predator was sent to the Cornell Institute for Genomic Diversityand extracted DNA of the tipulid prey was sent to University of Wisconsin-Madison Biotechnology centre to conduct GBS and sequencing. I performedthe bioinformatics, wrote the model and the manuscript under the supervisionof Diane Srivastava.Chapter 5I conceived the idea. I wrote the homework assignments with the help ofEllen Nikelski and the supervision of Matthew Pennell and Diane Srivastava.I analyzed the data and wrote the manuscript with comments from EllenNikelski, Matthew Pennell and Diane Srivastava. This work was conductedwith review and approval by the Behavioural ethics research board of theUniversity of British Columbia, H16-02319. The project title was "Evaluationof R instruction in Zoology undergraduate statistics courses"viiContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . vPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viContents . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiL ist of Tables . . . . . . . . . . . . . . . . . . . . . . . . . xiL ist of F igures . . . . . . . . . . . . . . . . . . . . . . . . . xiiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . xivDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . xvi1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 12 A precipitation gradient underlies change in macroinvertebratecomposition and interactions within bromeliads . . . . . . 102.1 Chapter summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323 Prey body mass and diversity determine food web persistence .333.1 Chapter summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524 Empirically determined differences between a predatorand its prey allow increased persistence in a metacommunity604.1 Chapter summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61viii4.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 624.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 654.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 724.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 805 Successful integration of data science in undergraduatebiostatistics courses using cognitive load theory. . . . . 845.1 Chapter summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 855.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 865.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 895.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 975.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1055.6 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1085.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1086 D iscussion . . . . . . . . . . . . . . . . . . . . . . . . . . .109B ibliography . . . . . . . . . . . . . . . . . . . . . . . . . .114Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . .137a Supplementary Information to Chapter 1 . . . . . . . . . .137a.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138a.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138a.3 Past and present metacommunity theory . . . . . . . . . . . . . . 141a.4 Spatial use properties and their consequences for pairwise trophicinteractions across scales . . . . . . . . . . . . . . . . . . . . . . . . 148a.5 Predicted effects of (co)variation in spatial use properties ontrophic metacommunity dynamics . . . . . . . . . . . . . . . . . . 160a.6 Future directions: building and testing future metacommunitytheory based on spatial use properties . . . . . . . . . . . . . . . . 162a.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170b Supplementary Information to Chapter 2 . . . . . . . . . .173b.1 Partitioning beta diversity . . . . . . . . . . . . . . . . . . . . . . . 173b.2 Environmental variation between sites . . . . . . . . . . . . . . . . 174b.3 Validation of Markov Network method . . . . . . . . . . . . . . . 179b.4 Supporting results . . . . . . . . . . . . . . . . . . . . . . . . . . . 181c Supplementary Information to Chapter 3 . . . . . . . . . .193c.1 Supporting results . . . . . . . . . . . . . . . . . . . . . . . . . . . 193c.2 Asymmetric competition . . . . . . . . . . . . . . . . . . . . . . . . 202ixd Supplementary Information to Chapter 4 . . . . . . . . . .207d.1 Modifications to DNA extraction protocols . . . . . . . . . . . . . 207d.2 Supporting results . . . . . . . . . . . . . . . . . . . . . . . . . . . 208e Supplementary Information to Chapter 5 . . . . . . . . . .213e.1 Homework assignments . . . . . . . . . . . . . . . . . . . . . . . . 213e.2 Surveys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220e.3 Codebooks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228e.4 Supporting results . . . . . . . . . . . . . . . . . . . . . . . . . . . 237xList of TablesTable 3 .1 Parameter values . . . . . . . . . . . . . . . . . . . . 46Table 3 .2 Estimated parameters in the functional response . . . . . . 48Table 4 .1 Parameter values used for simulations . . . . . . . . . . . 73Table 5 .1 Course structure . . . . . . . . . . . . . . . . . . . . 91Table 5 .2 Self-perceived emotions of the students . . . . . . . . . .100Table a .1 Competitive and trophic metacommunity response variables144Table a .2 Synthesis of metacommunity ecology . . . . . . . . . . .149Table a .3 Spatial use properties and measurable traits . . . . . . . .164Table b .1 Environmental gradients between sites . . . . . . . . . .175Table b .2 Interaction strengths in known module . . . . . . . . . .180Table b .3 Pairwise Tukey tests . . . . . . . . . . . . . . . . . . .181Table b .3 Pairwise Tukey tests . . . . . . . . . . . . . . . . . . .182Table b .3 Pairwise Tukey tests . . . . . . . . . . . . . . . . . . .183Table b .3 Pairwise Tukey tests . . . . . . . . . . . . . . . . . . .184Table b .4 Linear regression for relative interaction strengths . . . . .184Table b .4 Linear regression for relative interaction strengths . . . . .185Table b .5 Permutation test p-value . . . . . . . . . . . . . . . . .191Table c .1 Prey abundance used in feeding trials . . . . . . . . . . .194Table e .1 Perceived difficulty of the material . . . . . . . . . . . .238xiList of FiguresF igure 1 .1 Neoregelia cruenta at Jurubatiba national park . . . . . . . . 5F igure 1 .2 Bromeliad patch at Jurubatiba national park . . . . . . . . 6F igure 1 .3 Bromeliads form larger patches of habitat . . . . . . . . . 7F igure 2 .1 Map of sites along the coast of Brazil . . . . . . . . . . . 18F igure 2 .2 Community composition across sites . . . . . . . . . . . 24F igure 2 .3 Relative strength of species interactions . . . . . . . . . . 25F igure 2 .4 Tipulid’s interactions . . . . . . . . . . . . . . . . . . 26F igure 3 .1 Type II functional response . . . . . . . . . . . . . . . . 48F igure 3 .2 Time series of predator and prey abundance . . . . . . . . 50F igure 3 .3 Predator persistence with different prey size . . . . . . . . 51F igure 3 .4 Prey diversity has a unimodal relationship with predatorpersistence . . . . . . . . . . . . . . . . . . . . . . . 58F igure 3 .5 Food web persistence . . . . . . . . . . . . . . . . . . 59F igure 4 .1 Map of sites along the coast of Brazil . . . . . . . . . . . 66F igure 4 .2 Odonate and tipulid’s population structure . . . . . . . . 76F igure 4 .3 Site of origin for odonate and tipulid individuals . . . . . . 77F igure 4 .4 Estimated dispersal rate . . . . . . . . . . . . . . . . . 78F igure 4 .5 Persistence in trophic metacommunity model . . . . . . . 79F igure 5 .1 Students responses to the surveys . . . . . . . . . . . . . 99F igure 5 .2 Probability that students used R . . . . . . . . . . . . .104F igure a .1 Three forms of movement . . . . . . . . . . . . . . . .150F igure a .2 Trophic metacommunity simulation outcomes . . . . . . .152F igure a .3 Spatial use properties in a three species module . . . . . .171F igure b .1 Total precipitation using WorldClim data . . . . . . . . .176F igure b .2 Total precipitation using weather stations . . . . . . . . .177F igure b .3 Mean water volume increases with precipitation . . . . . .178F igure b .4 Predators have more negative interactions and prey havemore positive interactions . . . . . . . . . . . . . . . .186F igure b .5 Relative interaction strength and water volume . . . . . . .187F igure b .6 Permutation of interaction terms . . . . . . . . . . . . .188xiiF igure b .7 Permutation of negative slopes . . . . . . . . . . . . . .189F igure b .8 Permutation of positive slopes . . . . . . . . . . . . . .190F igure b .9 Presence vs. relative interaction strength . . . . . . . . . .192F igure c .1 Parameter functions vs. body size . . . . . . . . . . . . .195F igure c .2 Parameter space explored by MCMC . . . . . . . . . . .196F igure c .3 Time series of two prey species with high competition . . . .197F igure c .4 Time series of two prey species with low competition . . . .198F igure c .5 Jensen’s inequality . . . . . . . . . . . . . . . . . . .199F igure c .6 Predator persistence and prey diversity . . . . . . . . . .200F igure c .7 Predator persistence and prey body size . . . . . . . . . .201F igure c .8 Time series of two prey with assymetric competition . . . .204F igure c .9 Predator persistence with assymetric prey competition . . .205F igure c .10Prey diversity decreases predator persistence . . . . . . . .206F igure d .1 Identity by state similarity . . . . . . . . . . . . . . . .209F igure d .2 Cross validation error and loglikelihood of major clades . . .210F igure d .3 Population segregation of potential sub-clades . . . . . . .211F igure d .4 Cross validation error of different population structures . . .212xiiiAcknowledgementsDiane Srivastava has been a very patient mentor and supervisor. I am gratefulfor all her guidance and her endless effort to improve my writing.I want to thank my committee members: Mary O’Connor, Sally Otto,Loren Rieseberg and Vinicius Farjalla. Your guidance and support have beenindispensable.In particular I want to thank certain members of the committee for excep-tional help: Vinicius for Brazilian fieldwork logistics, Sally for help with modelconstruction, Loren for providing lab space free. I also want to thank BramVanschoenwinkel for allowing me to come and do research in Brussels.The working groups during my Ph.D. have been an integral part of my edu-cation. The trophic metacommunity working group was one of the best part ofmy Ph.D. Thank you for meeting every week and having awesome discussionsabout ecology. I want to thank: Patrick Thompson, Rachel Germain, SamStrauss, Coreen Forbes, Dominique Gravel, Adam Ford, Mary O’Connor andDiane Srivastava. The sTURN working group helped me push the boundariesof what metacommunity theory means, and what we can do with it. In particu-lar I want to thank: Jon Chase, Zsofi Horváth, Robert Ptacnik, Luc De Meester,Stéphanie Gascón, Maria Anton-Pardo, Pieter Lemmens, Alienor Jeliazkov,Duarte Viana and Bram Vanschoenwinkel. Finally, the bromeliad workinggroup let me meet all the great people that love bromeliads, in particularRegis Cereghino, Ignacio Barberis and Kurt Trzcinski.This whole Ph.D. couldn’t have happened without key support of numer-ous people. I want to thank some of the people who made this possible: in thefield by Juliana Leal and Nayara Gomez, in the lab Anita Poon, Sadie Garcia,xivKathleen Higgins and Winnie Cheung, and finally for the R assignments EllenNikelski.A large part of my Ph.D. was trying to improve the way we teach R. Iwanted to thank the people who showed me that research on teaching ispossible, and fun: Miranda Meets, Lacey Samuels and Sunita Chowira.I want to thank past, present and new members of the Srivastava lab:Sarah Amundrud, Natalie Westwood, Pierre Rogi, Nadia Paez, KeerthikruthaSeetharaman, Angie Nicolas, Alathea Lethaw, and last but definitely not leastAndrew McDonald.I am thankful to everyone in the BRC (and adjacent buildings) that havemade these past years a lot of fun. In particular I want to thank LuchoCamacho, Alejandra Echeverri, Santiago David, Manny Boehm.I want to thank my family Sonia Uribe and Carlos Guzman for all yoursupport, enthusiasm and love that have helped me get here. I also want tothank my new family, Brenna, Richard, Alec, Steve and Laura Pennell. Thankyou for welcoming me to your family.Matthew Pennell, thank you. Thank you for celebrating everything withme and for being a shoulder to cry on. Your love and support have made thisexperience be the best it could have been.xvDedicationTo my parentsSonia Uribe and Carlos Guzmanxvichapter 1Introduction1chapter 1The theories of island biogeography (MacArthur and Wilson, 1967), andmetapopulation ecology (Hanski et al., 1997) have long encouraged ecologiststo think deeply about the role of space and dispersal on community dynam-ics. More recently, the theory of metacommunity ecology has highlightedthat species interactions, in combination with space and dispersal, also havedynamical consequences for communities at local and regional scales (Leiboldet al., 2004). In a pioneering paper, which set the stage for the next 15 years ofresearch in metacommunity ecology, Leibold et al. (2004) summarized the theo-retical literature and found four major combinations of processes that enabledspecies that would otherwise competitively exclude each other, to coexistregionally (i.e., across multiple populations). These four combinations, whichthey originally term paradigms (and more recently renamed as "archetypes";(Leibold and Chase, 2017)) were: i) species sorting, where intermediate levelsof dispersal allow species to track their environmental optima; ii) mass effects,where high dispersal allows species to persist in sub-optimal environments;iii) patch dynamics, where dispersal-colonization trade-offs between speciescould allow regional persistence; and iv) neutral dynamics, where species areecologically equivalent but stochastic dispersal and drift leads to co-existence.These four paradigms have been so successful as a rhetorical tool that theyhave become nearly synonymous with the term metacommunity ecology.After a decade or so of empirical studies classifying metacommunitiesinto these paradigms (typically following variance partitioning proceduresoutlined by Cottenie (2005)), researchers have increasingly recognized thatthe four metacommunity paradigms are neither mutually exclusive nor com-prehensive, and that multiple mechanisms may promote coexistence simul-taneously (Logue et al., 2011; Thompson et al., 2017) (to their credit, Leiboldet al. (2004) recognized this in this original paper). Not only can multiplemechanisms promote coexistence, but these paradigms are just points along2chapter 1a multi-dimensional continuum of community dynamics that results fromvariation in dispersal, the strength of the abiotic niche and the outcome ofspecies interactions (Thompson et al. in prep).Furthermore, while species interactions are widely recognized as key tounderstanding the dynamics of communities, both theoretical and empiricalwork, guided by the paradigms, has focused primarily on interactions betweencompetitors. A number of researchers have recognized this limitation andtried to incorporate trophic interactions into metacommunity thinking (e.g.Holt, 2002; Gravel et al., 2011); however, these efforts are quite scattered anddisconnected. During my Ph.D. I co-led a collaborative network of researchersthat aimed to create a coherent vision for a truly multi-trophic theory of meta-communities (see Appendix a of this thesis and Guzman et al. (2019)). Thisconceptual work, while not part of my dissertation, provides an overarchingtheme for the research presented here. In our synthesis paper, we argue thata theory of trophic metacommunities is necessary (i) when we need to predictfood web properties, which are incompatible with a competitive framework,and (ii) when interacting species use space at different scales; for example,when a predator population interacts with multiple smaller-scale prey popula-tions. In addition, we argue that trophic metacommunity dynamics arise wheninteracting trophic levels differ in the way they use space. These differencesin space use arise from differences in ‘spatial use properties’, which we defineas population level properties that reflect how species use space. These spatialuse properties include three forms of movement — dispersal, migration, andforaging —, as well as the abiotic niche and spatial information processing.Spatial information processing refers to the ability of individuals to direct andcontrol their movement based on biotic and abiotic conditions.This trophic metacommunity framework is well suited for a system like themacroinvertebrate food webs that inhabit bromeliads. Bromeliads have inter-3chapter 1locking leaves which form a tank that collects water, referred to as a phytotelm(Figure 1.1); the phytotelm provides a habitat for aquatic macroinvertebrates.Bromeliads are an ideal system to study metacommunity ecology since everybromeliad is a discrete patch of habitat (i.e., a sensu stricto metacommunity),and bromeliads are clustered in space, often forming patches of bromeliads(Figure 1.2 and 1.3). They create a hierarchical patchy spatial structure forthese insect communities. In my research I focused on the communities livingin a particular species of bromeliad — Neoregelia cruenta. N. cruenta is foundalong the sand dunes (called restingas) of coastal Brazil, from the north of Riode Janeiro state to São Paulo state. Bromeliad macroinvertebrate communitiesare often comprised of aquatic larvae which include filter feeders, scrapers,shredders, collectors, and top predators. Both the spatial distribution of theplants and the diversity of invertebrates make the phytotelms of N. cruenta anideal system to study trophic metacommunities.As a result of decades of observational and experimental studies (many ofthese spearheaded by my advisor, Dr. Srivastava and other members of theBromeliad Working Group), we know a lot about the ecology of these commu-nities including that there is substantial variation in different species spatialuse properties. For instance, the species within this food web have differenttolerances to drought (Amundrud and Srivastava, 2015), which results in vari-ation in species composition across the landscape. We also know that thereis substantial variation in body size among the invertebrates (Céréghino et al.,2018), which suggests that they might also differ in foraging scale or dispersaldistance. However despite these results, our knowledge of the spatial useproperties of the insects remains far from complete.For my Ph.D., I decided to study trophic metacommunities in the bromeliadsystem using three different approaches. For my first chapter, I studied theeffect of environmental gradients on species interactions. We often think of an4chapter 1F igure 1 .1 : Collecting water from a bromeliad using a turkey baster. Someinsects, especially culex mosquitoes that live in the water column are collectedthis way. This picture was taken at the Jurubatiba national park in Rio deJaneiro, Brazil.5chapter 1F igure 1 .2 : A patch of bromeliads close together under a shrub. This picturewas taken at the Jurubatiba national park in Rio de Janeiro, Brazil.6chapter 1F igure 1 .3 : Under each shrub a patch of bromeliads aggregates forminglarger patches of habitat. This picture was taken at the Jurubatiba nationalpark in Rio de Janeiro, Brazil.7chapter 1environmental gradient as a series of filters selecting which species can persistat different points on the gradient. However, environmental conditions canalso change the way species interact. I evaluated the effect of a regional en-vironmental gradient on community composition and the strength of speciesinteractions. The species interactions were inferred from co-occurrences usingMarkov Networks.For my second and third chapters, I parameterized theoretical modelswith data from bromeliad communities (consumption rates and dispersal, re-spectively). I was motivated to parameterize these models because, despitethe remarkable theoretical advances that these models represent, many com-munity ecology models are primarily heuristic and are often disconnectedfrom natural systems. In particular, although the general predictions of sometheoretical models have been tested using clever experimental designs, thesemodels are rarely parameterized with empirical data. For my second chapter,I specifically looked at the persistence and coexistence mechanisms that shapefood webs at the local scale, which will in turn affect trophic metacommunitydynamics at the regional scale. To do this, I studied the effect of trait diversityand body size at the local scale on food web dynamics. I did feeding trialswith the top predator and multiple prey species of different size and I usedthis data to parameterize a food web model. For my third chapter I empiricallyestimated the dispersal kernel of a predator and a prey pair using populationgenetics, and I combined this information with the feeding rate of predatorsto create a trophic metacommunity model. I evaluated whether observeddifferences in dispersal were sufficient to generate differences in the spatialoccupancy of landscapes between the predator and the prey.None of this work could have been possible without the strong statisticaland programming skills, that I developed over the course of my Ph.D., andwhich, more broadly, have been found to be important and necessary for8chapter 1many quantitative areas in ecology. Using this knowledge, I wanted to em-power future generations of biologists before they became graduate studentsby teaching them programming. I decided to approach this task with the samescholarly rigor that I applied to my ecological research. I studied whether wecould teach R programming in biostatistics courses using cognitive load theory.The results of this educational research comprise my final chapter.9chapter 2A precipitation gradient underlies change inmacroinvertebrate composition and interactionswithin bromeliads. 11Previously published as Guzman, L. M., Vanschoenwinkel, B., Farjalla, V. F., Poon,A., Srivastava, D. S. (2018). A precipitation gradient drives change in macroinvertebratecomposition and interactions within bromeliads. PloS one, 13(11), e0200179.10chapter 22 .1 chapter summaryEcological communities change across spatial and environmental gradientsdue to (i) changes in species composition and (ii) changes in the frequency orstrength of interactions. Here we use the communities of aquatic invertebratesinhabiting clusters of bromeliad phytotelms along the Brazilian coast as amodel system for examining variation in multi-trophic communities. We firstdocument the variation in the species pools of sites across a geographicalclimate gradient. Using the same sites, we also explored the geographicvariation in species interaction strength using a Markov network approach.We found that community composition differed along a gradient of spatiallycorrelated water volume within bromeliads due to the spatial turnover of somespecies. From the Markov network analysis, we found that the interactionsof certain predators differed due to differences in bromeliad water volume.Overall, this study illustrates how a multi-trophic community can changeacross an environmental gradient through changes in both species and theirinteractions.11chapter 22 .2 introductionEcological communities can change across spatial and environmental gradi-ents in three main ways: the composition of species can change, the strength ofinteractions between species can change, or the presence of the interactions canchange (Tylianakis and Morris, 2017; Poisot et al., 2012). Species compositioncan vary across an environmental gradient if the environment filters partic-ular traits (Leibold et al., 2004; Kraft et al., 2015) and across space if speciesdiffer in their dispersal abilities (Leibold et al., 2004; Kraft et al., 2015). Evenwhen species are found together across a gradient, the presence or strengthof interactions between these species can vary between sites on the gradient.For example, consumers may find prey more efficiently in structurally simplehabitats, resulting in stronger interactions than in complex habitats (Lalibertéand Tylianakis, 2010). Consumption rates can also be higher in warmer sites,due to temperature-dependence of metabolic rates (Rall et al., 2012). Here wecombine multiple analyses to show how environmental and spatial gradientsaffect both the composition and interactions of species in a multi-trophic eco-logical community.Estimating changes in species interaction strengths between sites is noto-riously difficult, much more so than estimating changes in community com-position (e.g. Anderson, 2001; Borcard et al., 2011). For example, pairwisecompetition experiments consider interactions between two species. Theseexperiments would need to be performed at multiple environments to esti-mate changes in interaction strengths (Maser et al., 2007). Even then, suchexperiments would ignore the influence of other species in the estimates ofinteraction strengths. In order to measure interactions in a community context(i.e. including indirect effects), researchers have experimentally removed onespecies from the system and assessed the impact on the whole community.However, this approach cannot reconstruct the strength of the interactions be-12chapter 2tween all members of a community, only the interactions between the removedspecies and the rest of the community (Paine, 1966).Inferring species interactions from observational data, as opposed to ex-perimental manipulations, has the advantage of observing the end result ofmultiple direct and indirect interactions. For instance, combining observationsof prey abundance and predator foraging rates can provide information oninteraction strengths (Wootton, 1997). However, this method cannot estimateindirect interactions. Another popular method, checkerboard analyses, candetermine if observational patterns in species co-occurrence differ from ran-dom assembly (Stone and Roberts, 1990; Gotelli, 2000); that is, checkerboardanalyses attempt to estimate the effect of competition in shaping the distribu-tion of species. However, such analyses do not explicitly test for differences ininteraction strengths.Markov networks are a promising method to get information about speciesinteraction strengths from observational data while controlling for indirectinteractions between species (Harris, 2016). A Markov network relates theprobability of the occurrence of multiple species at a site to (i) one parameterfor every species α which determines how much the presence of a givenspecies contributes to the probability of observing the presences and absencesof all species in that site and (ii) one parameter for every pair of speciesβ which determines how much the co-occurence of a given pair of speciescontributes to the same probability. Given an observed vector of presences andabsences, we can use maximum likelihood estimation to obtain the parametersα and β (Harris, 2016). If species are less likely to occur together, theirinteraction strength (parameter β) will be negative. And, conversely, if speciesare more likely to occur together, their interaction strength (parameter β) willbe positive. Some weaknesses of this approach are that Markov networkanalyses only calculate symmetrical interaction strengths, if a species is very13chapter 2rare at the regional scale it may appear to be negatively interacting with manyspecies, and this approach does not explicitly relate occurrences to environ-mental drivers. This method was developed for competitive communitiesthat show a checkerboard distribution. A checkerboard distribution refersto an arrangement where two species are found to always occupy differentpatches. This distribution might be the outcome of some exclusion process(competition or predation) (Stone and Roberts, 1990). This reasoning suggeststhat we can infer interaction strengths in certain types of simple multi-trophiccommunities that also display checkerboard distributions (see also Harris,2016).Although a predator cannot persist in the absence of its prey in a closedsystem, open systems with a high colonization rate of the prey and a highpredation rate can also display a checkerboard distribution between the preda-tor and the prey. When the predator consumes its prey to extinction, wemay find the predator on its own. If the prey has a high colonization rate,it can colonize patches where the predator is absent. These colonization -extinction dynamics can lead to a system with patch dynamics (e.g. Englundet al., 2009). In other words, the spatial scale can affect the degree of co-occurrence observed between predators and prey; at small scales, effectivepredators should reduce or eliminate their prey (negative co-occurrence) whileat larger scales predators and prey should positively co-occur (Freilich et al.,2018).Here we define interaction strength as a measure of the degree of co-occurrence between pairs of species, akin to measuring the correlation betweenthe occurrence of two species (Berlow et al., 2004). Note that this definition ofinteraction strength does not map to biomass or energy flux between trophiclevels, but rather conforms to one of Berlow et al.’s (2004) definitions of in-14chapter 2teraction strengths as a statistical pattern of co-occurrence at a given spatialscale.Despite their potential, Markov methods have thus far not been used toreconstruct interactions in real food webs along environmental and spatialgradients. Good candidate ecosystems for such analyses are insular systemswith simple food webs that occur over wide geographic areas. In such ecosys-tems, species interactions are contained within each replicate of the systemand the environment can vary between systems. A classical food web modelsystem that fits these criteria are the aquatic communities that live insidebromeliad plants in the Neotropics; these communities often occur as clus-ters that exchange species via dispersal. Bromeliad plants have leaves thatinterlock, forming a cavity where water accumulates. Inside these cavities,communities of aquatic invertebrates form a food web (Figure 2.1). In thesecommunities, a suite of voracious predators can limit the abundance of preyspecies (Hammill et al., 2015a), and prey colonization is rapid (Hammill et al.,2015b). In addition, multiple studies have shown that environmental variation(such as water volume) can determine the presence of certain species andmediate the interactions between some predators and their prey (Amundrudand Srivastava, 2016, 2015). Thus bromeliad communities are a suitable modelsystem to test how environment and space can affect species interactions andcommunity composition (Petermann et al., 2015; Farjalla et al., 2012).Making use of this model system, we explored three main questions. First,we tested whether environmental conditions varied between our samplingsites, located along a geographic gradient. Due to spatial variation in pre-cipitation at the time of sampling, we would expect that sites will vary inthe amount of water present in the plants. Second, we described change incommunity composition along this geographic gradient, and then partitionedbeta diversity into either spatial turnover or nestedness of species assemblages15chapter 2— specifically nestedness of community composition as a geographic pattern.We expect that beta diversity would be driven mostly by nestedness of speciesassemblages. Specifically, since the amount of water in the bromeliads de-termines habitat size, we expect that lower water volumes reduce diversityin the community, and that sites with lower water volumes would have asubset of the species of the sites with higher water volumes (Patterson andAtmar, 1986; Baselga, 2010). Third, we used Markov networks to quantifyspecies interactions at each site. We explored whether differences betweensites in the strength of species interactions could be explained by geographicvariation in environmental conditions. We expect that species interactionswould vary along this gradient, because water volumes determine the abilityof some predators to persist.2 .3 methods2 .3 .1 Model systemTank bromeliads accumulate water inside their leaf axils, providing habitatfor communities of aquatic macroinvertebrates (Kitching, 2000). Inside eachbromeliad, these aquatic macroinvertebrates interact to form a food web com-prised of detritivores, filter feeders, intermediate predators and top predators.Bromeliad macroinvertebrate communities are known to be particularly sensi-tive to changes in precipitation, since this can change the amount of habitatavailable for the invertebrates (Pires et al., 2016). For example, drought inbromeliads is known to reduce growth rates of some invertebrate species(Amundrud and Srivastava, 2015). Therefore, we expect that changes in pre-cipitation have the potential to substantially affect species interactions andcommunity composition.16chapter 22 .3 .2 Study AreaThe study area was located in the sand dunes of coastal Brazil (Figure 2.1),in the states of Rio de Janeiro and São Paulo. We sampled ten sites, sevenof which were within the Jurubatiba National Park in Rio de Janeiro state,Brazil. The other three sites were located in the sand dunes of Arraial doCabo (Rio de Janeiro), Marica (Rio de Janeiro), and Ilha Bela (São Paulo).This sampling design resulted in the sites closest to Jurutabita National Parkreceiving low precipitation, the sites close to Marica receiving intermediateprecipitation, and the sites closest to Ilha Bela and Arraial do Cabo receivinghigh precipitation in the month immediately before sampling (February andMarch 2015, Appendix b, Figure b.1, b.2).2 .3 .3 SamplingWe sampled all macroinvertebrate communities between March and May 2015.In each site, we dissected ten bromeliads (totalling 100 bromeliads across allsites) to collect all the invertebrates in each plant. The invertebrate sampleswere preserved in 99% ethanol. Macroinvertebrates were counted and iden-tified to genus level whenever possible. Overall we identified between 11and 16 genera for each site. For every bromeliad, we measured a suite ofenvironmental variables to assess the amount and quality of habitat availableto the invertebrates (Appendix b). For example, actual water volume (mL) wasmeasured by emptying the plant and calculating how much water it containedand maximum water volume (mL) was calculated by emptying the plant andcalculating how much water the plant could hold before it overflowed. Sincebromeliad invertebrates prefer particular bromeliad sizes (Srivastava et al.,2008), we chose the same broad range of bromeliad sizes for every site, toensure that we obtained the spectrum of species present in the site.17chapter 2F igure 2 .1 : Sites are located along the eastern coast of Brazil. A site iscomprised of ten bromeliads found within 100 meters of each other. Tensites were sampled, with a hierarchy of distances between bromeliads (nestedboxes, right side of diagram). The mean water volume found in the bromeliadsfrom each site is shown. Bars represent mean and standard error of the mean.Sites 1 to 10 are ordered from north to south. A community is the set ofspecies found in one bromeliad. The bromeliad macroinvertebrate communityis comprised of predators and prey.18chapter 22 .3 .4 Data analysisEnvironmental variation between sites — In order to test whethersites did indeed vary in environmental conditions, we performed an ANOVAfor most of the environmental variables. For two variables measured on apercentage scale, oxygen saturation and canopy cover, this ANOVA procedurewas inappropriate so we used an analogous generalized linear model specify-ing a binomial family error distribution (Appendix b: Table b.1).Compositional variation between sites — We tested for differ-ences in community composition between sites using permutational multi-variate analysis of variance using distance matrices (function adonis in Rpackage vegan, hereafter referred to as Adonis). Multivariate tests of disper-sion (function betadisper in R package vegan) were used to test for differ-ences in community variation (beta diversity) between geographic sites. Wesummarized abundances according to genus so that these results would becomparable with the species interactions analyses. For the Adonis analysis,we tested if bromeliads from different sites and containing different watervolumes differed in community composition. We used water volume in thisanalysis since, of all the environmental variables, it differed the most betweensites (Appendix b, Table b.1). For the multivariate test of dispersion, we testedif bromeliads from different sites differed in their beta diversity, where within-site beta diversity was measured as the average dissimilarity of bromeliadinvertebrate communities from the centroid in multivariate space (Anderson,2001, 2006). To visualize the differences in community composition and disper-sion, we used non-metric multidimensional scaling (NMDS) plots (Anderson,2001) (Figure 2.2b). An NMDS plot shows both the differences between sitesin their average community composition (position of centroids) as well as19chapter 2differences between sites in beta diversity (the standardised residuals aroundthe centroids).To further understand our results, we partitioned beta diversity: by nested-ness of assemblages and by spatial turnover of species. Nestedness of speciesassemblages occurs when some sites have a smaller subset of the species thanother richer sites (Baselga, 2010). This pattern could result if lower watervolumes in bromeliads exclude certain species without replacement. Spatialturnover of species occurs when some species are replaced by others (Baselga,2010). This pattern could result if some species can persist in low watervolumes and other sets of species can persist in high water volumes. Tocalculate the different portions of beta diversity we used Baselga’s method(Baselga, 2010), where Sørensen dissimilarity (βSOR) is partitioned into purespatial turnover (βSIM) and nestedness (βNES) (See Appendix b for details inthe equations used). βNES is not an absolute measure of nestedness but insteada measure of the dissimilarity of communities due to the effect of nestednesspatterns. To visualize nestedness and turnover we used a nestedness anddegree fill plot (Figure 2.2c).Overall, we tested differences in community composition between sitesusing Adonis, compared the differences in beta diversity between sites usingBetadisper, and finally evaluated if the differences in community compositionbetween sites can be attributed to species nestedness or turnover using parti-tioning of beta diversity. Adonis tests if the differences in community compo-sition between sites are significant, and partitioning of beta diversity relatespatterns in either nestedness or turnover to the compositional dissimilaritybetween sites.Species Interactions — To obtain species interactions strengths, weused Markov network analysis (Harris, 2016). This method does not makeany assumptions about the topology of the food web, nor do we have to20chapter 2define which species might interact with each other. The method calculatesthe conditional species interaction strength given the presence/absence datausing maximum likelihood estimation. We summarized abundances accord-ing to genus, to reduce computational and taxonomic complexity. The trophicrole of bromeliad aquatic invertebrates is highly conserved at the genus level(Poff et al., 2006), so we likely have not averaged over different trophic inter-actions with this approximation. The abundance data of each genus weretransformed into presence/absence data. We performed Markov Networkanalysis separately for each site (Harris, 2016). The output of this analysisis the relative interaction strength for every pair of species in the site. We useda logistic density function for the prior distribution of interaction strengths;after running the model the final distribution of interaction strengths tendedto be normal with a mean close to zero. We performed two validations for theMarkov Network analysis (Appendix b).Effect of environment on species interactions — Once we wereable to confirm that Markov Network analysis correctly distinguished betweenpredators and prey in terms of the predominant sign of interactions, we couldthen examine if the environment explained differences between sites in therelative strength of either positive or negative interactions. For this analysis,we separated negative from positive interactions to assess how interactionstrength (within a particular sign) changes with the environmental variables,based on linear regression. We also used quantile regression to assess howinteraction strengths (positive and negative) change with the environmentalvariables. Quantile regressions are useful when there is unequal variationin the data and therefore there might be more than one slope describing therelationship between response variable and predictor. Quantile regression isalso more robust to outliers than mean regressions (Cade and Noon, 2003).The linear regression and quantile regression p-values were adjusted using21chapter 2the Holm correction for multiple comparisons. To confirm the robustness ofour results, we performed a permutation analysis by shuffling communitycomposition (Appendix b: Permutation results, Figure b.6, b.6, b.6, Table b.5).For the species interaction analyses we used the rosalia package (Harris,2015), all multivariate analyses were performed using the vegan package (Ok-sanen et al., 2018), mixed effect models were performed using lme4 (Bates et al.,2015) and car (Fox and Weisberg, 2011), and all analyses were done using theR programming language (Team, 2018).2 .4 results2 .4 .1 Environmental variation between sitesThe only two environmental variables that significantly differed between siteswere maximum and actual water volume in bromeliads (Appendix b: Tableb.1), and of these two, the most pronounced gradient was observed in theactual water volume in the bromeliads (F10,90 = -3.854, P = 0.0003, Figure2.1). We therefore focus on actual water volume as the major environmentalgradient for the remainder of the analyses, hereafter just water volume.2 .4 .2 Community variation along an environmental gradientCommunity composition differed between sites, depending on the water vol-ume in the bromeliads (F9,90 = 4.649, P = 0.001, Figure 2.2a, b). However,beta diversity, measured as multivariate dispersion in composition around sitecentroids, differed only marginally among sites (F9,90 = 1.966, P = 0.052). Thesesite differences in beta diversity were mainly driven by the sites that were thefurthest apart geographically and differed the most in the water containedin bromeliads (Appendix b: Pairwise multivariate analysis of variance andpairwise Tukey tests for community dispersion, Table b.3). The difference22chapter 2in community composition between sites was mostly due to species turnover(70%) and not due to nestedness (30%, Figure 2.2c). Therefore, contrary to ourinitial predictions, species were not progressively lost along the gradient ofwater in the sites and species richness per site was relatively constant acrossthe gradient (Figure 2.2a).2 .4 .3 Effect of environment on species interactionsAs the majority of genera were found in most sites, we could ask how eachgenus differed across the large scale environmental gradient in terms of inter-action type (i.e. sign) and strength (i.e. magnitude) with other communitymembers. For every pair of genus we obtained an interaction strength inevery site (Figure 2.3). These interactions, however, did not correlate betweensites either using the Pearson’s correlation between interactions or using aSpearman’s rank correlation. Therefore species inteactions are changing fromsite to site. Using site means of water as the environmental gradient, we foundthat the relative strength of positive and negative interactions remain constantbetween sites for most genera, but for Tipulidae, Wyeomyia and Elpidium therelative strength of negative interactions diminished with site water volume(Appendix b: Regression results, Figure b.5, Table b.4). That is, sites whosebromeliads contained less water on average tended to have stronger negativeinteractions between community members and either Tipulidae (linear regres-sion: β = 1.179 x 10-3, P value = 0.017), Wyeomyia (β = 8.254 x 10 -4, P value =0.062) or Elpidium bromeliarum (β = 1.257 x 10 -3, P value = 0.016, all P valueshave been adjusted for multiple comparisons). Arguably, quantile regressionmight be better suited to detecting changes in the distribution of interactions,in which case only the Tipulidae interactions remain related to the mean watervolume, even after the results were adjusted for multiple comparisons (firstquantile regression: β = 1.151 x 10 -3, P value = 0.05, Figure 2.4a).23chapter 2F igure 2 .2 : Community composition across sites. a) Richness is relativelyconstant between sites. b) The community composition of every bromeliad iscompressed into two axes. Each site is represented by a polygon containingall bromeliads within that site. The polygons with higher overlap suggestthat those sites have more similar community composition. The area of thepolygons represents the differences in community composition within a site(beta diversity). While most of the polygons have a relatively similar area(resulting only in a marginal difference in community dispersion), we findthat there are three main clusters of overlap between the sites (Sites 1, 2, 3, 4and 7 overlap and then sites 5 and 8, and 10 and 9 overlap). The stress of theNMDS (non-metric multidimensional scaling) plot was 0.26, consistent witha good, but not great, representation of the communities in two dimensions.c). A genera (columns) by sites (rows) matrix with sites ordered based onmean actual water, where sites with low water volumes are at the top of thegraph and sites with high water volumes are at the bottom of the graph. Ifdifferences in beta diversity occur mainly through nestedness, the sites at thetop would have emptier communities (more white) than the sites at the bottom.Beta diversity is mostly due to species turnover and not nested loss of speciesalong the gradient.24chapter 2F igure 2 .3 : Relative strength of species interactions in every site. Speciesinteractions are scaled to 1. Where rows or columns are empty, that particularspecies is not in that site. Blue indicates positive interactions and red indicatenegative interactions. Positive interactions represent species than tend to co-occur, negative interactions represent species that do not tend to co-occur. Thesize of the points and intensity of the colour represent the interaction strength25chapter 2F igure 2 .4 : a) The tipulid has more negative interactions at low watervolumes (Intercept = -0.98, se = 0.27, slope = 0.001, se = 0.0004). The red linerepresents the first quantile regression, because the major change in interactionstrength occured with the negative interactions. Tipulids are absent from site2, so this site is absent from this regression. Dashed lines represent predictedconfidence intervals. b). Image of a Tipulid larvae.26chapter 2Even though difference between sites in interactions strengths could be dueeither to changes in the per capita interaction strengths between specific taxa,or changes in the pool of species available for interactions, we find that lowvolume sites do not progressively lose species (i.e. there is no nested loss ofspecies, Figure 2.2c). We also checked whether if a species was missing due tolow water volume (slope between presence and absence of a species vs watervolume) was related to the interaction strength between the given speciesand the tipulid. We focused on the tipulid because the tipulid consistentlyshowed a pattern of interaction strength related to water volume. (Appendixb: Relative interaction strength vs. presence, Figure b.9)2 .5 discussionThe main conclusions of this study were threefold. First, we found that, dueto variation in precipitation, the water contained in the bromeliads was themain variable that consistently differed between sites. Second, we foundthat sites differed in both the average composition within bromeliads and thedifference between bromeliads in composition (beta diversity). However, mostof the effect of sites on beta diversity was due to the turnover of some speciesand not due to sequential loss of species being filtered by the environmentalgradient (i.e. between-site turnover vs. between-site nestedness). Third, aftervalidating that the Markov network approach could identify trophic levels,we found that interactions between tipulids and other species changed alonga site gradient in actual water volume; sites with lower water volume hadmore intense negative interactions.Our sites were located along a precipitation gradient with those in thesouth-west of our gradient receiving less rainfall than those towards the north-east (Appendix b: Figure b.1, b.2). This gradient was reflected in the amount27chapter 2of actual water found in the bromeliads (Appendix b: Figure b.3), but notother aspects of the bromeliad environment (e.g. water chemistry). Low watervolumes can affect bromeliad communities through a multitude of mecha-nisms: (i) low water volumes can select species whose traits allow them tobe tolerant to drought (Dézerald et al., 2015); (ii) low water volumes decreasehabitat size thereby decreasing the size of the community (Dézerald et al., 2014)(iii) low water volumes tend to lose higher trophic levels due to demographicstochasticity (Amundrud and Srivastava, 2015).Overall, community composition differed along the geographic gradientin bromeliad water volume. However, this difference is not driven by thesequential loss of species along this gradient, but instead turnover in speciesidentity. For example, the oligochaete Dero superterrenus was more common inthe drier sites, and Polypedilum chironomids in the wetter sites. Such turnovermay be related to the life history of organisms: oligochaetes reproduce withinbromeliads, and so are resident year round, whereas larval chironomids re-quire terrestrial adults to oviposit eggs, and adults may delay oviposition untilmost bromeliads in the site are water-filled. Previous studies have shown thatthe functional traits of bromeliad invertebrates determine their response towater levels within bromeliads: taxa able to survive low water conditions arecharacterized by small size and deposit or filter feeding whereas taxa able torapidly colonize full bromeliads are characterized by drought-tolerant eggsand short generation times (Dézerald et al., 2015). Since traits determine theresponse of species to altered environmental conditions, selection of speciesthrough their traits can alter not only the size of a community but also itsstructure (Tylianakis and Morris, 2017). More generally, if species differ intheir optimal environment due to their life history and tolerance traits, wewould expect that the arrangement of sites along an environmental gradientwould cause a turnover in species composition due to species sorting mech-28chapter 2anisms or when early successional species are gradually lost (Leibold andChase, 2017; Brendonck et al., 2015). Note that this species turnover occursdespite constant species richness between sites, regardless of water volume.However, within site, species richness increases with bromeliad water volume,as shown in previous studies of bromeliad invertebrates (Jabiol et al., 2009).The biggest advantage of the Markov network approach is that it considersindirect interactions such as intraguild predation, which commonly occurs incontainer habitat food webs (Edgerly et al., 1999; Fincke, 1994). However, thelow number of degrees of freedom in compositional data only allow us toestimate one interaction value per species pair (Harris, 2016). Even thoughMarkov network analyses only calculate symmetrical interaction strengths,we argue that it is suitable for analysing trophic asymmetrical interactionswhen other information is available (Harris, 2016). For example, we can useinformation from the natural history of the system to allow us to interpretthese interactions (Harris, 2016; Freilich et al., 2018). We looked at the typeof interactions that prey and predators participated in, knowing prior to theanalysis which species were predators and which species were prey. We foundthat the top predator Leptagrion andromache dominates negative interactions, asexpected from a generalist predator known to have high per capita impact onits prey, and therefore it is more likely to eat its prey at the local scale (Hammillet al., 2015b). Furthermore, we found that predatory species were more likelyto participate in net negative interactions and prey species were more likelyto participate in net positive interactions, meaning that the Markov Networkapproach has different outcomes for different trophic levels. This, howeverdoes not mean that all predator-prey relationships are necessarily detected vianegative interaction strengths. Another shortcoming of this method is that, ifa species is very rare at the regional scale due to dispersal limitation or habitatfiltering, it may appear to be negatively interacting with many species. This29chapter 2occurs because a species that is rare in the region will not co-occur with themajority of the species. To reduce this problem, we only used species thatwere present in at least two bromeliads and the analysis was done at the sitescale where most bromeliads experience the same climatic conditions.Our Markov analyses indicated that, while overall the mean value of speciesinteractions are similar in sign and strength along the water volume gradient,for three genera there is a consistent pattern of strengthening negative inter-actions in sites with lower water level. This pattern was particularly robustfor tipulids. There are two possible mechanisms for this result. First, speciesthat have only weak interactions with the three genera may become absentat sites with low water volumes, allowing stronger negative interactions toinfluence the mean. If this mechanism was operating, then the pattern shouldweaken with quantile regression. Indeed for two genera it does, but not fortipulids. The second mechanism is that many of the negative interactionsintensify in strength as site water volumes diminish. This mechanism isconsistent with the patterns seen in the tipulids. Tipulids may show strongernegative interactions at low water volumes because they switch from detri-tivores to generalist predators. This mechanism is supported by previousresearch, which found that tipulids in Costa Rican bromeliads supplementdetritivory with opportunistic predation under drought (Amundrud and Sri-vastava, 2016). These researchers hypothesized that decreasing water volumein a bromeliad restricts the space for prey movement, and therefore the tip-ulids can become more effective predators. Other manipulative experimentsconfirm that bromeliad predators are more effective in smaller water volumes(Srivastava, 2006). Generally, from a biomechanical perspective, consumptionrates of predators should depend on habitat dimensionality because it influ-ences the cost of locomotion and the probability of prey escape (Pawar et al.,2012).30chapter 2Tipulids thus appear to be facultative predators, opportunistically switch-ing from detritivory to predation. Facultative predators feed both on plantmatter and animals at the same developmental stage; they represent a caseof non-obligate omnivory (Albajes and Alomar, 2004). Facultative predationmay constitute an adaptive strategy in habitats with high variability of foodsources and allow species to withstand changing environments (Srivastavaet al., 2008; Albajes and Alomar, 2004). Bromeliad habitats are known to behighly variable, with water levels that fluctuate year around (Scarano, 2002).Therefore facultative predation may be a favourable strategy in these systems.Our study adds to the evidence that trophic interactions may change withclimate in bromeliad infauna. Over a much larger geographical gradient,Romero et al. (2016) found that cooler, less seasonal climatic conditions re-sulted in stronger top-down control from predators, based on biomass ratios oftop predators to detritivores as a proxy for interaction strength. In their study,Romero et al. focused on odonate larvae as top predators. Here, we find thattipulid predation intensified in warmer, more seasonal sites. An intriguingtopic for future study is whether seasonal droughts in Rio de Janeiro state,Brazil, shift predation from odonates to tipulids. Our study cannot pull apartother gradients that vary simultaneously with out sites such as latitude or time— since our sites were sampled at different times. To de-confound these effects,future studies can sample communities in the same site through time after aprecipitation event, where bromeliads would start empty and eventually fillup. In addition, future studies can also perform experiments to establish thecausal effect of water volume on interaction strength, not only for the tipulid,but also for the other predators in this system.Our study reinforces the general point that ecological communities canchange along an environmental gradient through three main mechanisms (i)through the turnover of species, (ii) through the change in species interactions,31chapter 2or (iii) through the presence or absence of interactions (Tylianakis and Morris,2017). Here we found the first two mechanisms are contributing to the changesin community composition along a gradient of water within bromeliads.2 .6 conclusionIn this study we provided evidence for changes in community structure alongan environmental gradient through two mechanisms. First we showed thatcommunity composition differed along a gradient of water volumes in macroin-vertebrate communities due to the turnover of some species. Second weshowed that species interactions also differed along this gradient. In our sys-tem, lower water levels likely changed the effectiveness of different predationstrategies reflected in negative species interactions. Broader applications ofthe Markov approach to assess interaction strengths could assist studies thataim to explain differences in functional aspects of ecosystems that cannot beattributed to differences in species composition.32chapter 3Prey body mass and diversity determine food webpersistence.33chapter 33 .1 chapter summaryPredators and prey often differ in body mass. The ratio of predator to preybody mass influences the predator’s functional response (how consumptionvaries with prey density), and therefore the strength and stability of the predator-prey interaction. The persistence of food chains is maximized when preyspecies are neither too big nor too small relative to their predator. Nonetheless,we do not know if (i) food web persistence requires that all predator-preybody mass ratios are intermediate; nor (ii) if this constraint depends on preydiversity. We experimentally quantified the functional response for a singlepredator consuming prey species of different body masses. We used theresultant allometric functional response to parameterize a food web model.We found that predator persistence was maximized when the minimum preysize in the community was intermediate. We also found that as prey diversityincreased the range of values that this intermediate body mass prey couldhave became broader. This last result occurs because of Jensen’s inequality:the average handling time for multiple prey of different sizes is higher thanthe handling time of the average sized prey. Our results demonstrate that preydiversity mediates how differences between predators and prey in body massdetermine food web stability.34chapter 33 .2 introductionClassical food web theory concludes that abstracted complex ecological net-works are unstable (May, 1972). Yet most natural communities are comprisedof complex, interconnected networks where species depend on other speciesfor food and compete with other species for resources (Pascual et al., 2006).To address this discrepancy, researchers have shown that natural food webs,rather than having random network structure as assumed in the classicalapproach, have more weak than strong interaction strengths (Gross et al., 2009;McCann et al., 1998; Neutel et al., 2002), and that this non-random networkstructure actually promotes stability compared to May.The strength of a trophic interaction that occurs via consumption (as op-posed to non-consumptive effects), is determined by the flux of biomass trans-ferred from prey to predator (McCann, 2011). A strong interaction betweena single predator population and single prey population is unstable, lead-ing to the extinction of the species pair (McCann, 2011; Berlow et al., 2004;Holling, 1959). When we model food webs, reducing the flux of biomasstransferred from the prey population to the predator population stabilizes theinteraction. Similarly, when multiple species interact in a food web, one weakinteraction among multiple species interactions can stabilize other interactions.For example, when two prey species share a predator population, the preywith the weaker interaction with the predator can reduce the efficiency ofthe predator in attacking the other prey, stabilizing an otherwise strong anddestabilizing interaction (McCann et al., 1998). Generally, food webs becomestable when they contain more weak interactions. However, the increase instability depends on the size of the food web: small food webs become stable,whereas larger food webs do not (Gross et al., 2009).The stability of food webs depends on the mechanisms that determine in-teraction strengths between species. One important determinant of interaction35chapter 3strengths, at least amongst animals, is the relative body masses of predatorsand prey (Emmerson and Raffaelli, 2004; Kalinkat et al., 2013). For example, anempirical test with crustacean predators showed that the predator-prey bodymass ratio is correlated with the per capita interaction strength (Emmersonand Raffaelli, 2004). The per capita interaction strength between predators andprey depends on the predator’s functional response (the relationship betweenpredation rate and prey density). How the predator’s functional responseis modeled is in turn determined by parameters that depend on the bodymass of both the predator and the prey (Kalinkat et al., 2013). This functionalresponse is composed of the attack rate (a measure of a predators huntingefficiency), the handling time (the amount of time needed to kill, ingest anddigest an individual prey) and the efficiency rate (the fraction of prey biomassconsumed and turned into predator biomass) (McCann, 2011; Berlow et al.,2004; Holling, 1959; Jeschke et al., 2002). This relationship between the ratio ofpredator and prey body masses and interaction strength has been integratedinto population dynamic models, specifically by relating interaction strengthsto the mean body masses of interacting species. Using these models, ecologistshave found that species coexistence is restricted to a narrow range of preybody mass relative to that of their predator — specifically predator-prey bodymass ratios between 10 and 100 for both invertebrate and vertebrate predator-prey pairs (Brose, 2010; Brose et al., 2006; Otto et al., 2007). Coexistence isrestricted to these intermediate body mass ratios because at high body massratios, population dynamics are unstable and at low body mass ratios, thepredators do not consume enough energy to persist in these models.This body of literature has allowed ecologist to understand when pairwisepredator and prey interactions are unstable, and how the presence of otherspecies’ populations may stabilize those interactions. Yet, we still do not knowif predator and prey persistence requires that all the body mass ratios between36chapter 3the predator and its prey species are intermediate in value. Jensen’s inequal-ity suggests that when relationships are not linear, such as the relationshipbetween attack rate and handling time with body mass, then variation inbody size within a prey population (or among prey species consumed by thepredator) can alter the average interaction strength, thereby influencing thedynamics of the system (Bolnick et al., 2011). Given Jensen’s inequality, it isnot clear if the narrow range of intermediate body mass ratios that stabilizefood chains (one consumptive link between trophic levels) are also required tostabilize large food webs (multiple consumptive links between trophic levels).We took a three-pronged approach to answering these questions. First, weempirically determined how body mass ratios between a generalist predatorand various prey species of different size affects the functional response pa-rameters of a natural food web: the aquatic invertebrates that inhabit bromeli-ads. Although previous studies have examined this question by pooling databetween systems, the same pattern may not apply within a system — and it isat this scale that allometric effects of body size on food web persistence is rel-evant (Kalinkat et al., 2013). We then used this empirically-derived allometricfunctional response to simulate a food web with one predator and multipleprey, and confirmed that predator and prey persistence was maximized atintermediate prey body masses when the predator had only one prey. Finally,we tested (i) how differences between prey species in body mass affects thepersistence of the entire food web or subcomponents and (ii) how the numberof prey affects the distribution of prey body masses required for the entirefood web or subcomponents.37chapter 33 .3 methods3 .3 .1 Study systemTank bromeliads accumulate water inside their leaf axils, providing habitatfor communities of aquatic macroinvertebrates (Kitching, 2000). Inside eachbromeliad, these aquatic macroinvertebrates interact to form a food web com-prised of detritivores, filter feeders, intermediate predators and top predators.All the species we used in our experiment were identified to morphospecieslevel. We distinguished the morphospecies based multiple characteristics andnot body mass.3 .3 .2 Predator consumption ratesWe quantified the consumption rate for one damselfly larvae predator andmany of its prey. The top predator Leptagrion andromache (Zygoptera: Odonata,dry mass = 3.31 mg, se = 2.45, n = 29) was fed several densities of each prey(Table c.1). The prey were chosen because they were the most abundantprey in bromeliads. All prey are aquatic insect larvae. We chose Culex sp 1(Culicidae: Diptera, density range = 1- 50, mean dry mass = 0.17 mg, se = 0.04,n = 25), Culex sp 2 (Culicidae: Diptera, 1-20, 0.09 mg, 0.02, 14), Forcipomyia(Ceratopogonidae: Diptera, 1-60, 0.07 mg, 0.01, 5), Dero superterrenus (Naidi-dae: Haplotaxida, 1-60, 0.12 mg, 0.01, 2), Psychodidae (Psychodidae: Diptera,1-30, 0.22 mg, 0.11, 18), Scirtes sp 1 (Scirtidae: Coleoptera, 1-30, 0.33 mg, 0.12,13), Scirtes sp 2 (Scirtidae: Coleoptera, 1-6, 0.43 mg, 0.27, 65), and Trentepohlia(Tipulidae: Diptera, 1-7, 0.29 mg, 0.19, 43). The predators were acclimatizedto laboratory conditions for 72 h or more; the prey, were acclimatized tolaboratory conditions for 6 h. Prior to each trial, the predator was starvedfor 24 h. Kairomones — signaling chemicals — emitted by predators havebeen shown to alter the behavior of the prey, altering functional responses38chapter 3(Hammill et al., 2015a), but because our focus was on body size we did notwant interspecific differences in kairomone sensitivity between prey to affectour estimations of allometric functional responses. Therefore, for each trial,the predator was placed in a 250 mL dark cup with 200 mL of fresh mineralwater and the prey were immediately introduced, preventing the water tobe filled with kairomones before the prey was introduced. We recorded thenumber of prey individuals that were eaten during a two hour period. Forthe Trentepohlia and Scirtes trials, a leaf of approximately 25 cm2 was placedin the experimental containers, as these species move along benthic surfacesrather than swim in the water column. We used five to eight densities perspecies increasing the total density, until feeding rates reached an asymptote(Table c.1). All species-by-density combinations were replicated three timesfor a total of 162 trials.3 .3 .3 Body MassThe average measured dry body mass of each prey species was obtained frompreviously established allometric equations (Median number of individuals =21 and R2 = 0.75-0.94, depending on the species) (Marino, 2015). We measuredall prey used to the nearest mm and calculated the average dry body mass ofthat prey species in mg.3 .3 .4 Allometric functional responseWe fit a general functional response to the consumption data of each preyspecies:Ne =aNq+11+ ahNq+1(3.1)39chapter 3where Ne is the number of prey consumed, N is the starting prey density, ais the attack rate of the predator, h is the handling time of the predator, that is,the time taken to search and consume the prey (Real, 1977). The parameter qdetermines the shape of the functional response, allowing a range of responsesincluding type II (q = 0) and type III (q = 1). We initially fitted a fullmodel with all three parameters (a, h and q). However q was not significantlydifferent from zero, and we thus restricted q = 0 throughout our analyses(type II functional response). Because the prey were not replaced during theexperiment, we used numerical integration to calculate the true proportion ofprey consumed (Hammill et al., 2015a, 2010; Bolker, 2012).We calculated a single allometric functional response that allows the attackrate and handling time to vary with the body mass of the prey and thepredator. Since we used the same species of predator in all experiments, thisallometric functional response need only consider variation in attack rate andhandling time with respect to the mean prey body mass. We fit a simplifiedpower relationship with fixed allometric-scaling exponents (eq. 3.2 and 3.3)following Yodzis and Innes (1992):a = a0m−1i (3.2)h = h0mi (3.3)as well as an allometric relationship (eq.3.4 and 3.5) based on Kalinkat et al.(2013):a = a0mα 3.3mii eδ 3.3mi (3.4)h = h0mϕi mγc (3.5)40chapter 3The allometric relationship between attack rate and body mass based onKalinkat et al. (2013) combines a power function with a Ricker function thatallows the attack rate to have a humped relationship with body mass.Because the body mass of our predator was constant, we used a simplifiedversion of equation 3.5 (eq.3.6):h = h0mϕi (3.6)where mi is the body mass of the prey and mc is the body mass of thepredator. For equation 3.4 mc = 3.3.3 .3 .5 Food web modelWe built a stochastic food web model for a predator that consumes any num-ber of prey with a type II functional response. If the model contained two ormore prey, then the prey competed for resources. We chose a stochastic modelto allow for competitive exclusion, as under a deterministic model, prey wouldcontinue to co-exist even if their body sizes were identical. The stochasticitywas incorporated in the birth terms of the prey and predator equation. Forboth predators and prey this means that variance in lambda was obtained froma Poisson distribution. For the prey, lambda was calculated by multiplying thethe intrinsic growth rate and the abundance of the prey in the previous timestep. For the predator lambda was calculated from the consumption of prey,the predator’s conversion efficiency and the abundance of predators in theprevious time step.41chapter 3The abundance of prey is given by:Ri(t+ 1) = Ri(t)+ θ(m, t)(1− Ri(t) +∑Rj=1 αijRj(t)K(mi))− a(mi)Ri(t)P(t)1+∑Ri=1 a(mi)h(mi)Ri(t)P(t)(3.7)andθ(m, t) ∼ Poisson(λ = r(mi)Ri(t)) (3.8)In eqns. 3.7 and 3.8, Ri(t) is the abundance of prey i at time t. The growthrate of prey i is given by a stochastic Poisson process, where λ is the product ofr(mi), the intrinsic growth rate of prey (e.q. 3.9), and Ri(t), the abundance ofthat prey at time t. The prey experiences logistic growth in where its carryingcapacity K(mi) is determined by its body mass mi (e.q. 3.10).r = rmaxmρi (3.9)K = kkmki (3.10)We explicitly added a term, αij, signifying the intensity of competitionbetween prey i and j, to our equation, as otherwise non-linear functional re-sponses can transform apparent competition into apparent mutualism (Abramset al., 1998). The attack rate, a(mi), as well as the handling time, h(mi), aredetermined by the body mass mi of prey i as given by eqns. 3.4 and 3.6.The intensity of competition αij was dependent on the amount of nicheoverlap, which was given by the body mass of the prey:αij = α(mi, mj) = (1+ (mi −mj)2/2σ2α)−1 (3.11)42chapter 3where mi is the body mass of species i and mj is the body mass of speciesj. σα represents the niche width. The competition coefficient is based ona decaying function between the body masses of species i and j (Johansson,2008). This equation assumes that competition is symmetrical. Evidencesuggests that larger organisms outcompete smaller ones, and that competitionis often asymmetrical (Persson, 1985; Lawton and Hassell, 1981). We evaluatethis scenario in Appendix c using equation 3.12:αij =(11+ (mi −mj + β)/(2σ2α))(1+β22σ2α)(3.12)where β determines the asymmetry of the competition coefficients (VanDen Elzen et al., 2017). When β = 0 competition is symmetric (Johansson,2008), on the other hand when β > 0 the competition is asymmetric, wherelarger individuals outcompete smaller individuals.The predator will saturate not only from consuming prey i but also fromother prey that it also consumes (McCann et al., 2005). The abundance of thepredator is therefore given by:P(t + 1) = P(t) + ϑ(m, t)− CP(t) (3.13)withϑ(m, t) ∼ Poisson(λ =P(t)B∑Ri=1 a(mi)Ri(t)1+∑Ri=1 a(mi)h(mi)Ri(t)P(t))(3.14)where P(t) is the abundance of the predator at time t. The growth ofthe predator is given by a stochastic Poisson process, where λ is equal tothe amount of prey (all species) consumed at time t. The caloric value of acaptured prey individual is assumed to be constant across prey species, andis signified by B. The per capita mortality rate of the predator is C.43chapter 33 .3 .6 Simulations based on all possible combinationsWe ran the simulation for prey body masses starting at 0.05 mg and increasingat 0.01mg intervals until reaching 1 mg.For the one and two prey scenario, we ran every combination of preybody masses 10 times. The starting abundances were 10 individuals for eachprey and 7 individuals for the predator. All simulations were run for 500generations. As previously mentioned, the attack rate, handling time, intrinsicgrowth rate of the prey and the carrying capacity were all determined by thebody mass of the prey (Table 3.1, Figure c.1).We used a random Poisson process to simulate stochastic dynamics (e.q.3.8 and 3.13), and one property of the Poisson distribution is that the varianceis equal to the mean. Therefore, any increase in λ increases the possiblerange of values that the Poisson process can take, resulting in large spikesin population size as λ increases. To stabilize the model and reduce theamplitude of the spikes in population size, we decreased the maximum valueof the attack rate and handling time but kept the shape of the relationshipconstant for all parameter combinations (Figure c.1).3 .3 .7 Simulations based on sampled parameter spaceScenarios with three or more prey are computationally difficult, as the po-tential combinations of prey body masses increases exponentially with thenumber of prey. Fortunately, a recently proposed Monte Carlo strategy forsampling parameter space helps to make this tractable (Leigh and Bryant,2015). In this sampling process, we begin by defining an binary outcomeof interest as R specific (for example, whether the predator persisted). Foreach outcome R we followed the following five recursive steps:S1: If at parameter θ, then propose a move to θ′. A step size drawn from a44chapter 3random normal distribution centered at zero, truncated between a minimumand maximum value. The first step in the MCMC is to propose a new set ofparameters θ′ given an initial value of θ. For example, if the initial body massof three species was a vector (0.1, 0.3, 0.4), we might drew a random valuefrom a normal distribution (say 0.1) and add it to each body mass. This newvector (0.2, 0.4, 0.5) would be θ′.S2: Run the simulation using θ′ and assess R The second step of theMCMC is to run the simulation using the new parameters and to determinewhether R. occurred (e.g. whether the predator persisted or not).S3: IfRoccurs, then accept θ′, otherwise stay at θ. In this third step, if R occurred,we take θ′ as the new starting value, otherwise we go back to the initial valuein step 1. This ensures that as the number of iterations increases, the MCMCconverges towards the body masses (θ) where the predator is more likely topersist.S4: Record θ, θ′ and R as well as the final abundance of all species in thecommunity at the end of the simulationS5: Return to S1This sampling processes allowed us to sample through the space of θ withouthaving to run the simulation for every combination of prey body masses. Inall cases, the only parameters that were sampled were the body masses of theprey. Therefore they could be sampled from the same distribution.The outcomes R that we required were that (i) all species survived, (ii)only prey survived and (iii) at least one prey and the predator survived.We ran the sampling process for 10,000 steps for one and two prey and for20,000 steps for three or more prey. For the first 10,000 steps,we used a step45chapter 3size of 0.3, and then increased this to 0.5 for the next 10,000 steps. Parameterspace was well sampled with the Monte Carlo sampling strategy (Figure c.2).Table 3 .1 : The parameter values used for the simulations of the food weband their relationship with the body mass of the prey. Assigning k = −1implies that K ∗mi is constant.Parameter Description Body mass scaling Estimatesa Attack efficiency ofthe predator a = a0mα 3.3mii eδ 3.3mia0 = 0.0005,α = 1.30, δ = 0.071h Handling time ofthe predator h = h0mϕi h0 = 5, ϕ = 2.41K Carrying capacityof the prey K = kkmki k0 = 6, k = −1rMaximumpopulation growthrate of the preyr = rmaxmρirmax = 0.05,ρ = −0.20BCaloric value of acapture individualof prey species i(this is assumed tobe constant acrossspecies)Constant 0.2C Predator death rate Constant 0.4σ Niche width Constant 0.025βDegree ofasymmetry incompetitionfunctionConstant0 (0.5 in Appendixc)To examine the impact of Jensen’s inequality on food web dynamics, wecompared parameters of the functional response calculated as the mean forall species versus based on the mean mass of the species. Specifically, forevery run where all the prey species and the predator persisted, we calculatedthe attack rate and the handling time for each prey species and averaged thesevalues over species to obtain a(m) and h(m). Then we averaged the body massof all prey species before calculating the attack rate and the handling time to46chapter 3obtain a(m) and h(m). Due to the non-linearity and the upward curvature ofthe attack rate and the handling time with body mass (Figure c.1), we wouldexpect that a(m) = a(m) and h(m) = h(m) only when prey diversity is one.As diversity increases we expect that a(m) > a(m) and h(m) > h(m) (Figurec.5).All analyses were performed using R (Team, 2018) and the bbmle package(Bolker and Team, 2017).3 .4 results3 .4 .1 Allometric feeding ratesWe compared two potential models that have often been used in the literature,describing the relationship between feeding rate and prey body mass: a powerfunction model and an allometric model (Kalinkat et al., 2013). In the powerfunction model, the attack rate decreases proportionally to the negative powerof body mass and the handling time increases linearly with body mass. In theallometric model, the attack rate decreases exponentially with body mass andthe handling time increases in a power function (Figure c.1). We fit each modelto all prey simultaneously, using the mean body mass of each species as a fixedeffects (Figure 3.1, Table 3.2). Of these two models, the best fit model was theallometric model (Allometric model BIC = 621.74, df = 5, Power model BIC =732.38, df = 3). We therefore use the allometric model for our simulations.3 .4 .2 Simulation:We found that when only one prey species was available for the predatorand when this prey species was very small, this one predator-one prey foodchain did not persist. When prey body masses were small, the attack rate47chapter 3F igure 3 .1 : Fitted type II functional response for all prey separated betweensmall, medium and large prey.Table 3 .2 : Estimated parameter values for the relationship between attackrate, handling time and prey body mass.Parameter Estimate Std error P valuea = a0mα 3.3mii eδ 3.3mi a0 0.012 0.008 0.121α 1.30 0.6113 0.033δ 0.071 0.022 0.001h = h0mϕi h0 19.837 0.002 2x10−16ϕ 2.418 0.083 2x10−16of predators on prey is so high that the predator consumed the prey quickly,driving the prey species extinct, which consequently led to the collapse ofthe predator population (Figure 3.2a). On the other hand, when the one preywas large, the handling time was so long that the predator could not meet48chapter 3its energetic demands (Figure 3.2c). Only at intermediate body masses of theprey were both prey and predator able to persist through time.Similarly, when two prey were present, the predator required at least oneprey to have an intermediate body mass in order for the predator to persist(Figure 3.3a). Surprisingly, the body mass of the second prey could be almostany mass except for very small, including a prey body mass that was so largethat, on its own, the prey could not sustain the predator. When the bodymass of the second prey was small, only the predator and the larger of thetwo small prey persisted, as the smallest prey was driven to extinction dueto the high attack rate of the predator (Figure 3.3c). By contrast, when bothprey species were very small, the whole community went extinct, and whenboth prey species were very large, the prey persisted but the predator wentextinct (Figure 3.3b). We only observed competitive exclusion in the presenceof the predator. When the predator went extinct, competition between preyonly generated differences in their abundances (Figure c.3, and c.4).In food webs with more than two prey species, predator persistence showsa unimodal relationship with prey diversity, increasing with modest numbersof prey species but decreasing with larger numbers of prey species (Figure3.4a). Within this overall effect of prey diversity, different effects of prey bodymass can be discerned. At low prey diversity, predator persistence requiresthe prey communities have neither small or large species (Figure 3.4b, c). Thatis, the prey species are the ‘optimal’ intermediate mass. At high prey diversity,predator persistence increases when large prey are added to the community(Figure 3.4c). Regardless of prey diversity, predator persistence decreasedas the proportion of the community with small prey increased (Figure 3.4b).By contrast, the proportion of prey species that strongly competed had onlymodest effects on predator persistence (Figure c.6). Although these results49chapter 3F igure 3 .2 : Time series for the abundance of the predator and one prey atthree different prey body masses. Predator and prey persistence is maximizedat intermediate prey body masses. a) When the prey is small (0.07), the attackrate of the predator is very high and the predator consumes all the prey,driving the prey and itself extinct. b) When the prey has intermediate bodymass (0.12) both predator and prey can persist. c) When the prey has highbody mass (0.25) the handling time is too long and the predator is limited bythe amount of energy it can obtain.pertain to the initial prey diversity, the patterns are unchanged even when weuse the final prey diversity as the determinant (Figure c.7).For a given diversity of prey, we found that predator persistence requires aminimum body mass for at least one prey species. As prey diversity increases,this minimum body mass first takes a wider range of values, but at highprey diversity again is constrained to a narrow range of values (Figure 3.5a).The broadening of the minimum body mass that allows all species to persistis due to the increasing importance of Jensen’s inequality as we increase50chapter 3F igure 3 .3 : Predator persistence is constrained only by the body mass of oneprey, where one prey must have an intermediate body mass but the secondprey can be of any mass. On the x axis is the body mass of prey 1, and on they axis is the body mass of prey 2. Panels a-c show the proportion of the runswith a certain outcome, where yellow represents all the runs and purple noneof the runs: a) both prey species and the predator persists; b) the predator goesextinct and only the two prey persist;. c) one prey and the predator persistand one prey goes extinct (in every case the smaller prey). These scenarios aredetailed in the food web modules: the grey circles represent species that goextinct and the black circles represent species that persist.prey diversity. When we plotted a(m) against a(m) and h(m) against h(m)(Figure 3.5b and c), we find that for both parameters the effective attack rateor handling time initially increases with diversity and then decreases. Allscenarios, when prey diversity is greater than one, fall above the 1:1 line.Therefore initially, as prey diversity increases, the attack rate and the handlingtime increase allowing then predator to persist at larger body masses (Figure3.5a). As diversity continues to increase, the effective attack rate decreasesmore than the effective handling time, reducing the body masses of the preywhere the predator can persist.51chapter 33 .5 discussionIn this study, we tested: (i) how differences in body mass between prey speciesaffect the stability of the entire food web or its subcomponents; and (ii) howthe diversity of prey determines the distribution of prey body masses neededfor food web persistence. To answer these questions, we first experimentallydetermined how body mass affected the parameters of functional responseswithin a single food web. We then used these parameters to simulate afood web consisting of a generalist predator and multiple prey; we kept thebody mass of the predator constant and we varied the diversity and bodymass distribution of the prey. We found that when the predator had oneprey, predator persistence required the prey to be of intermediate body mass.As prey diversity increased, the range of prey body masses that allowed forpredator persistence became first broader and then narrower. We also foundthat prey diversity had a unimodal relationship with predator persistence. Atlow prey diversity, increasing diversity increased predator persistence, whereas,at high prey diversity, increasing diversity decreased predator persistence. Fur-thermore, the effects of prey body mass on predator persistence reversedbetween low and high prey diversity conditions. We now consider each ofthese main results.We found that the effect of prey body mass on the functional response ofdamselfly larvae in bromeliads largely conformed to the general form of theallometric functional response found by Kalinkat et al. (2013). This conver-gence in results suggests a generality to these allometric functional responses,despite differences in scale (our analysis was within a food web, Kalinkatet al.’s was between food webs) and hunting mode (our predator was sit-and-wait, whereas multiple hunting modes were considered by Kalinkat et al.).While this points to a qualitative generality in the effect of body mass onfunctional responses, we caution against any quantitative extension of the52chapter 3parameters to other systems. Our estimates of the predator’s functional re-sponse may underestimate the attack rate for other types of predators or othertypes of prey. The effectiveness of a predator depends not only on prey bodymass, but also predator hunting mode, prey defensive behaviour or traits,the relative preference of the predator for prey, prey refuges and the identityof other species present in the community (Jonsson et al., 2018). Predatorhunting mode (such as sit-and-wait, sit-and-pursue or active predators) canaffect the activity of the prey and therefore the prey mortality. Sit-and-waitpredators have been found to cover small distances and kill fewer prey thaneither sit-and-pursue and active predators (Miller et al., 2014). Therefore, ourestimates of the predator’s functional response may underestimate the attackrate for other types of hunting strategies. In natural systems, even whena predator is generalist, it may only rely on a handful of species due todifferences in prey vulnerability and habitat complexity (Weber et al., 2010).Furthermore, any variation in the biomass of prey species and conspecificdensity can result in preferences of predators for particular prey sizes (Costa-Pereira et al., 2018). Finally, as we only allowed the predator to eat onetype of prey at a time, our estimates of the functional response may not berepresentative of the predator’s effectiveness in real bromeliads, which arecomplex habitats (Srivastava, 2006).Our first main result from the model was that predator persistence in-creased when its sole prey had an intermediate body mass. As in other studies(Brose et al., 2006; Otto et al., 2007), this occurred because of the opposingeffects of body mass on two parameters of the predator’s functional response.If the prey had a very small body mass, then the predator had a high attackrate and consumed all prey individuals, driving the prey and itself extinct.If the prey had a large body mass, then the predator had a long handlingtime and it could not offset its mortality via reproduction and went extinct.53chapter 3Even when the food web contained multiple prey, only the body mass of thesmallest prey largely constrained predator persistence; the body mass of theother prey species could be either large, intermediate or small. This resultin consistent with the case of asymmetrical competition between the prey, aslong as the prey can coexist (Appendix c). These results extend previousstudies of the effects of prey body mass on food web stability, which eitherconsidered only a single prey species (Otto et al., 2007) or multiple prey speciesbut with a narrow range of body masses (Brose et al., 2006). These studiesfound that intermediate predator-prey body mass ratios maximize food webpersistence, similar to our single prey results. Our novel result is that witha wide range of prey body masses, persistence depends on the smallest preybeing of intermediate body size.Even though the body mass of only one prey species constrained predatorpersistence, this optimal body mass may still change with increasing diversity.Indeed, we found that increasing prey diversity broadens and then narrowsthe range of body masses that promote predator persistence. Prey with bodymasses too high to allow predator persistence on their own, could, as part ofa diverse prey community, now allow the predator to persist. The mechanismhere relates to Jensen’s inequality: since the attack rate and the handling timeare non-linear with respect to prey body mass, variation around the meanbody mass (i.e. when diversity increases) increases the effective attack rateand handling time. Therefore the predator experiences a much higher attackrate and handling time than expected from the mean body mass of all prey,allowing the predator to persist when otherwise it would not (Bolnick et al.,2011). Intermediate prey diversity effectively relaxes the bottom-up energeticconstraint imposed by having only one prey, allowing the attack rate and thehandling time to be higher and resulting in an overall high total intake forthe predator. Gibert and DeLong (2017) found a similar pattern, where the54chapter 3predator’s total intake is maximized at low diversity when prey is optimallymatched in phenotype (e.g. body mass) to the predator and at higher diversitywhen the prey is poorly matched in phenotype to the predator.Our results also are consistent with previous observations that weak inter-actions can stabilize a system with strong interactions (McCann et al., 1998).In our study, the differential in body mass between predators and prey deter-mined interaction strength: prey species with a small body mass had stronginteractions with the predator, and prey species with a large body mass hadweak interactions with the predator. When a predator had a strong interactionwith one prey, leading to the extinction of both the predator and the prey,adding a larger prey species would often allow the predator to persist. Eventhough adding a large prey would stabilize many strong interactions betweena predator a small prey, as shown by McCann et al. (1998), we found that somestrong interactions between a predator and a very small prey could not bestabilized even in diverse communities (e.g. Figure 3.3).So far, we have shown that predator persistence is constrained by the pres-ence of at least one prey of intermediate body mass. This result helps explainwhy, at low prey diversity, adding more prey species can increase persistenceof the predator: increasing diversity increased the probability that at leastone prey has the optimal body mass. This sampling mechanism is consistentwith models that show only intermediate body mass ratios between predatorsand prey can result in a positive relationship between food web stability andprey diversity (Brose et al., 2006). However, our analysis not only allows us toconfirm this result, but also to test the interaction between body mass ratiosand diversity. We discovered that prey diversity had a unimodal relationshipwith predator persistence, which is mediated by the body mass distributionof the prey. The increasing portion of this relationship, at low prey diversity,reflects sampling of an optimal body mass prey. At high prey diversity, adding55chapter 3prey species generally decreased predator persistence but this depends on thebody mass distribution of added prey. Specifically, adding large prey speciesincreased predator persistence whereas adding intermediate and small preyspecies decreased predator persistence. As before, the mechanism here is aweakening in interaction strength as prey body size increases relative to thatof their predator, allowing for stabilization of the whole food web (McCannet al., 1998). Consequently, we found that the food webs with the highestprey diversity at the end of the simulation were comprised of many large preyspecies. This result, however, is different when prey compete asymmetrically.In this scenario, higher diversity only reduces predator persistence. Addingsmall prey species has the same effect as in the symmetrical competition sce-nario, but adding large prey species now decreases predator persistence sincelarge species drive intermediate species extinct due to competition (Appendixc). The implication of the symmetrical competition results is that we wouldexpect the largest food webs in nature to have large-sized prey relative to theirpredators. Some food webs have shown a pattern where slow energy channels,which have weaker interactions, are more diverse than fast energy channels(Rooney and McCann, 2012). While some invoked explanations of this patternsuggest that is due to higher habitat complexity, another explanation can bethat slow channels with weaker interactions are more stable. Our resultswould support the latter explanation.Taken together, these results suggest that: (i) Only a few prey species, notall, constrained predator persistence; (ii) increased prey diversity can lead toincreased predator stability if the additional prey contain at least one speciesof optimal body mass (low prey diversity) or enough large prey to weakeninteractions with the predator (high diversity). That is, not all diversity isequal in terms of food web stability: the body mass of those gained or lostspecies has major consequences for food webs stability. This conclusion but-56chapter 3tresses earlier findings that food web stability is more influenced by variationin the body mass ratios of predators and prey than by prey diversity alone(Brose et al., 2006); (iii) The food webs we see in nature are only the observedsurviving configurations. We expect that larger food webs will be skewedtowards having larger prey species per predator when competition betweenprey is symmetrical.57chapter 3F igure 3 .4 : Prey diversity has a unimodal relationship with predatorpersistence. a) Increasing diversity initially increases the proportion of runswhere the predator and at least one prey survived. At higher diversity thetrend reverses. b) As the proportion of small prey in the community increases,the proportion of runs where the predator persists decreases. The unimodalrelationship is maintained regardless of the proportion of small prey in thecommunity. c) At low diversity, a high proportion of large species in thecommunity reduces the proportion of runs where the predator persists. Athigh diversity, the trend reverses and predator persistence is maximized whencommunities have a high proportion of large prey species.58chapter 3F igure 3 .5 : Food web persistence depends on the number of prey and thebody mass of the smallest prey species. Circles of different colours representfood webs that successfully persisted. a) Some combinations of prey numberand smallest body mass did not lead to food web persistence, due either toextinction of at least one prey (shaded red area) or predator extinction (shadedblue area). The food web modules illustrate these scenarios of food webpersistence and extinction; the dashed circles represent species that may, butdo not necessarily go extinct, the grey circles represent species that go extinctand the black circles represent species that persist. b) Jensen’s inequality isdemonstrated by the mean attack rate, a(m), being higher than the attack rateon a species with mean mass a(m), but this effect is strong at low diversity andweak at high diversity given the deviation from the black 1:1 line. As diversityincreases, both a(m) and a(m) decrease. c) Jensen’s inequality has a greaterimpact on handling time, as the mean handling time, h(m), is higher than thehandling time on a species with mean mass, h(m). The deviation from the 1:1line is particularly pronounced at low prey diversity, and approaching the 1:1line at high diversity.59chapter 4Empirically determined differences between apredator and its prey allow increased persistence ina metacommunity60chapter 44 .1 chapter summaryTrophic metacommunity theory has pushed the boundaries of our understand-ing of spatial dynamics in food webs, yet empirical tests of theory have laggedbehind. A key reason for this mismatch is that most empirical studies ofmetacommunities do not parameterize models. To bridge this gap, we esti-mated the dispersal rate and kernel of a predator-prey pair using genotyping-by-sequencing (GBS) and a Bayesian approach. We found that the prey dis-persed up to 25 km while the predator dispersed up to 200 m. We alsomeasured the interaction strength between these two species experimentally(from a previous study). Using our estimates of dispersal and feeding rates,we parameterized a metacommunity model and found that differences indispersal rates were sufficient to generate differences in occupancy of ourmodelled landscape, without requiring variation in the abiotic niche. Moresurprisingly, the observed asymmetry in dispersal was more likely to generatedifferences in occupancy than the reverse asymmetry (higher predator thanprey dispersal) generated.61chapter 44 .2 introductionFood webs are inherently spatial, and species within a food web often livein different parts of a landscape. The movement of organisms via dispersalis critical to determining food web structure at small and large scales (Ama-rasekare, 2008). A food web metacommunity then, is a set of connected foodwebs which inhabit patches linked by dispersal (Leibold et al., 2004). Trophicmetacommunity theory has provided valuable insight into the stability andpersistence of food webs (Holt and Hoopes, 2005). For example, trophicmetacommunity theory has provided us with tools to understand the per-sistence of otherwise unstable predator-prey dynamics in a landscape. Specif-ically, the movement of individuals can create negative density dependencethat stabilizes multi-species communities, allowing recovery when popula-tions reach low abundances (Holt, 1984, 1985; Huxel and McCann, 1998; Briggsand Hoopes, 2004). Trophic metacommunity theory has also allowed us tounderstand the emergence of complexity and higher trophic levels in foodwebs (Pillai et al., 2011). However, until recently, most metacommunity studieshave relied on the assumption that all species within a food web disperseequally. In natural communities, this assumption is unlikely to be met (Guz-man et al., 2019). When species at different trophic levels differ in dispersal,classic patterns in metacommunity ecology, such as the humped relationshipbetween diversity and dispersal rate, may be altered (Haegeman and Loreau,2014). More broadly, differences in dispersal ability — and the directionalityof the difference — between any two interacting species are expected to havediverging consequences on metacommunity dynamics, (Guzman et al., 2019).For example, when prey populations disperse less than predators, the preydensity will vary in the landscape. On the other hand, when the predatordisperses less than the prey, the prey is able to persist in patches free ofpredators (McCauley et al., 1993; Pedersen and Guichard, 2016).62chapter 4While both theoretical and empirical research on metacommunity ecol-ogy has pushed the field in remarkable directions, research that integratesboth at once has lagged behind. Specifically, the parameters often used inmetacommunity models are rarely quantified empirically. The majority ofempirical metacommunity studies have instead compared patterns observedin real communities with potential patterns originating from metacommunitymodels. For example, variation partitioning analysis (Logue et al., 2011) es-timates the amount of community variation explained by environmental orspatial components, and then these estimates are interpreted as signatures of aparticular metacommunity dynamic (Cottenie, 2005). This approach has beenextended to study differences between generalist and specialist species (Panditet al., 2009), species of different body sizes and dispersal modes (Bie et al.,2012), and even among different taxonomic groups along an isolation gradient(Driscoll and Lindenmayer, 2009). In parallel, other empirical studies havealso considered the effects of dispersal mode (Jones et al., 2015) or constraintsof spatial drivers (Grainger et al., 2017) on metacommunity distribution anddiversity, yet these studies were not designed to estimate the parameters thatare used in metacommunity theory (e.g., dispersal rates). Studies that com-pare observed and predicted patterns, without parametrizing models, mayfall into the trap of assuming that a particular process underlies the patternwhen in fact the pattern could be generated in multiple ways (Gilbert andBennett, 2010). The main reasons we find this mismatch between theoreticaland empirical trophic metacommunities is: (i) the lack of clear and concisepredictions of trophic metacommunity theory (Guzman et al., 2019) and, (ii)the challenge of quantifying dispersal kernels - especially as we expect eachspecies to have a unique dispersal kernel (Borthagaray et al., 2015).To integrate trophic metacommunity theory with empirical estimates, weused a model system for metacommunity research (Srivastava et al., 2004),63chapter 4which consists of multiple interacting macro-invertebrates that inhabit theaquatic habitat created by the leaves of bromeliads. From this system, we esti-mated (i) the dispersal rate and kernel and (ii) the feeding rates of a predator-prey pair (the top predator Leptagrion andromache (Zygoptera: Odonata) andone of its prey Trentepohlia sp. (Tipulidae: Diptera)). To estimate the dispersalkernel, we sampled individuals from multiple populations at different spatialdistances and then used population genetics to estimate dispersal betweenthese populations. Specifically, we used a genotyping-by-sequencing approach(Elshire et al., 2011) with a Bayesian method that uses individual genotypes toestimate rates of dispersal between populations (Wilson and Rannala, 2003).Genotyping by sequencing (GBS) does not rely on any previous knowledgeof a species genome (for example to develop primers) and does not requirea reference genome. Instead, GBS uses restriction enzymes to digest thegenome at multiple sites and PCR to introduce adapters used for Illuminasequencing. The result is short sequences that can be aligned to identifyindividual genotypes. Once the genotypes have been identified, Bayesiananalysis can extract information about recent dispersal from disequilibriumat individual genotypes of migrants.Using these estimates of dispersal, we asked: (i) whether the predator andthe prey were dispersal limited by the same geographical barriers at largespatial scales; (ii) whether the dispersal rate and kernel were the same for thepredator and the prey; (iii) whether a simple metacommunity model couldpredict differences in space use based on the estimated differences in dispersalparameters; and (iv) whether the observed dispersal kernels led to greaterpersistence or occupancy of either the predator or the prey.64chapter 44 .3 methods4 .3 .1 Study systemTank bromeliads accumulate water and detritus inside their leaf axils, pro-viding habitat for communities of aquatic macroinvertebrates (Kitching, 2000).Inside each bromeliad, these aquatic macroinvertebrates interact to form afood web comprised of detritivores, filter feeders, intermediate predators andtop predators. These communities have been identified as useful study sys-tems for metacommunity ecology (Srivastava et al., 2004). Each bromeliadis perceived as a patch of habitat and overall bromeliads form a naturallypatchy landscape for the food webs of macroinvertebrates. Previous studieson bromeliad metacommunities have shown that ten isolated bromeliads areinsufficient habitat to sustain the metacommunity through time (LeCraw et al.,2014).4 .3 .2 SamplingThe study area was located in the sand dunes of coastal Brazil (Figure 1), inthe states of Rio de Janeiro and São Paulo. We sampled ten sites, seven ofwhich were within the Jurubatiba National Park in Rio de Janeiro state, Brazil.The other three sites were located in the sand dunes of Arraial do Cabo (Riode Janeiro), Marica (Rio de Janeiro), and Ilha Bela (Sao Paulo). Our sites wereselected so that the distance between adjacent sites increased logarithmically(Figure 4.1). Sampling was done between February and May of 2015. In eachof our sites we collected 10-20 individual larvae of two species in order to haveenough replication of genetic variation within each site and make meaningfulcomparisons between sites; the top predator Leptagrion andromache (Zygoptera:Odonata) and one of its prey Trentepohlia sp. (Tipulidae: Diptera).65chapter 4F igure 4 .1 : Sites were located in the sand dunes of coastal Brazil, in thestates of Rio de Janeiro and São Paulo. We sampled the sites such that siteswere increasingly further apart. Sites one to four were within 1 km, while sitesone to ten were 430 km apart.66chapter 44 .3 .3 DNA extractionsWe extracted DNA from the odonate predator larvae using Qiagen DNA bloodand tissue kit (Qiagen, Inc., Valencia, California, USA) and concentrated theDNA using Agencourt AMPure XP beads. We extracted the tipulid prey larvaeusing Qiagen DNA blood and tissue kit and the OmniPrepTM kit from G-Biosciences (St. Louis, MO) for the smaller individuals (modified protocolsare in Appendix d).4 .3 .4 Genotyping - by - sequencing (GBS)Extracted DNA of the odonate predator was sent to the Cornell Institute forGenomic Diversity (Ithaca, NY, USA) and extracted DNA of the tipulid preywas sent to University of Wisconsin-Madison Biotechnology centre since theCornell Institute for Genomic Diversity lost its patent throughout our study.In both cases, the extracted DNA was processed with GBS. GBS (Elshire et al.,2011) is a simple technique for constructing reduced representation librariesfor the Illumina sequencing platform. In GBS, DNA from each individualis digested using a restriction enzyme (in this case PstI (CTGCAG)). Thefragmented DNA is then ligated to an adaptor that matches long PCR primers.During PCR, these long primers add a length of sequence to the fragments,that bind to the Illumina flow cell.4 .3 .5 SNP callingBecause neither of our species has a reference genome, raw sequences wereconverted into individual genotypes using a UNEAK pipeline (Lu et al., 2013).The UNEAK pipeline clusters identical reads into tags. All unique tags aremerged and their counts stored. Then pairwise alignments of tags are per-formed and tags with 1-bp mismatch are considered candidate SNPs. Of67chapter 4those candidate SNPs, only reciprocal tags, which involve only two tags with1-bp mismatch are more likely to be true SNPs than those which belong tocomplicated networks of tags. Rare tags are considered to be sequencingerrors, so tags that have relative counts of less than 0.03 are removed. Afteridentifying the SNPs, counts of each tag (or allele) are output for each locusand each individual. Within the pipeline we excluded tags that were presentless than 15 times, and set the minimum minor allele frequency to 5% andthe minimum proportion of individuals covered by at least one tag to 10%(Stansell et al., 2018; Lu et al., 2013; Michalski et al., 2017).After the UNEAK pipeline output the SNPs for each individual, we filteredthe SNPs so that the maximum number of times a tag was present was 2000,heterozygosity at each locus was less than 0.5, and loci had at most 40%missing data. For this filtering we used the Tassel 5.0 software (Bradbury et al.,2007). The resulting data consisted of 4161 SNPs for the odonate predator and1675 SNPs for the tipulid prey.4 .3 .6 Historical ancestryWe estimated the genetic distance between each individual pair using the 1 -identity-by-state metric (1 - IBS), which is the probability that alleles drawn atrandom from two individuals pairs at the same locus are the same (Bradburyet al., 2007). After finding that some individuals were very similar and otherindividuals were very dissimilar (Figure d.1), we ran an admixture analysisto identify major groups of individuals (Alexander et al., 2009). We ran theadmixture analysis five times with a different random seed and performed across validation procedure to find the best number of clusters (from one tofive). We chose the number of clusters that had the lowest cross-validationvalue, yielding two clusters for both the odonate predator and the tipulid prey.68chapter 4We separated the individuals for each of these clusters and then re-ran theadmixture analysis for each cluster for both species.4 .3 .7 Recent dispersalTo estimate recent rates of dispersal (within the last few generations) we usedthe software Bayesass (Wilson and Rannala, 2003). Bayesass is a Bayesianmethod that uses individual genotypes to estimate rates of recent dispersalusing transient disequilibrium observed in individuals that migrated. Thismethod does not assume that genotypes are at Hardy-Weinberg equilibrium.We ran Bayesass for 107 iterations, discarding the first 106 iterations as burn-in, and sampled every 1000 iterations. We adjusted the mixing parameters forthe migration rates to 0.3, allele frequencies to 0.6 and inbreeding coefficientsto 0.1 for the odonate and 0.2 for the tipulid such that the acceptance rate ofthese parameters was within the recommended range by the software. Werepeated this process four times for each species, assessed the convergence ofthe MCMC and pooled the outcomes of the four chains.4 .3 .8 Dispersal kernelWe inferred a dispersal kernel for both the odonate predator and the tipulidprey by regressing the estimated dispersal rates between each population(from Bayesass) with the distance between each population. We filtered thedistance to only include sites one to seven, because only two individuals fromsite eight were present in the major clade of the odonate and the tipulid.We fit: (i) a GLM with a Gamma family and a log link; (ii) an exponentialdecay function; and (iii) model the distance between patches as a continuousfunction of their physical distance, x, but treated sites within a patch asspatially identical (x=0). We also used a hurdle function, which allowed for a69chapter 4probability, D0, that an individual would stay in the same site, coupled withan exponential distribution among those individuals that leave a site:D(x) =if x = 0 : D0if x > 0 : D1e−bx (4.1)4 .3 .9 Feeding trialsWe fit a type II functional response (eq. 4.2) to a consumption experiment ofthe odonate predator with the tipulid prey. This experiment was previouslyreported in Guzman Srivastava (In review) and the data is publicly available(Guzman and Srivastava, 2018). We fit a type II functional response becausethe parameters that determined a type III functional response were not signif-icantly different from zero.Ne =aN1+ ahN(4.2)Ne is the number of prey consumed, N is the starting prey density, a is theattack rate of the predator, h is the handling time of the predator, that is, thetime taken to search and consume the prey (Real, 1977).4 .3 .10 Trophic metacommunity modelUsing the dispersal and consumption parameters, we built a simple metacom-munity model, based on a Rosenzweig-MacArthur (Rosenzweig and MacArthur,70chapter 41963) model with a type II functional response in a 2-dimensional grid with25 patches. The abundance of the prey N at time t+ 1 in patch j was given by:Nt+1,j = Nt,j + rNt,j(1−Nt,jK)− aNt,jPt,j1+ ahNt,j+∑i 6=jDN(x)Nt,i − (1− DN0)Nt,j(4.3)where Nt,j is the abundance of the prey at time t in patch j, r is the intrinsicgrowth rate of the prey, K is the carrying capacity of the prey, a is the attackrate of the predator and h is the handling time of the predator. DN(x) is thedispersal rate of the prey as a function of the distance x between the patchesj and i and Nt,i is the abundance of the prey at time t in patch i. DN0 is theproportion of individuals of the prey that stay in patch j. The abundance ofthe predator at time t + 1 in patch j was given by:Pt+1,j = Pt,j + rpPt,j(1−Pt,jKp) +Pt,jBaNt,j1+ ahNt,j−CPt,j +∑i 6=jDP(x)Pt,i − (1−DP0)Pt,j(4.4)where Pt,j is the abundance of the predator at time t in patch j. Sincethe odonate in this system is top predator that could persist through theconsumption other prey species, we included a growth term rP and carryingcapacity term KP which allow the predator to persist without the tipulid prey.The caloric value of a captured prey individual is signified by B. The percapita mortality rate of the predator is C. DP(x) is the dispersal rate of thepredator as a function of the distance x between the patches j and i andPt,i is the abundance of the prey at time t in patch i. DP0 is the proportionof individuals of the predator that stay in patch j. DP(x) and DN(x) weredetermined using equation 4.1. DN(x) and DN0 are parameterized based onthe tipulid’s dispersal kernel, DP(x) and DP0 are parameterized based on the71chapter 4odonate’s dispersal kernel. Because the odonate has a generation time of 9months while the tipulid larvae has a generation time of 2 months, and thedispersal rates were estimated per generation, we divided the dispersal rateby the generation time to obtain a dispersal rate per day. The attack rate andthe handling time were parameterized based on the consumption data (Table4.1).We ran the simulation model over several combination of parameters ofB, C, r, K, rP and KP and found combinations of parameters that yieldedpersistence -non-zero abundance after 2000 time steps- for both the predatorand the prey. We evaluated the occupancy of the predator and the prey, wherethey differed in occupancy as long as the prey was present in at least one patchwithout the predator. We also ran the simulation (across the same combinationof parameter space) by interchanging the dispersal parameters of the predatorand the prey.The dispersal kernel was fitted using the package nlsTools (Baty et al., 2015)and all the simulations were run with the programming language R (Team,2018). This research was enabled in part by support provided by WestGrid(www.westgrid.ca) and Compute Canada (www.computecanada.ca).4 .4 results4 .4 .1 Historical ancestryEach species was clearly split into two distinct clusters (Figure d.1) both inthe identity-by-state distance and in an admixture analysis. The admixtureanalysis showed that the cross validation error was minimized between twoand five clusters depending on the run. However, the log likelihoods of thesecases differed by less than four. Therefore, we chose the simplest model forboth species (Figure d.2, d.3): two clusters for the odonate predator and two72chapter 4Table 4 .1 : The parameter values used for the simulations of themetacommunity model.Parameter Description Empiricalestimates Theoretical valuesa Attack efficiency of thepredator 0.170h Handling time of thepredator 1.170DP0Proportion of thepredator populationstaying in patch j0.850DP1Initial dispersal rate ofthe predator 0.020bPPredator’s exponentialdecay constant 0.003DN0Proportion of the preypopulation staying inpatch j0.807DN1Initial dispersal rate ofthe prey 0.035bNPrey’s exponentialdecay constant 0.030B Caloric value of acapture individual0.45, 0.48, 0.51,0.54, 0.57, 0.60,0.63, 0.66, 0.69,0.72, 0.75C Predator death rate0.10, 0.13, 0.16,0.19, 0.22, 0.25,0.28, 0.31, 0.34r Growth rate of theprey0.5, 0.6, 0.7, 0.8, 0.9,1.0K Carrying capacity ofthe prey9, 12, 15, 18, 21, 24,27, 30rPGrowth rate of thepredator 0.01, 0.05, 0.10, 0.50KPCarrying capacity ofthe predator 1, 5, 1073chapter 4clusters for the tipulid prey. For the odonate predator, we found that twoindividuals from site 8 are very similar to sites 1 to 4, and we found twoindividuals from site 4 that are very similar to site 8. This result may be dueto swapped labels. Since we used the entire individual for this analysis, wecannot confirm the provenance of these individuals, and we will assume fromnow they were indeed errors. We ran the analysis with the original labels butdid not interpret dispersal from these individuals.After separating the individuals of each species into the two separate clus-ters, we re-ran the admixture analysis separately for each cluster for eachspecies (Figure d.4). Hereafter, we refer to the major clade as the clusterthat had the majority of the individuals (odonate had 67 and the tipulid64 individuals). For the odonate, we found that the major clade (Figure4.2a) included individuals from sites 1 to 7 and two individuals from site8. The individuals from the major clade form two sub-clusters, where someindividuals draw some admixture. The odonate’s minor clade (Figure 4.2c),included two individuals from site 4, and all other individuals from site 8, 9and 10. The individuals of the minor clade, form three sub-clusters whichmirror major geographical barriers, as site 10 is in a small island and the cityof Rio de Janeiro separates sites 9 and 10. These are the sites that are furthestapart.For the tipulid, we found that the major clade (Figure 4.2b) has no sub-clusters, and therefore all individuals at this scale are inter-breeding. Themajor clade includes individuals from site 1 to 8. The minor clade (Figure4.2d) includes three sub-clusters, two of which mirror the same geographicalbarriers as the odonate (from sites 9 and 10). The last sub-cluster includesindividuals from sites 4 to 6 and site 8. This sub-cluster co-occurs in the samesites as the major cluster, yet they do not interbreed. Due to the prevalence ofcryptic species in insects (Bickford et al., 2007) and this evidence of reproduc-74chapter 4tive isolation, we decided to treat these major and minor clusters as separatetaxa for both the odonate and the tipulid and ran subsequent analysis only onthe taxa with most individuals.4 .4 .2 Recent dispersalBayesass provides the most likely source population for each individual, thegeneration at which they dispersed and the dispersal rate between each pairof populations. We plotted the source and sampling site for each tipulid andodonate individual from the taxa with most individuals (Figure 4.3). We findthat the majority of odonate individuals were assigned to the source site fromwhich they were sampled (Figure 4.3a). We interpret this result as indicatingthat individuals move little between one generation and the next. The onlyindividual that was assigned a different source site, had dispersed two gen-erations ago (Figure 4.3a) from site three to two, moving approximately 350m. On the other hand, many tipulid individuals moved from their assignedsource site and the site where they were sampled (Figure 4.3b). Some of theseindividuals moved within one generation or two generations ago. The longestdistance that a tipulid individual moved was from site 4 to 7, approximately23 km.We next considered how the dispersal rate between each pair of sites re-lated to the geographic distance between each pair of sites (Figure 4.4). Weonly build the dispersal kernels up to 25 km since we found that the longestany individual moved was 23 km and we were confident that the individ-uals at this scale belonged to the same taxa. We used AIC to distinguishbetween three different functions for this relationship. For the odonate preda-tor (Figure 4.4a), the hurdle function that included the exponential decay(AIC = −283.235, d f = 4) was a better function than the exponential de-cay alone (AIC = −234.655, d f = 3) and the generalized linear model with75chapter 4F igure 4 .2 : The odonate major clade (a) has two sub-clusters while thetipulid’s major clade (b) does not. Both the odonate (c) and the tipulid(d) minor clades have three sub-clusters. Every vertical bar represents anindividual, and the colours represent the ancestral population. Individualswho have multiple colours are said to be drawing ’admixture’, that is,individual who likely resulted from the interbreeding of multiple populations.The different colours delineate the ancestral populations for those individuals.76chapter 4F igure 4 .3 : The ancestry of individual odonates (a) and tipulids (b) isreconstructed from their genetic composition. Dispersal events from one siteto the next are represented by arrows, each circle represents a site. Loopsrepresent individuals whose source site was the same as their collection site.The ancestry of the odonate individuals was commonly assigned to the sitewhere they were collected (loops in a) and only one odonate individualwas assigned as dispersing within two generations. On the other hand, theancestry of tipulid individuals was commonly assigned to other sources site(b) including dispersal event within one generation and two generations.77chapter 4F igure 4 .4 : Estimated dispersal rate between sites at different distances forthe odonate predator (a) and the tipulid prey (b). Insets highlight the dispersalrate when the distance between sites is greater than zero.gamma distribution (AIC = −203.989, d f = 3). Similarly, for the tipulidprey (Figure 4.4b) the hurdle function that included the exponential decay(AIC = −213.281, d f = 4) was better than the exponential decay alone (AIC =−187.039, d f = 3) and the generalized linear model with gamma distribution(AIC = −179.799, d f = 3). Overall we found that the tipulid’s dispersal rateis higher than the odonate’s dispersal rate at all distances.4 .4 .3 Trophic metacommunity modelWe used the best fit models for the dispersal kernels of odonates and tipulidsto parameterize a simple trophic metacommunity model. We tested whetherthe observed differences between predator and prey in dispersal rate wouldbe predicted to result in differences in occupancy. We also tested whetherthe reverse pattern (i.e. the predator having a higher dispersal rate than theprey) would also produce the same difference in occupancy. Of the parameter78chapter 4F igure 4 .5 : Persistence of the predator and prey at the end of the simulationunder different parameter combinations. The percentage of simulation runswhere both predator and prey persists varies depending on the dispersalscenario. Similarly, the percentage of simulations runs where the predatorand prey differ in their occupancy depends on the dispersal scenario.combinations tested, the observed dispersal rates resulted in more scenarioswhere both the predator and the prey persisted than the reverse scenario(Figure 4.5), and more cases where the predator and the prey differed inoccupancy -the prey was found without the predator in at least one patch-than the reverse scenario (Figure 4.5).79chapter 44 .5 discussionWe found first, that at large spatial scales (100, 160 and 430 km), both thepredator and the prey are similarly structured — in each taxa, individualsfrom sites 8, 9 and 10 separated into different clusters. However, at interme-diate spatial spaces (0-23 km for the odonate and 0-100 km for the tipulid)the predator and the prey had a different structure — the prey consists ofone interbreeding population, while the predator consists of two spatiallystructured clusters. Second, we found parallel prey species or sub-species thatwere not interbreeding while occupying the same sites. Third, we estimatedhigher dispersal rates for the tipulid prey than the odonate predators. Thisresult is consistent with the previous finding at the same intermediate spatialscale: the prey had one interbreeding cluster, while the predator had twoclusters, with some individuals drawing admixture. In terms of the dispersalkernel, we found that the rate of dispersal of the tipulid prey was higher atlonger distances. Overall we found that while the odonate predator barelydispersed, the tipulid prey was able to disperse up to 25 km. Finally, wefound that when we parameterized the simple metacommunity model withthe estimated dispersal kernels, the predator and the prey were likely to differin their use of space. This was less frequently the case when the predator andthe prey had the reverse dispersal kernels.Dispersal variation within a metacommunity, while often deemed neces-sary for trophic metacommunity theory, has proven hard to quantify (Bortha-garay et al., 2015). For some systems, like streams, dispersal of multiplespecies has been easier to measure, due to the constrained nature of thesystem where individuals can be physically trapped by mesh (Elliott, 2003).Similarly, wind dispersed organisms from temporary rock pools have alsobeen readily measured, where individuals can be physically trapped usingsticky surfaces, and show higher rates of dispersal than previously thought80chapter 4(Vanschoenwinkel et al., 2008). Yet for many other systems, similar directmeasures of dispersal are not easily obtained, especially at a community level.In such systems, population genetics has been identified as useful tool forestimating dispersal (Robledo-Arnuncio and García, 2007; Ouborg et al., 1999;Broquet and Petit, 2009). Many studies have used different estimates of popu-lation differentiation to quantify dispersal for single species. In a communitycontext, measures of population differentiation have most commonly beenused in marine systems (Kinlan and Gaines, 2003; Weersing and Toonen, 2009).However, these studies often ignore how dispersal combines with speciesinteractions to affect metacommunity dynamics. Here we show not only thedispersal estimate of two interacting species using population genetics, but wealso show the consequences of the observed pattern of differential dispersalfor metacommunity dynamics using simulations.Both the odonate predator and the tipulid prey seemed to be comprised oftwo separate taxa. The identity-by-state results showed a bimodal distributionof distances between individuals, meaning that some individuals seem to beclosely related while others are not. Similarly, the admixture analysis ini-tially separated all individuals in two separate clusters, and by re-running theanalysis on each cluster separately we were able to find population structurewithin each cluster. The strongest evidence that supports the existence of twoseparate taxa, at least for the tipulid prey, is that individuals that occupiedthe same sites still segregated into different clusters that did not interbreed.This would be the case of sympatric cryptic species (Bickford et al., 2007). Inthe case of the odonate predator, we do not have the evidence to differentiatebetween cryptic species or simply isolation by distance since the two separateclades were allopatric. In our study we identified the insects at the larval stage,which for tipulidae hinders the proper identification of species that are oftendone by rearing the larvae to adults (Gelhaus, 2009).81chapter 4Based on scaling relationships between body mass and dispersal (Jenk-ins et al., 2007), we expected that the odonate predator, being larger, woulddisperse further than the tipulid larvae. However, we found the oppositeresult. One possibility is that, even though odonates have the capacity tofly further, some species are philopatric and therefore might oviposit in thesame area where they emerged as adults (Conrad et al., 1999; McCauley, 2007).While we do not have evidence of whether the odonate predator used in thissystem is philopatric, our population structure analyses are consistent withthis hypothesis. Another possibility is that the tipulid is not just an activedisperser, but it may have a mixed strategy which is facilitated by wind orbirds. For example, tipulid larvae have been found to be viable after beingingested by birds (Frisch et al., 2007) which may help explain the inferreddispersal over 20 km. Overall, we find that common scaling relationships —such as that between dispersal distance and body mass (Jenkins et al., 2007) —may apply generally to fauna but not necessarily to any particular species pair.However, our results only encompass two interacting species in a food web.The question of whether species within a food web follow the same scaling re-lationships for dispersal as entire taxonomic groups remains an understudiedquestion in ecology (Guzman et al., 2019).The question of whether predators or prey disperse more or less thanone another is most important when we are interested in the dynamic con-sequences of dispersal in a metacommunity. Trophic metacommunity modelshave found that differential dispersal may stabilize predator-prey dynamics.Many metacommunity models incorporate fixed differences between patchesin their conditions, which causes the dynamics of the patches to be asyn-chronous and therefore more stable (Briggs and Hoopes, 2004). For example,models of source-sink dynamics assume patches differ in quality (Holt, 1984).However, many of these models incorporate the differences in dispersal as ex-82chapter 4treme asymmetries (Holt, 1984) or by incorporating differences in the dispersalrate and not the dispersal kernel (Rohani et al., 1996). We expect that if specieshave differences in dispersal parameters, we would observe differences in theway they use space. Indeed, we found that the observed differences in the dis-persal rate and kernel, in combination with the way these two species interact,were sufficient to generate differences in space use between the predator andthe prey without invoking any differences in the abiotic niche. Surprisingly,we found in our model that the observed directionality in dispersal asymmetry,with the prey having a higher dispersal rate than the predator, was more likelyto generate differences in space use than the reverse. We urge ecologists touse population genetic methods to explicitly parameterize dispersal kernelsof interacting species, and combine these with studies of interaction strengthsbetween species. Only with empirical estimates of the relevant parameterscan we hope to apply metacommunity models to understanding communitydynamics over space.83chapter 5Successful integration of data science inundergraduate biostatistics courses using cognitiveload theory.84chapter 55 .1 chapter summaryBiostatistics courses are integral to many undergraduate biology programs.Such courses have often been taught using point-and-click software, but theseprograms are now seldom used by researchers or professional biologists. In-stead, professionals typically use programming languages, such as R, whichare better suited to analysing large and complex datasets. These coding skillsare valued not only in common "tech" fields, but also in non-traditionally-tech fields, such as healthcare. As a result, many biology programs are notproviding their students the skills they will need in the future. However, teach-ing statistics and programming simultaneously has the potential to overloadthe students and hinder their learning. We sought to mitigate this potentialoverload by using cognitive load theory to develop assignments for two bio-statistics courses (introductory and advanced). We evaluated the effectivenessof these assignments by comparing cohorts that were taught R using theseassignments to those that were taught R just through example scripts or wereinstructed on a point-and-click software program. We surveyed all cohortsafter the courses, and analyzed statistical and programming ability throughstudents’ lab reports or final exams. Students that learned R through ourassignments rated their programming ability higher and were more likely toput the usage of R as a skill in their CVs than control students. We also foundthat the treatment students were more motivated, less frustrated and lessstressed when using R. There was no cost of learning R for their understandingof statistical concepts. These results suggest that we can use cognitive loadtheory to teach challenging material and better prepare students for moderncareers in biology.85chapter 55 .2 introductionToday, more than ever, biology graduates need to be equipped with statisticaland programming skills. At the interface between statistics and programmingis data science. Biology graduates require these data science skills in the jobmarket or in graduate programs. Data science has been one of the fastestgrowing careers in North America. The employment site Glassdoor rated datascience as the best job in the USA in 2018 (Glassdoor, 2018) and being a datascientist is regarded as the "sexiest job of the 21st century" (Davenport andPatil, 2012). In environmental and conservation sectors, employers (includinggovernment, non-profit, and private) list technical and statistical skills as im-portant requirements they look for in their potential hires (Blickley et al., 2012).These technical skills are not only important for data science or professionalbiologist jobs, but also employers in ‘non-tech’ jobs are demanding them, suchas employers in marketing, engineering, finance, manufacturing, design andeven healthcare (Dishman, 2016). Biology graduates interested in researchalso need strong statistical and programming skills. With biology firmly inthe era of big data, biologists from multiple disciplines are starting to grapplewith handling, processing and analyzing large data (Marx, 2013). Not onlyis data becoming larger, but analyses are becoming more sophisticated. Inour own discipline of ecology, sophisticated and computationally intensivestatistical techniques, such as mixed models and Bayesian statistics, are re-placing more traditional frequentist-based tests such as ANOVAs or t-tests(Barraquand et al., 2014; Touchon and McCoy, 2016). The increased need fordata science solutions for biological data has resulted in a growing demand forsoftware that can do these analyses. Specifically, the programming languageR is in much higher demand and more commonly used both in commercialapplications and in academic research than point-and-click statistical softwaresuch JMP, SAS, and SPSS (Touchon and McCoy, 2016; Muenchen, 2017).86chapter 5Biology education, at undergraduate and graduate levels, rarely providesstudents with the statistical and programming skills that they need for theirfuture careers. One proposed solution to this problem, at the graduate stu-dent level, is to provide students with accelerated learning programs at thebeginning of their graduate programs (Stefan et al., 2015; Vale et al., 2012).However, a recent study by Feldon et al. (2017) found that short format trainingcourses, such as "bootcamps", do not provide students with the desired skills.One explanation for this result is that students learn quantitative skills bestwhen taught incrementally over a long time frame rather than intensively(Rohrer, 2015). It seems then, that a better place to introduce programmingand statistical skills is at the undergraduate level (Michener and Jones, 2012).Teaching data science skills to biology undergraduates will provide them withthe skills they need, not only for graduate school but also for a demanding jobmarket.Given that biology undergraduates require simultaneous training in statis-tics and programming, the question is how this can be most effectively achieved.Teaching either statistics or programming is challenging. Both statistics andprogramming are courses in which students report high levels of anxiety, withdebilitating effects on academic performance (Onwuegbuzie and Wilson, 2003;Wilson and Shrock, 2001). For example, the main predictors of student successin introductory programming courses is feeling comfortable while working oncomputer assignments and being able to ask questions (Wilson and Shrock,2001; Simon et al., 2006). Statistics and programming courses not only in-duce high anxiety in students, they also are perceived to be hard coursesto learn. Programming for example, requires that students use both deep(understanding application of concepts) and surface (e.g. memorization ofsyntax) learning at the same time, and therefore students have trouble learningwhen instruction is primarily through lectures (Bellaby et al., 2003) or when87chapter 5they do not have adequate support on assignments (Bellaby et al., 2003; Wilsonand Shrock, 2001; Jenkins, 2002). The simultaneous instruction of statisticsand programming will only increase the cognitive load on students. Onestrategy for this problem is to use cognitive load theory to design hands-onassignments (Wilson, 2018). Cognitive load theory deals with how cognitiveresources are distributed during learning and problem solving (Sweller et al.,1990).Cognitive load theory suggests that learners have a limit in their workingmemory. There are three components of cognitive load: (i) Intrinsic loadis the inherent difficulty of the instructional material. It is related to thenumber of elements that learners need to consider simultaneously to learna particular procedure and the prior knowledge of the learner (Sweller andChandler, 1994). (ii) Extraneous load is determined by the manner in whichthe instructional materials are presented. Since students have limited cognitiveresources, using cognitive resources to process the extraneous load reducesthe available resources for the intrinsic load (Sweller, 1993). Finally (iii) thegermane load is the processing and creation of mental models. The germaneload can be modified by instructors through the materials presented (Paaset al., 2004). By recognizing these three aspects of cognitive load, instructorscan design the scope and nature of their teaching so as to minimize theintrinsic and extrinsic loads while emphasizing the germane load.We used cognitive load theory to design regular homework assignments toteach R programming in two biostatistics courses. In particular, we used threepedagogical methods based on cognitive load theory to design our assign-ments: the worked-example effect, where studying worked examples resultsin better performance of the students (Renkl, 2005); the completion effect,where we required students to complete partially solved problems (Paas andVan Merriënboer, 1994); and the split-attention effect, where an integrated88chapter 5teaching of multiple concepts can improve learning compared to presentingthe concepts separately but concurrently in a "split" format (Ayres and Sweller,2005). We compared student cohorts that applied R using assignments basedon cognitive load theory with cohorts that either applied R strictly throughreference to example scripts or applied a point-and-click software. We investi-gated whether (i) the students effectively learned to use R, (ii) the introductionof R programming hindered the learning of statistics, (iii) the students felt thatthey learned a useful skill, (iv) the students felt frustrated or overwhelmedwith the assignments, and (v) the students were motivated because they feltthey were learning something useful and challenging.5 .3 methods5 .3 .1 Target coursesWe implemented this experiment at the University of British Columbia (Canada),in an introductory biostatistics course, Fundamentals of Biostatistics (here-after Biostatistics), and an advanced ecological statistics course, EcologicalMethodology (hereafter Eco-Methods). Biostatistics introduces the conceptsof hypothesis testing, probability, experimental design, and statistical testssuch as student’s t-test, linear regression and ANOVA. Biostatistics includesthree 50 minute lectures and one 2-hour optional computer laboratory perweek. Eco-Methods introduces the concepts of experimental design, statisticalpower and sample size, mark and recapture methods, metrics of communitydiversity and composition, as well as statistical tests such as ANOVA, multipleregression, ordination and clustering. Eco-Methods includes includes two 60minute lectures and one 3-hour field and/or computer laboratory per week.For each course, we had a control and a treatment term (Table 5.1). Allcourses included homework assignments for a relatively small reward in terms89chapter 5of overall marks. The main difference between the treatment and controlterms was the teaching of R using cognitive load theory in the homeworkassignments (Box 5.1, Appendix e). The assignments taught and tested theability to apply the statistical concepts in R. In Biostatistics we aggregatedthe previous homework assignments and introduced cognitive load theory forconceptual questions taken from the textbook. In this course we includedtwo R questions in the midterm and the final exams. The control terms weredifferent for each course. In Biostatistics the students in control term learnthow to use the point-and-click software JMP. In Eco-Methods the students inthe control term learnt how to use R using example scripts. In all courses andterms, the in-class sessions consisted of Socratic lecturing.Although the instructor differed between the control (2016) and treatment(2017) terms for Eco-Methods, both instructors taught from the same lectureslides. We note that in 2015 instructor D.S.S taught R from the same examplescripts as M.K.T. in 2016, and that their teaching evaluations were comparablebetween these two years, suggesting that there was not a strong effect ofinstructor identity.5 .3 .2 Homework assignmentsWe designed ten homework assignments for Biostatistics and seven homeworkassignments for Eco-Methods. In each of these assignments, we applied cogni-tive load theory to (i) reduce the extraneous load of students by taking advan-tage of the split-attention effect, the worked-example and completed problemeffect, (ii) reduce the intrinsic load of the material by managing the elementinteractivity and (iii) increased germane load by scaffolding the material withself-explanation questions (See examples in Box 5.1 and Appendix e - All thematerials have been submitted to CourseSource).90chapter 5Table 5 .1 : Course structure in control vs. treatment terms. The treatmentgroups for both courses completed assignments designed using the ideas ofcognitive load theory (CLT) as homeworkBiostatistics Eco-MethodsControl Treatment Control TreatmentYear 2016 2018 2016 2017n 155 116 26 30Instructor M.W.P. M.W.P. M.K.T. D.S.S.TAs 5 5 2 2GradebreakdownAssignments(3): 10%Homework(10): 10%Homeworkassignments(10): 20%Homework as-signments (5):25%Homework as-signments (7):28%Midtermexam: 30%Midtermexam: 30%Formal labreports (twoat 15% each):30%Formal labreports (threeat 11% each):33%Final exam:50%Final exam:50%Research pro-posal, groupproject: 10%Research pro-posal, groupproject: 11%Group projectpresentations:5%Group projectpresentation:5%Group projectwritten report:25%Group projectwritten report:21%Participation:5%Participation:2%Labs Labs usedJMPLabs used R Labs usedR/MicrosoftExcelTMLabs used RHomework as-signmentsHomeworkwereconceptualproblemsfrom thetextbookHomeworkassignmentsused R andCLTR scripts thatthey had torun on theirown time anddo conceptualstatisticshomeworkHomeworkassignmentsused R andCLT91chapter 5Box 5.1 - Homework assignment examplesSelected examples from the assignments showing how we used cognitive loadtheory to introduce R programming concepts in the statistics exercises.(i) Reducing the extraneous loadSplit attention effect: Worked example effect: Completed problem effect:Code is often presentedas multiple sources ofinformation. We incor-porated the code andthe explanations as asingle source to reducethe split attention ef-fect.We presented workedexamples of simpleand complex problems,both involving howto write code andhow to use code torun statistical tests.All worked exampleswere partitioned intodifferent parts.After presentingworked examples, wepresented partiallycompleted problemswere the scaffoldingwas introduced inthe steps to solvea question and thecode needed to run astatistical test.Question: Calculatethe mean of a vector ofall the integers from 1to 50.Third, construct yourbox plot using ggplot.Fill in the blanks in thefollowing code to doFirst, we must createthe vector.so:vector <- 1:50 > ggplot(data =92chapter 5Second, we must calcu-late the mean., aes(x = ,y = ))+> mean(vector) ()[1] 25.5Finally, we now haveour answers calculatedby R. The mean of avector from 1 to 50 is25.5.(ii) Reducing the intrinsic loadWe reduced the element interactivity of the material by:1. Presenting only one way to do a task. In R, every task can be done bymultiple functions. While understanding these different function is usefulfor more advanced programming, beginners can be overwhelmed by learningmultiple functions simultaneously.2. Presenting only the functions that were needed for a given statistical test.(iii) Increasing germane loadIn both worked examples and in partially completed problems, we askedthe students to reflect on a part of the question to engage in germane loadactivities such as self-explaining.Self-explanation questions:For you to think: Why did you use ":" instead of "c" to create a vector in"vector <- 1:50"?5 .3 .3 Evaluating the success of the homework assignmentsSurveys — We evaluated students’ perceptions using a survey at the end ofthe course (Appendix e). Student participation in the survey was requested by93chapter 5L.M.G., who was not a course instructor or TA, during lecture time. We did notoffer any incentive to complete the survey but it also presented no cost to thestudents, it was anonymous and it was conducted with the instructors absentfrom the room. Both surveys consisted of 29 closed-response questions and3 open-response questions. The survey included questions on the frequencyof using R before and after the course took place, as well as attitudes aboutthe difficulty of the course and their emotional response to the data sciencematerial during the course.Assessments of lab reports and final exams — To address thequestion of whether the students learned R effectively, we used analyses par-ticular to each course. For Eco-Methods we evaluated graphs produced bystudents for their final report. In these graphs we assessed whether studentwere able to customize graphs relative to the example graph provided in theassignments. For example, we recorded whether the students changed thecolour, type of lines, font, background of their figures, etc. We compared thecustomization of graphs between the control and the treatment groups. ForBiostatistics, we asked the students to upload and submit graphs as part oftheir assignments. The students were required to do nine graphs as the courseprogressed. We compared the proportion of students creating graphs by hand,in Microsoft ExcelTM, or in R, each week, from week 1 to week 10. We onlydid this temporal comparison in the treatment group, as we were interestedprimarily in the progression to R from other methods.We were also interested in determining whether the introduction of Rprograming would hinder the learning of statistics. Biostatistics was the onlycourse with a final exam. We ensured that this exam had one conceptualquestion in common between the control and the treatment group. We thencompared the scores for this question.94chapter 55 .3 .4 Data analysisSurveys : L ikert -type questions — Likert-type responses were con-verted into numerical values from 1 to 5. For these types of questions, weused a generalized linear model to test for differences in the response betweencontrol and treatment terms. We used a Poisson family with a logarithmic linkfunction since these data were comprised of integer responses from 1 to 5.Surveys : Conceptual difficulty questions — We tested whetherstudents perceived the difficulty of the conceptual material differently fromthat of the application of the material, and whether this difference âA˘S¸ ifany - depended on the topic taught (e.g. ANOVA v.s. linear regression) andthe course treatment (control v.s. treatment). Here our expectation was thatas the course progressed, the perceived difficulty of the conceptual materialwould increase while the perceived difficulty of the application would declinein the treatment group but not the control. To analyze these predictions, weused a generalized linear model with a Poisson family and a logarithmic linkfunction.Surveys : Emotional response questions — We asked the studentsto assess their emotions towards both the conceptual parts of the course andthe use of R or JMP. We transformed all positive feelings into values of 1and all negative feelings into values of 0. For these types of questions, weused a generalized linear model to test for differences in the response dueto the treatment (control vs. treatment) or due to the use of R v.s. JMP (forBiostatistics). We used a Binomial family with a logit link function.To investigate which particular feelings contributed most to this difference,we evaluated, for each feeling separately, the difference between the treatmentsusing a Chi-squared contingency test. We corrected the p-values for multiple95chapter 5comparisons using the false discovery rate method (Benjamini and Hochberg,1995). We excluded from this analysis all feelings that had less than tenresponses.Surveys : Open -response questions — We developed codes for eachof these questions using the method described in Guest et al. (2012). Twoobservers, E.N. and L.M.G., generated and reviewed the codes, the themesand the codebook (Appendix e).Assessments of lab reports , midterm and final exams —Eco-Methods Lab reports:To analyze the degree of customization of the graphs in the Eco-Methods labreports we summed the total number of customizations per person and thenused a generalized linear mixed effects model to test for differences betweenthe courses. We used the number of customized elements per person as theresponse and the treatment as the fixed effect. Since the lab reports weredone in groups of four students, the reports generated were not independent,therefore we used the group id as the random effect. We used a Poisson familywith a logarithmic link function.Graphs in the Biostatistics assignments:We used multinomial logistic regression to test for the odds of using R vsother methods as the term progresses.Biostatistics Final exam marks:We tested the differences in scores between the control and treatment groups96chapter 5in Biostatistics using paired questions in the final exam. Here we used ageneralized linear model using a Poisson family and logarithmic link functionwhere the response was the question score on this question and the explana-tory variable was the course.All analyses were done using the R programming language (Team, 2018).Mixed effect models were performed using lme4 R package (Bates et al., 2015)and lmerTest (Kuznetsova et al., 2017), analysis of variance was done using car(Fox and Weisberg, 2011), and multinomial regressions were done using nnetR package Venables and Ripley (2002).5 .3 .5 Human Subjects OversightThis work was conducted with review and approval by the Behavioural ethicsresearch board of the University of British Columbia, H16-02319.5 .4 results5 .4 .1 SurveysL ikert -type questions — Students in the control and the treatmentcohorts, for both courses, rated similarly their initial programming skills andthe frequency of using R (Figure 5.1: "Before this course started").For Biostatistics (Introduction to Biostatistics), we found that during thecourse the students in the treatment group self-rated their frequency of usingR higher in lab assignments and outside of class than the control group ratedtheir frequency of using JMP (Figure 5.1: "During this course"). This differenceoccurred even though the students in the control cohort started the coursefeeling more comfortable using statistical software than the experimental co-hort. By the end of the course, the students who used the R assignments97chapter 5designed with cognitive load theory self-rated a higher proficiency in R, ahigher willingness to put R as a skill in their CV and a higher chance that theywould continue using R in their future graduate and undergraduate studies.In Eco-Methods, we could compare the students’ comfort in using R whenit was taught traditionally (control cohort) or using cognitive load theory(experimental cohort). Here there were no treatment effects before or duringthe course, but by the end of the course students in the experimental cohortfelt more proficient in R and were more likely to include it as a skill on theirCV (Figure 5.1: "Having completed this course"). Both cohorts were likely touse R in future projects.Conceptual difficulty questions — For both courses, we found noeffect of teaching treatment on the perceived difficulty of the course, includingthe conceptual v.s. applied parts, or the different materials taught (Appendixe - Table e.1).Emotional response questions — We found that both the Biostatis-tics and the Eco-Methods students in treatment cohorts had more positivefeelings than the students who were taught JMP traditionally (Biostatistics) orwere taught R traditionally (Eco-Methods) (X21,517 = 25.68, P « 0.001 and X21,163= 11.57, P « 0.001 respectively). Specifically, the students in the Biostatisticstreatment cohort felt more excited, happy, motivated, proud and less bored,and the students in the Eco-Methods experimental cohort felt less frustrated(Table 5.2).Open -response questions — We focus on two questions (out of threequestions asked) for each course about the way the statistical software (eitherR of JMP) was taught. The third question, "did you have any other commentsabout the course", was too broad and resulted in many comments not relevant98chapter 5F igure 5 .1 : Students responses to the survey questions before, during andafter the course, in relation to teaching treatment (control vs. cognitive loadtheory treatment) and course identity. Student responses are ranked on aLikert scale (all but first question) or referring to year of undergraduate (firstquestion). Points and bars represent means and standard errors respectively.Control groups are coloured red and treatment groups are coloured blue.Significance is noted with stars.99chapter 5Table 5 .2 : Treatment students in Biostatistics significantly felt less bored,and more excited, happy, motivated and proud than control students.Treatment students in Eco-Methods felt less frustrated than control students.X2 and P-value of the X2 test for each emotion.Biostatistics Eco-MethodsEmotion X2 P X2 Pangry 0.02 0.98annoyed 0.005 0.98 0.73 0.59anxious 0.55 0.62 1.45 0.45bored 6.52 0.03 **excited 17.94 « 0.001 *** 0.20 0.66frustrated 0.51 0.62 10.89 0.01 **happy 8.92 0.009 ***motivated 30.04 « 0.001 *** 3.73 0.16overwhelmed 1.05 0.50 1.33 0.45proud 10.66 0.005 *** 0.26 0.66scared 0.001 0.98stressed 3.52 0.13 5.24 0.10supported 1.53 0.40 0.29 0.66100chapter 5to the assignments. For each question and each course we emphasize the top5 themes.BiostatisticsQuestion: If you could change anything about the way the statistical software(R or JMP) was taught, what would it be?The most prevalent themes we found in this question were (i) "Theme A:Course should use other software", which had 47 responses in total (Control= 47 out of 157 students, Treatment = 0 out of 117 students). In Biostatistics,the control cohort learnt JMP in the labs whereas the treatment cohort learntR. Overall, 30% of the students wanted to use another software, the studentsmentioned both R and Excel in their answers. (ii) "Theme N: The R assign-ments need improvement". Theme N had 29 responses (0, 29). 25% of thestudents responded in this theme. Specifically, seven students mentioned thatthe assignments needed more clarity, or better instructions. Four studentsmentioned that the assignments were too easy, while six mentioned it wastoo challenging and four mentioned that they were too long. Two studentsmentioned that the assignments were disconnected from the lectures or thelabs and finally four students did not like the layout in the online learningmanagement system (Canvas) since they had to scroll between instructionsand questions. (iii) "Theme B: The students want more activities to help orforce them to learn the software" which had 23 responses (8, 15). (iv) "ThemeH: The course should provide an incentive to come to the labs to learn thestatistical software". Theme H had 19 responses (13, 6). And (v) "ThemeC: The course should provide more support learning the statistical software"which had 16 responses (5, 11). Some of the suggestions that the students101chapter 5provided were: more help troubleshooting, provide demos or explain betternew commands, functions and concepts, give more walkthroughs and providemore information on online resources.Question: If I could keep anything about the way the statistical software (R orJMP) was taught, what would it be?The most prevalent themes we found in this question were (i) "Theme K: Keepsome part of the canvas R assignments" which had 49 responses (42% of thestudents) (Control = 0 out of 157 students, Treatment = 49 out of 117 students).In particular, 18 students suggested to keep the walkthroughs, 12 students thedetailed instructions, 5 students the step-by-step questions, 3 students the fill-in-the blank questions, the expected codes and graphs. 4 students mentionedthe assignments were informative and not overwhelming. (ii) "Theme A: Keepthe lab manual" which had 39 responses (26, 13). (iii) "Theme C: Keep thelabs" which had 15 responses (12, 3). (iv) "Theme N: Liked how R was taught/no changes" which had 14 responses, all in the treatment group. (v) "ThemeG: They did not like how JMP was taught" which had 9 students responses,all in the control group.Eco-MethodsQuestion: If you could change anything about the way the statistical software(R or JMP) was taught, what would it be?The most prevalent themes we found in this question were (i) "Theme B:Students want more R instructions on functions and packages" which had 28responses (Control = 17 out of 27 students, Treatment = 11 out of 30 students).102chapter 5(ii) "Theme E: More synchrony between the assignments, the lectures and labs"which had 13 responses (6, 7). (iii) "Theme C: More support outside of class"which had 11 responses (10, 1). (iv) "Theme A: the student wants to learnmore R" which had 9 responses (6, 3). Finally, (v) 8 students responded with"Theme G: the teaching of R was not good enough", which had 8 responses (7,1).Question: If I could keep anything about the way the statistical software (R orJMP) was taught, what would it be?The most prevalent themes we found in this question were (i) "Theme C: Rwas taught well", which had 21 responses (Control = 4 out of 27 students,Treatment = 17 out of 30 students). (ii) "Theme E: the students liked having anR Workshop" which had 19 responses (15, 4). Here we found that the studentsliked having the first in-lab session devoted to learning to start using R, whichoccurred for both the treatment and the control groups. (iii) "Theme I: Likedthe R/stats assignments" which had 16 responses (2, 14). (iv) "Theme F: Thestudents are grateful to have learned R" which had 5 responses (2, 3). Finally,"Theme A: Learning packages/analyses/functions was useful" which had 4responses (2, 2).5 .4 .2 Assessments of lab reports and final examsLab reports — Students in the control and treatment cohorts of Eco-Methodsdid not differ in the number of customized elements on their graphs (X21,58 =1.67, P = 0.19, project group as random effect).Graphs in the assignments — The students in the treatment group ofBiostatistics had to do two types of graphs: graphs from data provided in the103chapter 5F igure 5 .2 : a) The probability that Biostatistics students in the treatmentcohort made their graphs using R from previous assignment examples is highfrom the beginning of the course. b) The probability that Biostatistics studentsin the treatment cohort made their graphs using R from the textbook increasesas the term progresses and replaces use of Microsoft ExcelTM ("Excel") or handdrawing ("Hand") or other software.textbook, where they had to input and graph the data without an example, andgraphs from data provided in the labs, where the data was already formattedand easy to input and the graph was based on an example. We found thatwhen the students had an example, they were able to produce a graph of theirdata using R from the beginning of the term (Figure 5.2a). However, withoutan example, we found that at the beginning of the term they used MicrosoftExcelTM or drew the graph by hand, but by the end of the term, the majorityof the students were able to input and graph their data using R (Figure 5.2b).F inal exam marks — The treatment and control cohorts of Biostatisticsdid not differ in their scores on the same question in the final exam (X21,244 =0.64, P = 0.42).104chapter 55 .5 discussionOverall we found that students not only learnt to use R, but they felt that theymastered a useful skill, they had positive feelings when using the assignmentsand liked the assignments. Examining the final reports (Eco-Methods) and theprogression of the use of R for the graphs through the term (Biostatistics), wefound that the students learnt how to input, plot and analyze data. We alsofound that the introduction of R programming did not hinder the learning ofstatistics (at least in Biostatistics), since the results from the final exam werenot significantly different between the control and treatment.Overall we found that students appreciated learning R, regardless of theformat in which it was taught. For example, a student from the Biostatis-tics control group (which used the JMP program) wrote: "I wish I learned Rbecause it seems more relevant to my degree and I wish it was part of homeworkand assignments [C97]." As well, those students who were taught R generallyfelt it was valuable; one student wrote that they were "glad [they] learned R,as [they]’ve heard it’s very useful in biology especially." [E52 - Biostatistics] andanother thought the course could be improved by adding even more R into theclass as this was "probably the most useful part of this course moving forward" andthat they "would have liked more assignments that required more problem solving"[E113 - Biostatistics].Self-determination theory states that there are multiple sources of extrinsicmotivation. When a student identifies the value or utility of a task, theextrinsic goal is self-endorsed and thus adopted. Identifying the utility oftask is a form of extrinsic motivation that has been associated with greaterengagement, performance, higher quality learning, among other outcomes(Ryan and Deci, 2000). Students who learnt R using our assignments based oncognitive load theory felt that they learnt a useful skill and they would ratetheir programming proficiency as high after the treatment level. Similarly,105chapter 5they would put the ability to use R as a skill in their CV. Regarding thestudent’s affect, we found that the students reported feeling more motivatedwhen learning R than when learning JMP. Additionally, we found that thestudents felt more positive when using the treatment assignments to learn Rthan when either learning JMP or using only scripts to learn R. Specifically,the students who used the R assignments in Biostatistics felt more excited,happy, motivated, proud and less bored than the students who used JMP.In Eco-Methods, the students who used the CTL-based R assignments feltless frustrated than the control students who used the R scripts. Part of thispositive response may be due to the students liking some elements of cognitiveload theory that we introduced in the assignments. For examples, when weasked the students what they would keep about the way the software wastaught they wrote that they liked how the assignments "walked you through thequestions almost step-by-step" [E3], how "everything was broken down and explainedto a very basic level [as] it made it very enjoyable to learn for someone who reallystruggles with computer programming" [E19] and how they "made sure your codewas right and gave hints too if you were on the right track" [D14]. Consistent withthe principles behind cognitive load theory, we also found that the design ofthe assignments influenced whether students perceived that they were able tobe successful. For examples, one student wrote: "I liked the fill-in-the-blanksespecially the question with the expected graphs because I could test it out and it gaveme some sense of support" [E74]; and another "really liked how the instructionswalked us through the process so it was less overwhelming" [D7].Previous studies have found that when teaching novice students, boredomand frustration were negatively correlated with learning, while transitioningbetween confusion and engagement were positively correlated with learning(Bosch and D’Mello, 2015). While we do not measure affect throughout theterm, we found that using assignments designed with cognitive load theory106chapter 5reduces the frustration compared to plain R scripts, and reduces boredomcompared to a point and click software JMP.Cognitive load theory has been used successfully in a variety of courses.For example, Mason et al. (2016) used cognitive load theory to re-design acourse in database systems. They found that the failing rate of mid to lowerperforming students was reduced by 34% after the redesign on identical finalexams. Student satisfaction also increased and feedback was very positive(Mason et al., 2016). Similarly, on an Advanced Web Applications coursefor graduate students, cognitive load theory was used to develop an onlineprogramming tool, and they found that students performed best when theywere able to view examples of code during the learning of new material(Heo and Chow, 2005). Similarly, when cognitive load theory was appliedto teaching math to middle school students, researchers found that studentperformance was improved by signaling important information, improvingthe aesthetic of item organization and removing extraneous content (Gillmoret al., 2015). Previous studies on teaching programming to novice learnershave also found that using cognitive load theory led to better learning as wellas an increase in self-efficacy and reductions in the perception of difficulty(Mason and Cooper, 2013).When we designed the assignments, we included multiple types of scaf-folding, including procedural scaffolding (helps the learners use appropriateresources as well as tools), and metacognitive scaffolding (helps the learnersto reflect about what they are learning). Metacognitive scaffolding and self-questioning have been shown to support student learning of programming(Nurulain et al., 2017). In addition, affect can have metacognitive effects, suchas feelings of difficulty (Efklides, 2017). For example, a negative mood canincrease the self-reported difficulty in math problem solving (Efklides andPetkaki, 2005).107chapter 55 .6 limitationsThe perceptions expressed by the students may not be generalizable to a largerpopulation. The students who were surveyed were those present on the lastday of class, which may reflect a more motivated subset of the class. Further-more, many students in the University of British Columbia Biology programwho take these classes are interested in medical school or graduate school, andthis motivation may not extend to students situated in other environments orthose enrolled in other programs. This study was unable to control for thepossibility of temporal differences in either course or that instructors differedin teaching ability (Eco-Methods). We view these explanations less likely sincesimilar effects were seen in both courses.5 .7 conclusionThis is the first evidence, to our knowledge, that using cognitive load theoryincreased learning success for the introduction of data sciences practices andthe integration of programming and statistics, based on two courses in thebiology undergraduate program. Each course teaches different concepts in bio-statistics, but we found congruent results in terms of affect and performanceof the students. The findings presented here suggest that data science is ofinterest to students, and cognitive load theory can be useful in introducingprogramming not only in statistics but also in other courses. Even though wedesigned these assignments with biology students (and novice programmers)in mind, other disciplines will face the same data heavy method demandsand challenges of having to teach quantitative skills to novice undergraduatestudents. We think that these methods can be applied to other disciplines withdiscipline-specific examples.108chapter 6Discussion109chapter 6More generally, through the projects that I did during my Ph.D. I foundthat empirical approaches that infer processes from observational data arelimited. While both competitive and trophic metacommunity theory haveadvanced incredibly quickly, and have improved our understanding of therole of space in community dynamics, our empirical approaches remain be-hind. Experiments have been critical at testing whether the predictions madeby theoretical models could happen in nature (e.g. Forbes and Chase, 2002;Staddon et al., 2010; Cadotte, 2006b; Altermatt et al., 2011). Yet we are still farfrom confirming these predictions using observational surveys. Often, we usestatistical tools to analyze observational data, that do not infer the processeswe are interested in. For instance, variation partitioning is a general tool thatallows us to examine the degree to which variation in environment or in spacecan explain variation in community composition. However, this tool is onlyloosely tied to the processes we are interesting in inferring, i.e. dispersal,abiotic niche and species interactions. In fact, while we attribute processes tothe different variance components, multiple processes can produce the samepatterns (Gilbert and Bennett 2010). Without explicitly testing and comparingthese processes, we will be hopeless in trying to infer process from pattern.Some of the statistical tools that metacommunity ecologists can use, to linkthe processes we are interested in to the patterns we observed, have alreadybeen developed and adopted in other fields. For example, population geneticsand phylogenetics often use Bayesian statistics (Falush et al., 2007), approxi-mate bayesian computation (Aeschbacher et al., 2012) and machine learning(Sukumaran et al., 2016). These tools allow them to infer population structurefrom allelic data or whether dispersal is constrained by traits in radiations ofbirds.New studies in ecology seem to be incorporating specific statistical models(Martin et al., 2018; Pontarp et al., 2019), and it is time we start applying them110chapter 6to metacommunity ecology. A potential worry for ecologists, is that some ofthese methods do not encapsulate all possible processes that could be drivingcertain patterns. However, by using specific models that tie the patterns wemeasure to the processes we want to infer, we show explicitly which processeswe are taking into account and which ones we are not. Using these methodsthat tie directly our observations to the inferences we actually are interestedin, will push the field further than using general methods that do not answerthe questions we are asking.The development of new inference techniques for metacommunity ecologyis a huge mountain to climb, that will take decades of research to develop.In the meantime, we can use better approximations to directly link patternsto the processes we are interested in inferring. For example, while not formy thesis, I am currently using machine learning methods identify whichmetrics can allow us to distinguish metacommunity processes from time seriesdata. This concept has been applied previously to differentiate the differentmetacommunity paradigms (Münkemüller et al., 2011), but since the meta-community paradigms are only a subset of all combinations of the possiblemetacommunity processes (Thompson et al., in prep), we need an updateon the metrics that will allow us to differentiate the three metacommunityprocesses — the abiotic niche, dispersal and the strength of local competition— rather than the paradigms. This will enable ecologists to have a richerunderstanding of the processes that maintain biodiversity.After completing this dissertation, I found some aspects which could beexpanded to allow a more thorough understanding of the bromeliad system.Given that species interactions vary with environmental variables, I think feed-ing trials should be done in multiple environments, especially those identifiedas important for the organisms. While metabolic theory focuses mostly onthe variation of feeding rates due to body size and temperature, bromeliad111chapter 6macroinvertebrates might be more sensitive to changes in water volume thanto changes in temperature. The relationship between water volume and feed-ing rate has only been quantified for one predator in the bromeliad food web(Amundrud accepted paper), and could profitably be expanded to many more.Since Jensen’s inequality is important whenever the relationship between twovariables is not linear, future experiments should repeat the feeding experi-ment while incorporating intra and not only interspecific variation in bodysize.Parameterizing theoretical models in metacommunity ecology allow us toget closer to understand the effect of the different processes in nature. WhileI parameterized a simple model with the dispersal kernel of two species andtheir feeding interaction, there are still plenty of parameters that I had toignore. For example, growth rate, carrying capacity and mortality of thepredator are all parameters which I did not estimate. Next steps shouldalso include, not just which environmental conditions promote growth of thedifferent species, but also, how do abiotic gradients change the functionalresponse or dispersal propensity.Throughout my dissertation, I realized how important computational ap-proaches are for biology. Every single one of my chapters relied on intensecomputation, often through the access of clusters. I often helped other grad-uate students with their statistical and computational needs. This led me torealize that many biology programs are not preparing their students for thedemands of the job industry or academia. While not all biology undergradu-ates need strong computational skills, those going into ecology and evolutionare likely to need them. All of my chapters inspired me help undergraduatestudents in biology studying biostatistics to learn R programming. 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Body size and consumer-resource dynamics. Am.Nat. 139:1151–1175.136appendix aSupplementary Information to Chapter 1 - Towards amulti-trophic extension of metacommunity ecology.22Previously published as Guzman L.M., Germain R.M., Forbes C., Straus S., O’ConnorM.I., Gravel D.,Srivastava D.S., and Thompson P.L.2019. Towards a multi-trophic extension ofmetacommunity ecology. Ecology letters 22137appendix aa .1 abstractMetacommunity theory provides an understanding of how spatial processesdetermine the structure and function of communities at local and regionalscales. Although metacommunity theory has considered trophic dynamicsin the past, it has been performed idiosyncratically with a wide selectionof possible dynamics. Trophic metacommunity theory needs a synthesis offew influential axis to simplify future predictions and tests. We propose anextension of metacommunity ecology that addresses these shortcomings byincorporating variability among trophic levels in "spatial use properties". Wedefine "spatial use properties" as a set of traits (dispersal, migration, foraging,and spatial information processing) that set the spatial and temporal scales oforganismal movement, and thus scales of interspecific interactions. Progresstowards a synthetic predictive framework can be made by (i) documentingpatterns of spatial use properties in natural food webs, and (ii) using theoryand experiments to test how trophic structure in spatial use properties affectsmetacommunity dynamics.a .2 introductionMetacommunity theory formalizes the role that dispersal plays in determiningthe diversity, stability, and function of ecological communities at local and re-gional scales (Leibold et al., 2004; Holyoak et al., 2005). This rich body of theoryhas allowed ecologists to understand that ecological dynamics observed at thescale of local habitat patches are, in part, determined by dynamics in otherhabitat patches via the exchange of dispersing individuals. To date, metacom-munity ecology has been most successful at providing a theoretical predictiveframework for competitive metacommunities (Holyoak et al., 2005). However,we still lack a cohesive framework for trophic metacommunities (Leibold and138appendix aChase, 2017). The need for a general theory of trophic metacommunity arises(i) when we need to predict food web properties, which are incompatiblewith a competitive framework, and (ii) when interacting species use spaceat different scales; for example, when a predator population interacts withmultiple smaller-scale prey populations.A growing effort has been dedicated to exploring the consequences oftrophic interactions in metacommunities (Holt, 2002; Pillai et al., 2011; Gravelet al., 2011; Haegeman and Loreau, 2014; Beger et al., 2010; Treml et al., 2012).Despite recent empirical and theoretical advances that have laid a solid foun-dation for a synthetic theory of trophic metacommunities, our understandingremains fragmented due to the diversity of response variables (e.g., diversity,stability, network structure, energy flow) and representations of spatial con-straints (eg., perception of scale, types of movement). Traditional metacom-munity theory focuses on only one type of movement: dispersal. Dispersalis often related to reproduction (e.g., seed, larvae ,and gamete dispersal, ordispersal in search of mates), and therefore relates to only one particularcomponent of life-history. A recent review of metacommunity ecology sug-gested that future development of this theory must allow species to vary intheir abilities to experience the spatial environment (Leibold and Chase, 2017).As a consequence, we suggest that it is time to rebuild trophic metacommu-nity theory, using spatial processes as pillars of a more cohesive theory formetacommunity dynamics. We focus on five characteristics of "spatial useproperties" that we suggest should be at the center of a coherent and broadtheory of trophic metacommunities. We define "spatial use properties" aspopulation-level properties that reflect how species use space, and includethree forms of movement relevant to trophic metacommunities — dispersal,migration, and foraging (Gounand et al., 2017). We emphasize that speciesvary in their responses to the environment and to each other, that movement139appendix ais not just about dispersal, but an array of processes that each have their ownconsequences for population dynamics and, we highlight that differences inthe way species use space — a dynamic critical to metacommunity dynamics— is due to differences in these spatial use properties.We propose a framework as a first step to bridge the rapidly advancingfields of spatially-structured food web ecology, movement ecology and meta-community ecology. This framework: (i) builds on competitive metacom-munity theory to make it applicable to trophic dynamics, and (ii) explicitlyconsiders a set of 5 spatial use properties relevant to the spatial and temporaldimensions of trophic interactions. We emphasize the distinction between thethree forms of movement — dispersal, migration and, foraging — becausethey occur at different stages of an organism’s life-cycle, they couple differenthabitat types (e.g., different nearby habitat patches vs. summer and winterhabitats), they are initiated by different environmental cues, and they gener-ally occur over different spatial and temporal scales. Therefore, we expecteach form of movement to differ in their consequences for metacommunitydynamics. Future progress in trophic metacommunity ecology can be made bydocumenting the distribution and variation of these five spatial use propertieswithin and among food webs to generate empirical and theoretical predictionsfor how patterns in spatial use properties within a food web can affect meta-community dynamics the diversity and structure of food webs at local andregional scales. We also outline empirical and theoretical avenues to test ourpredicted consequences of spatial use properties in trophic metacommunities.140appendix aa .3 past and present metacommunity theorya .3 .1 Recent advances and challenges in trophic metacommunity researchWhile the theory for competitive metacommunities offers clear predictions,trophic metacommunity theory is remarkable in the diversity of topics ex-plored despite lacking an overarching organizational framework. The firstmodels were inspired by Huffaker’s 1958 famous experiment exploring thepopulation dynamics of herbivorous and predatory mites in an experimentalmetacommunity. Seminal metapopulation models by Holt and Hoopes (2005),Hanski (1999), and others investigated how spatial predator-prey dynamicscan contribute to regional coexistence. For example, predators may stabilizeprey populations that would otherwise overexploit their resources in the ab-sence of predators (Holt, 2002). The spatial nature of food webs has also beenconsidered previously (Holt, 2007). A greater geographic range of highertrophic level populations was noted by Elton (1966) and its implications forthe spatial scale of communities by Holt (1996) and Polis et al. (1996). Species(and resources) moving on different scales was recognized to result in spatialsubsidies between otherwise seemingly discrete food webs (Polis et al., 1997).Despite these early advances, the effects of spatial processes on food websdynamics has not been explored in a metacommunity context though they arebecoming increasingly apparent (Ward et al., 2015). Metacommunity config-urations can determine whether dispersal stabilizes or destabilizes predator-prey dynamics (Jansen, 2001; McCann et al., 2005; Amarasekare, 2008; Gravelet al., 2016b) and this understanding has pushed food web models towards amore general patch dynamics approach of predator and prey assembly. In aneffort to map different metacommunity paradigms to food webs, Baiser et al.(2012) found that pitcher plant inquiline community structure is best explainedby the species-sorting archetype (because of co-variation in response to theenvironment) and patch dynamics (because of a predominance of local inter-141appendix aactions). Other studies have used the source-sink framework to investigate themaintenance of food web structure, not only directly through the dispersal ofindividuals to poor quality patches, but also indirectly via the spatial exchangeof nutrients and energy (Gravel et al., 2010b,a). Such exchanges were furthershown to buffer spatial variation in patch productivity, potentially stabilizingtrophic metacommunities subject to the paradox of enrichment (Gounand et al.,2014).Emerging models of trophic metacommunities have demonstrated howtrophic interactions can help to understand basic ecological patterns and pro-cesses, such as species-area relationships, the co-distribution of predators andprey, range limits, and the restructuring of food webs in response to globalchange. For example, Holt et al. (1999), followed by Ryberg and Chase (2007),proposed that predator species richness should accumulate faster with in-creasing area than prey species richness. Similarly, Stier et al. (2014) showedthat predator species richness is less sensitive to isolation than prey speciesrichness. This difference between trophic levels has significant consequencesfor the interaction network-area relationship (Galiana et al., 2018). This phe-nomenon results from a sequential assembly of food webs, starting with gen-eralist species at the trophic base of the food web, followed by higher trophiclevels and more specialized species (Pillai et al., 2011; Gravel et al., 2011). Theco-distribution of predators and prey in trophic metacommunities appears tobe key to understanding spatial variation in local network structure (Cazelleset al., 2016). In addition to species turnover among patches, interaction net-works also vary in space due to spatial turnover in the realization of potentialinteractions (Poisot et al., 2012), with cold and hot spots of network beta-diversity (Poisot et al., 2016; Stier et al., 2014).Although existing metacommunity theory provides a guiding predictiveframework for how spatial processes affect the dynamics and structure of142appendix aspecies belonging to the same trophic level (Table a.1A; Calcagno et al., 2006;Mouquet and Loreau, 2003), those predictions are not applicable to the uniqueresponse variables that arise when trophic levels interact. When trophic levelsinteract, the local and regional food webs that are formed can be characterizedby network properties, such as connectance (Dunne et al., 2002), diversity ateach trophic level (Gamfeldt et al., 2005), and spatial turnover in pairwiseinteractions in a network (Poisot et al., 2012). Local communities that containidentical numbers of species might differ in their ratio of predators to prey, orin the average number of prey species that predators consume (i.e., linkagedensity Winemiller et al., 2001; Banasek-Richter et al., 2009). Additionally,because trophic levels are linked through consumption, the flow of energyand matter through local food webs might differ through space (Table a.1B).The greater array of metacommunity properties that characterize multi-trophicsystems may reveal spatial processes that are missed by the traditional suite ofmetacommunity response variables (Pillai et al., 2010) despite being essentialto food web stability (Rooney and McCann, 2012; Dunne et al., 2002).a .3 .2 Reformulating the assumptions of competitive metacommunity theoryLeibold et al.’s 2004 proposal of four metacommunity paradigms has guidedempirical research for much of the past decade (Table a.2A) though, subse-quent research demonstrates that communities rarely conform to any singlearchetype (Cottenie, 2005; Leibold and Loeuille, 2015). Rather, the distributionof organisms across habitat patches can reflect a combination of mechanisms,such as species sorting into some patches and mass effects into others, evenwithin a single species (Thompson et al., 2017). Others have suggested thatmetacommunity dynamics do not fit into discrete paradigms and instead arebetter represented as a continuum (Holyoak et al., 2005; Cottenie, 2005; Logueet al., 2011; Thompson et al., 2017). We argue that this continuum perspective143appendix aTable a .1 : Comparison of response variables of competitive metacommunityvs. trophic metacommunity theoryResponse class A. Competitive meta-community ecologyB. Trophic metacom-munity ecologyStructure Coexistence CoexistenceDiversity DiversitySpecies distribution Species distributionSpecies co-distributionComplexity/connectanceTrophic lengthTrophic modulesDynamics Stability StabilitySynchrony SynchronySpecies turnover Species turnoverInteraction turnoverTrophic regulation (top-down vs. bottom up)Energy Energy flow Energy flowProductivity ProductivityTrophic biomass pyra-mid144appendix ais more critical when we are interested in studying the dynamics of trophicmetacommunities, since different trophic levels are more likely to differ inthe way species use space than single trophic levels. Therefore, adoptingthis continuum perspective is necessary to extend metacommunity theory toencompass trophic interactions.Competitive metacommunity theory assumes that the suitability of habi-tat patches is determined only by the abiotic environment, and competitioncan allow species to exclude one another (Leibold et al., 2004). In a trophicmetacommunity perspective, patch suitability also depends on the interac-tions between species, because predators can only persist in patches that havesufficient prey (Gravel et al., 2011). Effectively, the presence of prey increasespredator persistence (i.e., a form of "niche construction"), whereas the presenceof predators decreases their persistence (i.e., "niche destruction") (Holt, 2009).Because the population dynamics of species linked by trophic interactions areinterdependent, patch suitability is dynamic through space and time, even inthe absence of abiotic heterogeneity. In this context, distinguishing amongpatch dynamics and species sorting archetypes becomes difficult (Table a.2A)because species sort into habitat patches based on the presence of predatorsand prey.It is clear that these systems where scales of movement and dispersal differamong interacting species violate the assumption inherent in most metacom-munity theory: species interacting and coexisting within the metacommunityexperience the environment at the same spatial and temporal scales. Thisassumption is reflected in three ways in competitive metacommunity models:(i) by forcing species to share a common dispersal rate (the proportion of thepopulation that disperses to another population in each generation), (ii) byconsidering only dispersal and not other forms of movement among popula-tions, such as migration or foraging, and (iii) by assuming species share the145appendix aspatial resolution at which they perceive the environment and their abilityto act on this information. Variation in dispersal rates has generally beenconsidered in competitive contexts where competition-colonization trade-offspromote coexistence (Cadotte, 2006a). In empirical studies, however, bulk dis-persal is the most commonly used method for altering dispersal rates, whichprevents detection of interspecific differences in dispersal abilities (Graingerand Gilbert, 2016). Grainger and Gilbert (2016) argue that the heterogeneitythat many experimenters choose to remove is necessary to detect metacom-munity processes, leading to an inability to robustly test a growing body oftheory. Variation in dispersal rates has also been applied to simple predator-prey systems where coexistence is promoted by a higher colonization rate inthe prey species (Holt and Hoopes, 2005). In particular, studies of host-parasiteinteractions revealed that differences in dispersal rate and/or scale could havehuge impacts on metacommunity dynamics because parasitoid infection wasfound to be dependant on host dispersal rate (Holt and Hoopes, 2005) anddifferences in host vs. parasitoid dispersal rate was found to destabilizedynamics (Rohani et al., 1996). In a two-parasitoid model, the less mobilespecies was able to persist only in small pockets of high host density, resultingin a competition-colonization trade-off for the competing parasitoids (Neeet al., 1997). However, beyond two-species systems, differences in dispersalbetween species of different trophic levels are only recently being considered(Haegeman and Loreau, 2014; Pedersen and Guichard, 2016; Thompson andGonzalez, 2017; Jacquet et al., 2017). Differences in dispersal rates betweentrophic levels are expected to be much greater than differences within trophiclevels because, for example, species at different trophic levels tend to differ inbody size and life history (Haskell et al., 2002; McCann et al., 2005). Thishas consequences for the structure of local and regional trophic networks(Woodward et al., 2005). With larger body size also comes longer lifespans146appendix aand greater energetic requirements (Speakman, 2005), and thus the need forother forms of movement, such as foraging and migration, to track daily andseasonal variation in resource supply, respectively. It is for these reasons thatwe will explore the consequences of differences between interacting speciesnot only in dispersal but also in foraging and migration, and how species-specific differences in these "spatial use properties" affect the structure of foodwebs.Metacommunity theory has not yet explicitly integrated the effects of move-ment governed by perception of the environment on spatial biodiversity pro-cesses, even though perception and behaviour are central to the interactionsbetween species (Table a.2B). Existing metacommunity models implicitly as-sume that demographic consequences of behaviour are captured in local pop-ulation dynamics. Metacommunity models based on patch dynamics andspecies sorting assume that the probability that an organism exists in a habitatpatch (often equated to a population) is based on its colonization and extinc-tion probabilities (Levins and Culver, 1971; Law and Morton, 1993). In reality,this probability is not fixed but varies with patch quality and the experience ofthe dispersing organism through prey seeking, predator avoidance, avoidanceof competition and selection of suitable habitat, all of which occur at the levelof the organism but which have consequences for stability of the entire foodweb (Kondoh, 2003). For example, predators might leave habitat patches whentheir prey reach low abundances, buffering prey populations from extinction(Holt, 1984), or prey might avoid dispersing to habitat patches that containpredators, bolstering the prey’s regional fitness and allowing predators andprey to coexist regionally (Resetarits, 2005). Similarly, individuals may chooseto leave patches with high densities of intra- or interspecific competitors allow-ing more stable, regional coexistence (Fronhofer et al., 2015). Movement andbehaviour of individuals that link patches can affect the population dynamics147appendix aand persistence of other species. The latter is traditionally the domain ofmetacommunity concepts, but a food web perspective highlights that individ-ual decisions about movement in space can couple these population dynamics(McCann et al., 2005).a .4 spatial use properties and theirconsequences for pairwise trophicinteractions across scalesSpatial use properties must be considered beyond abiotic niches and dispersalin order to expand metacommunity theory. We propose to incorporate addi-tional ones related to temporal and spatial scales of migration, foraging, andspatial information processing, all of which with very different implicationsfor population dynamics. We propose to differentiate these forms of move-ment since they happen at different times in an organism’s life, they coupledifferent habitats in space and in time, they occur at different temporal fre-quencies and each may have varied consequences across scales of observation.In this section, we draw on theory from movement ecology and food webecology to consider explicitly how to integrate the consequences of species’differences in spatial use properties (Figures a.4 and a.4.1), and provide ex-amples where spatial use properties vary with trophic level in natural systems.We also consider how spatial use properties may be estimated in terms ofmeasurable organismal traits.a .4 .1 Abiotic nichesSpecies’ abiotic niches, and their overlap, play a major role in determiningthe spatial distribution of species in metacommunities. Interactions are onlypossible between species that overlap in their abiotic niches, except for speciesthat can transiently forage in or disperse through environments that are other-148appendix aTable a .2 : A synthesis of ideas in metacommunity ecology (formalized inLeibold et al. (2004)) and food web ecologyProcess Application to compet-itive communitiesExtension to trophicmetacommunitiesIncompatibilitywith trophicmetacommunitiesSpatial use propertiesrelevant to coexistenceA. Metacommunity ecologyPatch dynamics(Levins and Culver,1971; Levin and Paine,1974)Competition-colonization tradeoffsallow the regionalcoexistence ofspecies that differin competitive abilityPrey must dispersemore than theirpredators; predatordistributions must be anested subset of theirpreyNone Dispersal; niches (incl.biotic environment)Species sorting (Tilman,1982; Leibold, 1998;Chase and Leibold,2003)Species differ in whichpatches are suitable,with suitability definedby abiotic conditionsand competitive inter-actionsThe presence ofpredators and prey (i.e.,trophic interactions)also affect patchsuitabilityPatches must containprey to be suitable toa predator, thus preda-tors and prey can nevercompletely sort intodifferent patchesDispersal; Niches (incl.biotic environment)Mass effects (Shmidaand Wilson, 1985)High dispersal erodesthe effects of speciessorting such that abun-dance does not fullyreflect patch suitabilityThe presence ofpredators and preyalso affects patchsuitability; predatorsand prey maintained inneighbouring patchescan impact each otherNone Dispersal; Niches (incl.biotic environment)Neutral interactions(Hubbell, 2001)Species are competi-tively equivalent, con-suming the same re-sourcesNot extendable Neutral interactionsare not possiblebetween species thatdo not consume thesame resourcesDispersalB. Food web ecology*Process Application to foodweb ecologyApplication to foodweb ecologyExtension to trophicmetacommunitiesIncompatibilitywith trophicmetacommunitiesSpatial coupling (Mc-Cann et al., 2005)Predators forage atlarger spatial scalesthan their prey,linking local foodwebs togetherPromotes food web sta-bility when predatorsare generalistsPredators forage atlarger scales than preyForaging scaleBehavioural adaptiveforaging (Kondoh,2003)Dynamic shifts in for-aging strategies to opti-mize prey captureCurrently not incorpo-ratedCurrent formulationsof metacommunitytheory do not allow forchanges in interspecificinteractions and theresponse to space dueto behaviourForaging scale and spa-tial information pro-cessing149appendix aF igure a .1 : (a) Schematic representation of the three forms of movementhighlighting the differences of the three forms of movement based on habitatand timescale. The differences between the types of movement for spatialscale are dependent on the organism. (b) A hypothetical distribution ofspecies spatial use properties, where each axis dimension is one of the threemovement types, and each point is a species’ characteristic movement distance.Dark blue points correspond to those with high levels of migration, andlight blue to those with low levels of migration. Data are simulated withmultivariate normal distributions, and the empty regions represent ecologicalor evolutionary constraints. We present two scenarios with no covariancebetween movement types or covariance between movement types. When thereis no covariance between movement types, knowing the scale of one type ofmovement can not allow for predictions about the others. We highlight threeexamples of organisms that vary in their scales of movement among the threemovement types (1 = Tallman Healey 1994, 2 = Dickson Beier 2006), 3 =Pineda et al., 2007). Three spatial use properties are shown for visualisation,but all five are possible.150appendix awise lethal (Holt, 1993; Mouquet and Loreau, 2003; Rahel and Nutzman, 1994).We expect abiotic niches to correlate between trophic levels when predatorsare specialists and need to track their prey. Generalist predators are notconstrained to their prey distribution and therefore their abiotic niches maynot correlate with their prey’s abiotic requirements. Incomplete overlap ofabiotic niches may allow for spatial refugia from predation or competition,or constrain species ranges for species that depend on other species for per-sistence (e.g., specialist predators). In addition, we expect that changes inenvironmental conditions will determine not only a species’ spatial distribu-tion, but also food web responses such as food chain length and the shape ofbiomass pyramids (Tunney et al., 2012).We expect that the consequences of partial overlap in abiotic niches shoulddepend on which trophic level has the narrower niche. If species belonging tolower trophic levels have wider niches, then prey populations might benefitfrom spatial refugia in environments outside their predators’ niche envelope.For example, mosquitofish are more tolerant to warm temperatures comparedto their bass predators, which allows them to escape predation by residingin warm habitats (Grigaltchik et al., 2012). Conversely, the abiotic niches ofspecies at higher trophic levels may be limited if their prey have lower abiotictolerances (e.g. Figure a.4.1b). For example, a butterfly with the physiologicaltolerance to handle high elevations, can be limited to low elevations by thelow elevation range of its host plant (Merrill et al., 2008).a .4 .2 Three forms of movementDispersal, migration, and foraging differ in in their frequency and timingwithin an organism’s life cycle; more importantly they have different conse-quences for the dynamics of trophic metacommunities (Figure a.4a). We firstdefine each movement process, and then unpack their unique consequences151appendix aF igure a .2 : Schematic representation of simulation outcomes for food webstructure in two patches and three time points. The food web consists of twoprimary producers (squares), one herbivore (circle) and one predator (triangle).We show five scenarios of species differences in spatial use properties. (a) Thespecies in this food web do not vary in spatial use properties and thereforethe food web does not vary through space or time. (b) The environment variesbetween patch 1 and patch 2 and because the herbivore has a narrower abioticniche, it cannot persist in the red patches. The predator consequently also goesextinct in these patches. (c) In this food web, the herbivore has a much lowerdispersal than any other species in the food web. Over time, the herbivore isable to reach distant patches. (d) In this food web, the herbivore has a largerforaging scale than any other species in the food web. The herbivore alternatesforaging between patches, frequently enough to allow the predator to persist.(e) The top predator migrates in and out of the region, (here presented as amodule, each module has two patches) with little effect on the persistenceof other species (although abundances may change). (f) In this food web,plants have lower spatial information processing and they are unable to trackchanging abiotic conditions in patches. The herbivore and the predator trackthe abundance of the plants.152appendix a153appendix afor spatial food web structure, particularly when they differ among trophiclevels. The first form of movement, dispersal, occurs once in a lifetime viathe movement of individuals to new habitat patches. When an individualdisperses, it permanently leaves a patch and enters another patch of the sametype of habitat. As such, dispersal can allow a species to colonize a patch thatwas previously unoccupied or can contribute individuals to existing popula-tions, affecting population size and stability. The second form of movement,migration, is the tracking of seasonally available resources or mates by indi-viduals, and typically occurs annually or once in a lifetime. Unlike dispersal,individuals or their progeny complete migration by returning to their originalhabitat type; migration does not act to link populations together like dispersalbut tends to move single populations through many food webs. Migrationis a more predictable event, with proximate cues depending on body condi-tion and climatic and phenological processes. The last form of movement,foraging, is the frequent exploration of space by organisms as they search forresources. Species differ in the spatial scales over which foraging takes place,from very localized for some (e.g., plants through roots) to highly mobileand integrating resources across many habitat patches in a region (Dobson,2009). Foraging behaviour is highly variable, with decisions depending onthe availability and preference of different prey types as well as predator risk(Figure a.4a). We provide the following example to clarify the differencesbetween the types of movement: Dragonflies forage when they are larvaewithin ponds. Although they are sit and wait predators, they can still foragewithin ponds to find higher abundances of prey (Johansson, 1991). Thenthey undergo metamorphosis, an ontogenetic habitat shift. We categorize thisontogenetic habitat shift as the first part of a migration, as aquatic habitatsand terrestrial habitats are different types of habitats, and terrestrial adultswill eventually return to ponds to oviposit, completing the cycle between154appendix ahabitats. Finally, adult dragonflies may stay in their natal pond, or disperseto a different pond (McCauley, 2007). Here the movement as adults betweenponds is a dispersal event since they are moving between habitats of the sametype. While each of these three forms of movement may occur over distinctspatial and temporal scales, each form of movement will likely have differentconsequences for food web structure and stability across multiple scales ofspace and time. For example, at the local scale of a marine rocky reef system,sea urchins may be extirpated by foraging sea otters, however, urchins mayrecover locally due to the dispersal of urchin gametes from distant populationsor alternatively, by the migration of transient orcas that eat sea otters. Here,multiple types of movement, each primarily occurring over different scalesof space and time and by organisms at different trophic levels, interact toproduce dynamics at a single scale that could not be fully understood withoutconsideration of each simultaneously. We consider dispersal, migration andforaging to be different types of movement (i) because they are not necessarilycorrelated, and therefore, it is difficult to infer anything about the scale ordynamic consequences of these processes from knowledge of another of theseprocesses; (ii) they have dramatically different effects on the trophic dynamicsof a metacommunity since they occur at different stages in an organism’slife cycle and because they couple different habitats. These three spatial useproperties have recently been highlighted as key to understanding spatialflows of energy in meta-ecosystems (Gounand et al., 2017), but their effectson metacommunity dynamics and coexistence are not well understood.Consequences of dispersal — Differences in dispersal rates amongtrophic levels may stabilize population dynamics and lead to more complexfood webs than would exist in the absence of dispersal (Hauzy et al., 2010).Spatial asymmetries in dispersal among interacting consumer and resourcepopulations can produce distinct spatial distribution of resources. For ex-155appendix aample, when resource populations have limited dispersal and the consumerhas global dispersal, the resource density becomes highly variable in space(e.g. Figure a.4.1c). On the other hand, when the consumer has limiteddispersal and the prey disperses regionally, the prey is able to persist insubsets of patches that do not contain their predators (de Roos et al., 1998;McCauley et al., 1993; Pedersen and Guichard, 2016). It is expected that ratesof dispersal often vary systematically with trophic level, e.g., larval dispersalis greater in predator versus prey species in Pacific reefs (Stier et al., 2014).More generally, we expect that specialist predators require a higher dispersalrate than generalist predators because they need that a particular prey speciesto be present before it can colonize new habitats (Holyoak et al., 2005).Consequences of migration — Species’ migration determines the move-ment of species among habitat type patches, for reproduction and resourceconsumption. Migration links patches of different habitat type, where speciescomposition is different. In contrast, when individuals disperse and forage,they typically move between habitats of the same type, with similar speciescomposition. In the case of foraging, the movement of individuals betweenthese compositionally-similar habitats may be driven by variation in resourceabundance. Classic examples of migration include whales migrating towardsthe poles in the search of food resources during the summer and migratingtowards the tropics during their breeding season in the winter months (Stoneet al., 1990), wildebeest following the flush of grass growth across the Serengeti(Holdo et al., 2009), and waterfowl migrating across latitudes to follow thegrowing season of plants (Van der Graaf, 2006). In addition, some speciesswitch habitats at some point in their life cycle if they require sequential hosts(i.e., parasites) or resources to complete development (Molnár et al., 2013). Forexample, many insects transition between aquatic and terrestrial life histories,or between belowground and aboveground dwellers as they develop from156appendix alarvae to adults. We aggregate migration and habitat switches as both actas spatial subsidies for the receiving food web and link different habitats.Migration can influence the structure and dynamics of local food webs,involving non-migrating species, by providing a temporal influx of energy,nutrients, and temporary competitors, natural enemies or facilitators. Forexample, migration may allow the maintenance of populations in low pro-ductivity ecosystems such as the Arctic, where large populations of migratorybirds disrupt the trophic interaction between terrestrial carnivores and smallrodents (Giroux et al., 2012). These spatial subsidies can occur at differenttrophic levels, for example, a prey species may migrate into a communityand provide resources to predators, which can release local prey from risk.Alternatively, predators may migrate which can depress prey populations andhave either stabilizing or destabilizing effects (Polis et al., 1997).Consequences of foraging — Foraging movements are within-populationmovements of one species that can affect the dynamics of other species. Foodwebs across habitats may be coupled when predators and prey differ in thespatial scales at which they forage (e.g. Figure a.4.1d) (Polis et al., 1997;McCann et al., 2005). For example, if predators forage at broader spatialscales (meaning, over greater areas) than their prey, prey populations in onehabitat patch can increase the abundance of predators in an adjacent habitatpatch. Because organisms can forage in habitat patches that are outside theirabiotic niches (Rahel and Nutzman, 1994), a predicted outcome of linkinglocal food webs via foraging activities is the realization of a greater range oftrophic interactions than a given habitat patch would otherwise support. Asa consequence of spatial coupling among habitat patches, local dynamics maybe decoupled, leading to otherwise unstable food web structures (McCannet al., 2005).157appendix aThe consequences of foraging on metacommunity structure depends on themismatch between species at different trophic levels in the use of space; somepredators forage over smaller spatial areas than their prey, whereas othersforage over larger areas than their prey. We must first consider two generalconstraints to understand the causes of mismatches in foraging extent amongtrophic levels: i) consumptive interactions are energetically inefficient, withonly 10% energy transfer from food consumed into the bodies of individualsof the consumer population (Trebilco et al., 2013), ii) foraging is also costlybecause of energetic demands and lethal risks of movement (Anderson andKarasov, 1981; Pyke, 1984). The spatial scale of foraging should thereforereflect the minimum area needed to meet energetic and nutritional require-ments given the spatial distribution of prey (DeLong et al., 2014; Laca et al.,2010). Foraging can be highly localized for predators with locally replenishingprey (e.g., web-building spiders with a sit-and-wait strategy), or integrate overmuch larger spatial scales for predators with scarce, depleted and patchilydistributed prey (e.g., predatory birds that must actively seek prey). Mis-matches in the spatial scale of foraging occur among trophic levels whentheir constituent species differ in spatial scales at which energetic/nutritionalrequirements are met (Higginson and Ruxton, 2015). Such differences inforaging scale between trophic levels will create spatiotemporal dynamics infood webs, and therefore are a critical part of understanding trophic metacom-munities.a .4 .3 Spatial information processingTraditional metacommunity ecology assumes that dispersal is passive. Thisassumption becomes problematic when studying food webs, especially forhigher trophic levels where movement involves cognitive and information pro-cessing systems that allow organisms to actively determine when and where158appendix ato move (e.g. Figure a.4.1f). Movement therefore often requires the capacityto receive, store, and process spatially explicit information about the environ-ment; we refer to this capacity as spatial information processing. Spatial infor-mation processing can affect any of the three forms of movement - dispersal,migration and foraging- and encompasses ‘habitat selectivity’, or the degree towhich individuals control their movement based on local conditions. However,spatial information processing requires organisms not only to sense their localenvironment (requiring ability to perceive environment), but also the environ-ment of adjacent patches (requiring spatial memory to integrate perceptions).Organisms must then use this information to aid their navigation and decidewhere to go (Nathan et al., 2008a). Spatial information processing can havelarge consequences for the distribution of species in space. For example,colonization rates can depend not only on the perceived quality of one patch,but also that of surrounding suitable patches, leading to spatial contagion(Resetarits and Silberbush, 2015). Mathematical models of animal movementssuggest that perception of environmental stimuli affects movement decisions(Hein and McKinley, 2012), and that increased spatial memory optimizes timespent foraging in suitable patches (Fagan et al., 2013).The ability to process spatial information likely differs between trophiclevels. In general, we expect selectivity to increase with trophic level, withplants and microbes being the least selective and top predators being the mostselective (but there are also counter examples). Organisms at higher trophiclevels tend to have greater cognitive function and brain size, both of whichcorrelate with greater habitat selectivity (Rooney et al., 2008). In particular,actively foraging consumers require more spatial memory to efficiently exploittheir environment (Edmunds et al., 2016), and so have larger hippocampalcomplexes and putative hippocampal homologues both across and within taxa(Krebs et al., 1989; Baird Day et al., 1999). Similarly, animals with larger brains,159appendix afor example mammals, have a greater degree of behavioural flexibility andare better able to successfully colonize new environments (Sol et al., 2008).However, increased brain size also comes with increased energetic demands(Fagan et al., 2013) and thus the need for increased foraging.The scale at which organisms perceive their environment reflects the scaleat which they use that environment. Some organisms, such as seabirds, forageacross multiple habitat types to meet their nutritional requirements (Oriansand Wittenberger, 1991) and so must be able to perceive the patchiness ofthe landscape and select for certain patches. Habitat specialists may perceivea higher degree of habitat heterogeneity than generalists, resulting in theirrestriction to small amounts of suitable habitat surrounded by perceived bar-riers (Holyoak et al., 2005). Larger species have longer viewing distancesand therefore a wider scale of perception (Kiltie, 2000), allowing them tomove farther and survive for longer in novel environments (Sol et al., 2008).However, faster moving animals also have less accurate perception, potentiallyexplaining changes in visual acuity with trophic level (Chittka et al., 2009).Indeed, the ability to navigate through sensory perception and memory haslikely co-evolved with movement capacity, and together these factors influencehow and where an individual may move (Fagan et al., 2013; Nathan et al.,2008a).a .5 predicted effects of (co )variation in spatialuse properties on trophic metacommunitydynamicsPredicting the consequences of different distributions of spatial use proper-ties will require deeper theoretical investigation than is possible here, butwe nonetheless propose a few general patterns as a starting point. As anillustration, we examine the dynamics of a simple food web of four species160appendix a(two plants consumed by one herbivore, which itself is preyed upon by onepredator) in two patches using the model presented in appendix S2. Weparameterized this model with simple scenarios where at least one species inthe food web varies in their spatial use properties from the rest of the food web(Figure a.4.1). The same food web will occur in all patches at all timepointsif species do not differ in their spatial use properties, the environment ishomogenous and dispersal between patches is null (Figure a.4.1a). Changes indiversity and food web composition through space or time arise with variabil-ity in spatial use properties (Figure a.4.1). For example, the herbivore cannotpersist in the red patch of Figure a.4.1b, only on the black patch when it hasa narrower abiotic niche and species do not disperse between patches. Sincethe herbivore is permanently absent from the red patch, the predator is alsoabsent because of starvation. Similarly, the herbivore will be absent from thesecond patch if it has very low dispersal (Figure a.4.1c). In this case however,the predator is only present via dispersal, where the second patch becomes asink population for the predator, given that there is no prey present (Figurea.4.1c). The predator can persist if it has a larger foraging scale because of theconsumption of herbivores on both patches. Even if there are no herbivoreson the patch that contains predators, the predator will be able to persist bycoupling the two patches and foraging on the second patch (Figure a.4.1d).In the case where the predators migrate in and out of a metacommunitymodule, they will affect the abundance of the herbivores only when they arepresent in that module (Figure a.4.1e). Finally, when the plants have lowerspatial information processing, they will be slower at tracking changes in theabiotic conditions of patches. This inertia could cascade to other trophic levelsif upper trophic levels track their resources more closely than they do theirenvironment (Figure a.4.1f). Overall, we expect increased network diversity,complexity, and stability when trophically-linked species are dissimilar in161appendix atheir spatial use properties. This should coincide with greater difference in thespatio-temporal dynamics of each species. These results, based on a relativelysimple model, show how differences in spatial use properties across trophiclevels can impact the dynamics, diversity, and food web structure of trophicmetacommunities. Further work is now needed to fully integrate spatial useproperties into trophic metacommunity models and theory.a .6 future directions : building and testingfuture metacommunity theory based onspatial use propertiesWe have argued that incorporating spatial use properties will provide a deeperunderstanding of trophic metacommunities; our challenge is now to use thisperspective to develop, test, and refine a body of trophic metacommunitytheory. To accomplish this goal, efforts are now needed to (i) documentthese five spatial use properties within food webs, (ii) use meta-analyticalapproaches to investigate patterns of spatial use properties across scales ofspace time and and organization, within and among food webs, (iii) developnew theory for how the relative scales of spatial use properties across trophicgroups affects metacommunity dynamics and their outcomes, and (iv) testwhether empirical biodiversity patterns in trophic metacommunities can beexplained by the scales of ecological processes related to spatial use properties.( i ) Documenting spatial use properties within food webs —Before new theory about trophic metacommunity dynamics (goals iii-v) canbe tested, we require quantitative measures of spatial use properties (usingtraits) within food webs. This is a challenge, because spatial use propertiesthemselves are rarely quantified directly in empirical studies. We propose a setof measurable traits that can be used as proxies of spatial use properties (Table162appendix aa.3), to quantitatively compare differences in the spatial scales and extentsmovement among interacting species. A single measurable trait may not besuitable to estimate differences in spatial use properties across all trophiclevels ranging from microbes to top predators. Experiments coupled withobservations from multiple techniques may be required to estimate spatialuse properties for whole food webs. For example, bacterial movement can bestudied using microfluidic devices (Englert et al., 2009), insect movement withharmonic radar (Chapman et al., 2011), and mammal movement with radiotags (Millspaugh, 2001).( i i ) Using meta -analytical approaches to investigate patternsof spatial use properties within and among food webs — Doc-umenting the scales and mechanisms associated with spatial use propertieswill provide the empirical evidence needed to answer the question of whetherthese properties vary systematically within and across food webs, using meta-analytical approaches. It will also allow us to test whether spatial use proper-ties are constrained by physiological, morphological or evolutionary trade-offs.In other words, can we use knowledge of one spatial use property within afood web to infer the the structure of another spatial use property in that foodweb? (Figure a.4b).The synthesis of metacommunity and spatial food web concepts we havereviewed here implies that within a food web, organisms vary in their spa-tial use properties and that this variation affects metacommunity dynamics.Species at different trophic levels have very different energetic needs and lifehistory strategies (Trebilco et al., 2013). Furthermore, both trophic level andspatial use properties such as dispersal, migration and foraging scale withbody size (Kalinkat et al., 2015; McCann et al., 2005; Hein et al., 2012). However,these scaling relationships have been generated by aggregating species acrossmany food webs and therefore little is known about how spatial use properties163appendix aTable a .3 : Spatial use properties and how they correspond both tomeasurable traits and parameters in the modelling framework described inthe text.Spatial usepropertiesMeasurable organismal traits Model parame-tersAbiotic niches Temperature tolerance (Magnuson et al., 1979;Huey and Kingsolver, 1989) Drought tolerance(Engelbrecht et al., 2007; Schimper et al.,1903) Range limits (Ehrlén and Morris, 2015;Parmesan et al., 2005; Sexton et al., 2009)Stoichiometric niche (González et al., 2017;Sterner and Elser, 2002)Species-specificenvironmentaloptima andenvironmentalbreadthDispersal scale Maximum dispersal distance (Nathan et al.,2008b; Levin et al., 2003; Cain et al., 2000)Dispersal rate (Hanski, 1991) Number ofpropagules (Shanks et al., 2003; Simberloff,2009) Gene flow (Palumbi, 2003; Slatkin, 1987)Mode of locomotion (Stevens et al., 2014; Ronceand Clobert, 2012)Dispersal rateand distanceMigration scale Migration propensity (Hanski et al., 2004; Aler-stam et al., 2003) Migration distance (Websteret al., 2002) Stable isotopic ratios (Hobson,1999)Migration rateand distanceForaging scale Home range size (Börger et al., 2008; Mitchelland Powell, 2004) Radio collars for dailymovement (Harris et al., 1990)The numberof patches thateach speciesuses to forageSpatialinformationprocessingRelative brain size (Fagan et al., 2013) 2d vs.3d perception (Pawar et al., 2012) Sensingappendages (Vickers, 2000; Mitchinson et al.,2007) Active vs. passive dispersal (Cottenie,2005; Van de Meutter et al., 2007)Changes tomovementdue toenvironmentalvariation164appendix aare structured within individual food webs. A related question that could beanswered through meta-analysis of is whether trophic structure in spatial useproperties varies systematically across different ecosystem types. We mightexpect such systematic differences between ecosystem types to arise becauseof differences in the evolutionary histories of their constituent species (e.g.,aquatic vs. terrestrial), regional environmental structure (e.g., patchiness), orbioclimatic differences on larger geographic scales (e.g., temperate vs. trop-ical). Identifying additional scaling relationships, and their causes, will notonly allow application of this framework with efficient use of data for param-eterizing models, but will also help understand how macro-ecological andphysiological constraints may influence spatial processes in metacommunities.Understanding covariances in spatial use properties across species canreveal biological or evolutionary constraints and tradeoffs of these properties,as well as variation in those constraints among ecosystems (Díaz et al., 2016).For example, relative brain size (a proxy for spatial information processing) issmaller in migratory than in non-migratory birds due to an energetic trade-offbetween neural tissue volume and migratory flight (Vincze, 2016). Similarly,traits relevant to particular types of movement (foraging, migration, dispersal)might be positively correlated (Bowman et al., 2002) as each has been shownto increase with body size (De Ryck et al., 2012; Kelt and Van Vuren, 1999;Greenleaf et al., 2007; Alerstam et al., 2003; Hirt et al., 2017); for this reason,we refrain from assigning body size as a proxy for any specific spatial useproperty (Table a.3). A high degree of covariation among spatial use proper-ties might simplify predictions in some ecosystems. Non-random covariationamong traits will constrain the range of local food web structures that arepossible for theoretical studies (Gravel et al., 2016a).( i i i ) Developing new theory for how the relative scales ofspatial use properties across trophic groups affects meta-165appendix acommunity dynamics and their outcomes — We can use theo-retical models to explore the consequences of different trophic structures inspatial use properties for the stability and network structure of food webs.By constraining this exploration based on documented patterns of spatial useproperties (goals i and ii) will allow us to focus on and contrast the predictedoutcomes of patterns that are found in specific food webs or ecosystem types.We have outlined how this could be done using a modelling approach thatincorporates the five spatial use properties (Figure a.4.1). This constrainedexploration will allow us to ask what are the commonalities and differencesin how the five spatial use properties affect food web stability? and how doestrophic metacommunity structure and persistence respond to environmentalchange and habitat loss? Given the importance of spatial use properties forthe dynamics and stability of trophic metacommunities as we suggest here,we hypothesize then that diversity associated with trophic status in traitsrelated to spatial use properties might be a particularly important dimensionof diversity for spatially structured food webs (McCann et al., 2005). Forexample, McCann et al. (2005) showed that when predators forage at largerspatial scales than prey, they can stabilize food webs. Similarly, differences indispersal between predators and prey can result in stability of the interactions(Pedersen and Guichard, 2016). We suggest that it should be addressed withtheory that is guided by observational patterns of spatial use properties (i.e.goals i and ii) and then tested using experiments. If, for example, fish inponds are observed to forage at larger scales but disperse at smaller scales thaninvertebrate prey, we can develop models that provide theoretical predictionsfor how these movement differences affect the spatial distribution of the twotrophic levels. We can test these predictions by experimentally manipulatingfish foraging and dispersal via movement restriction (i.e., size-specific mesh)and assisted dispersal, respectively.166appendix aMovement is a key process that determines how communities respond toenvironmental change and habitat loss (Loreau et al., 2003; Norberg et al., 2012;Thompson et al., 2017; Grilli et al., 2015). Despite the fact that we knowthat trophic level is a key predictor of how species will respond to suchchanges , we have limited theory that links this response to movement withina food web context (Thompson and Gonzalez, 2017). Theoretical modelsoffer the opportunity for developing expectations of how different patternsof spatial use properties affect the response of food webs to different forms ofenvironmental change or habitat loss. This theory is needed for informing andinterpreting experiments since the presence of predators has often interferedwith our ability for experiments to match theoretical predictions (Graingerand Gilbert, 2016).( iv ) Testing whether empirical biodiversity patterns in trophicmetacommunities can be explained by the scales of ecologi-cal processes related to spatial use properties — Inferring thespatial processes that govern the diversity and functioning of communities isa major goal in metacommunity ecology (Leibold and Chase, 2017). Yet, meth-ods for linking patterns of abundance to different metacommunity paradigms(Cottenie, 2005; Ovaskainen et al., 2017) do not have a systematic way ofincorporating trophic interactions, nor variation in movement between trophiclevels. We demonstrate how our framework can be used to link patterns ofabundance to spatial use properties with a food web module from a meta-community of bromeliad-dwelling invertebrates (Box 1). This example showshow observational data may be coupled with structural equation models tountangle how space affects food web structure. Additional efforts to formalizethese links in other systems with existing data would be one way to rapidlyadvance our empirical understanding of trophic metacommunities.167appendix aThe questions and avenues of research we highlight are underexploredand promise rich research opportunity. The feasibility of answering thesequestions will undoubtedly vary among food webs, particularly those forwhich spatial use properties are difficult to quantify with reasonable certainty.Trophic metacommunities are complex and and models will need to dealwith the rich natural history that underlies species interactions and movement(such as omnivory, territoriality, ontogenetic niche shifts, non-consumptiveeffects and cross-ecosystem subsidies). Experiments and observational studieswill guide theoretical studies to manage that complexity. Further develop-ment of trophic metacommunity theory requires a feedback between empiricalobservation, theory, and experiments. We believe that this approach offersexciting possibilities and has the potential to guide the development andtesting of the next generation of trophic metacommunity theory.Box 1: Trophic metacommunities in bromeliad-dwelling insectWe use a food web module from water-filled bromeliads in Costa Rica toconsider how shifts in the relative abundances of species along a habitat sizegradient can be understood in terms of species differences in their spatial useproperties (colonization rates, abiotic niches) and susceptibility to predators.Culex spp. and Wyeomyia spp. mosquitoes are potential competitors andare both preyed upon by Mecistogaster modesta damselflies. All three taxashow strong patterns with bromeliad size, with the abundance of Culex andMecistogaster increasing with bromeliad size, and Wyeomyia decreasing withbromeliad size (Figure a.6a). Bromeliad size affects species in three ways.168appendix a(1) Numerical effects on colonization. If colonization probability is relatedto available habitat, as often assumed in competitive metacommunity models,we would expect larger bromeliads to be colonized more frequently than smallbromeliads, such that species with small regional populations and thus fewcolonists (Mecistogaster) occur entirely in the large bromeliads whereas specieswith larger regional populations (Culex, Wyeomyia) occupy mainly large butalso some medium-sized bromeliads. Although such numerical effects explainthe distribution of Culex, Mecistogaster still occurs in larger bromeliads thanexpected and Wyeomyia in smaller bromeliads than expected.(2) Abiotic niche differences. Small bromeliads are at risk of drying outwhile insects are still aquatic larvae, and this risk is particularly acute forMecistogaster, whose larvae require ca. 9 months to develop. Culex andWyeomyia larvae require ca. 3 weeks to develop and have less exposureto drought risk (Figure a.6b). After correcting species abundance fornumerical effects on colonization probability, residual Mecistogaster abundanceis positively related to bromeliad size in a structural equation model —presumably reflecting its greater likelihood of drought exposure at some pointduring the larval stage. Wyeomyia residual abundance is negatively relatedto bromeliad size, potentially because drought-resistant eggs in this genus(unlike Culex) enable it to preferentially colonize small bromeliads.169appendix a(3) Trophic interactions. Finally, bromeliad size may affect species indirectlyvia predation or competitive interactions. In our structural equation model,Wyeomyia occurs in smaller than expected bromeliads because it is negativelyaffected by its predator, Mecistogaster, which in turn occurs disproportionatelyin large bromeliads. By contrast, Culex abundance is unaffected by effects ofbromeliad size mediated by Mecistogaster (Figure a.6c). This is consistent withthe documented ability of Culex — but not Wyeomyia — to chemically detectMecistogaster and avoid predation through a change in foraging behaviour(Hammill et al., 2015a). This example shows the power of combining statisticalanalyses with documented differences between species in their response toabiotic stress and predation to understand the distribution of the food webmodule between habitat patches. Deeper understanding of this module couldbe achieved by studying how other spatial use properties differ betweenthese species, such as spatial information processing by ovipositing adults,or dispersal (pupation) cues for mosquito larvae.a .7 conclusionWe argue that metacommunity theory must incorporate trophic interactionsto encompass the full range of dynamics that occur in real-world communi-ties. We began by outlining challenges to extending metacommunity ecologybeyond competitive systems, with suggestions for how to overcome thosechallenges by reformulating some basic assumptions. We then proposed thatprogress towards a trophic metacommunity framework could be achieved byaccounting for a wider array of spatial use properties than the traditionalmetacommunity framework allows. These spatial use properties are (i) abi-otic niches, (ii) spatiotemporal scales of dispersal, (iii) scales of migration,170appendix aF igure a .3 : (a) The observed abundance of three genera of insects changesacross a gradient in the maximum volume of bromeliads. A null modelthat assumes no per capita differences in colonisation probability, but purelynumerical differences driven by differences in regional abundance (‘predictedabundance’), can account for some of the positive effects of bromeliad size onCulex and Mecistogaster. (b) The Mecistogaster damselfly larvae experiencegreater risk of drought during their 9 month larval phase than the Culexand Wyeomyia mosquito larvae with a 3 week larval duration. (c) Aftercorrecting for the numerical effects of bromeliad size on colonisation rates,residual abundance of species may be related to bromeliad size either directly,for example by drought risk associated with small bromeliads, or indirectly,through effects on competitors and predators. Bromeliad size was correctedfor numerical effects on colonisation. Path coefficients are standardised effectsizes from structural equation models described in full in the SupplementaryMaterial; path widths are proportional to absolute standardised effect sizes.Significance of path coefficients: *P < 0.05; 1P < 0.10.171appendix a(iv) scales of foraging, and (v) spatial information processing. We end byreiterating priority questions to be answered towards a robust trophic meta-community theory. Answering these questions would allow metacommunityecology to fulfil its promise as a truly synthetic theory of food web ecology.172appendix bSupplementary Information to Chapter 2b .1 partitioning beta diversityWe used the procedure of Baselga (2010), where Sørensen beta diversity formultiple-sites can be expressed as:βSOR =[∑i<j min(bij, bji)]+[∑i<j max(bij, bji)]2[∑j Si − ST]+[∑i<j min(bij, bji)]+[∑i<j max(bij, bji)] (b.1)Where Si is the richness in each site, bij is the number of species in sitei not in site j and bji is the number of species in site j not in site i and STis total richness across all sites. Sørensen dissimilarity (βSOR) accounts forboth species turnover and nestedness. Beta diversity accounting only for purespatial turnover is (βSIM) :βSIM =[∑i<j min(bij, bji)]2[∑j Si − ST]+[∑i<j min(bij, bji)] (b.2)Therefore we can use Sørensen dissimilarity (βSOR) and spatial turnover(βSIM) to calculate the total nestedness of species assemblages (βNES):βNES = βSOR − βSIM (b.3)173appendix bTherefore,βNES =[∑i<j min(bij, bji)]+[∑i<j max(bij, bji)]2[∑j Si − ST]+[∑i<j min(bij, bji)]+[∑i<j max(bij, bji)]−[∑i<j min(bij, bji)]2[∑j Si − ST]+[∑i<j min(bij, bji)](b.4)b .2 environmental variation between sitesFor every bromeliad, we measured a suite of environmental variables to assessthe amount and quality of habitat available to the invertebrates: the height(cm) and diameter (cm, measured as the maximum distance between leaf tips)of the plant, maximum water volume (mL, calculated by emptying the plantand calculating how much water the plant could hold before it overflowed),actual water volume (mL), longest leaf length (cm), longest leaf width (cm),number of leaves, canopy cover (% of shaded pixels in photos taken lookingdirectly up from the bromeliad), total detritus (g dry mass), pH, oxygenconcentration (% saturation), salinity (ppt), temperature (°C), and turbidity(NTU). Water chemistry and temperature variables were measured using aportable multiparameter waterproof meter in the field as soon as the waterwas collected from the plant.To test for differences between sites in environmental variables, we useda linear model and for oxygen saturation and canopy cover we used a gener-alized linear model with binomial family between the environmental variableand the site number.We obtained precipitation information from World Clim for our sites. Thefinest resolution from World Clim is 30 seconds, or 1 Km2. Sites 1-4 of our174appendix bTable b .1 : F value, Chisq value when using a binomial family, and the Pvalue for comparing the environmental variables between sites. All treatmentdegrees of freedom are 9 and residual degrees of freedom are 90.Environmentalvariable F/Chisq P valueDiameter 1.501 0.159Height 0.987 0.455OxygenSaturation 3.914 (Chisq) 0.916Salinity 0.860 0.563Canopy cover 9.084 (Chisq) 0.429Chlorophyll 0.441 0.908Total detritus 1.417 0.192Turbidity 1.764 0.086MaximumVolume 2.232 0.0267**Actual Volume 3.854 0.0003**175appendix bF igure b .1 : Total precipitation (mL) for the closest 1 Km2 of every site usingWorldClim data. Sites not shown are within 1 Km2.sampling are all within 1 Km2, therefore we cannot obtain independent pre-cipitation data from World Clim for each of these sites [1].We also obtained precipitation data from the year we collected from theweather stations located close to the metacommunities where we sampled [2].We then related the cumulative precipitation in the closest weather stationto each of our sites to the actual volume of water present in the bromeliads.For each site we added the precipitation from February 1st to the date the sitewas sampled176appendix bF igure b .2 : Total precipitation (mL) for the closest weather stations to thetransect. This data represents the months of sampling in 2015.177appendix bF igure b .3 : The mean actual water volume in the bromeliads increases withthe cumulative precipitation until sampling date (Intercept = 279.65, se = 53.92,slope = 0.613, se = 0.167). For each site we added the precipitation fromFebruary 1st to the date the site was sampled. We used the data from theclosest weather station to the site.178appendix bb .3 validation of markov network methodWe validated the method by confirming it gave the same results as knowninteraction strengths and could predict trophic interaction strengths in simplebromeliad food webs. We took two different approaches to this confirmation.First, we ran the Markov Network analysis on a three species module fromCosta Rica where we compared the outcome of the Markov Netowork analysison the distribution of these species in Costa Rica vs. interaction strengths thathad been established based on experiments (Hammill et al., 2015b). Second,because we have prior knowledge on the trophic ranks of every genera in theBrazilian dataset, we could test whether the Markov Network method couldcorrectly assign the trophic positions of genera.b .3 .1 Markov Network analysis on a known species module:We were able to get similar interaction strengths as those expected basedon direct experimentation. Using a three species module prohibits us fromaccounting for the indirect interactions that these three species may have withthe rest of the community. However, from the experimental evidence, thesethree species have been shown to have strong effects on each other and wehad experimental data only on this module.We used a known species module to test the outcome of the MarkovNetwork analyses where species interactions have been studied in detail usingexperiments (Hammill et al., 2015a). In this species module, both the preyCulex and the predator Mecistogaster increase in abundance with bromeliadsize. However, wherever the predator is present, Wyeomyia’s numbers aregreatly reduced. Culex is tolerant to predation due to behavioural responsesand therefore is commonly found with the predator. Using Markov Networkanalysis, Culex and Mecistogaster have a positive interaction strength. On the179appendix bTable b .2 : Interaction strengths of the three species module studied inHammill et al. (2015a)Mecistogaster Culex WyeomyiaMecistogaster 0.000 1.013 -2.268Culex 1.013 0.000 0.936Wyeomyia -2.268 0.936 0.000other hand, Wyeomyia and Mecistogaster have a negative interaction strength(Table b.2).b .3 .2 Markov Network analysis for assigning trophic rank:For this analysis, we started by assessing the types and strengths of interac-tions for every combination of genera. Positive interactions mean that speciesare more likely to co-occur than expected by chance. Negative interactionsmean that species are less likely to co-occur than expected by chance. Wecalculated the number of positive and negative interactions for every species,regardless of the strength across sites. We classified every species as a predatoror a prey, to test if known differences in trophic positions have a differentpreponderance of positive (expected for prey) or negative (expected for preda-tors) interactions. If such a pattern is found it must reflect realized trophicstructure in the community since information on trophic position was notincluded in the estimation of interaction terms. The species or genera knownto be predatory are: the damselfly Leptagrion andromache nymphs, elephantmosquito larvae Toxorynchites, Corethrella midge larvae, horsefly larvae Taban-idae and cranefly larvae Tipulidae (Figure 2.1). For this analysis, we explainedthe total number of interactions for each genera as a function of the sign of theinteraction (either positive or negative) and the trophic position. Since individ-ual genera are present in different interactions, we included genera identity asa random effect in a generalized mixed effect model. The independent units of180appendix breplication are the sites. We used a Poisson error distribution, appropriate forleft-skewed count data. The interaction term of this model, between trophicposition and the sign of the between-genera interaction, tests if predators andprey differ in the sign of their biological interactions.The top predator Leptagrion andromache dominated negative interactions(Figure b.4a), which is expected since it preys on most species in the com-munity. In general, prey species had more positive interactions and predatorspecies had more negative interactions compared to random expectations (β =0.564, z value = 4.456, P value = 8.3 x 10- 6, Figure b.4). This result was robustto the matrix permutations of presences (P value = 0, Permutation results,Figure b.6 - b.8, Table b.5). We therefore conclude that the Markov Networkmethod assess trophic position from observational data.b .4 supporting resultsb .4 .1 Pairwise multivariate analysis of variance and pairwise Tukey tests for com-munity dispersionTable b .3 : F value, R2, p value and adjusted p value for pairwisemultivariate analysis of variance (adonis tests) and the difference between thedispersion of communities, lower and upper boundaries of the differences andadjusted p values for pairwise tukey-tests.Pairwise multivariate Pairwise Tukey-testanalysis of variance for community dispersionPairs ofsitesF R2 p.value p.adjust Diff Lower Upper p.adjust1 vs 2 1.634 0.083 0.205 1.000 0.043 -0.367 0.454 1.0001 vs 3 1.907 0.096 0.135 1.000 0.151 -0.260 0.562 0.9721 vs 4 1.892 0.095 0.158 1.000 0.178 -0.232 0.589 0.922181appendix bTable b .3 : F value, R2, p value and adjusted p value for pairwisemultivariate analysis of variance (adonis tests) and the difference between thedispersion of communities, lower and upper boundaries of the differences andadjusted p values for pairwise tukey-tests.Pairwise multivariate Pairwise Tukey-testanalysis of variance for community dispersionPairs ofsitesF R2 p.value p.adjust Diff Lower Upper p.adjust1 vs 5 12.887 0.417 0.001 0.045* -0.159 -0.569 0.252 0.9611 vs 6 9.186 0.338 0.001 0.045* 0.195 -0.216 0.605 0.8731 vs 7 4.272 0.192 0.010 0.450 0.103 -0.308 0.513 0.9981 vs 8 15.549 0.463 0.001 0.045* -0.163 -0.573 0.248 0.9551 vs 9 6.718 0.272 0.001 0.045* 0.062 -0.348 0.473 1.0001 vs 10 11.157 0.383 0.001 0.045* 0.036 -0.374 0.447 1.0002 vs 3 0.743 0.040 0.614 1.000 0.108 -0.303 0.518 0.9972 vs 4 2.355 0.116 0.052 1.000 0.135 -0.276 0.545 0.9872 vs 5 13.273 0.424 0.001 0.045* -0.202 -0.613 0.208 0.8462 vs 6 7.746 0.301 0.001 0.045* 0.151 -0.259 0.562 0.9712 vs 7 3.849 0.176 0.007 0.315 0.059 -0.351 0.470 1.0002 vs 8 15.564 0.464 0.001 0.045* -0.206 -0.617 0.205 0.8312 vs 9 7.690 0.299 0.001 0.045* 0.019 -0.392 0.429 1.0002 vs 10 7.988 0.307 0.002 0.090 -0.007 -0.418 0.403 1.0003 vs 4 1.717 0.087 0.165 1.000 0.027 -0.383 0.438 1.0003 vs 5 8.485 0.320 0.001 0.045* -0.310 -0.720 0.101 0.3113 vs 6 4.413 0.197 0.003 0.135 0.044 -0.367 0.454 1.0003 vs 7 4.304 0.193 0.002 0.090 -0.048 -0.459 0.362 1.0003 vs 8 13.604 0.430 0.001 0.045* -0.314 -0.724 0.097 0.2943 vs 9 4.701 0.207 0.001 0.045* -0.089 -0.500 0.322 0.9993 vs 10 6.041 0.251 0.001 0.045* -0.115 -0.525 0.296 0.996182appendix bTable b .3 : F value, R2, p value and adjusted p value for pairwisemultivariate analysis of variance (adonis tests) and the difference between thedispersion of communities, lower and upper boundaries of the differences andadjusted p values for pairwise tukey-tests.Pairwise multivariate Pairwise Tukey-testanalysis of variance for community dispersionPairs ofsitesF R2 p.value p.adjust Diff Lower Upper p.adjust4 vs 5 5.571 0.236 0.001 0.045* -0.337 -0.747 0.074 0.2054 vs 6 6.196 0.256 0.001 0.045* 0.016 -0.394 0.427 1.0004 vs 7 3.214 0.152 0.010 0.450 -0.075 -0.486 0.335 1.0004 vs 8 8.524 0.321 0.001 0.045* -0.341 -0.751 0.070 0.1934 vs 9 7.137 0.284 0.001 0.045* -0.116 -0.527 0.295 0.9964 vs 10 10.432 0.367 0.001 0.045* -0.142 -0.553 0.269 0.9815 vs 6 2.857 0.137 0.021 0.945 0.353 -0.057 0.764 0.1555 vs 7 6.691 0.271 0.001 0.045* 0.261 -0.149 0.672 0.5565 vs 8 4.122 0.186 0.007 0.315 -0.004 -0.414 0.407 1.0005 vs 9 6.496 0.265 0.001 0.045* 0.221 -0.190 0.631 0.7675 vs 10 12.187 0.404 0.001 0.045* 0.195 -0.216 0.605 0.8726 vs 7 5.470 0.233 0.001 0.045* -0.092 -0.503 0.319 0.9996 vs 8 6.412 0.263 0.001 0.045* -0.357 -0.768 0.053 0.1456 vs 9 3.823 0.175 0.004 0.180 -0.132 -0.543 0.278 0.9886 vs 10 7.344 0.290 0.001 0.045* -0.158 -0.569 0.252 0.9617 vs 8 10.299 0.364 0.001 0.045* -0.265 -0.676 0.145 0.5357 vs 9 7.227 0.286 0.001 0.045* -0.041 -0.451 0.370 1.0007 vs 10 10.481 0.368 0.001 0.045* -0.066 -0.477 0.344 1.0008 vs 9 8.375 0.318 0.001 0.045* 0.225 -0.186 0.635 0.7488 vs 10 16.800 0.483 0.001 0.045* 0.199 -0.212 0.609 0.8589 vs 10 2.282 0.113 0.073 1.000 -0.026 -0.437 0.385 1.000183appendix bTable b .3 : F value, R2, p value and adjusted p value for pairwisemultivariate analysis of variance (adonis tests) and the difference between thedispersion of communities, lower and upper boundaries of the differences andadjusted p values for pairwise tukey-tests.Pairwise multivariate Pairwise Tukey-testanalysis of variance for community dispersionPairs ofsitesF R2 p.value p.adjust Diff Lower Upper p.adjustb .4 .2 RegressionTable b .4 : Slope and the p value (corrected and uncorrected for multipletests) for the linear regression between positive or negative relative interactionstrengths and mean bromeliad volume.Species NegativeslopeP value Correctedp valuePositiveslopeP value Correctedp valueTipulidae 1.179e-03 0.0012** 0.0178** 7.12e-05 0.838 1.00Corethrella.sp.-3.58e-04 0.435 1.00 4.25e-04 0.291 1.00Leptagrion 2.44e-04 0.488 1.00 1.116e-03 0.020** 0.312Elpidium 1.251e-03 0.001** 0.0163** 1.82e-04 0.609 1.00Dero 9.69e-05 0.885 1.00 -5.53e-04 0.418 1.00Chironomid 3.42e-04 0.337 1.00 3.73e-04 0.209 1.00Scirtes 2.97e-05 0.938 1.00 -3.47e-04 0.34 1.00Ceratopogonid6.69e-05 0.872 1.00 -3.43e-04 0.34 1.00Culex 2.96e-04 0.295 1.00 3.27e-05 0.891 1.00Tabanid 1.19e-03 0.256 1.00 8.08e-04 0.277 1.00Toxorhynchtes4.3e-04 0.216 1.00 5.49e-04 0.300 1.00Wyeomya 8.24e-04 0.004** 0.06** -1.08e-04 0.794 1.00Psychodidae -7.78e-04 0.175 1.00 -4.67e-04 0.428 1.00184appendix bTable b .4 : Slope and the p value (corrected and uncorrected for multipletests) for the linear regression between positive or negative relative interactionstrengths and mean bromeliad volume.Species NegativeslopeP value Correctedp valuePositiveslopeP value Correctedp valueEphydridae 3.00e-03 0.057 0.690 1.66e-03 0.38 1.00Dasyhelea.B -2.91e-04 0.513 1.00 -4.25e-04 0.180 1.00b .4 .3 Permutation resultsSince we only obtain one set of interaction strength values for each site, andwe wanted to ensure that the results we obtained were not due to a randomcombination of presence and absences, we permuted the presence-absencematrix for each site, and then re-calculated the interaction strengths. Wepermuted the presence of the species by keeping the number of species ineach bromeliad constant across each permutation. For each of our sites, wecreated 10,000 reshuffled sites. After calculating the interaction strength foreach site, we recalculated 1) the effect of the type of sign and trophic positionon the number of interactions and 2) the effect of water volume on the positiveor negative interaction strength of the species.The effect of the type of sign and trophic position on thenumber of interactions : — To assess the effect of type of sign of inter-action and trophic position on the number of interactions we ran a generalizedlinear model. For this model, we used the number of interactions each specieshad for the full data set as a function of the the sign of the species interaction(either positive or negative) and the trophic position using the species identityas a random effect; the units of replication are the sites. The interaction termof this model, between sign of species interaction and trophic position, tests if185appendix bF igure b .4 : Predators have more negative interactions and prey have morepositive interactions. a) Negative interactions are dominated by Leptagrionandromache (top predator). b) Positive interactions are dominated by Culex(dipteran prey). Darker colours indicate known predatory species prior to theanalysis and lighter colours indicate prey species. c) Predators have a highernumber of negative interactions while prey have a higher number of positiveinteractions. Blue indicates positive interactions and red indicate negativeinteractions. Bars represent mean and standard error of the mean. Positiveinteractions represent species than tend to co-occur, negative interactionsrepresent species that do not tend to co-occur.186appendix bF igure b .5 : Relative interaction strength against mean bromeliad watervolume. Every panel represents a different focal species. Blue regression linesrepresent the positive interactions and the red regression lines represent thenegative interactions.187appendix bF igure b .6 : Distribution of interaction terms after the presence of specieswas permuted 10,000 times. Red line represents 0 and the black line representsthe actual interaction term found in our original data.predators and prey have different distributions of the sign of their interactions.Here we show the distribution of the interaction term of the model from allthe permutations vs the interaction term we obtained from our data.Here we see that the interaction term of the model we obtained from ourdata does not overlap the distribution. We are calculating the P value for thispermutation test by the proportion of values from the distribution that aregreater than the value we obtained from the original data. Here the p-value is0.The effect of water volume on the positive or negative in-teraction strength of the species : — To assess the effect of watervolume on the positive or negative interaction strength of the species we useda linear regression. Here we compare the slope of that regression for each188appendix bF igure b .7 : Distribution of negative slopes after the presence of species waspermuted 10,000 times. Red line represents 0 and the black line represents theactual slope found in our original data.species vs the distribution of slopes obtained from the permutation of thepresence matrix.We are calculating the P value for this permutation test by the proportionof values from the distribution that are greater than the value we obtainedfrom the original data.189appendix bF igure b .8 : Distribution of positive slopes after the presence of species waspermuted 10,000 times. Red line represents 0 and the black line represents theactual slope found in our original data.190appendix bTable b .5 : P value for the permutation test for linear regression betweenpositive or negative relative interaction strengths and mean bromeliad volume.Species P value for posi-tive interaction val-uesP value for nega-tive interaction val-uesTipulidae 0.448 0.001 **Corethrella.sp. 0.175 0.845Leptagrion 0.0005 ** 0.360Elpidium bromelar-ium0.320 0.001 **Dero superterrenus 0.897 0.545Scirtes 0.911 0.569Chironomid 0.118 0.209Ceratopogonid 0.886 0.481Culex 0.513 0.252Tabanid 0.165 0.115Toxorhynchtes.sp. 0.077 0.149Wyeomya 0.698 0.019 **Psychodidae 0.812 0.892Ephydridae 0.169 0.080Dasyhelea.B 0.947 0.881b .4 .4 Relative interaction strength vs presenceThe negative interaction strength between two species can be due to the ab-sence of one caused by the local community environment (for example, lowwater volume filters out certain species). Therefore, we wanted to test if191appendix bF igure b .9 : The estimate of a logistic regression between actual watervolume in the bromeliad and the presence of the species versus the relativeinteraction strength with the tipulid at each site.the slope between the presence of any given species and water volume ina bromeliad was related to their interaction strength to other species. Theexpectation here was that if the interaction strength at the site scale is drivenby the filtering of the local environment, then they would be more likelyto engage in negative interactions if the slope between presence and watervolume is positive. Here we plotted the slope of the relationship betweenthe presence of each species and water volume in the bromeliad, againstthe interaction strength value that they have against the tipulid on that site.We find that there is no relationship between this slope and the interactionstrength with the Tipulid.192appendix cSupplementary Information to Chapter 3c .1 supporting results193appendix cTable c .1 : The prey species used for the feeding trials with the predatorLeptagrion, their average body mass and the densities we used for the feedingtrialsPrey Mean Body Mass(mg)DensitiesCulex sp 1 0.1771 1, 2, 5, 7, 10, 20, 30, 50Culex sp 2 0.0906 1, 2, 5, 7, 10, 20Forcypomia 0.0737 1, 2, 5, 7, 10, 20, 30, 60Oligochaete 0.1242 1, 2, 5, 7, 10, 20, 30, 60Psychodidae 0.2198 1, 2, 5, 10, 30Scirtes sp 1 0.3286 1, 2, 5, 10, 30Scirtes sp 2 0.4344 1, 2, 3, 4, 5, 6Tipulid 0.2935 1, 2, 3, 4, 5, 6, 10, 17194appendix cF igure c .1 : The attack rate, carrying capacity and growth rate decrease withprey body size, the handling time increases with prey body mass. The attackrates and the handling times of the model had to be reduced in magnitude(but not in shape) to reduce the amplitude of the dynamics (Parameters intables 1 and 2)195appendix cF igure c .2 : Parameter space is well covered in the Monte Carlo sampling.As diversity increases, most values for body mass of the prey 1 and 2 arerepresented. All other prey show a similar coverage. Each panel shows thediversity being considered196appendix cF igure c .3 : Time series of two prey species and the predator. If the bodymass of both prey is high the predator will go extinct. Body masses of eachprey species are presented above each graph. All a-d show prey species thathave high competitive interaction strengths since they are close in body mass.a) and b) show two prey species with intermediate body mass, c) and d) showtwo prey species with large prey mass197appendix cF igure c .4 : Time series of two prey species and the predator. The bodymass of each prey species is presented above each graph. Panels a- d showprey species that have low competitive interaction strengths since they differin body mass. a) The predator and the largest prey persist, the prey withthe smaller body mass goes extinct due to predation and competition. b) andc) Both prey species and the predator persist through time since the smallestprey has an intermediate body mass. d) The predator goes extinct when bothprey are large198appendix cF igure c .5 : Jensen’s inequality alters the effective attack rate and handlingtime as prey diversity increases. a) As diversity increases, the average bodymass of the prey increases causing an increase in the handling time h(m) buta decrease in the attack rate a(m). b) Due to Jensen’s inequality, increasingdiversity increases the combination of effective attack rates and effectivehandling times (compare to panel a). Given the upward curvature of theattack rate c) and the handling time d), we expect that the effective attack ratand the effective handling time will be higher than the attack rate and thehanding time of the mean body mass199appendix cF igure c .6 : The probability that the predator persists has a unimodalrelationship with prey diversity. Since prey that are close to each other inbody mass have higher competition coefficients, we calculated the proportionof species in a run that had the same body mass. As the proportion of preyspecies with the same body mass increases, predator persistence decreases.But this decrease is relatively small compared to the effects of having small orlarge prey (Figure 3.4)200appendix cF igure c .7 : a) As the proportion of small prey in the community increases,the proportion of runs where the predator persists decreases slightly. b) Forany given predator persistence, higher final prey diversity occurs when therun had a higher proportion of large prey species201appendix cc .2 asymmetric competitionThe model we presented assumes that competition is symmetrical with re-gards to the trait. That is, there is no benefit of being large or small inthe outcome of competition. Arguably, this may not be the case. Evidencesuggests that the outcome of competition is dependent on the body size of theindividuals, where larger individuals outcompete smaller individuals Persson(1985); Lawton and Hassell (1981). In certain cases smaller individuals canalso outcompete larger individuals Winder et al. (2008). Here, however, wewill only analyze the case where larger individuals outcompete smaller indi-viduals.Asymmetric competition reduces the window of persistence of the wholecommunity (Figure c.8, c.9). Persistence only occurs when both prey areintermediate in body mass and the competition is not vastly asymmetric, thatis, their body masses are close (Figure c.8c). If both prey are small, but oneprey is very small, the latter will go extinct due to predator overconsumption(Figure c.8a). Similarly, if the both prey are large, where the predator cannotpersist, and the larger prey will outcompete the smaller prey. Due to theasymmetry in competition, the smaller prey will extinct much faster than inthe case of symmetric competition (Figure c.8d vs Figure c.4d).Predator persistence occurs less frequently when prey species competeasymmetrically (Figure c.10a) and it decreases with diversity. Similarly, as inthe case of symmetric competition, a higher proportion of smaller prey speciesdecreases the predator’s persistence. Contrary to the case of symmetric compe-tition, a higher proportion of large prey species now decreases the predator’spersistence. This occurs due to an increase in competitive exclusion at highdiversity and larger prey outcompeting the intermediate prey necessary forpredator persistence. In this scenario, large prey species do not interact weakly202appendix cin the system (so they do not stabilize the system), but instead destabilize themdue to a larger competitive advantage.203appendix cF igure c .8 : Time series of two prey species and the predator. The bodymass of each prey species is presented above each graph. Panels a- d showprey species that have low competitive interaction strengths since they differ inbody mass. a) The predator and the largest prey persist, but the smaller preygoes extinct. b) and c) Both prey species and the predator persist through timesince the smallest prey has an intermediate body mass. d) The predator goesextinct when both prey are large204appendix cF igure c .9 : Predator persistence is constrained to two intermediate similarlysized prey or one intermediate and one large prey. Prey competitively excludeeach other unless they are similarly sized (1:1 edge). On the x axis is the bodymass of prey 1, and on the y axis is the body mass of prey 2. Panels a-c showthe proportion of the runs with a certain outcome, where yellow represents allthe runs and purple none of the runs: a) both prey species and the predatorpersists; b) the predator goes extinct and only the two prey persist;. c) oneprey and the predator persist and one prey goes extinct (in every case thesmaller prey). These scenarios are detailed in the food web modules: the greycircles represent species that go extinct and the black circles represent speciesthat persist205appendix cF igure c .10 : Prey diversity decreases predator persistence. a) Increasingdiversity decreases the proportion of runs where the predator and at least oneprey survived. b) As the proportion of small prey in the community increases,the proportion of runs where the predator persists decreases. c) The range ofbody masses that allow the predator to persist becomes narrower with preydiversity. d) As the proportion of large prey in the community increases, theproportion of runs where the predator persists decreases206appendix dSupplementary Information to Chapter 4d .1 modifications to dna extraction protocolsd .1 .1 Modifications of the Qiagen protocolBased on the purification of Total DNA from Animal Tissues (Spin-ColumnProtocol):1. Let ethanol evaporate and macerate samples before adding ATL buffer.2. Add 30 µL of proteinase K instead of 20 µL.3. Incubate for seven days instead of 6-8 hours. Vortex, flick and spinsamples daily.4. Add 250 µL of buffer AW1 and AW2 instead of 500 µL.5. Incubate for 15 minutes in buffer AE instead of 1 minute.6. Repeat AE incubation.d .1 .2 Modifications of the Ommiprep protocolBased on the Ethanol or Formalin Fixed Tissue Protocol:1. Let the insect dry and then re-hydrated in water for 1 hour.2. Freeze in liquid nitrogen and lyse with beads.207appendix d3. Add 6 µL of Proteinase K instead of 5 µL4. Incubate the sample at 55-60°C overnight instead of 60 minutes.5. Always centrifuge at 22°C.6. Added 4 µL instead of 2 µL Mussel Glycogen.7. Incubate for 1 hour after adding the Mussel Glycogen.8. Centrifuge at max speed for 20 minutes instead of 1.9. Add 35 µL TE Buffer to the pellet, instead of 50 µL. Incubate in the fridgeat 4°C for several days.d .2 supporting results208appendix dF igure d .1 : Individuals of both the odonate predator and the tipulid preyform two groups of individuals by the identity by state similarity.209appendix dF igure d .2 : Both the odonate predator (a, c) and the tipulid prey (b, d) havetwo major clusters of individuals as shown by the cross validation error andloglikelihood results from Admixture. Different colours represent differentmodel runs with a different random seed.210appendix dF igure d .3 : The odonate predator (a) and the tipulid prey (b) both have twomajor clusters with little admixture. We separated these clusters for furtheranalysis.211appendix dF igure d .4 : The major cluster of the odonate predator (a) is best representedby two subclusters, while the minor cluster of the odonate predator (b) is bestrepresented by three subclusters. The major cluster of the tipulid (a) is bestrepresented by one clusters, while the minor cluster of the tipulid prey (b) isbest represented by three subclusters.212appendix eSupplementary Information to Chapter 5e .1 homework assignmentsThe homework assignments were designed to (i) reduce the extraneous load,(ii) reduce the intrinsic load and (iii) increase the germane load.e .1 .1 (i) Reducing the extraneous loadSplit attention effect — Code is often presented separate from itsexplanation, for example:binom.test(c(463, 850), 0.5)Where 0.5 is the probability of success, 463 is the number of successes, 850 is thenumber of failures and binom.test is the function to run a binomial test.We minimized the split attention effect for the students learning new codeby providing code with the english explanations of each part:And by providing explanations of the code output:213appendix eWorked example effect — For conceptual questions (in Biostatistics)and for programing questions, we included a worked example in every as-signment. For each worked example, we also highlighted the different partsthat must be completed to do a question correctly.Conceptual question:From Whitlock and Schluter:Ch 3: 15 The data in the accompanying table are from an ecological study of theentire rainforest community at El Verde in Puerto Rico (Waide and Reagan 1996).Diet Breadth is the number of types of food eaten by an animal species. The numberof animal species having each diet breadth is shown in the second column. The totalnumber of species listed is n = 127.a) Calculate the median number of prey types consumed by animal species inthe community.First, order your list of numbers from smallest to largest.214appendix eLuckily, this step has already been completed for us in the table. Thelowest diet breadth is 1 and the greatest diet breadth is >20. Keepin mind that this is a condensed list as multiples of each diet breadthare counted up in the frequency columns. If we wrote out this listwith full, it would begin with twenty-one "1"s followed by eight "2"sand so on.Second, determine how you will obtain or calculate your median number.Because this list contains an odd number of observations, our medianwill be equal to Y([n+1]/2) meaning that the median will be equal toY64.Third, find the 64th number in your list. This will be your median.Add together the multiples of each diet breadth starting at "1" untilyou reach 64.21+ 8 = 2921+ 8+ 9 = 3821+ 8+ 9+ 10 = 4821+ 8+ 9+ 10+ 8 = 5621+ 8+ 9+ 10+ 8+ 3 = 5921+ 8+ 9+ 10+ 8+ 3+ 4 = 6321+ 8+ 9+ 10+ 8+ 3+ 4+ 8 = 71From these calculators we know that numbers 64 - 71 in our list are"8"s. Therefore our median is 8 prey species.Programming question:215appendix eQ1 Using the "titanic" dataset mentioned above, create three histograms: one for"Passenger Class", one for "Age" and one for "Survive".First, we need to read the "titanic" data frame into R. This is done usingthe following line of code:> titanic <- read.csv(file = ‘titanic.csv’)**Note, after uploading your csv, you should see the item, "titanic", underthe "Data" heading in the "Environment" tab of the upper right panel ofyour R console. If you would like to view the data frame in a spreadsheetformat, simply click on this item or employ the View() function in thefollowing line of code:> View(titanic)Second, now that we have read our data into R, we can use "ggplot2" tocreate our histograms. Start by using the library() function to load thispackage onto your console.> library(ggplot2)Third, construct your first histogram using the "Passenger Class" variable.This can be done using a single line of code. Please return to the previoussections if you do not remember what the different parts of the followingcode represent.> ggplot(data = titanic, aes(x = Passenger.Class))+geom_histogram(stat= ‘count’)For you to think: What kind of data is "Passenger Class"? Why do weneed to include the ‘count’ statistic in this line of the code?Fourth, view your graph. It should look like this:216appendix ePartially completed problem — Similar to the worked example prob-lems, we included partially completed questions in conceptual (Biostatistics)and programming questions. We scaffolded both the different parts to aquestion and the steps needed for each part of the question. As the assignmentprogressed, both types of scaffolding was reduced.Conceptual question:From Whitlock and Schluter:Ch 3: 21 Researchers have created every possible "knockout" line in yeast. Eachline has exactly one gene deleted and all the other genes present (Steinmetz et al.217appendix e2002). The growth rate–how fast the number of cells increase per hour–of each ofthese yeast lines has also been measured, expressed as a multiple of the growth rateof the wild type that has all the genes present. In other words, a growth rate greaterthan 1 means that a given knockout line grows faster than the wild type, whereas agrowth rate less than 1 means it grows more slowly. Below is the growth rate of arandom sample of knockout lines:0.86, 1.02, 1.02, 1.01, 1.02, 1, 0.99, 1.01, 0.91, 0.83, 1.01a) What is the mean growth rate of this sample of yeast lines?First, review the formula for calculating the mean of a list of numbers.mean = ∑ni=1 YinFinally, use this formula to calculate the meanb) What is the median growth rate of this sample?First, order your list of numbers from smallest to largestSecond, count how many observations are in your list.Finally, based on the results from the previous step, determine what yourmedian is.Programing question:Question: Construct a boxplot plotting the "growthexpt2" column against the"fertexpt2" column in the "fertilized_block" data set.First, make sure that you have ggplot2 installed by using the library()function.Second, decide which column is your independent and dependent variable.Independent: Dependent:For you to think: Can you explain how you made this distinction?218appendix eThird, construct your box plot using ggplot. Fill in the blanks in thefollowing code to do so:> ggplot(data = , aes(x = , y = )) + ()e .1 .2 (ii) Reducing the intrinsic loadWe reduced the element interactivity of the material by presenting (i) only oneway to do one job and (ii) presenting only the functions that were needed forthat assignment. In R, there are many synonymous ways to do the same task.For example, if we wanted to select one column out of a table these are thepossible ways of doing it:my_table$column1my_table[,1]select(my_table, column1)We decided to choose only one option and consistently use it throughoutthe course. Additionally, in every assignment the students learned only ahandful of new functions, but throughout the course they gained practice in adiverse assortment of functions. For example, they learned to input data intoR, graph data, manipulate data and do multiple statistical tests.e .1 .3 (iii) Increasing the germane loadBoth in worked examples and in partially completed problems we asked thestudents to reflect on a part of the question to engage in germain load activitiessuch as self-explaining.Self-explanation questions:219appendix eFor you to think: What kind of variable is "fertexpt2" and what kind of variable is"growthexpt2"?e .2 surveyse .2 .1 Biostatistics2201	of	4Page	1What	year	of	your	undergraduate	degree	are	you	in?Before	this	course	started...Excellent Above	Average Average Below	Average Very	PoorMy	programming	skills	(in	any	programminglanguage)	wereMy	skills	in	any	statistical	software	(JMP,	SPSS,etc)	wereBefore	this	course	started	I	used	R...Before	this	course	started,	I	was	interested	in	learning	a	programming	languageStudents	attitudes	to	programming	in	R	for	BIOL	30012345+DailyWeeklyMonthlyYearlyNeverStrongly	AgreeAgreeNeutral	/	UndecidedDisagreeStrongly	Disagree2	of	4Page	2During	this	course	I	felt	that	the	...Strongly	Agree AgreeUndecided	/NeutralDisagreeStronglyDisagreeNAstatistics	concepts	were	easy	to	understand(Normal	distribution,	t-test,	ANOVA,	regression)programming	concepts	in	R	were	easy	tounderstand	(Data	input,	visualization,	writingcode)statistical	software	JMP	was	easy	to	understandstatistical	software	(R	or	JMP)	sessions	werehelpful	to	understand	the	statisticsDuring	this	course,	the	level	of	difficulty	of	was...The	concept	refers	to	the	material	you	saw	in	the	lecture	and	the	application	refers	to	doing	the	analysis	in	the	software	(either	R	or	JMP)Too	high High Right Low Too	lowProbability	(Concept)Probability	(Application)Contingency	analysis	(Concept)Contingency	analysis	(Application)t-test	(Concept)t-test	(Application)ANOVA	(Concept)ANOVA	(Application)I	felt	...Mark	all	that	applyHappy Excited Motivated Supported Overwhelmed Anxious Bored Frustrated Stressed Angry Annoyed Proud Scared NAWhile	working	on	theconceptual	parts	of	thestatistics	assignmentsWhile	using	the	statisticalsoftware	RWhile	using	the	statisticalsoftware	JMPI	used	...Daily Weekly Monthly Once	in	the	term NeverR	outside	of	classJMP	outside	of	classR	in	the	laboratoriesJMP	in	the	laboratories3	of	4R	in	the	lecturesJMP	in	the	lecturesDaily Weekly Monthly Once	in	the	term NeverHaving	completed	this	course	I	would	...Extremely	likely Very	likely Moderately	likely Slightly	likely Not	at	all	likelyrate	my	programming	proficiency	as	highput	the	ability	to	use	R	as	a	skill	on	my	CVcontinue	using	R	in	my	own	projects	for	myundergraduate	or	graduate	schoolLong	answer	questionsDo	you	have	any	other	comments	about	the	course?Type	hereIf	you	could	change	anything	about	the	way	the	statistical	software	(R	or	JMP)	was	taught,	what	would	it	be?Type	hereIf	I	could	keep	anything	about	the	way	the	statistical	software	(R	or	JMP)	was	taught,	what	would	it	be?Type	hereappendix ee .2 .2 Eco-Methods2241	of	5Page	1What	year	of	your	undergraduate	degree	are	you	in?Who	was	your	instructorBefore	this	course	started...Excellent Above	Average Average Below	Average Very	PoorMy	programming	skills	(in	any	programminglanguage)	wereMy	skills	in	any	statistical	software	(JMP,	SPSS,etc)	wereBefore	this	course	started	I	used	R...Before	this	course	started,	I	was	interested	in	learning	a	programming	languageStudents	attitudes	to	programming	in	R	for	BIOL	40412345+Diane	SrivastavaKurt	TrzcinskiDailyWeeklyMonthlyYearlyNeverStrongly	AgreeAgreeNeutral	/	UndecidedDisagreeStrongly	Disagree3	of	5Page	2During	this	course	I	felt	that	the	...Strongly	Agree AgreeUndecided	/NeutralDisagreeStronglyDisagreeNAstatistics	concepts	were	easy	to	understand(ANOVAS,	regression,	ordination,	etc)programming	concepts	in	R	were	easy	tounderstand	(Data	input,	visualization,	writingcode)statistical	software	JMP	was	easy	to	understandstatistical	software	(R	or	JMP)	sessions	werehelpful	to	understand	the	statisticsDuring	this	course,	the	level	of	difficulty	of	was...The	concept	refers	to	the	material	you	saw	in	the	lecture	and	the	application	refers	to	doing	the	analysis	in	the	software	(either	R	or	JMP)Too	high High Right Low Too	lowTwo	way	ANOVA	(Concept)Two	way	ANOVA	(Application)Randomized	block	ANOVA	(Concept)Randomized	block	ANOVA	(Application)Multiple	regression	(Concept)Multiple	regression	(Application)Ordination	(Concept)Ordination	(Application)I	felt	...Mark	all	that	applyHappy Excited Motivated Supported Overwhelmed Anxious Bored Frustrated Stressed Angry Annoyed Proud Scared NAWhile	working	on	theconceptual	parts	of	thestatistics	assignmentsWhile	using	the	statisticalsoftware	RWhile	using	the	statisticalsoftware	JMPI	used	...Daily Weekly Monthly Once	in	the	term NeverR	outside	of	classJMP	outside	of	classR	in	the	laboratoriesJMP	in	the	laboratories4	of	5R	in	the	lecturesJMP	in	the	lecturesDaily Weekly Monthly Once	in	the	term NeverHaving	completed	this	course	I	would	...Extremely	likely Very	likely Moderately	likely Slightly	likely Not	at	all	likelyrate	my	programming	proficiency	as	highput	the	ability	to	use	R	as	a	skill	on	my	CVcontinue	using	R	in	my	own	projects	for	myundergraduate	or	graduate	schoolLong	answer	questionsIf	you	could	change	anything	about	the	way	the	statistical	software	(R	or	JMP)	was	taught,	what	would	it	be?Type	hereIf	I	could	keep	anything	about	the	way	the	statistical	software	(R	or	JMP)	was	taught,	what	would	it	be?Type	hereDo	you	have	any	other	comments	about	the	course?Type	hereappendix ee .3 codebookse .3 .1 Biostatistics228Biol 300 - Question: If I could keep anything about the way the statistical software (R or JMP) was taught, what would it be?Theme Total responses Child nodes Keywords Example answerControl responsesTreatment responsesK - Keep some part the canvas R assignments 49K1 - Step by step questionsQuestions, step-by-step, assignments“I like how they walked you through the questions almost step-by-step” [E3] 0 5K2 - Practice calcultion/ walkthroughspractice calculation, walkthrough, example, helpful“I appreciated the walkthroughs- I learn by example so that was great.” [E113] 0 18K3 - Informative and not overwhelming informative, not overwhelming“I love how informative the assignments are; not overwhelming to complete them.” [E11] 0 4K4 - Detailed instructions/ intro Instructions, intro, tutorial, guide“The guide before each assignment. Very helpful.” [E102] 0 12K5 - expected code/graph/values code, expected graphs/values,“Showing the code and the expected graphs/values to make sure you did it correctly in R.” [E22] 0 3K6 - Fill in the blank Fill in the blank“I liked the fill-in-the-blanks especially the question with the expected graphs because I could test it out and it gave me some sense of support.” [E74] 0 3K7 - Pictures Pictures “pictures were a great help.” [E92] 0 1K8 - Assignments in generalquestions, assignments, homework "Assignments were helpful." [E95] 0 3A - Keep the lab manual 39A1 - It was clear and easy to understandLab manual, clear, understand, easy to follow“Lab manual guides were easy to follow and understand.” [C120] 9 2A2 - Detailed instructions and lots of examplesExamples, helpful, detailed, instructions“Detailed instructions with lots of examples.” [C110] 5 2A3 - Step-by-step Step by step, lab manual“I appreciate the step-by-step process outlined in the lab manual.” [C38] 2 2A4 - Images (screen shots) Screenshots, images, lab manual“I think the images on the lab manuals for JMP instructions was very useful/helpful.” [C5] 2 0A5 - Overview pages with formulas summaries, formula, commands“I liked the summaries of R commands.” [E68] 0 4A6 - Liked the lab manual lab manual, helpful, Keep"The lab manual is a very useful way for new users to get started." [C28] 8 3C - Keep the labs - students like being in the labs 15C1 - How JMP was broken down in labs JMP, labs“I liked how JMP was broken down in the labs so that it became easy to use.” [C149] 2 0C2 - Can work on JMP on computers in lab computer, lab “the computer lab space” [C143] 1 0C3 - No homework, purely practice labs, marks“I liked that the labs were straight-forward and not for marks, it made it a very stress-free way to learn.” [C49] 1 0C4 - Length was good hours “Two hours is great.” [C18] 2 0C5 - Intro before labs concepts, first, problems“It was really useful to have the going over the concepts first then applying them to problems.” [E57] 0 1C6 - Liked the labs tutorial, lab, keep, teaching"I liked that the labs were straight-forward and not for marks, it made it a very stress-free way to learn." [C49] 6 2N - Liked how R was taught 14N1 - no changes useful, keep, everything “Everything! Taught well” [E73] 0 6N2 - Everything was broken down into small bite sized chunks broken down, clear“I liked that everything was broken down and explained to a very basic level; it made it very enjoyable to learn for someone who really struggles with computer programming.” [E19] 0 2N3 - Examples examples, code“I really liked the examples. I would keep those.” [E23] 0 2N4 - Application skills in questions application, questions“Good application skills put into questions.” [E51] 0 1N5 - Going over concepts and then attempting problemsconcepts, problems, example, question“It was really useful to have the going over the concepts first then applying them to problems.” [E57] 0 2N6 - well written and straightforward straightforward, well written“It was super straightforward and well written, despite being taught for the first time.” [E71] 0 1G - They did not like how JMP was taught 9G1 - not useful didn't like"Nothing. Maybe we could learn a program that is still current in the field." [C6] 2 0G2 - Labs unhelpful and disorganized didn't find useful"I never went to labs as I didn't find them useful." [C97] 3 0G3 - Teach R instead or as well teach, R"JMP just seemed a bit dated. It would be nice if we were able to use R instead." [C61] 4 0E - No changes to how JMP was taught 7E1 - No changes JMP, good"JMP taught well, teaching of software and practicing using JMP was good. The lab manual was a little out of data w/ links but otherwise really good." [C34] 6 0E2 - Easy and straightforward easy, straight-forward"The easiness and straight-forwardness." [C70] 1 0M - Didn't like how R was taught 7M1 - Nothing Nothing "Nothing at all." [E16] 0 1M - Didn't like how R was taught 7M2 - Wants more practical marked experience practical, marks"More practical [R] experience. Make it marked. Have a competition." [E10] 0 1M3 - Labs should be worth marks grades, labs, marks"Labs aren't worth marks, for correctness but we should get participation grades for attending." [E12] 0 1M4 - Wants reference command page Reference, commands page"Keep some key points for easier reference? Like the commands page in lab." [E20] 0 1M5 - More lessons on basics basics, fundamentals "more lessons on the basics" [E55] 0 2M6 - More class interaction class, interaction "More interaction in class." [E72] 0 1B - Ability to work on software and problems idependantly (ie from home) 6B1 - Work from home at home, online, independently"I liked that it was mostly independently self-taught with the aid of the manual and TA." [C32] 3 1B2 - Labs not mandatory labs, optional, not mandatory"I liked that labs were optional because if something conflicted you weren't stressed about it." [E15] 1 1D - Keep statistical software 6D1 - Software makes calclations easier calculate, homework"Being able to use [software] for homework answers." C53 2 0D2 - Good for plotting graphs plot, graph"The way to quickly generate and analyze graphs." [C20] 2 0D3 - Put it on exams exams"If R was taught, then use R all the way, even for final exams." [E47] 0 2F - TA/instructor assistance with stat software 5F1 - TA walkthrough TA, help, time, instructor, support"Providing time to spend with an instructor who will walk you through it." [C52] 4 0F2 - Wish TAs would teach from lab manual before students attempt teach, first, lab book"We read the lab book and did it on our own; maybe teach it first (I can read it at home)" [C20] 1 0H - JMP Activities/assignments 5 H1 - JMP Activities/assignmentsAssignments, questions, keep, activities"Keep the problems and questions." [C135] 5 0O - Learning how to graph data with R 5O1 - Learning how to graph data with R ggplot, graphing"I loved producing graphs- it felt like I had to process the information and explore." [E54] 0 5L - Didn't like R assignments 4L1 - Make instructions more concise "instructions, concise" [E8] Make the instructions more concise. 0 1L2 - Separate instruction doc instructions, separate, "Have the instructions written on a doc" [E62] 0 1L3 - Too easy too easy"I just think it was a bit too easy when [R] was in the week assignments" [E39] 0 1L4 - Link to previous assignment explanations link, previous"In [questions] link to previous lessons." [E55] 0 1I - Use JMP in lecture 2 I1 - Use JMP in lecture lecture, use, class, JMP"Use it more during lecture to showcase its advantages/disadvantages." [C58] 2 0J - Never used stat software 1 J1 - Never used stat software Never, used "Never used either" [C54] 1 0Biol 300 Q2: Question: If you could change anything about the way the statistical software (R or JMP) was taught, what would it be?Theme Total responses Child nodes Keywords Example answerControl responsesTreatment responsesA - Course should use other software 47A1 - R R, teach, instead "Learn more about R" [C95] 31 0A2 - Excel Excel, teach, instead "Excel should be used instead" [C134] 11 0A3 - other other, teach, option, newer, not JMP"Teach excel or a newer program" [C59] 5 0N -The R assignments need improvement 29N1 - Assignments need more clarity, better instructions Confusing, understand, difficult"Have hints or more thorough walk-throughs- sometimes I would do exactly what the instructions said and nothing outputted." [E24] 0 7N2 - R questions too easyUnnecessary, assignments, easy, challenging"I think the assignments shouldn't have the R walkthrough. It made them too easy and encouraged me not to go to lab." [E39] 0 4N3 - Disconnect between assignments and lecture Compared, assignment, class“Conceptually some of the assignments seemed off compared to what we saw in class” [E5] 0 1N4 - Didn't like help questions Help question“I feel like instead of having to debunk the code through the "Help" tab, it is more efficient if it's laid out because it should be an application question rather than trying to spend time trying to find it.” [E7] 0 1N5 - Scrolling Separate, document, scrolling“Have a separate document instead of a walkthrough in the assignment- too much scrolling.”[E22] 0 5N6 - Graphing questions were challenging graphs, help, explain, graphing“Explain how to deal with graphing questions more.” [E49] 0 3N7 - assignments were too longtoo long, instructions, assignments, quicker“The questions were long and difficult, and sometimes way too many numbers needed to be typed in to do a test.” [E87] 0 4N8 - Disconnect between assignments and lab Assignment, lab, reflect“Assignment R questions were not what was done in labs should reflect lab material” [E40] 0 1N9 - Too challenging Difficult, easier, questions“One change would be to make the R parts easier/quicker to do for a beginner (mostly)” [E92] 0 3B - The students want more activities to help or force them to learn the software 23B1 - Make learning it more interesting Interesting more “Make it more interesting” [C78] 1 0B2- Show application of softwareAppilcation, program, use, implement"How to use R in more applicable ways" [E79] 1 2B3 - Present exam style R questions R, exam, tested, questions"More exam sytle R questions on assignments" [E112] 0 3B4 - big project project"create a project to demonstrate our [R] skills" [E54] 0 1B5 - More practice softwareMore, practice, program, software, homework, R"Make homework or assignments that test knowledge of the programs" [C52] 6 9H - The course should provide an incentive to come to the labs to learn the statistical software 19H1 - Make labs mandatory labs, mandatory"some of the labs should be made mandatory" [C74] 7 4H2 - Labs worth markslabs, marks, marking scheme, quiz, attendance"Maybe make labs mandatory and with some form of marking scheme or small quiz?" [C18] 3 1H3 - Force people to work together/in grops group, partners, work, learning"I would like to have worked in the [lab] portion in a group or in parnters" [C116] 1 1H4 - Provide incentive for labs incentive, labs, forces, mandatory""Just make there an incentive to go to labs and to learn [JMP]" [C129] 2 0C - The course should provide more support learning the statistical software 16C1 - Make learning more organized and structured organized, sturctured, even spread"I wish it could be an even spread between R material and lecture material" [E73] 1 1C2 - Help troubleshooting troubleshooting, tips"some troubleshooting tips for us" [E92] 0 1C3 - Demo/ better explanation of new commands/functions/ concepts Demo, concepts "Demo new R commands" [E44] 0 4C4 - Provide reading provide, readings"encourage further exploration by providing reading" [E54] 0 1C5 - More walkthroughs explanation, functions, work"better explanation of how functions work" [E86] 0 2C6 - Provide information on online resources online, eduation, sites"Maybe do R-online assignments [with] online eduacation sites such as edx." [E104] 0 1C7 - More support teach, TA, help, program, R""Have the TA teach us how to use the program, rather than have us self-taught through the lab manual"" [C147] 4 1I - Improve labs 16I1 - Improve in general labs, waste, improve "Improve tutorial/labs" [E10] 3 1I2 - Integrate labs into lecture labs, integrated, lecture[Labs] were not integrated into lecture" [C123] 1 0I - Improve labs 16I3 - Too long labs, shorter"Making [labs] shorter and more helpful[.] We never finished a lab!" [C98] 1 0I4 - Review at beginning of lab review, before, labs"Provide a 15 minute review session before students begin working on the labs." [C12] 0 2I5 - Provide answers for lab questionsanswer, key, questions, manual, assignments"It would be useful to have an answer key for the lab assignments to be able to see if I did the questions correctly." [E85] 0 6I6 - More R activities more, activites, R"The labs could have more activities that enhance R" [E56] 0 1I7 - More comprehensive comprehensive, tutorials"Have slightly more comprehensive tutorials [near] the end." [E95] 0 1P - Liked how R was taught 13 P1 - Liked how R was taught Understand, taught, good, clear, R"No changes! It was easy to understand and easy to complete. Thanks for making it doable." [E58] 0 13D - Integrate statisical software into lecture 11D1 - Integrate statisical software into lectureIntegrate, lecture, software, class, R, JMP, demo, teach"Teach R in lectures as well as lab[.] Maybe cover concepts simultaneously in writeen and software based formats" [C113] 10 1G - JMP was a waste of time/take out 10G1 - JMP was a waste of time/take outwaste of time, JMP, didn't learn, Don't teach"I would get rid of JMP and use the more useful and universal R." [C51] 10 0F - Liked how JMP was taught/keep it 9F1 - Liked how JMP was taught/keep it Straightforward, teach, JMP, fine "JMP is excellent as it is" [C106] 9 0O - Liked R assignments 7O1 - Instructions were very clear Clear, help, instructions"All the instructions on how to use R for the assignments was very clear." [E13] 0 6O2 - Visualization of code Visualization"The visualization part was really good." [E101] 0 1L - Wants online video tutorials 5 L1 - Wants online video tutorials online, tutorial, video"I find video tutorials of anything is more useful/effective than reading a bunch of instructions." [E8] 2 3Q - Provide list of commands 5 Q1 - Provide list of commands list, command, cheat sheet"Provide an abbreviated list of all commands used in the course." [E27] 0 5M - Ensure TAs understand statisical software 4M1 - Ensure TAs understand statisical softwarebetter training, TA, understanding, program"Ensure that the TAs actually have a thorough understanding of the program before they teach it to us." [C6] 2 2J - Make statsical software mandatory 3J1 - Make statsical software mandatory software mandatory"For statistical software to be mandatory" [C110] 3 0K - Liked lab manual 3 K1- Liked lab manual lab manual, helpful, guide"Following a guide and doing things along with the guide helped familiarize myself with the program" [C19] 3 0E - Doesn't want statistical software taught 1E1 - Doesn't want statistical software taught Remove "Remove [R] entirely" [E16] 0 2R - Liked labs 1 R1 - Liked labs Liked, labs, useful"I really liked the labs. I felt that the TAs were really helpful in explaining R and how to use it." [E41] 0 1appendix ee .3 .2 Eco-methods233Biol 404 - Question: If you could keep anything about the way the statistical software (R or JMP) was taught, what would it be?Theme Total responses Child nodes Keywords Example answerControl responsesTreatment responsesC - R was taught well 21C1 - R was taught well R, taught"Overall, I liked the way R was taught and that we were provided with a lot of reasons behind the code we were typing so we could use them going forward." [D19] 0 1C2 - Liked examples and clarification in R code, examples, clarification, hints"Like how assignments made sure your code was right and gave hints to if you were on the right track" [D14] 2 1C3 - Liked having code to go along with lectures lectures, code, work-alongs"Including code to follow along with lectures was helpful for learning new concepts." [B14] 2 0C4 - Explanations for each questionExplanations, question, assignments"Including code to follow along with lectures was helpful for learning new concepts." [D1] 0 1C5 - Explanations for each element of the code explanation, code, R, element, part"Present R code, explaining what each element does" [D2] 0 7C6 - Had lots of opportunities for practice practice"The quizzes provided lots of opportunity for practice" [D4] 0 1C7 - Fill in the blank questions fill in the blank"The fill in the blank questions were helpful in figuring stuff out" [D16] 0 3C8 - Liked instructions in the quiz instructions, quiz"The instructions on the quizzes were very helpful" [D11] 0 2C9 - Liked hints hints, quizz"Like how assignments made sure your code was right and gave hints to if you were on the right track" [D14] 0 1E - Liked having an R workshop 19E1 - Liked having an R workshop R, workshops "Keep the R-script tutorials. Very helpful." [B19] 6 0E2 - Script was step by step/ having a script code, step by step, example"Walking through programming techniques step by step was valuable" [B8] 4 0E3 - Workshop during lab hours Workshop, lab"First instroductory tutorial allowed for smooth entry into R" [D6] 5 2E4 - Step by step instructions instructions, guided, walk through"I really liked how the instructions walked us through the process so it was less overwhelming" [D7] 0 2I - Like the stats assignments 16 I1 - Like the stats assignmentsassignments, understanding, learn, explain, quiz, practice, R"Liked the way the R assignments guided us through the steps and showed us how to do the parts necessary" [D21] 2 14F - The students liked learning something useful 5F1 - They learned something they wanted to learn skill, wanted, learn"The course forced me to learn a skill I wanted to learn, but I didn't know where to start." [B8] 1 0F2 - They learned something that has practical usage practical, realistic, going forward"Overall, I liked the way R was taught and that we were provided with a lot of reasons behind the code we were typing so we could use them going forward." [D19] 1 2F3 - They learned to simplify code simpler, code"Learning about the different functions and how they can be used to make code simpler" [D10] 0 1A - Learning packages/analyses/functions were useful 4A1 - Variety of things they found useful functions, code"Learning about the different functions and how they can be used to make code simpler" [D10] 1 2A2 - Anova ANOVA, R"I think the part of the course on ANOVAs and how to do them in R made sense." [B9] 1 0G -Like the tutorials 3 G1 - Like the tutorials Tutorial"The tutorials were very helpful because the teaching was more personal and more go-at-your-own-pace." [B10] 3 0H - Like the lectures 3H1 - Like the lectures lectures, notes"the class lectures and diagrams were very (underlined) helpful" [B20] 2 0H2 - Like the diagrams in lecture diagrams, lecture"the class lectures and diagrams were very (underlined) helpful" [B20] 1 0D - Liked the labs 2 D1 - Liked the labs lab, useful "Lab sessions were useful" [B23] 2 0B - Questions were useful 1B1 - Question selection and order was useful Selection, questions, order"A lot of thought was obviously put into selection of questions and order. Generally [] this was done well in a way that help build an understanding." [D9] 0 1J - Assignments were a good level of difficulty 1J1 - Assignments were a good level of difficulty difficulty, level. assignments"Stats assignments where pretty helpful and good level of difficulty" [D12] 0 1Biol 404 - Question: If you could change anything about the way the statistical software (R or JMP) was taught, what would it be?ThemeTotal responses Child nodes Keywords Example answerControl responsesTreatment responsesB - More R instruction on functions and packages 28B1 - More instructionsfunctions, teach, code, statisical analysis"Go into the details of how to actually write the codes and what items/functions mean. When introducing concepts such as regression or ordination plots have an R lab to accompany it." [B6] 3 1B2 - Instructions on the code/outputcode, output, feedback, explanation, write, structure"I think the lectures had too much random code without adequate explanation about what parts of the code were referring to or even how to interpret the results. Most of what I learned about R was reading blogs online or watching videos outside of class to teach myself." [B9] 7 2B3 - Provide csv files/ R files to follow in classR data, csv files, example, class"Please also give us the companion csv files so we can follow along lectures." [B10] 3 0B4 - Have a referece/ faq/guideoverview, reference guide, document, FAQs, resources"However, it would be nice if the explanations of the R inpus were put together in a short manual to reference throughout the term opposed to get at the beggnining of the R quizzes or in the lab manuals" [D28] 3 7B5 - More practical examples practical, apply, code"More practical use [of R] during labs and course" [B4] 1 1E - More synchrony between the assignments, the lectures and labs 13E1 - Spend time doing/explaining R in lectures/labsteaching, R, labs, lecture, more time"Include more R components to the lecture as well, in addition to the labs" [D3] 1 4E2 - Teachers/TA need to know assignments in greater detail Instructors, TA, assignments"Instructors and TA need to understand assignment better (they know how to code, but were often unprepared to answer questions specific to quizzes)" [D6] 0 1E3 - More synchrony between R and lecturesR, lectures, concepts, code, theory"Do better job of linking the theory with the statistics produced in R." [B22] 5 1E4 - More synchrony between labs and assignments codes, lab,"I think that basic graphs and codes should be instroduced early to assist with lab reports and there should be a reference page or something to refer to." [D23] 0 1C - More help outside of class 11C1 - More R homeworkmore, assignments, exercises, R"Please give us exercises for R; the stats assignments were overwhelming." [B10] 3 0C2 - More tutorialstutorials, code, more, workshop"More explanations for tutorials, go through [R] with template data together." [B5] 7 0C3 - R specific office hours Office hours, R "Add R office hours" [D8] 0 1A - More R 9A1 - Generally more R More, code"I would add more on how to make the code faster to type. i.e. loops, learn plyr. -These could just be provided as examples and then people can figure out how they work if their interested" [D10] 0 1A2 - Want R earlier in the course more, R, introduction, start, "A more thorough introduction of the basics of the course/R would have been valuable at the start" [B8] 2 0A3 - Want more teaching in R generally Overview, teach, R, code"I would have liked to given lesson on how to use R and told what the different codes were" [D25] 4 2G - R teaching in general not good enough 8G1 - Stats assigngments were overwhelmingstats assignments, overwhelming, challenging"Change the stats assignments. They were too challenging and I didn't feel like I learned anything from them." [B19] 2 0G2 - Explanations unclear and insufficientexplanation, unclear, unhelpful, code, discouraging"The explanations given in lecture were unclear, insufficient and, simply put, frustrating." [B17] 3 1G3 - Need to break down stepsBreak it down, step by step, smaller sections"Break it down more, step by step. Rather than give lines of code for a concept, break down how to write the code (what does a comma, or bracket mean?)." [B18] 2 0 K - Assignments were not clear 7K1 - Assignments generally not clearAssignments, do not make sense, questions"Assignments need to be more clarified. Some questions do not make sense" [D2] 0 1K2 - R help file questions not clear help file, question"Simpler concepts, more breakdowns of what exactly each function is doing instead of "read the help file"." [D14] 0 5K3 - Multiple choice questions not clear multiple choice, questions"A lot of the multiple choice questions felt more like careful reading and interpretation exercises and not R competence questions, they weren't super clear and were way too wordy" [D5] 0 2F - Too fast 6F1 - Generally too fast quickly, slower"Maybe go slower because I had no previous experience and was lost" [D27] 1 1F2 - Professor was too fast too fast, "Please just slow down the teaching pace so everything can be digested" B10 1 0F3 - R workshops were too fast rushed, slower, workshop"Some assignments felt a bit rushed, and because of that felt like was unable to comprenhend all the material. Slower pace would be great" [D8] 2 1H - Not enough support 5 H1 - Not enough support teach, support, R, guidance"Actually teach it! I felt like we were not taught a thing in class. Any skills I gained were from the online workshops or google. I didn't feel like I had any support." [B16] 4 1N - Layout in canvas not great 5N1 - Layout in canvas not greatscroll, assignment instructions, canvas, layout"The assignment on canvas made us scroll up to see the question and down to answer it which got confusing" [D18] 0 5L - Assignments not challening enough 4L1 - Assignments not challening enoughassignments, independent thought, figure out"Let students figure out how to do things on their own more without always giving step by step instructions. Id learn more if I was forced to figure things out on my own" [D17] 0 3L2 - Not sure if retained info retained, assignments"Some assignments walke us through it but I'm not sure how much I retained" [D18] 0 1M - Labs unclear 4M1 - Need to have correct code for labsincorrect code, labs, assignments"Ensure that all the code given to students works, sometimes we received incorrect code which made assignments and labs difficult to understand" [D20] 0 3M2 - Labs overwhelming labs, overwhelming"More intro- the beginning was overwhelming because there wasnt enough time to figure things out (ie labs took too long)." [D21] 0 1I - More lecture material 3 I1 - More stats explanation clarification, method, statistics"Learn exactly what each statistics means better" [B27] 2 1D - Wanted R in prereq course (BIOL300) 1D1 - Wanted R in prereq course (BIOL300) learn, earlier, R"As someone who had no programming knowledge before this, basic programming skills and logic would have been helpful to learn earlier on." [D16] 0 1J - More feedback 1 J1 - More feedback feedback"Provide more feedback (which stats when following assignment)" [B3] 1 0appendix ee .4 supporting results237appendix eTable e .1 : The perceived difficulty of the material did not change based onthe format (application or concept), nor the treatment, nor the concepts learnt.X2 and P-value of the X2 test for each main effect and interaction.Perceived difficulty ofthe materialBiostatistics Eco-MethodsX2 DF P X2 DF PFormat 0.24 1 0.62 0.006 1 0.93Course 0.74 1 0.39 0.00 1 1.00Material 0.32 3 0.95 1.60 3 0.66Format:Course 0.007 1 0.93 0.11 1 0.73Format:Material 0.21 3 0.97 0.24 3 0.97Course:Material 2.68 3 0.44 0.30 3 0.96Format:Course:Material 0.22 3 0.97 0.14 3 0.99238

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