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Factors influencing the coexistence of bromeliad-dwelling chironomids on Ilha do Cardoso, Brazil Letaw, Alathea Diana 2016

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Factors influencing the coexistenceof bromeliad-dwelling chironomidson Ilha do Cardoso, BrazilbyAlathea D iana LetawB.A. (Hons), University of Oregon, 2007M.Sc., University of Oregon, 2009A 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)June 2016© Alathea Diana Letaw, 2016AbstractSpecies interactions can influence the spatial distribution of organisms and thecomposition of local communities. To investigate how interactions influencethe coexistence of invertebrates living in bromeliad phytotelmata, I combinedmethodological development and empirical exploration with the aim of under-standing: 1) Which species in a community show signs of strong interactions,2) Whether predators influence the outcome of competitive interactions and 3)Whether equalizing or stabilizing interactions between species change depend-ing on context. To detect interactions between species given observational fielddata, I designed a method of finding negative co-occurrence patterns (usingcheckerboard units) between species based on their abundances in nature.Using this method, I found that three chironomid (Diptera: Chironomidae)species showed very strong negative co-occurrence patterns, suggesting thatthey experience net negative interactions (e.g. competition) or habitat filtering.Next, I performed a predator-addition experiment to assess the importance ofpredators in mediating the coexistence of the three chironomid species. Threepredator species were added to bromeliads containing the three chironomidspecies. Although field observations suggested that at least one chironomidspecies should improve performance in the absence of predators, there wasonly a slight differential response to predators. Furthermore, one speciesof chironomid was competitively superior to the others in both the presenceand absence of predators. We suspect that differing habitat preferences andthe presence of other prey may be more important to coexistence than thepresence or absence of predators alone. Finally, I performed an experiment toassess how habitat and ontogeny affect the outcome of competition betweeniithe two most common chironomid species. When reared at the same bodysize, the two chironomids exhibited a stable relationship that we term hereasymmetric equivalence: in one species experiences the world neutrally butthe other does not. However, when species differed in their ontogenetic stage,the asymmetric equivalence disappeared. Taking all three studies together, Ifound that competition, but not predation, is an important factor in chirono-mid coexistence, but that differences in context lead to different coexistenceoutcomes.iiiPrefaceAll chapters in this thesis are the original work of A. D. Letaw. The ideas forall chapters were developed by A. D. L. with supervisor D. S. Srivastava. Allchapters were written by A.D.L. in the form of manuscripts and edited by theco-authors. Chapter 2 is co-authored with D. S. S., who also collected the dataused in that chapter. Chapter 3 is co-authored with D. S. S. and G. Q. Romero,who contributed to the ideas and manuscript. Demographic models used inthis chapter were developed with A. Andrew M. MacDonald. Chapter 4 isco-authored with D. S. S. Experimental design for all chapters was developedby A. D. L. with D. S. S. Empirical work was completed by A. D. L. with fieldassistants Robert Fisette and Aline Nishi. All programming and analysis forall chapters was completed by A. D. L.ivTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTable of Contents . . . . . . . . . . . . . . . . . . . . . . . vL ist of Tables . . . . . . . . . . . . . . . . . . . . . . . . . viL ist of F igures . . . . . . . . . . . . . . . . . . . . . . . . . viiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . viiiDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . x1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Assessing species associations using abundance -weighted checkerboard patterns and null modelanalysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 Predator-mediated competition does not facilitatecoexistence of bromeliad -dwelling Chironomidaein Brazil . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314 Asymmetric ecological equivalence and context -dependent competition between chironomids inbromeliads . . . . . . . . . . . . . . . . . . . . . . . . . . . 535 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 88B ibliography . . . . . . . . . . . . . . . . . . . . . . . . . . 94Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . .106a Supplementary Information to Chapter 4 . . . . . . . . . .106vList of TablesTable 2 .1 Matrices with higher AWCU than at least 95% of shuffledmatrices. . . . . . . . . . . . . . . . . . . . . . . 22Table 2 .2 Checkerboard (C), abundance checkerboard (AC) andabundance-weighted checkerboard (AWC) units for themost highly segregated species pairs under each analysis . 29Table 2 .3 Abundances of four species in 25 bromeliads from Brazil . 30Table 3 .1 Mean and predicted emergence in the presence and absenceof predators . . . . . . . . . . . . . . . . . . . . . 43Table 4 .1 Outcome of local and regional coexistence . . . . . . . 59Table 4 .2 Summary of models for the equivalence experiment . . . 72Table 4 .3 Summary of models for the ontogeny experiment . . . . 73Table a .1 Results of likelihood-ratio tests in the equivalenceexperiment . . . . . . . . . . . . . . . . . . . . .108Table a .2 Results of likelihood-ratio tests in the ontogenyexperiment . . . . . . . . . . . . . . . . . . . . .109viList of FiguresF igure 1 .1 The study site . . . . . . . . . . . . . . . . . . . . 7F igure 3 .1 Set up of the predator-addition experiment . . . . . . . 41F igure 3 .2 Days to first emergence in the presence and absence ofpredators . . . . . . . . . . . . . . . . . . . . . . 44F igure 3 .3 Demographic model fits . . . . . . . . . . . . . . . 45F igure 3 .4 Comparison of emergence and death rates . . . . . . . 46F igure 3 .5 Relationship between Polypedilum abundance and predatorbiomass in survey data . . . . . . . . . . . . . . . . 47F igure 3 .6 Relationship between C. detriticola abundance and plantsize and predator biomass in survey data . . . . . . . . 48F igure 4 .1 Possible results for the ecological equivalence . . . . . . 60F igure 4 .2 Experimental design of the ontogeny and equivalenceexperiments . . . . . . . . . . . . . . . . . . . . . 68F igure 4 .3 Response of C. detriticola in the equivalence experiment . . 74F igure 4 .4 Response of C. detriticola to total larval abundance . . . . 75F igure 4 .5 Response of P. marcondesi in the equivalence experiment . 76F igure 4 .6 Response of P. marcondesi to total larval abundance . . . . 77F igure 4 .7 Response of C. detriticola in the ontogeny experiment . . . 78F igure 4 .8 Response of P. marcondesi in the ontogeny experiment . . 79F igure 4 .9 Density resistance and fitness ratio in the equivalenceand ontogeny experiments . . . . . . . . . . . . . . 80F igure 4 .10 Null and observed plant size occurrence . . . . . . . . 81viiAcknowledgementsThank you:Diane Srivastava – a brilliant supervisor with incredible patience who pro-vided the impetus to move forward at several crucial moments;My advisory committee, who were generous with feedback and advice:Leticia Avilés, Jedediah Brodie, Mary O’Connor, John Richardson and RoyTurkington;My examination committee, whose questions and comments led to a muchimproved final product: Amy Angert, Mark McPeek, Mary O’Connor andJennifer Williams;Alice Liou, the mastermind behind the Zoology department;My lab mates, who were amazing motivators and companions: SarahAmundrud, Angélica Gonzalez, Melissa Guzman, Bill Harrower, Pavel Kratina,Robin LeCraw, Andrew MacDonald, Gennifer Meldrum, Angie Nicolás, Vir-ginia Noble, Fabiola Ospina, Jana Petermann, Martin Videla and Xinxin Xue;Robert Fisette and Aline Nishi – two amazingly tough, positive and tal-ented field assistants;Gustavo Q. Romero and his students Paula Omena, Tiago Bernabé, SandraBenavides & Alexandre Neutzling (thank you, you two for all of the trips tothe bank!), Adriano, Pablo Antiqueira, Gustavo Cauê and Gustavo Miglorini– who took extremely good care of us in Brazil, and without whom all fieldwork would have been impossible;Eduardo Pereira and his family, who made us welcome on the island;John R. and Larissa Letaw, who provided an abundance of programmingadvice and guidance;viiiNicholas Gotelli and Werner Ulrich, who kindly answered my questionsabout their own null models and checkerboard analyses;Stilianos Louca, who crossed a C#/C language barrier to provide com-ments on Chapter 2;Andrew MacDonald, who co-developed the demographic model of Chap-ter 3;Sally Otto, who supplied some of her genius to help with mathematicalmodels;Rich FitzJohn, who provided his LaTeX dissertation formatting templateson GitHub;Rob Miles, who wrote a free and really good C# book;Amazon Web Services, for their AWS in Education Grant award;and Robert Fisette, for his excellent work on A-Infinity Algebras.All R code developed here was greatly improved on reading Advanced R byHadley Wickham, available on-line for free.ixFor my familyxchapter 1Introduction“In that murky zone girdled byWhere have we come fromand Where are we boundWe exist.Sometimes science can shine a lightinto this dark regionbetwixt Whence and WhitherSometimes not.”–Marcia E LetawThe most basic questions in community ecology concern the distribution oforganisms across the biosphere. Why are species where they are? Answeringthis question could help us predict how environmental changes might leadto changes in species distributions over time. At the global scale, it is notdifficult to understand why species are where they are: Organisms are theproduct of the environment in which they have evolved and therefore cannotpersist under any arbitrary set of conditions. However, as we consider everfiner geographical scales, it becomes more difficult to understand which forceslead to the particular composition of a local community.At a local level, species interactions may be one of the most importantdeterminants of species distributions. In fact, according to early theory, verysimilar species that have highly overlapping resource use should not be able1chapter 1to coexist at all (Gause, 1934; Grinnell, 1904; Hardin, 1960; Hutchinson, 1957;MacArthur and Levins, 1967) because one will always be better on average atobtaining or assimilating resources. Under this premise, it is then difficultto understand why similar species can be found in the same communitytogether and how they can coexist. Fortunately, there are multiple explana-tions for how various aspects of a community and environment can main-tain similar species at the metacommunity scale. These include explanationsthat utilize niche-based models, such as: habitat/spatial heterogeneity (Ama-rasekare, 2003; Chesson, 2000b; Loreau, 2004), phenology/temporal hetero-geneity (Chesson and Warner, 1981; Godoy and Levine, 2014), multi-speciesinteractions (Holt et al., 1994; Spiesman and Inouye, 2015) and species traits(Bassett, 1995; Miner et al., 2005); as well as explanations that propose alterna-tives to niche based models, such as neutral models (Connor and Simberloff,1979; Hubbell, 1997, 2001); and combinations of niche and neutral (Cadotte,2007; Gravel et al., 2006). While niche models employ species differences tounderstand coexistence, neutral models consider species to be ecologicallyequivalent (equivalent in terms of competition and fitness), and explain coexis-tence as a result of random processes. Importantly, niche models usually focuson stable coexistence, in which species could theoretically cooccur togetherindefinitely, whereas neutral models accept an unstable version of coexistence,in which species may go extinct over time (Chesson, 2000b; Hubbell, 1979,1997).Modeling coexistence is difficult, both because community compositionis often the result of multiple processes, and because the identity of thoseprocesses often vary between systems. Having a library of well understoodsystems could help us find larger scale ecological patterns. Some researchprograms have attempted to get at this deeper understanding. For example:studies of interactions between Tribolium spp. beetles investigated multiple2chapter 1factors contributing to the outcome of competitive coexistence, including tem-perature, humidity, and relative abundance (Leslie et al., 1968; Park, 1948,1954, 1957); interspecific interactions such as competition and predation havebeen found to limit the distribution of barnacles in the intertidal zone inboth Scotland and the San Juan islands (Connell, 1961a,b, 1970); competition,predation and dispersal are all factors affecting the distribution of zooplanktonin lakes (Shurin, 2001; Shurin and Allen, 2001). Not only are these studiesuseful for providing a foundation from which to seek out patterns that crossgeographic and ecosystem boundaries, they can also lead to the developmentof new ideas. For example, the unpredictable outcome of coexistence betweenTribolium beetles under some environmental conditions is a good example ofstochasticity in ecology; Connell’s intertidal zone studies provide a textbookexample of fundamental and realized niches.In the following body of research, I study the factors that lead to co-existence (both stable and unstable) in a bromeliad invertebrate mesocosm.Bromeliads are a family of neotropical plants that provide habitat for aquaticinvertebrates, primarily insect larvae. The bromeliad system consists of adetritus-fed food web maintained by fallen leaves from the surrounding canopy.In some cases, especially in open-canopy areas, algae replace detritus as theprimary basal energy source (Brouard et al., 2011, 2012; Frank and Lounibos,2009). Allochthonous material is reduced from its whole form to fine particu-late organic matter via an invertebrate-facilitated processing chain (Starzomskiet al., 2010). In turn, bromeliads obtain increased nitrogen input, especiallywhen predators are present (Ngai and Srivastava, 2008), or terrestrial fauna(Gonçalves et al., 2014; Romero et al., 2006, 2010). Many species of invertebratesare supported by this system, most of which are larval Dipterans, includingseveral species of mosquitoes (Culicidae) and chironomids (Chironomidae).The top predator is usually a damselfly, though leeches, corethrellids, ta-3chapter 1banids and tanypodine chironomids are often present as well (Frank andLounibos, 2009). Bromeliads are excellent systems for community ecologyresearch because the invertebrate communities that live among their leavesare possible to delineate and easy to manipulate (Srivastava et al., 2004). Thisease of manipulation makes it possible to modify community structure inorder to study the effects of species interactions and habitat characteristicson populations or the community as a whole.The body of research concerning bromeliad-invertebrate community ecol-ogy has been growing rapidly over the past several years. We are startingto formulate ideas about which large-scale processes are the main factorsinfluencing food-web structure. Macroinvertebrate diversity often increaseswith bromeliad size or water volume (Armbruster et al., 2002; Dézerald et al.,2014; Jabiol et al., 2009; Jocque and Field, 2014); community composition maychange with canopy cover, with predators favoring more open areas (Brouardet al., 2012; Dézerald et al., 2013). Furthermore, biotic interactions, especiallypredation (Dézerald et al., 2014; Hammill et al., 2015a,b; Starzomski et al.,2010), but also competition (Lounibos et al., 2003) are known to influencecommunity composition, and sometimes ecosystem function as well. Nowthat the importance of these factors has been highlighted, more work is neededto understand how they work in combination to influence species coexistenceat the local level.In order to answer the question of how similar species can coexist inbromeliad food webs, I manipulated invertebrate communities in the statepark of Ilha do Cardoso, Brazil (see more about the study site below). Istarted with the development and application of a new methodological ap-proach to predict which species exhibit strong negative interactions based onobservational data. I followed this with two empirical methods to determinewhether species interactions and environmental variables led to coexistence of4chapter 1the species indicated in the first portion of the research. I sought the answersto three main questions:1. Which species exhibit signs of competition?2. Is competition between the target species mediated by predators?3. Do habitat and species-level traits change the outcome of competitionbetween the target species?To answer the first question, I modified a method of finding negativeco-occurrence patterns called checkerboard analysis (Gotelli, 2000; Stone andRoberts, 1990). In checkerboard analysis, observational field data are used toidentify cases of mutual exclusion between species in a community. Existingforms of the analysis use species incidence data, a practice that can compro-mise the biological relevance of the analysis. In Chapter 2, I modify the exist-ing method to use species abundances and to differentially weight observedpatterns based on those abundances. Then I use diagnostic testing to comparethe abundance-based method with the original incidence-based version ofcheckerboard analysis. Questions two and three are answered by applyingempirical methods to the species pairs identified in Chapter 2. Chapter 3involves the addition of predators to whole bromeliads to determine whetheror not they mediate the coexistence of competing detritivores. Following thepredator-addition experiment, I compare total emergences between speciesand use a demographic model to compare their demographic (emergence anddeath) rates as well. The analysis of demographic rates allows us to get moreinformation about how predators impact the three species differently than wecan obtain from final measures. The development of this three-fate model alsorepresents a methodological contribution to ecological analyses. In Chapter 4,I manipulate bromeliad size, ontogeny (body size) and relative abundance oftwo species to determine whether habitat type and phenotypic differences5chapter 1change the outcome of competition. Manipulations of relative abundanceallow us to answer questions about local coexistence, while manipulationsof habitat and ontogeny lead to conclusions about regional coexistence.1 .1 the study site : ilha do cardoso , brazilMy research was carried out in the state park of Ilha do Cardoso in São Paulo,Brazil (Figure 1.1). The habitat at the field site is comprised of restinga forest,a type of low canopy forest with sandy soil. Bromeliads are ubiquitous in theregion, making it an ideal research site for bromeliad food web ecology. Allexperiments, were performed using the terrestrial bromeliad Quesnelia arvensis- the most common bromeliad species in the area. This species has serrated leafmargins and sharp spines at each leaf tip. The richness of bromeliad-dwellinginvertebrate species is high in this area compared to other regions (BromeliadWorking Group, unpubl. data), with at least 166 species now documented(Romero and Srivastava 2010; P. M. Omena and G. C. Piccoli, pers. comm.).The high abundance of species makes Cardoso a great place to study speciescoexistence, as many taxonomically similar species cooccur in the region.6chapter 1F igure 1 .1 : Quesnelia arvensis in the restinga of Ilha do Cardoso, Brazil.7chapter 2Assessing species associations using abundanceweighted checkerboard patterns and null modelanalysis2 .1 introductionEcologists have long been interested in understanding patterns of communitystructure. Earlier research often assumed that habitat filtering and bioticinteractions are the most important determinants of species distributions (Van-dermeer, 1972; Whittaker and Levin, 1975). More recently, greater consider-ation has been given to random events, such as dispersal and drift, whenexplaining species distributions (Hubbell, 1997, 2001; Vellend, 2010). Earlyefforts in disentangling these drivers of community structure were limited bythe restrictions of empirical inference. However, modern computing powerhas made it feasible to perform large-scale simulations in order to understandthe impact of random events on community assembly.Checkerboard analysis was developed with the intention of distinguishingbetween communities structured primarily by competitive interactions andrandomly assembled communities (Diamond, 1975; Gotelli, 2000; Stone andRoberts, 1990), and is still used to make inferences about community structure(e.g. Barberán et al. 2012; Bik et al. 2010; Horner-Devine et al. 2007; Presley et al.2010). Checkerboard analysis works by measuring numbers of checkerboardunits (CU) between species pairs. A checkerboard unit is a 2 x 2, species-by-site sub-matrix in which one species is present in the first site only, and the8chapter 2second species is present in the second site only. In other words, the twospecies are mutually exclusive at the two sites. When repeated over multiplespecies pairs, this generates a checkerboard-like pattern to occurrence, therebygiving the name checkerboard unit. Usually, researchers are interested not inthe CUs between species pairs, but in the average number of CUs per speciespair for a community, known as the checkerboard score (C-score). Using anull model to shuffle the original data matrix, the C-score can be comparedto C-scores generated from shuffled matrices. The null model is intendedto simulate random processes and thus produce a community without thestructuring effects of deterministic processes, such as competition (Gotelli andUlrich, 2012). Thus, if the original C-score is higher than 95% of shuffledmatrices, we can say that the community is likely structured more by thoseforces that lead to checkerboard patterns than by random events.Although checkerboard analysis was designed to highlight the structuringeffects of competitive interactions (Diamond, 1975), checkerboard patterns canalso arise when species have a predator-prey relationship (Englund et al., 2009;Jackson et al., 1992), or when they are adapted to different sub-habitats. In thecase of a predator-prey relationship, we note that this interaction should leadto elimination of the prey unless there is some other factor allowing the preyto coexist with or avoid predators. Therefore, it is likely that even in the caseof predation-driven checkerboarding, environmental factors are also present.These alternative interpretations of checkerboard patterns add potential fordiscovering not only which species pairs are driving community-level patterns,but also which underlying mechanisms are responsible for mutual exclusion.Historically, checkerboard analysis has been performed on presence-absencematrices. In these matrices, columns represent sites and rows represent species.The matrix is then filled with 1s and 0s to represent the presence or absence9chapter 2of a particular species at a particular site. A checkerboard unit (CU) is thendefined as a sub-matrix with the form:Site x Site ySpecies A 1 · · · 0......Species B 0 · · · 1where Species A is found in Site x but not y, and Species B is found in Sitey but not x. (The dots above illustrate the fact that the two sites and speciesneed not be found next to each other in the data matrix; other numbers mayoccur between them.) Full details of the methodology can be found in Stoneand Roberts (1990).Unfortunately, there are two problems with using presence-absence, ratherthan abundance data. First, sub-matrices that nearly comprise a CU are notcounted under the strict presence-absence regime. For example, consider thefollowing abundance-based sub-matrix:A1 =100 01 98Ecologically speaking, sub-matrix A1 shows strong evidence for competi-tive exclusion or habitat filtering. However, the presence of a single individualoutside of the checkerboard pattern means that this sub-matrix will not countas a CU. This is a major fault with standard checkerboard analysis for threereasons: First, species that experience strong competition will not necessarilycompete to the point of exclusion of one or the other. For example, speciesthat change habitat at different life stages (e.g. aquatic larvae vs. terrestrialadults) experience a limited period of competition before moving on to theirnew environment. Second, species distribution data are merely a snapshot of10chapter 2the state of a community. A species that is in the process of extinction (e.g. asthe result of competition) at a site could still have a few lingering individualsat the time of data collection. Third, single individuals are associated withhigh error because they could have been misidentified or recorded incorrectlyduring data collection.A second problem with using presence-absence data over abundance datais that sub-matrices that qualify as CUs may actually provide only weak evi-dence of competitive exclusion because of overall low abundances of individ-uals; these sub-matrices still contribute equally to the overall checkerboardscore. Low abundances correspond with high error rates, reducing our confi-dence in the pattern. For instance, consider sub-matrix A2 below:A2 =1 00 2A2 is considered to be a CU following the traditional definition, but theprobability that this is a real checkerboard pattern as opposed to a randomdistribution of three individuals is quite low. The three individuals presentin sub-matrix A2 may be in the process of going extinct from the site, mayhave been misidentified, or may be in the process of moving to another site.Therefore, the low abundances reduce confidence in the ecological relevanceof the pattern. In contrast, A1 has high abundances and the relative dif-ference between high abundance and low abundance cells is much largerin absolute terms. From a purely biological perspective A1 provides muchstronger evidence of a biologically important relationship than A2. Thus, thestrength of checkerboard patterns varies depending on observed abundances,but patterns of varying strength are given the same weight, and some strongpatterns are not included at all.11chapter 2To summarize, two problems exist in the current use of checkerboardanalysis: 1) weak patterns are incorporated with equal weight to strong ones,and 2) strong patterns are eliminated completely due to the presence of asingle or a few individuals. A recent method by Ulrich and Gotelli (2010)began to address the problems with checkerboard analysis by presenting anabundance checkerboard unit (ACU). Using these ACUs ensures that sub-matrix A2 above would be included in the analysis. However, the moreimportant problem of strong and weak ACUs both receiving equal weightsstill remains.As mentioned above, checkerboard analysis is normally paired with a nullmodel to test whether the score for the data matrix differs significantly fromwhat is expected if random processes are responsible for species distributions.The null model takes the original data matrix and shuffles the values in amanner that is supposed to “randomize” the data, removing the mechanismof interest (Gotelli and Ulrich, 2012). However, there are a variety of possiblealgorithms that could be used to shuffle a data matrix and the best one de-pends on what mechanism is being studied. In incidence-based checkerboardanalysis, the preferred algorithm shuffles presences and absences by preserv-ing row and column totals (Gotelli, 2000; Stone and Roberts, 1990). Sincecolumns represent sites and rows represent species, this is the same as forcingspecies richness per site and the number of sites per species to be constant.Although this method works well for incidence-based checkerboard analysis,the same is not true when abundances are introduced; Checkerboard analysison abundances has favoured a probabilistic model, where row and columnsums are not fixed but the probability of placement in rows and columns isbased on those sums (Ulrich and Gotelli, 2010). Because it is difficult to knowa priori which method may be best for a particular analysis, it is essential to12chapter 2test a range of null model algorithms on sample matrices to calculate the TypeI and Type II error rates associated with each (Gotelli and Ulrich, 2012).In this paper, we present and test a new method for measuring speciessegregation using abundance data, solving existing problems with checker-board analysis. With this method, we define an abundance checkerboard unit(ACU) and apply a weight and strength to this unit to generate an abundance-weighted checkerboard unit (AWCU). Finally, we generate an abundance-weightedcheckerboard score, or AWC-score to replace the traditional C-score as a metricof species segregation in a community. To determine the best null modelfor use with our new metric, we tested nineteen null model algorithms withsample matrices to find the Type I and Type II error rates associated with eachone.As a follow-up to developing this new method of checkerboard analysis,we were interested in comparing our method with the incidence-based (Stoneand Roberts, 1990) and abundance-based (Ulrich and Gotelli, 2010) methodsthat have preceded it. To this end, we conclude by analysing one of our owndatasets using all three methods.2 .2 methods2 .2 .1 Abundance Weighted CheckerboardsAn abundance checkerboard unit (ACU) is defined as follows. Given any 4-cell sub-matrix ABxy, where A and B are species, x and y are sites, and Ax,Ay, Bx, and By are abundances of the respective species at the respective sites:ABxy =Ax · · · Ay......Bx · · · By13chapter 2ABxy comprises an abundance checkerboard unit if:[1] Ax > Bx and By > AyOR[2] Ax < Bx and By < AyTo distinguish between high and low abundance ACUs, we created a weight-ing method. Abundance weighting is performed in two steps. First, wedefined a weight, W, for each ACU:W =∣∣∣∣AxAt − BxBt∣∣∣∣+ ∣∣∣∣AyAt − ByBt∣∣∣∣ (2.1)where At and Bt are equal to the total abundance of species A and B, respec-tively. This generates a value between 0 and 2. The differences calculated givea measure of the amount of overlap between species at the given sites. If thedifference is small, then species show a near absence of exclusion, which willgenerate a small weight. Dividing by species abundance totals standardizesthe abundance measures, accounting for species that naturally occur at widelydifferent abundances. For example, in bromeliad invertebrate communities inIlha do Cardoso, Brazil, damselfly nymphs Leptagrion spp. are comparativelymassive and the average observed abundance is three per bromeliad (D. S. Sri-vastava and G. Q. Romero unpubl. data). At the same site, ostracods Elpidiumbromeliarum are barely visible to the eye and have been observed at abundancesinto the thousands (D. S. Srivastava and G. Q. Romero unpubl. data). Thus,using ratios avoids skewing the data in favour of species combinations thatinvolve naturally abundant species paired with naturally rare species.14chapter 2The inclusion of the weight is still not sufficient to solve all problems,however. Using the above calculation for W, we generate some ACUs withequivalent values of W but different strengths corresponding with differentoverall abundances. For example, suppose we have three ACUs as follows:ACU1 =200 100100 200with At = 300 and Bt = 300ACU2 =20 1010 20with At = 30 and Bt = 30ACU3 =2 11 2with At = 3 and Bt = 3. Because the ratios Ax/At, Ay/At, Bx/Bt andBy/Bt are equal in all three sub-matrices, all three ACUs have weight, W =0.667. However, ACU1 represents a stronger checkerboard than ACU2 andACU3 because of higher overall abundances. We therefore create a measureof strength based on abundances only, in order to increase the value of theabundance-weighted CU when abundances are high but ratios are equivalent.Strength, S, is calculated as:S = logNmax(Amax) + logNmax(Bmax) (2.2)where Nmax is the maximum abundance value in the matrix, and Amax andBmax are the maximum values of species A and B within the sub-matrix. This15chapter 2generates a value between 0 and 2 (the same range as W). Using log baseNmax scales the values such that the cell with highest abundance will give avalue of 1. This means that S is scaled to the abundance distribution of eachspecific matrix. Assuming the above three sub-matrices come from a matrixwith Nmax = 200, the strengths are as follows:S(ACU1) = 2S(ACU2) = 1.131S(ACU3) = 0.262Finally, these values are added to W, to get a set of abundance-weightedcheckerboard units (AWCU):AWCU1 = S1 +W1 = 2.667AWCU2 = S2 +W2 = 1.798AWCU3 = S3 +W3 = 0.929To calculate an abundance weighted checkerboard score for an entire ma-trix, AWCUs are calculated for each unique 2 x 2 sub-matrix in the data set(i.e. every pair of species at every pair of sites). The abundance weightedcheckerboard score is the mean of all AWCUs for the matrix.2 .2 .2 Null ModelsWhen converting from an incidence-based to an abundance-based matrix, thenumber of possible null model algorithms increases. We evaluated nineteennull model algorithms for shuffling matrices. Nine of these were previously16chapter 2employed by Ulrich and Gotelli (2010) and the remaining ten were of our owndesign.Null models for shuffling abundance data can be categorized in two mainways. First, zero cells in the original data can either be retained or ignoredin the null matrices. Fixed zero null models retain the placement of zero cellsand floating zero models allow species to be placed in sites where they did notexist in the original matrix (Ulrich and Gotelli, 2010). Second, null models canbe categorized based on whether populations, or individuals are rearrangedbetween the cells. In population-based models, the entire population of onespecies at one site is shuffled into another cell. In individual-based models,species are placed one-by-one into new cells (Ulrich and Gotelli, 2010). Bio-logically, a population-based model assumes that dispersal is clustered. Thebromeliad-dwelling ostracod Elpidium bromeliarum, for example, is largely un-able to migrate between bromeliads, so offspring remain together after repro-duction. Individual-based models, on the other hand, assume that dispersal isindividualized, as in bromeliad-dwelling frogs of the Scinax perpusillus group,which oviposit one egg at a time, splitting their clutch between bromeliads(AlvesSilva and da Silva, 2009).We constructed nineteen null models and named them based on the fol-lowing conventions: 1) As the first letter, I = individual-based, P = population-based; 2) As the second letter, X = fixed-zero, L = floating-zero. D is usedas a stand-in in the individual-based models to represent “dropped” zeros.In other words, the zeros are neither preserved by “fixing” them, nor by“floating” them; they are merely dropped; 3) As the third, and possibly fourthletter(s), R means row sums are preserved, C means column sums are pre-served, RC means both row and column sums are preserved, and M meansthe sum of the entire matrix is preserved (but row and column sums mayfluctuate); 4) As the final letter(s), U means there is a uniform probability of17chapter 2being placed in any cell, (though this is not strictly true if row and/or columnsums are preserved), R or C means placement probabilities are proportionalto row or column sums, and RC means probabilities are proportional to rowAND column sums. Following is the complete list of null models that weretested:• PXRU, PXCU: Population-based models with fixed zeros and row orcolumn sums, respectively, preserved.• PXMU: A population-based model with fixed zeros and populationsplaced in any cell with equal probability.• PLRU, PLCU, PLMU: Population based models with preserved row,column, or matrix sums, respectively. Same as PXRU, PXCU, and PXMUabove, but with floating zeros.• IDRU, IDCU: Individual-based models with row or column sums, re-spectively, preserved.• IDRCU: An individual-based model with preserved row and columnsums.• IXRU, IXCU: Same as IDRU and IDCU above, but with fixed zeros.• IDMR, IDMC: Individual-based models with placement probabilitiesproportional to, respectively, row or column sums.• IDMRC: An individual-based model with placement probabilities areproportional to both row and column sums.• IXMR, IXMC, IXMRC: Same as IDMR, IDMC and IDMRC above, butwith fixed zeros.• IDMU, IXMU: Individual-based models with, respectively, fixed or droppedzeros where placement in any cell is equiprobable.18chapter 22 .2 .3 Diagnostic TestingWe ran diagnostic tests to determine the ability of each null model to correctlydistinguish random from structured (checkerboarded) data. We estimatedType I and Type II error rates of each null model by creating 400 each of ran-dom and structured test matrices and performing the null model analysis oneach one. For each test matrix, we ran each null model 1000 times, generating1000 shuffled matrices per test matrix.Diagnostic testing was performed first on the random test matrices inorder to obtain a Type I error rate. Random matrices were created in twodifferent ways (designated as MR and MS) by sampling from a log-normaldistribution. A full description and defence of the diagnostic testing can befound in Ulrich and Gotelli (2010; see also Gotelli and Ulrich, 2012). Type Ierror was calculated as the number of test matrices showing significantly highor low (α = 0.05) amounts of structure compared to shuffled versions of thematrix (either k ≤ 0.025 or k ≥ 0.975 where k is the proportion of shuffledmatrices with a lower AWC score than the test matrix). Only models thatgenerated p ≈ 0.05 were tested for Type II error. This corresponded to 10 outof 400 test matrices with k ≤ 0.025 and 10 with k ≥ 0.975.Type II error rates were calculated by adding structure to random matricesto find the point at which structure was detected. Rows of structure wereadded one at a time and then the new matrix was run through the nullmodel again. Each row was selected randomly from a uniform distribution.Structure was generated by taking the maximum value, rmax in the selectedrow, and alternating that value with 0s. Depending on whether the row andcolumn index were even or odd, we switched between alternating in a 0, rmax,. . . pattern or a rmax, 0, . . . pattern. This ensured that 0s would be offset andACUs generated. Once the matrix showed more structure than 95% (k ≥ 0.95)of the shuffled matrices, we stopped adding structure and the proportion of19chapter 2structured rows was recorded. After all 400 test matrices were analysed, wegenerated a mean proportion of structure needed for the model to generatek ≥ 0.95.2 .2 .4 Analysis of Community DataTo compare the results of using incidence-based, abundance-based and abundance-weighted checkerboard analysis, we performed all three methods on a dataset of bromeliad-invertebrate communities (D. S. Srivastava and G. Q. Romerounpubl. data) using the null model algorithm best suited to each one. TheBromeliaceae is a neotropical plant family that collect water in their leaf ax-ils, providing habitat for aquatic insect larvae and other small fauna. Ourdata were collected from Ilha do Cardoso, an island off the coast of SãoPaulo province in Brazil. This community is home to over 100 species ofinvertebrates (Romero and Srivastava 2010; Srivastava 2015 pers. comm.),many of which may have strong interactions. In particular, three speciesof Chironmidae (Chironomus detriticola, Polypedilum kaingang and Polypedilummarcondesi) are observed to occur in different mean bromeliad sizes (Letaw,2015), but also co-occur frequently. We therefore expected that these mightdisplay strong checkerboard patterns in the abundance-weighted metric, butnot the incidence- or abundance-based ones.For each analysis, we ran the best suited null model 5000 times. For theincidence-based analysis, we used null model IDRCU, with fixed row andcolumn sums (Gotelli, 2000). For the abundance-based analysis we used nullmodel IDMRC, with probabilistic placement based on row and column sums(Ulrich and Gotelli, 2010). For our own abundance-weighted analysis, we usedthe optimal null model as determined by this research.Each of the aforementioned analyses generates a community-level scoreand a p-value describing whether the community differs significantly from20chapter 2the null expectation of random species segregation. In the event of significantcheckerboarding, we were interested in determining which species pairs weredriving the pattern. We did this by analysing the distribution of units (CU,ACU, or AWCU) for every species pair. From this distribution, we found themean number of units and the standard deviation. Any species pairs that hadmore than the mean + 2 SD were designated as the highly segregated speciespairs driving the checkerboard pattern.2 .3 resultsAs a result of the diagnostic testing, we found that most null models had veryhigh Type I error rates, with test matrices exhibiting lower AWCU scores thantheir corresponding shuffled matrices (Table 2.1). This pattern held acrossboth MR and MS type matrices. Models that had some constraint on bothrow and column values gave the lowest error rates, although this did not holdwhen zeros were fixed. The model with lowest Type I error was IDRCU, amodel that fixes both row and column sums, which generated an error rate of0.025 for MR matrices and 0.05 for MS matrices.Because all other models had unacceptably high error rates, we only as-sessed Type II error for model IDRCU. In the MR type matrices, the meanfraction of structured rows needed to generate k ≥ 0.95 was 0.221± 0.223. 11of the 200 matrices never generated k ≥ 0.95. For the MS type matrices, themean fraction of structured rows was 0.132± 0.161. 8 of the 200 matrices nevergenerated k ≥ 0.95. Those matrices that never generated k ≥ 0.95 correspondto a Type II error rate of 0.04 to 0.055.21chapter 2Null ModelMR MSk < 0.025 k > 0.975 k < 0.025 k > 0.975PXCU 172 [0.860] 0 [0.000] 193 [0.965] 0 [0.000]PXRU 115 [0.575] 0 [0.000] 193 [0.965] 0 [0.000]PXMU 174 [0.870] 0 [0.000] 194 [0.970] 0 [0.000]PLCU 176 [0.880] 0 [0.000] 197 [0.985] 0 [0.000]PLRU 191 [0.955] 0 [0.000] 196 [0.980] 0 [0.000]PLMU 190 [0.950] 0 [0.000] 199 [0.995] 0 [0.000]IDCU 147 [0.735] 0 [0.000] 196 [0.980] 0 [0.000]IDRU 125 [0.625] 2 [0.010] 192 [0.960] 2 [0.010]IDRCU 2 [0.010] 3 [0.015] 4 [0.020] 6 [0.030]IDMU 175 [0.875] 0 [0.000] 199 [0.950] 0 [0.000]IXCU 169 [0.845] 0 [0.000] 195 [0.975] 0 [0.000]IXRU 177 [0.885] 1 [0.005] 193 [0.965] 0 [0.000]IXMU 158 [0.790] 5 [0.025] 197 [0.985] 0 [0.000]IDMC 133 [0.665] 2 [0.010] 191 [0.955] 0 [0.000]IDMR 70 [0.350] 4 [0.020] 185 [0.925] 2 [0.010]IDMRC 0 [0.000] 33 [0.165] 1 [0.005] 11 [0.055]IXMC 125 [0.625] 19 [0.095] 168 [0.840] 1 [0.005]IXMR 0 [0.000] 167 [0.835] 130 [0.650] 5 [0.025]IXMRC 0 [0.000] 196 [0.980] 0 [0.000] 193 [0.965]Table 2 .1 : Number of matrices with higher AWCU than at least 95% ofshuffled matrices. A model with a standard Type I error rate of α = 0.05should generate around 5 matrices with k > 0.975 and 5 with k < 0.025 wherek is the proportion of shuffled matrices with a lower AWC score than the testmatrix. Error rates are calculated in square brackets.2 .3 .1 Analysis of an Example Community DatasetWe now consider the performance of the AWC approach, as compared toC and AC approaches, in terms of analysing a real ecological dataset: thebromeliad macroinvertebrate communities of Ilha do Cardoso, Brazil. Allthree checkerboard metrics generated significant checkerboard scores when22chapter 2tested against the relevant null model: incidence-based (CS = 7.46, p =0.0056), abundance-based (ACS = 9.98, p = 0.0002), abundance-weighted(AWCS = 10.14, p = 0.0002). However, each model generated a very differentset of highly segregated species pairs (Table 2.2), with C and AC approachessharing 22% of species, AC and AWC sharing 37% of species, and C and AWCsharing only 2.6% of species; only a single species pair was preserved acrossall three methods.2 .4 discussionHere we developed a novel method of performing checkerboard analysis onabundance data and weighting checkerboard scores based on these abun-dances. Further, we found that a null model that preserves matrix columnand row sums was the best choice for using with AWC analysis.Evaluating new analyses with diagnostic testing is an essential part ofensuring the analysis is robust (Gotelli and Ulrich, 2012). In the case of nullmodel shuffling algorithms, each one should be tested for Type I and Type IIerror rates to confirm that the model is creating random matrices as expected(Gotelli, 2001; Gotelli and Ulrich, 2012). In other words, a shuffling algorithmshould neither reject the null hypothesis that a data matrix is random too often(α = 0.05), nor should it falsely reject the alternate hypothesis that the datamatrix is structured too often (β). For our AWC analysis, we found that mostnull model algorithms had error rates well above the desired α level, and weretherefore unsuitable for use (Table 2.1). In fact, this is not unusual; previousanalyses using similar diagnostic tests have also shown that many null modelalgorithms are prone to high Type I error (Gotelli, 2000; Ulrich and Gotelli,2010). In our case, the only model with low susceptibility to Type I errorwas IDRCU, the “fixed-fixed” model that fixes the sum of row and column23chapter 2abundances. This result is not surprising because the fixed-fixed model is alsoconsidered to be the best null model for incidence-based checkerboard analy-sis (Gotelli, 2000). A good null model algorithm will attempt to remove themechanism of interest, and in all checkerboard analyses that is the structuringcaused by net negative species interactions or habitat filtering.Because model IDRCU was the only model with reasonable Type I errorrates, this model was the only one tested for Type II error. When rows ofstructure were added to the model, 13% to 20% of an otherwise randommatrix had to be filled with structured rows in order to generate a p < 0.05.This value is similar to the abundance-based metric, which found significantstructure when checkerboarding was increased by 1-10% (Ulrich and Gotelli,2010). Compared to the incidence-based metric, however, these values aresomewhat lower (Gotelli, 2000). In that analysis, Type II error was measuredby adding randomness to structured matrices, the reverse process to thatemployed here and by Ulrich and Gotelli (2010). Structure was still detectablewhen up to∼50% of the matrix had been randomized. This difference betweenincidence and abundance-based methods is likely related to the probabilityof generating checkerboard units at random in each method. If CUs appearfrequently by chance, a large percentage of structure should be required togenerate a significantly high level of checkerboarding because the averagenumber of checkerboards in shuffled matrices will be high. In contrast, ifCUs appear rarely by chance, a smaller percentage of structure will be re-quired to push the matrix to the alpha level of significance. In fact, logictells us that the probability of generating CUs by chance must be lower whenabundances are used. Because the random matrices are generated using a log-normal distribution (see Methods), some species are much more abundantthan others and it is unlikely for very abundant species to form checkerboardpatterns with rare species; rare species will frequently not have high enough24chapter 2abundances to be more abundant at a given site than the common species.However, if abundances are converted to incidences, the effect of high andlow abundances is removed and any species can randomly checkerboard withany other species.The relative ease of producing a CU by chance under different types ofcheckerboard analysis can inform us about the differences between the meth-ods. Because ACUs are more difficult to generate by chance than incidenceCUs, and because it takes a smaller fraction of structure in the matrix togenerate a significant AC- or AWC-Score, abundance methods should givehigher significance levels to matrices with equal or lower amounts of checker-boarding. In practice, we found this to be true. Our analysis of an empiri-cal data matrix showed significant amounts of checkerboard structure in allthree analyses. However, the level of significance was much higher in bothabundance-based methods than in the standard incidence analysis.Checkerboard analysis has primarily been used to assess the level of com-petition and species segregation within a whole community. An extension ofthis is to consider which species pairs are driving the pattern of segregation.This information can lead to fruitful empirical examinations of species insitu. We analysed our empirical data to find out which highly segregatedspecies pairs were driving the patterns of checkerboarding in the commu-nity. To illustrate the usefulness of analysing segregated pairs, we draw thereader’s attention to response of midge larvae in the family Chironomidae.Three species of Chironomidae – Polypedilum kaingang, Polypedilum marcondesi,Chironomus detriticola – are known competitors with different preferences forplant size (Chapter 4). On average, P. kaingang are found in small plants(∼ 250 mL), P. marcondesi are found in medium plants (∼ 525 mL) and C.detriticola are found in large plants (∼ 875 mL). However, the three speciesalso experience some overlap and do not show complete mutual exclusion,25chapter 2suggesting that abundance and incidence measures of co-occurrence will notbe identical. Under incidence-based checkerboard analysis, no pairwise combi-nation of the three species showed high levels of segregation (Table 2.2). Onceabundances were used by either the AC or AWC method, P. marcondesi andP. kaingang had ACUs in the high end of the distribution. Furthermore, usingour abundance-weighted metric, C. detriticola and P. marcondesi also appearedas highly segregated. The findings from our AWC analysis pair well with ourown knowledge and experimental results on the interaction between the threespecies. In particular, C. detriticola and P. marcondesi have been found to havean interesting competitive relationship when reared together in bromeliads(Chapter 4). However, using incidence-based or abundance-based CA, wewould not have detected this species pair as a duo of interest.Interestingly, there was little overlap between the highly segregated speciesaccording to incidence-based checkerboard analysis and those found withthe two abundance-based analyses. This suggests that the incidence-basedpatterns we found in our data matrix were often weak or rare when 1s and 0swere converted to abundances. Switching from incidence-based to abundance-based, if there are many more ACUs than CUs, the species pairs with high CUswill be moved to the middle or lower part of the distribution and no longerappear as highly segregated. Furthermore, converting to AWCUs, the actualvalue of abundances becomes important. If pairs with high CUs or ACUsare comprised of low total abundances, they may be moved even lower inthe distribution and disappear from the list of highly segregated species pairswhen the abundance-weighted analysis is used. It is instructive to comparespecies abundances underlying a species pair from Table 2.2 with high CU(Corethrellidae sp.1, Wyeomyia sp.) and one with high AWCU (P. marcondesi,Scirtes sp.). In Table 2.3, abundances are shown for these two species pairs.The high CU pair show a high degree of apparent mutual exclusion, but26chapter 2overall abundances are relatively low. Interestingly, this is a predator-preycombination (Corethrellids consume mosquito larvae, including Wyeomyia).Wyeomyia mosquito larvae are known to avoid their predators by occurringin smaller bromeliads than most other bromeliad-dwelling insects, (Hammillet al., 2015a). In comparison, the high AWCU pair have a lot of species overlapat sites, but high abundances and apparent mutual suppression have led to ahigh number of AWC units. Once again, this highlights the utility of AWCanalysis in detecting structured patterns between species pairs; when putativepairs of interacting species co-occur, standard incidence-based CA is unable todetect them.In spite of the advantages of using AWC analysis, incidence-based CAmay still be a useful method for some purposes. We have seen that theincidence-based method tends to be more conservative in its estimates of theamount of structure in a community. The fact that approximately 50% of thecommunity must be structured to generate a significant C-score (Gotelli, 2000)means that the incidence-based method gives a score more representative ofthe community as a whole than do the abundance-based and abundance-weighted methods. Combined with its strict adhesion to complete mutualexclusion, these qualities suggest that standard CA would be useful for detect-ing a strong environmental filter within a community. If the area of interestis actually species-level interactions, then we recommend the AWC analysisdescribed here. Because our analysis is more sensitive to the presence ofcheckerboarding and better at detecting interactions between species, it is agood way to find strong interactions between species that may actually beco-occurring within sites. Furthermore, following the AWC analysis with apost-hoc test to find highly segregated species pairs, as we did here, can leadto the identities of competing species and open the door to further empiricalstudy.27chapter 2Species 1 Species 2 C AC AWCOrthocladiinae sp. Tanytarsus sp. 49 67 –Ephydridae sp. Monopelopia caraguata 50 – –Bezzia sp. Polypedilum kaingang 51 – –Corethrellidae sp. 2 Polypedilum kaingang 51 – –Dasyhelea sp. Polypedilum marcondesi 51 – –Polypedilum kaingang Psychodidae sp. 52 72 –Corethrellidae sp. 1 Dasyhelea sp. 52 – –Tubificidae sp. Wyeomyia sp. 52 – –Elpidium bromeliarum Ephydridae sp. 56 72 –Ephydridae sp. Trentepohlia sp. 56 72 –Dasyhelea sp. Tubificidae sp. 56 – –Leptagrion andromache Wyeomyia sp. 56 – –Elpidium bromeliarum Wyeomyia sp. 60 73 –Trentepohlia sp. Wyeomyia sp. 60 – –Scirtes sp. Wyeomyia sp. 64 68 64.7Diptera sp. Elpidium bromeliarum 64 – –Diptera sp. Trentepohlia sp. 64 – –Corethrellidae sp. 1 Wyeomyia sp. 65 – –Polypedilum kaingang Trichoptera sp. – 68 87.7Culex sp. Elpidium bromeliarum – 72 91.2Polypedilum kaingang Tubificidae sp. – 75 67.1Polypedilum kaingang Polypedilum marcondesi – 76 92.8Corethrellidae sp. 1 Polypedilum kaingang – 81 80.5Polypedilum kaingang Scirtes sp. – 82 99.1Polypedilum kaingang Tanytarsus sp. – 87 73.5Polypedilum kaingang Trentepohlia sp. – 87 81.928chapter 2Species 1 Species 2 C AC AWCElpidium bromeliarum Polypedilum kaingang – 118 125.8Culex sp. Trentepohlia sp. – – 64.7Elpidium bromeliarum Trentepohlia sp. – – 65.8Elpidium bromeliarum Monopelopia caraguata – – 65.8Polypedilum marcondesi Wyeomyia sp. – – 67.0Chironomus detriticola Polypedilum kaingang – – 73.6Elpidium bromeliarum Tubificidae sp. – – 77.8Elpidium bromeliarum Trichoptera sp. – – 78.4Culex sp. Polypedilum kaingang – – 78.9Chironomus detriticola Elpidium bromeliarum – – 84.8Polypedilum marcondesi Scirtes sp. – – 100.5Elpidium bromeliarum Scirtes sp. – – 107.8Elpidium bromeliarum Polypedilum marcondesi – – 117.3Table 2 .2 : Checkerboard (C), abundance checkerboard (AC) and abundance-weighted checkerboard (AWC) units for the most highly segregated speciespairs under each analysis. “Highly segregated” species are those from a com-munity with a significant checkerboard score (incidence-based, abundance-based, or abundance-weighted) and whose number of units exceeds the mean+ 2 SD for the dataset.29chapter 2BromeliadHigh CU pair High AWCU pairCorethrellidae sp. 1 Wyeomyia sp. P. marcondesi Scirtes sp.B1 23 0 76 90B2 18 0 89 65B3 10 0 82 69B4 10 0 19 0B5 8 0 57 63B6 8 0 11 39B7 6 0 31 13B8 5 0 29 55B9 4 0 21 22B10 2 0 0 17B11 1 0 12 0B12 1 0 7 37B13 1 0 7 1B14 0 0 14 4B15 0 0 11 9B16 0 0 4 7B17 0 0 2 4B18 0 0 0 1B19 0 0 0 0B20 0 0 0 0B21 0 1 33 6B22 0 2 0 0B23 0 6 0 0B24 0 11 0 0B25 0 15 14 0Table 2 .3 : Abundances of four species in 25 bromeliads from Brazil. Thefirst two columns show a species pair with high numbers of checkerboardunits, while the second pair has high abundance-weighted checkerboard units.The high-CU pair has many instances of mutual exclusion, whereas the high-AWCU pair has higher overall abundances and a lot of species overlap.30chapter 3Predator-mediated competition does not facilitatecoexistence of bromeliad-dwelling Chironomidae inBrazil3 .1 introductionAccording to classical niche theory, the coexistence of identical species is im-possible (Hutchinson, 1957) because one species will ultimately exploit sharedresources more efficiently than the other. In ecosystems where similar speciescooccur, a conceptual challenge therefore arises in understanding how speciesavoid local extinction. Fortunately, several possible solutions to this puzzlehave already been formulated - including neutrality, and niche differentiationthrough trade-offs in species performance. Under neutral theory, speciescoexistence is unstable and stochastic events (e.g. drift, dispersal) determinewhich species coexist (Chave, 2004; Hubbell, 1997, 2001); Species may coexistfor multiple generations, but the ultimate fate is extinction. Further, speciesin the model are assumed to be equivalent, so species similarity in reality isnot a problem. Niche differentiation leads to coexistence of similar speciesby reducing overlap in their use of resources or microhabitats, as is the casefor mosquitoes that divide space vertically within bromeliad tanks (Gilbertet al., 2008). This occurs because of trade-offs in performance under differentconditions. Differential exploitation of multiple resources (Tilman, 1977, 1990)and differences between species in their competitive and colonization abilities(Turnbull et al., 1999; Levine and Rees, 2002) are classic examples of trade-offs31chapter 3that have been used to explain coexistence of similar species. We focus on therole of trade-offs in coexistence for the remainder of this work.There are numerous types of trade-offs that could lead to coexistence, anumber of which involve the effects of predators. Predators can have largeimpacts on the abundance of prey populations, and species may trade-offsensitivity to predation with sensitivity to other biotic or abiotic stressors.For example, trade-offs may occur between predator resistance and droughtresistance, as in bromeliad-dwelling mosquito larvae (Hammill et al., 2015a)or between predator resistance and competitive ability, as in larval anurans(Werner and Anholt, 1996; Werner and McPeek, 1994). The trade-off betweenpredator resistance and competitive ability in particular can result in coex-istence of similar species in the same habitat under predator-mediated co-existence (PMC). PMC has been shown to be important in several systems,including insect larvae in container habitats (Bradshaw and Holzapfel, 1983;Kesavaraju et al., 2008), as well as amphibians (Peacor and Werner, 2000; Reichet al., 2000), marine invertebrates (Wulff, 2005), fish (Persson, 1993), mites(Karban et al., 1994), and birds (McKinnon et al., 2013). The classic test for PMCis a difference in competitive outcomes following the exclusion (or inclusion)of the predator.In this study we examine whether trade-offs in predator resistance leadto PMC in aquatic invertebrate communities within the water-filled tanks ofbromeliads. In bromeliads, multiple invertebrate species of the same family, oreven genus, are often found co-occurring within a single plant, suggesting thatstrong competitive interactions may be present. Further, predation has beenshown on multiple occasions to be an important factor in invertebrate speciesdistributions among bromeliads (Gilbert et al., 2008; Hammill et al., 2015a,b).We conducted our research on Ilha do Cardoso in São Paulo, Brazil (seeChapter 1). In this area, there are many species in closely related taxonomic32chapter 3groups, suggesting that these species may have a high degree of niche overlapand may be involved in strong interspecific interactions. In particular, there areat least 4 species of chironomid midge in Cardoso, two of which are congeneric(G. Q. Romero, unpubl. data). We studied the relationship between the threemost common of these chironomids: Chironomus detriticola Correia & Trivinho-Strixino 2007, Polypedilum marcondesi Pinho & Mendes 2010, and Polypedilumkaingang Pinho, Mendes & Andersen 2013.In addition to being closely related, the three study chironomid specieshave previously been shown to have negative co-occurrence patterns accord-ing to abundance-weighted checkerboard analysis (AWCA; see Chapter 2).AWCA detects species segregation using relative differences in abundancesbetween species at overlapping sites. Negative co-occurrence patterns suggestthat the species either have differential responses to an abiotic aspect of thehabitat, or are undergoing net negative interactions. If the latter, competitioncould be driving their negative co-occurrence, though we cannot tell withAWCA alone whether predators are involved in mediating coexistence.Here we experimentally test whether the metacommunity-scale co-occurrenceof three chironomid species, including two congenerics, is due to PMC. If so,we predict that:1. Chironomid species differ in their vulnerability to predation.2. Chironomid species show different competitive outcomes within bromeli-ads, depending on the presence or absence of predators.3. The distribution of chironomid species among bromeliads is primarilydetermined by the distribution of predators, rather than any other habi-tat attribute of bromeliads (e.g. size).We conducted a predator-addition experiment to determine whether or notexpectations (1) and (2) were met. We followed this with an analysis of33chapter 3observed co-occurrence patterns of predators and chironomids in differently-sized bromeliads to determine whether expectation (3) was met.3 .2 methods3 .2 .1 Predator-addition experiment (Expectations 1 and 2)We conducted a predator-addition experiment to examine the effects of acommunity of three different predators on the three focal chironomid species.If PMC was important, we would expect chironomid species to differ in theirsusceptibility to predators, and for predators to alter the outcome of competi-tion between chironomids.Our experiment was carried out between January and April of 2011. Threespecies of predators were used: Leptagrion andromache (a damselfly; Odonata:Coenagrionidae), Monopelopia caraguata Mendes, Marcondes & Pinho 2003 (apredatory chironomid; Diptera: Chironomidae), and Hirudinea sp. (a greenleech). These species were chosen due to their relative ubiquity as well as theirphenotypic differences; We used three unrelated but common predator speciesin order to sample the multiple types of predator behaviour that chironomidsnormally experience in bromeliads. In this study site, bromeliads generallycontain 5 to 11 (mean ± SD) species of predators, so chironomids usuallyco-occur with a multi-species predator community. L. andromache is the mostcommon of a few odonate species found in Cardoso. Odonates are the toppredators in bromeliad food webs when present (Frank and Lounibos, 2009).They are sit-and-wait predators that lurk in the bottom of the leaf well andgrab approaching prey with their extensible labium. M. caraguata is a smallTanypodine chironomid with piercing mouth-parts. In spite of their small size,Tanypodine chironomids have been observed to consume prey as large as, orlarger than, themselves (A. A. M. MacDonald and D. S. Srivastava, unpubl.34chapter 3results). The green leech, Hirudinea sp., feeds by draining blood from its prey.These leeches were observed to feed on many invertebrates in the bromeliadfood web, including chironomids (A. A. M. MacDonald and D. S. Srivastava,unpubl. results).All invertebrates were collected from naturally occurring bromeliads by re-moving the contained water with a large pipette. Bromeliad water was sievedsequentially through sieves of two mesh sizes (850 and 150 µm) to separateorganisms from fine particulate organic matter. Once the invertebrates ofinterest were obtained, remaining organisms were returned to bromeliads inthe field.Two treatments were used to determine the effects of predators on differentchironomid species: a predator-present treatment and a predator-absent con-trol. In the predator treatment, the three species of chironomids and the threepredator species were added to cleaned (the cleaning process is describedbelow) bromeliads. In the predator-absent control, chironomids were addedto cleaned bromeliads without predators. In all treatments, every bromeliadreceived 10 individuals of each chironomid species. In the predator treatment,we also added one individual each of L. andromache and Hirudinea sp., andtwo individuals of M. caraguata. Densities of chironomids and predatorswere chosen based on the range of densities found in a 2008 field surveyof bromeliads (described below; D. S. Srivastava and G. Q. Romero, unpubl.data). Chironomids are known to benefit from detrital shredding, which cancreate the small detrital and fecal particles that they collect (Starzomski et al.,2010). Therefore, in both treatments, a nymph of Trichoptera sp. (a caddisfly)was added to promote shredding of the coarse detritus. Each treatment wasrepeated in 15 replicate bromeliads.Each replicate was run within an entire bromeliad, which was returnedto the forest after cleaning, for the duration of the experiment. Bromeliad35chapter 3sizes ranged from 100 to 200 mL. Bromeliads were prepared by first removingthem from the soil and pipetting out all water. They were then washed outthoroughly with a hose and submerged, upside down, in a tank of waterfor 24 hours to promote the exodus of any remaining organisms. Finally,bromeliads were hung upside down to dry for 48 hours so that any remainingorganisms would desiccate. Three bromeliads were cleaned to test the cleaningmethod. In the three test bromeliads, only two living organisms were found:a partially desiccated chironomid larva, and an individual of the ostracodspecies Elpidium bromeliarum. Washing Q. arvensis bromeliads has previouslybeen estimated to remove 94% of existing fauna (Romero and Srivastava, 2010).Chironomid communities were added to bromeliads along with fine de-tritus (to provide food and materials for the chironomid cases) and driedleaves (to provide the habitat complexity found naturally). Fine detritus wascollected from bromeliads using a 150 µm sieve. Detritus was then boiled toensure that no living organisms remained, and concentrated by allowing thedetrital material to settle overnight and pipetting off the remaining water. Weinoculated all bromeliads with 44.4 mL of this same batch of detritus solution,ensuring that the water to detritus ratio remained constant. Whole leaves werealso collected from bromeliads and dried in an oven at the lowest possibletemperature. After measuring out 7.9 g of dried leaves per bromeliad, leaveswere soaked in water overnight to avoid eutrophication of the bromeliadcaused by the initial influx of nutrients, and then distributed evenly betweenthe axils of each bromeliad. Chironomids were placed in bromeliads 24 hoursprior to predators to allow dispersal through the bromeliad.Bromeliads were placed in three different sections of the forest. In eachsection, the experiment was initiated two weeks subsequent to the previoussection, creating three temporal-spatial blocks, all run for the same length oftime (six weeks). The temporal staggering allowed us to perform an experi-36chapter 3ment with many replicates while reducing mortality in the captive chironomidlarvae, which tend to have poor survivorship in captivity. Furthermore, theincorporation of time and location as random variables allows us to test thegenerality of the experimental treatments, ensuring that results are not deter-mined by the date or physical placement of the bromeliads.Bromeliads were covered with mesh cages to prevent migration into andout of the experimental units. Attached to the top of each cage were collectiontraps for corralling adult chironomids (Figure 3.1). Traps were constructedfrom inverted, 2-liter, clear beverage bottles that had been thoroughly cleanedprior to the start of the experiment. The dispensing-end of the bottle wasremoved, turned upside-down, and attached to the interior of the bottle creat-ing a funnel type trap. Traps were checked daily for emerged insects, whichwere identified and released. If any predators emerged as adults, they werereplaced with another individual of the same species as soon as possible.The experiment was carried out for six weeks, which should have been asufficient amount of time for all chironomids to emerge under normal condi-tions (Canteiro and Albertoni, 2011; Oliver, 1971), after which the bromeliadswere removed and dissected, and the contained communities censused.3 .2 .2 Analysis of survey data (Expectation 3)We analysed an observational data set from our field site in Ilha do Cardoso,Brazil, collected in 2008 (D. S. Srivastava and G. Q. Romero, unpubl. data)to determine whether chironomid species differed in their relationship witheither predator biomass or bromeliad size. If predator-mediated coexistence(PMC) is important, we would expect predators rather than plant size todetermine differences between chironomid species in their distribution. Plantsize is examined in particular here as, of all bromeliad attributes, it is the mostcommon correlate of invertebrate composition in bromeliads (e.g. Amundrud37chapter 3and Srivastava 2015; Gilbert et al. 2008; Srivastava et al. 2008). We used linearmodels to predict how chironomid abundance was related to total predatorbiomass, bromeliad size and their interaction. Models were fit separatelyfor each chironomid species (Chironomus detriticola, Polypedilum kaingang andPolypedilum marcondesi). Non-significant terms were removed and the modelswere compared with AIC (Akaike’s Information Criterion) and ANOVA toselect the best one. We assessed model residuals and QQ-plots to confirm thatthe selected models fit well.3 .2 .3 Statistical Analysis of Experiment DataAll analyses were performed using the statistical computing language, R (RCore Team, 2014). Experimental data were analysed using a two-way analysisof variance (ANOVA) to compare the survival and emergence of the threespecies at the end of the experiment. The response variable (either survival oremergence) was transformed using a log10 transformation.To get an idea of how emergence rates were affected by the treatments, weanalysed the number of days until first emergence for each species within eachtreatment using two-way ANOVA.Because our data were right-censored (the experiment was ended on a fixeddate regardless of the fate of chironomids), we needed to model emergencesover time to determine whether chironomids might have emerged after theend of the experiment. Survival analysis is able to deal with data with binaryfates (e.g. dead, alive), but our data had three fates (dead, alive but notemerged, alive and emerged). Therefore, we created a demographic modelto predict the final values of survival and emergence for each species in eachtreatment. We used a density independent model of population growth (A.D. Letaw and A. A. M. MacDonald, unpubl. results) to predict the adult38chapter 3population size based on the larval population size, emergence rate, and deathrate. The model construction is as follows:First, larval population decline over time (t) is modelled as a function ofnumber of larvae (L), larval death rate (d) and adult emergence rate (a):dLdt= −(a+ d)L (3.1)Solving the differential equation gives:L(t) = L0e−(a+d)t (3.2)where L0 is the number of immature individuals at the start of the experiment.Next, we model adult population growth as:dAdt= aL (3.3)where A is the adult population size. Since we have already solved theequation for larvae, we can substitute that into the formula above, getting:dAdt= aL0e−(a+d)t (3.4)Now, solving the equation for the adult population gives:A(t) =aL0e−(a+d)t(e(a+d)t − 1)a+ d(3.5)which can be simplified, giving:A(t) =aa+ dL0(1− e−(a+d)t) (3.6)To estimate the parameters of our demographic model, we first calculatedthe cumulative emergence over time, within treatments and replicates, for eachchironomid species in our data set. Next, we fit our model to the cumulative39chapter 3data using two rounds of non-linear least squares (NLS) estimation. In thefirst round, we used a “brute-force” technique that generates 1000 randomparameter values within a given starting grid. The starting grid was cre-ated by establishing upper and lower bounds for each parameter (e.g. deathrate could not be higher than 10 as there were only 10 individuals of eachspecies per replicate). This process was completed using the R package nls2(Grothendieck, 2013). Using the estimates generated in the first round offitting as new start values, we performed NLS a second time, this time withthe Levenberg-Marquardt algorithm (Marquardt, 1963) to generate a betterfit. We used the R package minpack.LM (Elzhov et al., 2015) for the secondfit. Error in model parameter estimates was calculated using bootstrapping toresample the data 100 times and perform the two rounds of NLS on resampleddata. Percentile-based 95% confidence intervals were calculated based on thebootstrap residuals and used to compare parameter estimates.3 .3 results3 .3 .1 Predator-addition experimentChironomids took longer to start emerging in the presence of predators (treat-ment: F1,82 = 9.440, p = 0.00289 ; Figure 3.2), but this effect of predators ondays to first emergence did not differ between species (species x treatmentinteraction: F2,82 = 0.993, p = 0.375). In fact, there was no overall differencein days to first emergence between species (species: F2,82 = 1.365, p = 0.261),though P. kaingang tended to have a higher median in days to first emergencethan the other species (Figure 3.2). There was a significant block effect (F1,82 =8.302, p = 5.21× 10−4).Overall, predators reduced the survival and emergence of chironomids(survival: F1,82 = 24.836, p < 0.0001 ; emergence: F1,82 = 18.983, p < 0.000140chapter 3F igure 3 .1 : Set up of the predator-addition experiment. Bromeliadswere enclosed in mesh cages to prevent organisms from entering or exitingthe experiment. Cages were topped with traps to capture emerging adultchironomids.41chapter 3; Table 3.1). However, predators had proportionally similar effects on allchironomid species, both in terms of survival (species x predation: F2,82 =0.375, p = 0.688) and emergence (species x predation: F2,82 = 0.239, p = 0.788).In fact, regardless of treatment, there was little difference between chironomidspecies in their survival (species: F2,82 = 0.427, p = 0.654) and emergence(species: F2,82 = 0.205, p = 0.815). Both survival (F2,82 = 10.280, p =1.04× 10−4) and emergence (F2,82 = 11.195, p < 0.0001) showed block effects.We caution that, in addition to being performed on censored data, theseANOVAs consider only the total number of emergences or surviving larvaeby the end of the experiment. By considering how the number of emergenceschange over time we can gain additional insight into the underlying rates ofthese processes.Our models of adult population growth were a reasonable fit to adultemergence considering the amount of noise in the data (Figure 3.3). Predictedestimates of overall emergence from these models were often similar to theobserved values at the end of the experiment, but in four cases, the modelpredicted further emergences after the end of the experiment (Table 3.1) sug-gesting that some information was lost by using censored data for the ANOVA.According to the models, all chironomid species had significant decreases(around 2 to 3-fold) in emergence rates in the predator treatment (Figure 3.4)suggesting the species tend to delay emergence under threat of predation(also supporting the analysis of days until first emergence, above). All threespecies had similar emergence rates in the control treatment. However, whenpredators were present, P. kaingang emergence was lower than the other twospecies. Predators also led to non-significant increases in death rate for P.marcondesi (2-fold) and C. detriticola (3-fold), but did not change the death ratefor P. kaingang (Figure 3.4). Both P. marcondesi and C. detriticola had similardeath rates in both the control and predator treatments. However, while P.42chapter 3Control with PredatorsEmergence Survival Emergence SurvivalC. detriticola Obs. 2.67± 0.61 3.33± 0.72 1.13± 0.33 1.27± 0.36Pred. 4.90 NA 1.50 NAP. kaingang Obs. 3.27± 0.73 4.20± 1.00 1.27± 0.45 1.40± 0.51Pred. 9.10 NA 7.52 NAP. marcondesi Obs. 2.33± 0.37 2.40± 0.38 1.00± 0.24 1.07± 0.27Pred. 4.00 NA 1.34 NATable 3 .1 : Mean ± SE emergence and survival (Obs), and predicted(Pred) emergence (out of 10 individuals per replicate), for each species xtreatment combination. Gray cells represent those treatments in which furtheremergence is predicted after the end of the experiment (emergences greaterthan µ + 2 SE). P. kaingang was predicted to have the most emergences in bothcontrol and predator treatments.kaingang overlapped with C. detriticola in the control treatment, P. kaingangdeath rate was lower than the other two species in the predator treatment.These differences suggest a species-by-treatment interaction in which speciesrates are the same or nearly so in the control treatment, but P. kaingang isdistinguished by having lower emergence and death rates in the predatortreatment.3 .3 .2 Analysis of survey dataChironomid species differed in which factors (predator biomass or bromeliadsize) best predicted their abundance (Figure 3.5, 3.6). Polypedilum marcondesiabundance increased with predator biomass (t16 = 3.683, p = 0.00201; Fig-ure 3.5A); P. kaingang abundance was best fit by a model including a negativeeffect of predator biomass, but the slope of the relationship did not differ fromzero (t16 = −0.799, p = 0.436 ; Figure 3.5B); C. detriticola abundance increasedwith plant size (t4 = 5.759, p = 0.00451) but decreased with predator biomass(t4 = −2.839, p = 0.04692 ; Figure 3.6).43chapter 3F igure 3 .2 : Days to first emergence increased (F1,82 = 9.440, p = 0.00289)from the control to predator treatments, suggesting that chironomids delayedemergence in the presence of predators. However, although predationincreased time to first emergence in all species, there were no differencesbetween species (species: F2,82 = 1.365, p = 0.261 ; species x treatmentinteraction: F2,82 = 0.993, p = 0.375)44chapter 3F igure 3 .3 : Demographic model fits to the emergence data for bothtreatments. The coloured prediction lines are backed with the actualcumulative emergence data displayed as boxplots. Emergence was slowedand reduced in the predator treatment. Model fits suggest that P. kaingangwould have had the highest emergence values if the experiment had been runfor a longer period of time.45chapter 3F igure 3 .4 : Comparison of the parameter estimates from the demographicmodel for each species by treatment combination. Points show means andconfidence intervals. All species showed significant decreases in emergencerate (a) when predators were present. Compared to C. detriticola and P.marcondesi, P. kaingang had lower death rates (d), suggesting higher fitnessin the conditions of the experiment.46chapter 3F igure 3 .5 : Survey data showing the relationship between the twoPolypedilum species and predator biomass. Points show the actual data whilelines are the predicted values generated by linear models. A: P. marcondesiabundance increased with predator biomass (p = 0.00201). B: P. kaingang wasbest fit by a model containing only predator biomass, but the slope of thisrelationship was not different from zero (p = 0.436).47chapter 3F igure 3 .6 : Survey data showing the relationship between C. detriticola andplant size and predator biomass (log scale). Points show the actual data whileisocline lines depict the predicted values generated by the linear model. C.detriticola abundance increased with plant size (p = 0.00451) but decreasedwith predator biomass (p = 0.04692). The biological significance of therelationship with predator biomass was lower at small plant sizes in the sizerange we used in our experiment (due to the log scale).48chapter 33 .4 discussionHere, we combine observational and experimental data to test whether thecoexistence of three chironomid species in bromeliad tanks is mediated by thepresence of predators. Our predator-addition experiment suggests that theremay be differential responses to predator-presence between the three species.This was supported by the survey data, in which each species respondeddifferently to increased predator biomass. We conclude that predators havedifferent effects on different species, but that this does not result in predator-mediated coexistence because the identity of the highest performing speciesremains constant across treatments.Predators had strong negative effects on all chironomid species, realizedmore through reductions in the emergence rate than increases in the deathrate (changes in the death rate were not significant). Consequently preda-tors increased the time to first emergence in all species (Figure 3.2). De-layed development in response to predators has been found in many otherinsect communities as well (e.g. McKie and Pearson 2006; Stoks 2001; vanUitregt et al. 2012). The importance of non-consumptive effects such as thisis increasingly being highlighted (Davenport et al., 2014; Preisser et al., 2005;Werner and Peacor, 2003). In the bromeliad system, predators have previouslyexhibited non-consumptive effects on the community, leading to differencesin community composition and ecosystem function (Hammill et al., 2015a;Marino et al., 2015). Though non-consumptive effects have yet to be studiedfor the species used in our experiment, other species of chironomids changetheir behaviour in the presence of predators, increasing burrow depth (Hölkerand Stief, 2005) and reducing foraging (Ball and Baker, 1996; Hölker andStief, 2005). Reduced foraging can increase development time, which wouldnaturally lead to decreased emergence rates as we saw here.49chapter 3Although predators affected all three species of chironomids, the strengthof this effect differed between species. Results of the predator-addition ex-periment suggest a difference between P. marcondesi and C. detriticola on theone hand and P. kaingang on the other. Specifically, demographic rates werenearly equivalent between species in the control, with only P. kaingang and P.marcondesi differing slightly in death rate (Figure 3.4). When predators wereadded, however, the death rates of P. marcondesi and C. detriticola increasedsuch that P. kaingang then had a lower death rate than both of the other twospecies (Expectation 1; Figure 3.4). Emergence rates were also depressed inthe presence of predators for all three species, with P. kaingang standing outagain as having significantly lower emergence rate than the other two species(Figure 3.4). Even though P. kaingang larvae had low emergence rates in thepresence of predators, so many larvae survived to pupation that the totalnumber of predicted emergences was higher for this species than the othertwo species (Table 3.1). The results from our demographic model demonstratethat chironomid species differ in the extent to which predation depresses theirdemographic rates and that this led to differences in predicted numbers ofemergences (Table 3.1). Although our ANOVA of cumulative emergences doesnot show such a species-by-predation interaction, this likely is an artefact ofcensoring the data set for that analysis.In terms of the natural distribution of the three chironomids, all three haddifferent responses to predator biomass. Distributions of P. marcondesi andC. detriticola were both predicted by the biomass of predators (Expectation 3;Figures 3.5A, 3.6) but P. kaingang, differed, having no relationship with eitherpredator-biomass or plant size (Figure 3.5B). Furthermore, while C. detriticolawas negatively affected by predator biomass, P. marcondesi was actually pos-itively affected. Although both the survey and the experiments show that P.kaingang is the least affected by predators, we were expecting - based on the50chapter 3experimental results - for both P. marcondesi and C. detriticola abundance to benegatively (not positively) affected by predator biomass. The only way thatthis apparent contradiction in the response of P. marcondesi could be resolvedis if predation risk is actually lower in bromeliads with high predator biomass.This could occur if predators interfere with each other (Bruno and O’Connor,2005; Griffin et al., 2008), or if predators have alternate prey. Both of these seemplausible based on previous data from this system. Two studies have nowshown that predators in bromeliads have strong antagonistic effects, reducingtheir net predation rate (Atwood et al. 2014; A. A. M. MacDonald, unpubl.data). Thus, chironomids may obtain an advantage by occurring in bromeliadswith diverse predator assemblages (the number of predator species increaseswith predator biomass in our survey data: r = 0.891, p < 0.0001). Alter-natively, high predator biomass in bromeliads may reflect high biomasses ofalternate prey, including tipulids, scirtids and mosquitoes. Odonate predationon these alternate prey species has been shown, at our field site, to be greaterthan that on chironomids (LeCraw, 2014). Chironomids may escape predationin such situations.Notably, we found block effects showing differences in response when thelocation and time of experiment start was changed. Possibly there are differ-ences in the robustness of individuals that are the result of earlier colonizationcompared to those that develop later. There was no way to control for suchdifferences as our reason for blocking was to avoid high larval mortality incaptivity. However, these block effects may point to the importance of colo-nization timing, also suggested by Chapter 4. Further investigation is neededinto the role of time on chironomid survival, emergence and coexistence.Is there PMC in this system? Although predators had differential effectson the three chironomid species, the species that appeared to be the best atresisting predation, P. kaingang, was not competitively inferior in the absence51chapter 3of predators; In fact it had slightly lower larval mortality than the other specieseven in the absence of predators suggesting if anything it was the competitivedominant in all situations (a “Darwinian demon”). There are many possiblealternatives to PMC as the mechanism allowing these chironomid species toinhabit the same region. One is that the species do not compete, but our otherresearch does not support that conclusion (see Chapter 4). More likely, thereare other habitat variables mediating the coexistence of chironomids. Oneof these is likely plant size. Other studies of the system suggest that plantsize is an important factor in determining community composition (Gilbertet al., 2008; Hammill et al., 2015a). Field survey data showed that at least C.detriticola seems to have a positive relationship with plant size, meaning thisspecies may also be competitively dominant in larger plants. Any interactionbetween predation and plant size, could not be captured in our experiments,which were conducted in a single plant size.We therefore conclude that predation has little role in mediating coex-istence between bromeliad-dwelling chironomid species. Importantly, thisresult was not predicted by our analysis of observational data, which sug-gested that predator presence would benefit at least one species of chirono-mid. The mismatch between experimental and observational results suggestsfertile ground for future research. For example, manipulating predator ef-fects in conjunction with bromeliad size could determine whether effects arecontext-dependent; Examining the effects of alternate prey and predator an-tagonism on chironomid survival could answer questions about the positiverelationship between C. detriticola and predator biomass. Finally, future be-havioural or caged-predator studies could give more information about thenon-consumptive effects we suspect are driving chironomid response here.52chapter 4Asymmetric ecological equivalence andcontext-dependent competition between chironomidsin bromeliads4 .1 introductionSpecies coexistence can be explained by both deterministic, niche processesand stochastic, neutral processes (Chesson, 2000a,b; Vellend, 2010). Nichemodels explain coexistence by employing species differences whereas neu-tral models (Hubbell, 1997, 2001) explain coexistence through random events,such as drift and dispersal. Furthermore, neutral models assume species areecologically equivalent. Ecologically equivalent species interact as if they arethe same species, so the neutral processes of drift and dispersal determinelong-term dynamics. More specifically, ecologically equivalent species areequivalent in terms of both fitness (fitness equivalence; λi = λj , whereλ is the species average fitness) and competition (competitive equivalence;αii = αjj = αij = αji, where αxy is the effect of species y on species x).In a neutral model, ecological (fitness and competitive) equivalence ofspecies is sufficient for coexistence, albeit one that is vulnerable to drift orperturbation (unstable coexistence). In niche models, however, fitness or com-petitive differences among species do not guarantee coexistence. Instead, com-petitive differences must be such that they stabilize the multispecies system(stable coexistence) by increasing the strength of intraspecific (as comparedto interspecific) competition when a species is represented by an increasing53chapter 4proportion of individuals in a community (Chesson, 2000b). Conversely, com-petitive differences can destabilize the system if intraspecific competition di-minishes in importance as a species increases its relative proportion, generallyleading to local extinction of one species. Unlike competitive differences,fitness differences between species never promote coexistence at a local scale(although local fitness differences can promote coexistence at a metacommu-nity scale, as we discuss shortly). Fitness differences lead to competitiveexclusion when they cannot be offset by competitive stabilizing mechanisms(Chesson, 2000b).Between the extremes of ecologically equivalent species and niche-differentiatedspecies, lies a suite of other possible relationships. By mathematically ma-nipulating the relative importance of intra- and interspecific competition, itis possible to uncover alternative relationships. As previously shown (Adleret al., 2007; Chesson, 2000b; Godoy and Levine, 2014), when species exhibitfitness differences, coexistence occurs if the species with higher fitness also hasstronger intraspecific competition (competitive stabilization; Appendix a.1).However, under fitness equivalence, the strengths of competition for bothspecies determine whether or not this criterion is satisfied, and a few differentscenarios allow for coexistence (Table 4.1A; Appendix a.1). For example, onespecies may be equally affected by intra- and interspecific competition evenif the other is not, a phenomenon we call asymmetric ecological equivalence.In these scenarios, one species responds to the world neutrally while theresponse of the second species is decidedly non-neutral, being more limitedby either conspecifics or heterospecifics. The dynamics influencing the non-neutral species (i.e. competitive stabilization vs. destabilization) determinewhether or not the two species can coexist.Even if species do not coexist at the local scale, context-dependent fitnessdifferences can promote coexistence at the metacommunity scale (Table 4.1B).54chapter 4For example, environmental differences in local patches can lead to habitatpartitioning when each species performs better under a different environ-mental context. Many experiments on insects have shown differences in theoutcome of competition to be dependent on environmental variables suchas habitat size (Juliano, 2009), temperature (Park, 1954), humidity (Costanzoet al., 2005; Park, 1954), and resource distribution (Atkinson and Shorrocks,1981). Stochastic differences in colonization order can also lead to coexistenceby producing ontogenetic differences in body size; when both species havean advantage at one body size (e.g. the larger species always has higherfitness), variation in colonization timing can lead to variation in the identityof the superior competitor in a given patch - a priority effect (Rasmussenet al., 2014; Shorrocks and Bingley, 1994). Larger individuals often prey ontheir smaller counterparts (Fox, 1975; Polis, 1981; Schröder et al., 2009) whilesmaller individuals may be more adept at obtaining or utilizing resources(Claessen et al., 2000; Werner, 1994). Thus, even if species are identical in theircompetitive abilities in general, if one arrives earlier and is therefore largerat the time they interact, there may be some fitness or competitive differencedriven by colonization order and ontogeny alone (Gilbert et al., 2008).This research investigates local and regional coexistence by manipulatingrelative abundance, habitat type and body size in a bromeliad invertebratesystem using two species of chironomid larvae (Diptera: Chironomidae). Oneof the most important habitat variables for bromeliad insects is bromeliad size(Jocque and Field, 2014; Marino et al., 2011; Petermann et al., 2015). In surveysof bromeliad contents, many species appear to exhibit some preference forbromeliad size (Amundrud and Srivastava, 2015). Smaller bromeliads gen-erally dry out faster (Schmidt and Zotz, 2001; Srivastava et al., 2008) whilelarger bromeliads generally contain more predators (Amundrud and Srivas-tava, 2015; Srivastava, 2006; Srivastava et al., 2008). For example, coexistence55chapter 4in bromeliad mosquitoes may depend on a trade-off between the ability toresist desiccation and the ability to resist predation (e.g. Hammill et al. 2015b).Bromeliad size may also influence larval fitness by influencing resource avail-ability, such as detritus density and algal productivity (Marino et al., 2011).We performed two experiments with two chironomid species that are oftenfound coexisting within a single plant. We aimed to answer three questions:1. What type of competitive relationship, if any, do the two species have(e.g. competitive equivalence) and which mechanisms drive the relation-ship (e.g. stabilizing mechanisms)?2. Does context (habitat or ontogeny) alter the outcome of competition?3. Are the two species expected to coexist locally? Regionally?In the first “equivalence” experiment we tested the importance of intra-and interspecific competition by manipulating the relative abundance of thetwo species (Question 1). Recent research with congeneric damselfly nymphsused a similar experimental design and demonstrated ecological equivalence(Siepielski et al., 2010). In the second, “ontogeny” experiment, we tested theeffect of manipulating ontogeny by altering the relative body size of the chi-ronomid species (Question 2). In both experiments, we performed manipula-tions in two plant sizes to measure the effect of changing habitat conditions onlocal coexistence (Question 2). We crossed all treatments with a manipulationof absolute density. Species average fitness is related, in part, to their abilityto perform despite increased density of competitors, and differences betweenspecies in this component of fitness help predict whether species would coexistat the local scale (Question 3). We followed the experiments with an analysisof survey data to determine whether any habitat context-dependence seenin the experiment matched habitat-dependent patterns observed in naturalbromeliad communities (Question 2).56chapter 4In the equivalence experiment, we expected to find a combination of equal-izing and stabilizing processes consistent with local coexistence (Table 4.1A)as the study species are naturally found together within a patch. Two possibleoutcomes are consistent with local coexistence (Figure 4.1): 1) If the commu-nity was neutrally structured with ecological equivalence between species, therelative abundances of the two species are expected to have no systemic trendfrom the beginning to the end of the experiment (Figure 4.1), indicating thatspecies identity is unimportant in determining performance; 2) By contrast, ifthe community was structured by stabilizing mechanisms, intraspecific compe-tition is expected to increase as the relative abundance of that species increases.Therefore, when a species begins with high relative abundance, intraspecificcompetition should be strong leading to a lower per capita response (Fig-ure 4.1). A third possible outcome is that species interactions could lead toexclusion of one or the other species. This could happen either if the specieswith higher initial abundance also has higher final abundance (competitivedestabilization; Figure 4.1), or if one species always has higher final abun-dance (fitness inequality is not compensated by competitive stabilization). Asdescribed previously (Table 4.1A), the presence of competitive equivalence,stabilization, and destabilization can be asymmetric between the species, withdifferent combinations leading to different coexistence outcomes.Because we assumed density, that is, the ratio of organisms to food re-sources, not abundance, was the important factor in competition, our de-sign crossing habitat size and density necessarily resulted in a range of totalabundances or organisms even within density treatments. However, it isconceivable that organisms instead respond to abundance, for example iforganisms do not compete for food resources but instead for a scale-invariantresource. We therefore tested whether there was any relationship between thespecies response and total abundance. If total abundance were important, we57chapter 4would expect that equalizing mechanisms would show a decline in responsewith total abundance (Figure 4.1a), and stabilizing mechanisms would showthe steepest decline in response with total abundance of conspecifics only(rather than with heterospecifics, or both) (Figure 4.1b).In the ontogeny experiment and in the habitat manipulations, we expectedto find different responses to habitat and body size, especially if the resultsof the equivalence experiment led to local extinction of one species. Specifi-cally, species could still persist at the metacommunity scale, even with localextinction, if each species exhibited higher performance than the other speciesin a particular context (habitat or relative body size; Table 4.1B). However, ifspecies had the same performance in each context, then coexistence is expectedto be either unstable (neutral dynamics at local and metacommunity scales) orone species will go extinct in the metacommunity, in the absence of any otherstabilizing factors. Scenarios suggesting regional extinction of one specieswould be surprising because the two species have been observed in the sameregion over multiple years (G. Q. Romero unpubl. data, A. D. Letaw pers.obs.). If our results indicated such an outcome, we would postulate thatthere must be another mechanism besides those we investigate here, allowingcoexistence at the metacommunity scale.4 .2 methodsWe performed two experiments, manipulating relative abundance (ecologicalequivalence) and relative body size (ontogeny) in two chironomid species. Totest if performance in different plant sizes in experiments matched observedplant size preferences, we also analysed survey data for the two species froma previous year (D.S. Srivastava & G. Q. Romero, unpubl. data). Finally, we58chapter 4A: Outcome of local coexistence (λi = λj)αij = αii αij > αii αij < αiiαji = αjj Unstablecoexistence(ρij = λj/λi)No coexistence(asymmetricdestabilization)Coexistence(asymmetricstabilization)αji > αjj No coexistence(asymmetricdestabilization)No coexistence(destabilization)Contingentcoexistence:Species coexist if(αii × αjj) > (αij × αji)αji < αjj Coexistence(asymmetricstabilization)Contingentcoexistence:Species coexist if(αii × αjj) > (αij × αji)Coexistence(stabilization)B: Outcome of regional coexistenceλi,x = λj,x λi,x > λj,x λi,x < λj,xλi,y = λj,y UnstablecoexistenceSpecies j goes extinct Species i goes extinctλi,y > λj,y Species j goesextinctSpecies j goes extinct Coexistence via habitatpartitioning or priorityeffectsλi,y < λj,y Species i goesextinctCoexistence via habitatpartitioning or priorityeffectsSpecies i goes extinctTable 4 .1 : Outcomes of local and regional coexistence predicted for ourexperiments. A: Lighter grey cells exhibit asymmetric ecological equivalencewhile darker cells exhibit symmetric ecological equivalence (neutrality).Assuming fitness equivalence, local coexistence, depends on relative valuesof competition coefficients (αxy = the effect of species y on species x). Speciescoexistence is stable when ρij < λj/λi (ρij is a measure of niche overlap;Appendix a.1). The outcome of competition is driven by the non-equivalentspecies. If species do not have equal fitness, coexistence occurs throughcompetitive stabilization only. B: Dark cells are compatible with a hypothesisof neutrality at the metacommunity scale. Species can coexist via habitatpartitioning or priority effects if each species has higher fitness in one context(e.g. small plants vs. large plants) than the other species, where differentcontexts are indicated by x and y.59chapter 4F igure 4 .1 : Possible results for the ecological equivalence experiment. Therelationship between initial and final proportions of a species reveals the typeof mechanisms affecting the species interaction: A flat line suggests equalizingmechanisms because the per capita response is not affected by initial relativeabundance; Negative slopes suggest a stabilizing relationship in which specieswith high initial relative abundance limit their own population sizes; Positiveslopes suggest a destabilizing relationship in which one species excludes theother. Side plots show expected response to absolute density in a) Equalizingor b) Stabilizing scenarios. Species will either respond to the total abundanceof both species (a), to the abundance of conspecifics only (b), or have norelationship with abundance (a and b, dashed lines).60chapter 4estimated average fitness of species in order to predict whether coexistencewould occur (Table 4.1) in each treatment.Experiments were run between late February and early June of 2013. Twospecies of aquatic bromeliad-dwelling chironomid larvae were used: Chirono-mus detriticola Correia & Trivinho-Strixino, 2007 and Polypedilum marcondesiPinho & Mendes, 2010. These were chosen as focal species based on theirhigh relative abundance compared to other bromeliad invertebrates, includingother chironomid species.4 .2 .1 Equivalence ExperimentTo determine the relative importance of intra- and interspecific competition,we set up a 2 x 2 x 3 factorial experiment (Figure 4.2a), manipulating absolutechironomid density (low vs. high, described below), plant size (large vs. small,described below), and relative abundance. Relative abundance treatments fol-lowed a substitutive design, with each chironomid species making up either 25,50, or 75% of the total larval population. The substitutive design is necessaryfor detecting equivalence and frequency-dependence of species responses; anadditive design would confound the results because of the increased absolutedensity.4 .2 .2 Ontogeny ExperimentThe ontogeny experiment used a 2 x 2 x 2 factorial design (Figure 4.2a),manipulating absolute chironomid density (low vs. high, described below),relative body size (large vs. small), and plant size (large vs. small, de-scribed below). Relative body size was manipulated in order to representdifferences in colonization order (Hernandez and Chalcraft, 2012; Rasmussenet al., 2014), though we acknowledge that this fails to capture advantages inaccess to resources provided to early colonizers. This indirect manipulation61chapter 4of colonization order allowed us to ensure that all chironomids experiencedthe same length of the experiment; had we added one species before the other,the effects of the size difference would be confounded with differences in thenumber of exposure days. Larger bodied organisms were also put into theexperiment 24 hours prior to the smaller organisms.4 .2 .3 All ExperimentsIn all experiments, invertebrates were collected from bromeliads by removingdead leaves from the bromeliad tanks with large forceps and pipetting allimpounded water into a bucket using a large pipette. Bromeliad contents weresorted into coarse and fine organic matter, using an 850 µm sieve followed bya 150 µm sieve. Materials retained on sieves were then searched for larvae ofthe relevant species.Two plant size classes and two absolute densities of chironomids wereused. Plants were designated either as large or small, where small plants hadvolumes of 500 ml or less and large plants had volumes of 1500 ml or more.These volumes were determined based on data from bromeliads in naturalconditions (A. A. M. MacDonald and D. S. Srivastava 2010, unpubl. data); P.marcondesi tend to be found in small plants whereas C. detriticola are more oftenfound in large plants. Two levels of absolute density were used to examinethe response of chironomids to resource depletion, a component of averagefitness as defined by Chesson (2000). Under high density treatments, 8 larvaeper 15 ml were used; under low density, only 4 larvae per 15 ml were used(Figure 4.2b). Densities were based on the range of natural larval densitiesfound in bromeliads surveyed in the study area in 2008 (D. S. Srivastava & G.Q. Romero, unpubl. data).Fine particulate organic matter (FPOM), collected originally from bromeli-ads in situ, was added to tubes at a concentration of 0.008 g ml−1. FPOM62chapter 4provides food and habitat for chironomid larvae (Oliver, 1971; Walshe, 1951).The concentration added was again based on surveys of natural bromeliadsin the study area (D. S. Srivastava & G. Q. Romero, unpubl. data). Beforeadding FPOM to tubes, it was boiled to ensure that no invertebrate larvae oreggs remained alive. Samples of boiled FPOM were dried on filter paper andweighed to determine the wet volume equivalent of 0.008 g dry mass. FPOMwas added to tubes in liquid form because dried FPOM does not dissolve wellin water.In addition to FPOM, dead arboreal leaves were added to tubes to createhabitat structure as would be found in a natural setting. Leaves were collectedfrom bromeliads, cleaned thoroughly, and oven dried for sterilization. Theywere then standardized by size. A small leaf was added to small tubes, and alarge leaf was added to large tubes.Chironomid assemblages were placed in 15 or 50 ml centrifuge tubes forsmall or large plants, respectively. In preparation for the experiments, an 8.5mm hole was drilled through both sides of each tube. Holes were covered with80 µm Nytex mesh, which allowed bromeliad water and micro-organisms toflow into the tube, while preventing chironomids from escaping. Bromeliadsplay an important role in affecting the oxygen and nutrients within their tanks,and we wanted to ensure our experiment allowed for these processes (Benzinget al., 1972; Lopez et al., 2009). Tubes were placed in bromeliad leaf wells withone replicate of each treatment per plant. Thus, each plant held 4 (ontogenyexperiment) to 6 (equivalence experiment) tubes. The top of each tube wascovered with a mesh emergence trap to catch emerging insects and preventoviposition into the tubes. The emergence traps were checked daily. Followingidentification, adult insects were released.Performance was measured in terms of adult emergence (counted daily)and overall survival of each species. The experimental phase for each repli-63chapter 4cate lasted 8 weeks, which should have given both species sufficient time todevelop to adulthood (Canteiro and Albertoni, 2011; Oliver, 1971). At theend of the experiment, all remaining larvae were identified. Survival wascalculated as the sum of emergences and remaining larvae.4 .2 .4 Data AnalysisFour models were created for each experiment: a model for each of the twospecies with chironomid emergence as the response variable, and a modelfor each of the two species with chironomid survival as the response vari-able. The full model was used as a starting point for model fitting. The fullmodel included all treatments and all possible interactions between them. Foreach model, insignificant terms were removed one-by-one, starting with thethree-way interaction term, followed by the two-way interactions, and finallythe individual terms, if needed. Each simplified model was compared withthe more complex version using a likelihood ratio test (Zeileis and Hothorn,2002). When the likelihood-ratio test returned a significant p-value, the morecomplex model was retained.In the equivalence experiment, four additional models were created, fittingsurvival and emergence against total abundance. Models with total abun-dance of species and total abundance of conspecifics as explanatory variableswere compared using Akaike’s Information Criterion (AIC). Model fits includ-ing plant size were also tested, and compared to the simpler models usinglikelihood-ratio tests.In all cases, a binomial GLM was used with plant identity set as a randomeffect. Model fitting was done with the statistical software, R (R Core Team,2014) using the package lme4 (Bates et al., 2014). Models were assessed forgoodness of fit by examining the deviance residuals.64chapter 44 .2 .5 Fitness Proxy EstimatesAverage fitness in the context of Chesson’s (2000b) coexistence frameworkrefers to the ability of a species’ population to grow quickly despite resourcecompetition. Importantly, this ecological definition differs from Darwinianfitness. Empirically determining fitness differences is widely acknowledgedas one of the most difficult aspects of applying Chesson’s (2000b) frameworkto real systems. For example, the approach advocated by Adler et al. (2007)is to first fit a demographic model to each species and then force competitiveequivalence upon the model to reveal fitness differences. This approach hasbeen successfully implemented for an annual plant community (Godoy et al.,2014; Godoy and Levine, 2014; Kraft et al., 2015). However, such an approach isnot feasible for a system such as bromeliad chironomids, where it is extremelydifficult to obtain the necessary information on fecundity and adult mortalityto fit dynamic models. Instead, we return to the original definitions of averagefitness and first note that any definition of fitness as insensitivity to resourcecompetition requires that the density of both conspecifics and heterospecificsbe considered; for example, one term of the Godoy and Levine (2014) equa-tion for fitness considers the inverse of the product of the intraspecific andinterspecific competition coefficients. Therefore we expect that, in general, aspecies with high average fitness should show insensitivity in its vital ratesto changes in total density (combining conspecifics and heterospecifics). Wetherefore estimate a proxy of average fitness, density resistance, as:Density resistance =proportion survival at high densityproportion survival at low density(4.1)Here survival includes both larval survival and emergence, as both will con-tribute to the growth potential of the population. In practice, we added oneto the remaining survival proportions in order to avoid dividing by zero and65chapter 4removed replicates with no survival at both high and low density. We followKraft et al. (2015) in expressing average fitness differences between species asa ratio:Average f itness ratio =density resistance idensity resistance j(4.2)High values of this ratio indicate that species i is able to better resist thedeleterious effects of resource competition than species j, whereas a ratio notdifferent that one indicates fitness equivalence. We calculate 95% CI as 1.96 xSE to see if the ratio included the value one.We acknowledge that we have implicitly assumed that there are no fecun-dity differences between species that contribute to fitness differences. This isanalogous (although not numerically identical) to collapsing the Kraft et al.(2015) equation for average fitness to the term they refer to as “competitiveresponse”. We consider this assumption further in the Discussion. In theequivalence experiment, we evaluate the average fitness difference betweenspecies over a range of proportions. As the response of a species to total den-sity can depend on the relative proportion of conspecifics and heterospecifics(except in the case of competitive equivalence), estimates of fitness over a rangeof relative abundances allow us to evaluate how robust our conclusions are.True fitness differences should persist over all relative abundances (Kraft et al.,2015).4 .2 .6 Observed Plant Size PreferencesWe used survey data (D. S. Srivastava & G. Q. Romero, unpubl. data) toassess the observed plant size preferences of the study chironomids undernatural conditions. Regionally rare species are more likely to be found inlarger bromeliads due to the fact that larger bromeliads hold more individuals.To correct for this, we created a null model that placed individuals of each66chapter 4chironomid species in bromeliads one at a time (based on Amundrud and Sri-vastava 2015). Probabilities of placing an individual in a particular bromeliad(Pb) were based on the total abundance of all species in the bromeliad:Pb =nbN(4.3)where nb is the number of individuals in bromeliad b and N is the total numberof individuals in the data set. Next, the two target species were distributedinto bromeliads using the calculated probabilities, until all individuals ofthe species were placed. The abundance-weighted mean volume (in ml) inwhich each species was found was calculated after all individuals were placed,generating a mean expected bromeliad volume if species were distributedrandomly among bromeliads. This procedure was repeated 9,999 times togenerate a distribution of mean expected bromeliad sizes for each species.Finally, overall means were calculated by taking the mean of means for eachspecies. 95% confidence intervals were calculated based on the distribution ofmeans. Mean observed and mean expected plant sizes were compared using az-score to establish significance and determine whether or not observed plantsize preferences differed from the null expectation.4 .3 results4 .3 .1 Equivalence ExperimentChironomus detriticola responded to all manipulations of initial proportion, rel-ative abundance and plant size in terms of both survival and emergence(Table 4.2, Figure 4.3). C. detriticola had the highest survival at low density, insmall plants, and when it encountered more heterospecifics than conspecifics.The effects of these treatments were purely additive, that is, there were nointeractions. These patterns in survival largely translated into emergence rates,67chapter 4F igure 4 .2 : Experimental design of the ontogeny and equivalenceexperiments. a) Treatments for both experiments are shown. Circles representa top-view of the tubes used in the experiment. Black and white dots representthe two chironomid species: Chironomus detriticola (C. d.) and Polypedilummarcondesi (P. m.). b) Total numbers of chironomids used, where “High” and“Low” refer to absolute density and “Large” and “Small” refer to plant size.68chapter 4except the advantage of being in small plants disappeared for chironomidsat low density. That is, in addition to the main effects of treatments on C.detriticola emergence there were also interactions with density.Considering the response to total species abundance, C. detriticola emer-gence decreased with total abundance of conspecifics (Figure 4.4; Z = -4.469, p< 0.0001) as well as with plant size (Z = -2.175, p = 0.0296). The effect of plantsize disappeared when survival was assessed, such that survival was lowestat highest total abundance of conspecifics (Figure 4.4; Z = -3.982, p < 0.0001).Polypedilum marcondesi (Table 4.2, Figure 4.5) was unaffected, either in sur-vival or emergence, by the initial proportion of conspecifics. Like C. detriticola,P. marcondesi had highest survival and emergence at low absolute densities.Additionally, P. marcondesi had higher emergence - but not survival - in smallplants. These effects of absolute density and plant size were additive, that is,there were no interactions. The results of likelihood-ratio tests for both speciescan be found in the supplemental materials (Appendix a.2; Table a.1).P. marcondesi survival (Z = -3.575, p = 0.00035) and emergence (Z = -4.152,p < 0.0001) both declined with total abundance of all species (Figure 4.6).Models including plant size showed no improvement over these abundance-only models.4 .3 .2 Ontogeny ExperimentIn the ontogeny experiment, C. detriticola larvae survived best as small instarscohabiting with large instars of P. marcondesi (Table 4.3, Figure 4.7), rather thanthe reverse. The effects of plant size on C. detriticola survival depended on theabsolute density of larvae. At high densities, survival in small plants was dou-ble that in large plants, but at low densities the reverse was true: survival wasdouble that in large plants than small plants. Unlike survival, emergence of69chapter 4C. detriticola larvae was only affected by absolute density: survival decreasedslightly as absolute density increased.Larvae of P. marcondesi had the highest survival and emergence rates whenthey were large instars cohabiting with small instars of C. detriticola (Table 4.3,Figure 4.8). Survival was also greater in small, as opposed to large, plants.Results of likelihood tests for both species can be found in the supplementalmaterials (Appendix a.2; Table a.2).4 .3 .3 Fitness Proxy EstimatesWe estimated density resistance as a proxy for fitness in both experiments. Inthe equivalence experiment, increasing density in small plants reduced thesurvival of both species at the highest relative abundance, and of P. marcondesialso at the lowest relative abundance (Figure 4.9). The effects of density weresimilar for both species so the average fitness ratios were near one, indicatingfitness equivalence.In the ontogeny experiment, density dependence was unaffected by treat-ment for P. marcondesi, but dependent on both plant size and relative body sizefor C. detriticola. In small plants and at small body size, C. detriticola showedstrong density resistance; however, in large plants, C. detriticola was moresensitive to density. Consequently, neither species had a fitness advantagewhen they were the smaller species, but at large body sizes, P. marcondesi hada fitness advantage in large plants and C. detriticola had a fitness advantage insmall plants (Figure 4.9). Therefore, when the species differ in their relativebody sizes, fitness differences emerge in different plant sizes at large but notsmall body sizes.70chapter 44 .3 .4 Observed Plant Size PreferencesBoth C. detriticola (z = 25.39, p < 0.0001) and P. marcondesi (z = 10.38, p <0.0001) naturally occurred in larger plants than expected by chance (Figure 4.10).However, C. detriticola was found on average in even larger plants than P.marcondesi.4 .4 discussionIn this study, we deconstructed the competitive relationship between twochironomid species to determine whether the species experienced ecologi-cal (symmetric or asymmetric) equivalence, and how this relationship wasaffected by context (habitat and ontogeny). We found that competition af-fected the performance of both species differently, with signs of asymmetricequivalence and competitive stabilization, as we explain shortly. Furthermore,habitat size and ontogenetic differences in body size both had an effect onsurvival or emergence in one or both species, underlining a dependency ofthe outcome of competition on context.The results of both experiments confirm that competition plays a role inthis system. In the equivalence experiment, both species experienced reducedsurvival and emergence in response to increased absolute densities of organ-isms (Table 4.2). This was also true for C. detriticola in the ontogeny experiment,although P. marcondesi was largely unaffected by absolute density (Table 4.3).To explore the competitive relationship between the species and the mecha-nisms driving this relationship (Question 1), we first examine the response torelative abundance in the equivalence experiment. Under stabilization, levelsof intraspecific competition should be higher than interspecific competitionfor one (asymmetric equivalence) or both species (Table 4.1A). Therefore, wewould expect to see reduced performance (emergence or survival) in response71chapter 4Chironomus detriticola Polypedilum marcondesiEmergence Survival Emergence SurvivalPlant Size Z113 = 144.0p < 0.0001Z115 = 3.268p = 0.00108Z116 = 2.601p = 0.009288Z115 = 1.572p = 0.1159RelativeAbundanceZ113 = 18.4p < 0.0001Z115 = 3.441p = 0.00058Z115 = 0.523p = 0.6012Z116 = −1.576p = 0.1151Density Z113 = 431.8p < 0.0001Z115 = 2.318p = 0.02044Z116 = 3.464p = 0.000532Z117 = 4.792p < 0.0001RelativeAbundancex Densitya) Z113 = −4.3p < 0.0001Z112 = 0.122p = 0.9032Z113 = 0.769p = 0.442Z113 = 0.410p = 0.6819RelativeAbundancex Plant SizeZ112 = −1.1p = 0.251Z113 = 0.452p = 0.6516Z112 = 0.351p = 0.7252Z112 = −0.094p = 0.9253Plant Size xDensityb) Z113 = −167.3p < 0.0001Z114 = 1.081p = 0.2798Z114 = 0.899p = 0.3688Z114 = 1.564p = 0.1179Plant Size xRelativeAbundancex DensityZ111 = 17.1p < 0.0001Z111 = −1.643p = 0.1004Z111 = 0.706p = 0.4805Z111 = 1.679p = 0.0933Table 4 .2 : Summary of models for the equivalence experiment. Valueshighlighted in red indicate a negative relationship between the treatmentand response variables while those highlighted in blue indicate a positiverelationship. Green values are involved in an interaction (described below).Values in black were not significant. Shaded values were removed from themodel. Interactions are described here: a) Emergences were higher at lowdensity and high relative abundance than at low density and low relativeabundance; b) At high densities, emergence was higher in large than smallplants, while the reverse was true at low density.72chapter 4Chironomus detriticola Polypedilum marcondesiEmergence Survival Emergence SurvivalPlant Size Z81 = 1.597p = 0.1103Z82 = 2.160p = 0.0307Z84 = 0.887p = 0.375Z84 = 2.390p = 0.0168Body Size Z81 = 1.877p = 0.0606Z82 = 2.223p = 0.0262Z85 = 7.706p < 0.0001Z84 = 6.204p < 0.0001Density Z81 = 2.059p = 0.0395Z82 = 4.516p < 0.0001Z83 = 0.565p = 0.572Z83 = 1.594p = 0.1110Plant Size xBody SizeZ81 = −1.895p = 0.0581Z81 = −1.755p = 0.0792Z82 = 0.818p = 0.414Z82 = 1.143p = 0.253Plant Size xDensityZ81 = −1.747p = 0.0806a) Z82 = −2.748p = 0.0060Z81 = −0.697p = 0.486Z80 = −0.123p = 0.9018Density xBody SizeZ80 = −0.017p = 0.9866Z80 = −0.537p = 0.5910Z80 = −0.213p = 0.832Z81 = 0.440p = 0.6570Plant Sizex Density xBody SizeZ79 = −0.030p = 0.976Z79 = −0.742p = 0.4578Z79 = −0.517p = 0.605Z79 = 0.161p = 0.8718Table 4 .3 : Summary of models for the ontogeny experiment. Valueshighlighted in red indicate a negative relationship between the treatmentand response variables while those highlighted in blue indicate a positiverelationship. Green values are involved in an interaction (described below).Values in black were not significant. Shaded values were removed from themodel. Interactions are described here: a) At low densities, survival washigher in large plants whereas survival was higher in small plants at highdensities.73chapter 4F igure 4 .3 : Response of C. detriticola in the equivalence experiment. Linesshow the model predictions with variance due to the random effect of plantidentity in gray. Points represent the actual data (jittered). Under bothresponse variables, C. detriticola showed a stabilizing relationship with higherintraspecific competition at higher densities. a) Emergence Density*** + PctChironomus*** + Plant Size*** + Density:Pct Chironomus*** + Density:PlantSize*** + (1 | Plant ID). b) Survivors Plant Size** + Pct Chironomus*** +Density* + (1 | Plant ID).74chapter 4F igure 4 .4 : C. detriticola had decreased survival and emergence at higherabundances of conspecifics. Lines show the model predictions with thevariance due to plant identity in gray. Points show the actual data (jittered).a) Emergence Abundance of Conspecifics*** + Plant Size* + (1 | Plant ID). b)Survival Abundance of Conspecifics*** + (1 | Plant ID).75chapter 4F igure 4 .5 : Response of P. marcondesi in the equivalence experiment. Linesshow the model predictions with variance due to the random effect of plantidentity in gray. Points represent the actual data (jittered). Relative abundancewas not significant in either response, suggesting that P. marcondesi experiencescompetitive equivalence. a) Emergence Density*** + Plant Size** + (1 | PlantID). In this model, plant identity had a very weak effect so box plots are narrowand appear as lines. b) Survival Density*** + (1 | Plant ID).76chapter 4F igure 4 .6 : P. marcondesi had decreased survival and emergence at higherabundances of larvae. Lines show the model predictions with the variance dueto plant identity in gray. Points show the actual data (jittered). a) EmergenceTotal Abundance*** + (1 | Plant ID). b) Survival Total Abundance*** + (1 |Plant ID).77chapter 4F igure 4 .7 : Response of C. detriticola in the ontogeny experiment. Boxesshow the range of predicted values based on the random effect of plantidentity. Points represent the actual data. C. detriticola performed worse atlarge body sizes. a) Emergences Plant Size* + Body Size + Density*** + PlantSize:Density + Plant Size:Body Size + (1 | Plant ID). b) Survival Plant Size* +Body Size* + Density*** + Plant Size:Density** + (1 | Plant ID).78chapter 4F igure 4 .8 : Response of P. marcondesi in the ontogeny experiment. Boxesshow the range of predicted values based on the random effect of plantidentity. Points represent the actual data. P. marcondesi performed worse atsmall body sizes (when C. detriticola was larger). a) Emergence Body Size***+ (1 | Plant ID). b) Survival Plant Size* + Body Size*** + (1 | Plant ID).79chapter 4F igure 4 .9 : Density resistance and fitness ratio in the equivalence(top) and ontogeny (bottom) experiments. In the equivalence experiment,species tended to have similar density resistance in the same treatment andconsequently showed no mean fitness ratios different from 1. In the ontogenyexperiment, P. marcondesi had mean fitness just above 1 in large plants whenit was large and C. detriticola was small. When P. marcondesi was large in smallplants, C. detriticola had higher fitness. When P. marcondesi was small, therewere no fitness differences. Error bars are 95% CI calculated as mean +/- 1.96SE.80chapter 4F igure 4 .10 : Null and observed plant sizes for study chironomids. Starsshow the observed, abundance-weighted mean, representing the chironomidplant size preference. Points show the null model expectation if species arerandomly placed in bromeliads with 95% CI. Dashed lines show the plantsize for “small” (orange) and “large” (green) plants as we defined them in theexperiment. Both species were observed in plants significantly larger than thenull expectation, with P. marcondesi being found in plants close to the size ofthe “small plants” used in these experiments.81chapter 4to increased relative abundance. For C. detriticola, both emergence and sur-vival decreased at higher relative abundances (Table 4.2, Figure 4.3), revealingan increase in intraspecific competition with higher densities of conspecifics.This suggests that C. detriticola abundance is mediated by competitive stabi-lization. However, P. marcondesi (Table 4.2, Figure 4.5) did not exhibit thesame increase in intraspecific competition. P. marcondesi emergence dependedonly on plant size and absolute density, and survival depended on densityalone. P. marcondesi therefore appears to experience a competitively equivalentrelationship with C. detriticola - responding negatively to higher densities oforganisms in general, regardless of the identities of the organisms.Though we assumed the strength of competition would depend on thedensity of organisms - which was kept constant across treatments within agiven density treatment, model fits to absolute abundances suggested other-wise. Both P. marcondesi and C. detriticola had lower survival and emergenceat higher absolute abundances (Figures 4.4, 4.6). In the case of C. detriticola,only the abundance of conspecifics affected performance, while P.marcondesiresponded to total larval abundance - a pattern consistent with the resultsof the original models. It is unclear why abundance and not density mightbe important for the survival and emergence of these species. Possibly ourassumption that total volume of the experiment tubes would correspond toincreased usable habitat for the chironomids was faulty. Chironomids relyon detritus to construct cases and are often found deep in the bromeliadleaf well. It is possible that they remain at the bottom of the water column,which was roughly the same size in both large and small tubes. However,further empirical research is needed to delve into the mechanisms causingthis relationship with total abundance rather than density.Changing the relative body sizes of the two species (Question 2) also af-fected the nature of the interspecies relationship in an asymmetric way: Both82chapter 4species had lower performance when C. detriticola was the larger-bodied speciesthan when P. marcondesi was the larger species (Table 4.3; Figures 4.7, 4.8). Thenegative response of C. detriticola to a larger biomass of conspecifics is perhapsnot surprising given the demonstration of strong intraspecific competitionfor this species in the equivalence experiment (Figure 4.3). Asymmetry inthe competitive abilities of small and large versions of conspecifics has beenobserved frequently, often with larger individuals being superior competitors(Alcock, 2013; Bolund et al., 2007; Cameron et al., 2007; Livdahl, 1982; Werner,1994), although occasionally with smaller individuals being better (Bolundet al., 2007; Marshall and Keough, 1994). In our experiment, not only did largeC. detriticola suppress the performance of conspecifics, but also that of smallP. marcondesi. The lack of a symmetric response when P. marcondesi was largesuggests a change in relative competitive advantages, violating competitiveequivalence, and suggesting a context-dependency in the way P. marcondesiand C. detriticola interact.One possible reason for the negative response to C. detriticola by bothspecies is that C. detriticola may change trophic level as it grows, shiftingfrom a detritivore to a cannibalist and predator. This would be detrimentalto the small-bodied P. marcondesi, but C. detriticola might also be expectedto fare poorly when faced with a combination of intraspecific competitionand cannibalism. Facultative predation has been observed in other species ofthe genus Chironomus (Pinder, 1986). Furthermore, some models suggest thatspecies that engage in cannibalism often switch from competitive to cannibal-istic behaviour as they develop (Claessen et al., 2000; Persson et al., 2000). Thismay occur when smaller instars are better competitors for shared resourcesbecause the switch to cannibalism can allow large instars to coexist withsmall ones. If this were the case, the larger C. detriticola larvae might reducesurvival and emergence of all other larvae by consuming both conspecifics83chapter 4and heterospecifics. Larger P. marcondesi larvae, on the other hand, would nothave such an adverse effect on other organisms because they would retaintheir detritivorous diet throughout the larval stage.In addition to body size we also manipulated plant size (Question 2), whichseemed at first to play a prominent role in the relationship between the twochironomid species. In both experiments, there was a general trend of higherperformance in smaller plants. However, the effect of plant size was mostlylost once total abundance was considered (Figures 4.4, 4.6), though C.detriticoladid have higher emergences in large plants. Our analysis of observational data(Figure 4.10), shows P. marcondesi most frequently in bromeliads of similarvolumes to those used in the “small plant” bromeliads in the experiments,even when we corrected for sampling effects with a null model, and C. de-triticola is found in much larger plants (∼ 870 ml) than expected by chance(∼ 393 ml). Thus, there is some suggestion that plant size may be a factor inchironomid coexistence, but our experiments give no definite answers aboutwhat the effect may be and when it occurs. A follow-up experiment done inwhole bromeliads rather than tubes might help clarify some of the potentialissues with our design.While one of our experiments suggested a relationship of asymmetric com-petitive equivalence, and the second suggested that competitive equivalence iscontext-dependent, it is only with information about the relative fitness of thetwo species that we can make conjectures about whether or not ecologicalequivalence is present and make predictions regarding local and regionalcoexistence (Question 3). Conclusions about coexistence based on our fitnessproxy estimates come with some caveats. Most importantly, in our fitnessestimates, we did not consider the “demographic ratio” of Godoy & Levine(2014; see also Appendix a.1). The demographic ratio incorporates fecundityin the absence of competition, information which we do not have and would84chapter 4be difficult to obtain. Thus, our inferences about local and regional coexistencewill be most useful for illustrative purposes, and for directing future researchinto the particularities of chironomid coexistence.In the equivalence experiment, fitness estimates for chironomid specieswere equal in all treatments (Figure 4.9), garnering support for fitness equiv-alence. This suggests that these species experience fitness equivalence, andby extension, asymmetric ecological equivalence. According to our analysis(Appendix a.1), coexistence in such cases is dependent on the dynamics ofthe non-equivalent species. In this case, because C. detriticola experiencedcompetitive stabilization, the two species are expected to be able to coexist(Table 4.1A). In the ontogeny experiment, species differed in their relativebody sizes. Here we found a definite shift away from fitness equivalence.In large plants, large P. marcondesi had higher fitness than small C. detriticola(fitness ratio above one), and in small plants, large P. marcondesi had lowerfitness than small C. detriticola (fitness ratio below one; Figure 4.9). When thefocal species was the smaller of the two, there was no compensating effect ofplant size on fitness differences. Because each species had higher performancethan the other in a given context (small vs. large plants), the fitness data couldbe interpreted to suggest that when there is a relative size difference betweenspecies, metacommunity coexistence is achieved via habitat partitioning alonga bromeliad size gradient (Table 4.1A, cell labelled “Coexistence via habitatpartitioning or priority effects”) . However, note that (1) the effect of plantsize on fitness is exactly opposite to that observed in nature, and (2) anyfitness advantage dependent on the species being the smaller of the two willpresumably be lost as the species grows in size, and thus is inherently transientin nature. It is therefore premature to conclude that habitat partitioning in thissystem is key to coexistence of these species.85chapter 4Overall, this research suggests that context shifts the relationship betweenchironomids away from one of asymmetric competitive equivalence. Whiletheory (Adler et al., 2007; Haney et al., 2015; Leibold and McPeek, 2006) andexperiment (e.g. Almeida et al., 2015; Cadotte, 2007; Dumbrell et al., 2010;Prado and Rossa-Feres, 2014; Rominger et al., 2009) support the conclusionthat niche and neutral processes exist concurrently, it is still unknown in whichconditions one or the other type is more important. Existing research tendsto focus on the importance of neutral processes (i.e. dispersal) in colonization(Cadotte, 2007; Chu et al., 2007; Prado and Rossa-Feres, 2014; Püttker et al.,2015) or community structure (Almeida et al., 2015; Rominger et al., 2009).However, the local conditions that lead to ecological equivalence betweenspecies have not been widely investigated. One of the best examples of a pos-sible shift from equivalence may be the competition experiments of ThomasPark (1948; 1954; 1957), which pre-date neutral theory (Hubbell, 1997, 2001). Inthese experiments, the outcome of competition between Tribolium spp. beetleswas sometimes stochastic (suggesting ecological equivalence; Park 1948) andsometimes deterministic (Park, 1954, 1957), depending on initial conditions,similar to what we have found here.Research that manipulates relative abundances is invaluable for under-standing the role of competitive interactions in a community. While increasingnumbers of experiments address the relative importance of neutral and non-neutral forces in communities, few have determined what range of conditionslead to neutral or stabilizing dynamics. Furthermore, no research that weknow of has encountered asymmetric equivalence, or at least identified it assuch. Here, we found that what looked at first like coexistence via asymmet-ric competitive equivalence shifted in response to ontogeny. It is clear thatconsidering only one set of ecological conditions is not sufficient for under-standing competition and the presence or absence of ecological equivalence86chapter 4in a community. The interaction between ontogeny and competition is partic-ularly important to understand because changes in species interactions overdevelopment time could completely shift the relative success of the speciesconcerned. A stable or neutral relationship in one ecological context couldshift in a different context to a destabilizing one, thus ending in the exclusionof one species. We recommend that future research concerning neutrality inparticular should include exploration of the role of organism development andenvironmental context on the outcome of species interactions.87chapter 5ConclusionSpecies distributions can be understood in terms of the environmental condi-tions and biotic interactions that allow coexistence at local and regional scales.In this thesis, I set out to determine which factors are important for coex-istence in a community of bromeliad-dwelling invertebrates by identifyingspecies with strong negative co-occurrence patterns (Chapter 2), and studyingthe effects of predation and competition on the coexistence of these species(Chapters 3, 4), as well as the effects of habitat and body size (Chapter 4).Using multiple approaches, including null model analysis of observationaldata, demographic modelling, and empirical tests, I found that:1. Three species of chironomid have high rates of negative co-occurrencecompared to other species pairs in the community;2. Predators negatively affect performance, primarily through emergencerates, but do not mediate coexistence;3. Ontogenetic differences in body size manifested differently dependingon the identity of the larger species, indicating a context dependency tothe outcome of competition;4. Habitat size manipulations had an effect on species response, but habitatpartitioning is not expected to explain metacommunity coexistence.At the field site of Ilha do Cardoso (Chapter 1), several species pairs exhibitstatistically high negative co-occurrence rates (Chapter 2). Three species of88chapter 5chironomid (Diptera: Chironomidae) — Polypedilum marcondesi, Polypedilumkaingang, and Chironomus detriticola — were chosen for experiments becausethey are relatively common (A. D. Letaw, pers. obs.; D. S. Srivastava and G. Q.Romero, unpubl. data) and easy to identify at the larval stage (A. D. Letaw,pers. obs.). While all three species experience direct and indirect negativeeffects of predators (Chapter 3), one species (P. kaingang) is competitively supe-rior whether or not predators are present, suggesting that predator mediationis not responsible for the coexistence of these three species in nature. Two ofthe three study species (P. marcondesi and C. detriticola) were reared at differentbody sizes and in different bromeliad sizes (Chapter 4). Relative abundancemanipulations of these species suggested an asymmetric relationship in whichone species (P. marcondesi) appears to experience the world neutrally, whilethe other (C. detriticola) does not (Chapter 4), a relationship we term hereasymmetric equivalence. Both species respond negatively to the presence oflarge C. detriticola, but not to large P. marcondesi, indicating a shift away fromneutrality when ontogeny is manipulated. As for habitat size, both speciesgenerally have improved performance in smaller plants (Chapter 4).Taken together, the results suggest that the chironomids studied have acompetitive relationship the nature of which is changed primarily when onto-genetic differences in body size are present. While other factors contributeto performance (i.e. predators and habitat size), only ontogeny shifts thecompetitive outcome. To date very little is known about the importanceof ontogeny in the coexistence of bromeliad invertebrates or whether anytemporal colonization patterns are present, making it difficult to predict howimportant colonization order is at the community or metacommunity levels.In other systems, ontogenetic differences in body size have been found toeffect competitive outcome (Eichenberger et al., 2009; Hurd and Eisenberg,1990; Serrano-Meneses et al., 2007; Werner, 1994; Werner and Gilliam, 1984)89chapter 5and are often present naturally due to differences in colonization timing (Hurdand Eisenberg, 1990; Yang and Rudolf, 2010). Phenology has been pinpointedas a linking factor between species that can be broken when species responddifferently to environmental changes, such as those that occur due to climatechange (Both et al., 2009; Parmesan, 2006; Tylianakis et al., 2008; Visser andBoth, 2005; Yang and Rudolf, 2010). For example, many pollinators havetemporal coordination with the plants they pollinate (Hegland et al., 2009;J Memmot, 2007). However, differences in ontogeny generated by phenologycan also effect the nature of antagonistic interspecific interactions, such aspredation and competition (Kordas et al., 2011; Miller-Rushing et al., 2010;Tylianakis et al., 2008; Yang and Rudolf, 2010). Research conducted hereprovides the first evidence in this system in support of a relationship betweenphenology, ontogeny and the outcome of competition.In addition to insights gained from individual empirical results, here I ap-ply a variety of approaches to the study of coexistence in bromeliad-dwellingchironomids. Taken separately, each approach offers a new framework or anew way to analyse data. In Chapter 2, AWCA was developed to find negativeco-occurrence patterns in observational abundance data; in Chapter 3, a newmethod was used to model population growth on censored data while alsogaining insight about emergence and death rates; in Chapter 4, a theoreticalframework was developed, leading to new ideas about how ecological equiva-lence can be manifested. Each of these methods could be applied to any othersystem. For instance, there are many examples of checkerboard analysis beingused to find signs of competition structuring communities (e.g. Barberánet al., 2012; Beaudrot et al., 2013; Bik et al., 2010; Horner-Devine et al., 2007;Presley et al., 2010; Vernes et al., 2001). As pointed out in Chapter 2, traditionalcheckerboard analysis is not sufficient to determine whether competition isresponsible for community structure. However, using AWCA, it is possible to90chapter 5identify species pairs driving the checkerboard structure, to use backgroundinformation about those species to further postulate on whether competitionor something else (e.g. predation) is occurring, and to conduct experimentsthat support or refute the existence of competition as a structuring mechanism.For example, AWCA could be used to analyse other bromeliad-invertebratedatasets, which are available from multiple years and countries (BromeliadWorking Group, unpubl. data). Analyzing these data sets could help us findgeneralities in which species or functional groups drive community structurein the bromeliad system. Demographic models like the one used here (Chap-ter 3) could be applied to other experiments to find out how growth, death,or other rates vary between species in response to experimental treatments.Predators are known to reduce growth rates in many cases (McKie and Pear-son, 2006; Stoks, 2001; van Uitregt et al., 2012), however, besides predators,demographic models could predict the effect of any experimental factor on anyresponse. Finally, ecological equivalence could be studied in other systems tosee if there are other instances of asymmetry in species response, and howthese change depending on context. In particular, it would be interestingto know what range of conditions lead to niche or neutral processes. Forexample, chironomids exist across the geographic range of bromeliads, butthe richness of invertebrates tends to decline from South to North (BromeliadWorking Group, unpubl. data). Does overall community richness affect thepresence of neutral processes? Do these change when experiments are doneat the community, rather than population, scale?There are still many questions to be asked about how predators, habi-tat, and ontogeny effect the coexistence of chironomids and other bromeliadinvertebrates. Increasingly, research on bromeliad-invertebrate communitiesis revealing the importance of bromeliad size on species performance andcoexistence (Amundrud and Srivastava, 2015; Hammill et al., 2015a; Gilbert91chapter 5et al., 2008; Jocque and Field, 2014; Marino et al., 2011; Petermann et al., 2015).Further understanding of the role of predators in coexistence could be gainedby crossing predator-presence with a plant size manipulation. Another areaof exploration could involve looking at the effects of adding more predatorspecies or alternate prey; predators in bromeliads can interfere with one an-other, reducing their overall consumption rates (Atwood et al., 2014; A.A.M.MacDonald, unpubl. data), and alternate prey are preferred over chironomidsby odonates at the field site (LeCraw, 2014). A deeper look into the indirecteffects of predators is also warranted. At other field sites, predators reducecolonization (Hammill et al., 2015b), a phenomenon that may cascade downto affect resource distribution and ecosystem function. Analyses performedin Chapter 4 suggest that chironomid species have different plant size pref-erences. Differences in performance at different plant sizes may indicatedifferences in drought tolerance between the species (e.g. Amundrud andSrivastava, 2015), a supposition which could be tested experimentally. Resultsof the manipulations to ontogenetic stage, revealed a decline in performancewhen C. detriticola was larger. Experiments to study the temporal patternin oviposition could determine whether chironomids tend to colonize in aspecific order to avoid the negative effects of arriving second.Here I showed that multiple factors affect competition between chironomidspecies, and that ontogenetic body size differences in particular are crucial indetermining the outcome of competition. Further, I used a suite of meth-ods to answer each question. There is great value in applying a variety ofapproaches to the question of coexistence. Because nature is comprised ofcomplex systems, it is necessary to reduce these to just a few componentswhen studying them. 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R News 2:7–10.105appendix aSupplementary Information to Chapter 4a .1 how do relationships between competitioncoefficients effect coexistence?We aimed to solve equations for coexistence in terms of all possible combina-tions of intra- and interspecific competition. To do so, we follow Godoy andLevine (2014; see Appendix) in their model of coexistence, which is a modifiedversion of Chesson’s formulation of Lotka-Volterra competition (2000b; 2008):ρij =√αijαjiαiiαjj(a.1)where ρij is a measure of niche overlap, and 1− ρij describes the strength ofstabilization. In this model, fitness (λi , λj) differences are measured as:λjλi=(ηj − 1ηi − 1)√αijαiiαjiαjj(a.2)Here, ηi , ηj are demographic terms incorporating fecundity into the fitnesscalculation. This inclusion of a “demographic ratio” is the primary differencebetween Godoy and Levine (2014) and Chesson (2000b). Following Kraft et al.(2015), if we assume λj has the fitness advantage, species coexistence occurswhen:ρij <λjλi(a.3)106appendix aWhich, when combined with Eqn. a.2, is equivalent to:αjjηj − 1 >αijηi − 1 (a.4)This is the classic result requiring intraspecific competition to exceed inter-specific competition, rescaled to include the species’ effect on growth andfecundity (Godoy and Levine, 2014). If fitnesses are equal, however, we neednot know the value of λj/λi because Eqn. a.3 simplifies to:ρij =√αijαjiαiiαjj< 1 (a.5)Because of our experimental design, we can determine the relative strengthsof intra- and interspecific competition on a given species (i.e. αii by αij ; αjjby αji), and use these relationships to solve Eqn. a.5 and find out whethercoexistence can occur (Table 4.1A). It is of note that the formula for ρij isidentical in both Godoy and Levine (2014) and Chesson (2000b). Thus, ourconclusions about coexistence apply to either model.107appendix aa .2 results of likelihood -ratio tests for modelsimplificationChironomus detriticola Polypedilum marcondesiEmergence Survival Emergence SurvivalPlant Size – – – p = 0.1378χ2(4) = 2.2024RelativeAbundance– – p = 0.5985χ2(4) = 0.2773p = 0.1206χ2(3) = 2.4097Density – – – –RelativeAbundancex Density– p = 0.9039χ2(7) = 0.0146p = 0.4415χ2(6) = 0.5923p = 0.6849χ2(6) = 0.1646RelativeAbundancex Plant Sizep = 0.8636χ2(7) = 0.0295p = 0.6527χ2(6) = 0.2025p = 0.7252χ2(7) = 0.1236p = 0.9258χ2(7) = 0.0087Plant Size xDensity– p = 0.281χ2(5) = 1.1624p = 0.3663χ2(5) = 0.8162p = 0.1171χ2(5) = 2.4558Plant Size xRelativeAbundancex Density– p = 0.012*χ2(8) = 2.6873p = 0.4799χ2(8) = 0.499p = 0.0942χ2(8) = 2.8004Table a .1 : Results of likelihood-ratio tests for removal of specified terms inthe equivalence experiment. Low p-values (p < 0.05) indicate that the morecomplex model fits significantly better than the less complex one. * Althoughthe p-value was low, this term was removed because the model fit very poorlywhen the three-way interaction was retained.108appendix aChironomus detriticola Polypedilum marcondesiEmergence Survival Emergence SurvivalPlant Size – – p = 0.3796χ2(3) = 0.7719–Body Size – – – –Density – – p = 0.5737χ2(4) = 0.3165p = 0.1125χ2(4) = 2.5187Plant Size xBody Size– p = 0.0803χ2(6) = 0.0582p = 0.4058χ2(5) = 0.6911p = 0.25χ2(5) = 1.3233Plant Size xDensity– – p = 0.4849χ2(6) = 0.4877p = 0.919χ2(7) = 0.0152Density xBody Sizep = 0.9866χ2(7) = 0.0003p = 0.5922χ2(7) = 0.287p = 0.8327χ2(7) = 0.0446p = 0.6602χ2(6) = 0.1933Table a .2 : Results of likelihood-ratio tests for removal of specified termsin the ontogeny experiment. Low p-values (p < 0.05) indicate that the morecomplex model fits significantly better than the less complex one.109

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