vol. 193, no. 4 the american naturalist april 2019

E-Article Limiting Similarity? The Ecological Dynamics of Natural Selection among Resources and Consumers Caused by Both Apparent and Resource Competition

Mark A. McPeek*

Department of Biological Sciences, Dartmouth College, Hanover, New Hampshire 03755 Submitted December 31, 2017; Accepted September 8, 2018; Electronically published January 17, 2019 Online enhancements: appendix, MATLAB code, video. abstract: 1959). Most explorations of this idea have focused on one Much of ecological theory presumes that natural selection — should foster species coexistence by phenotypically differentiating particular type of species interaction competition among competitors so that the stability of the community is increased, but consumers for shared resources. Resource competition is an whether this will actually occur is a question of the ecological dynamics indirect interaction between consumers that is mediated by of natural selection. I develop an evolutionary model of consumer- their effects on and responses to shared resources (Levene resource interactions based on MacArthur’s and Tilman’s classic works, 1976; Tilman 1980, 1982, 1987). If multiple resource species including both resource and apparent competition, to explore what are involved, the indirect interaction of apparent competition fosters or retards the differentiation of resources and their consumers. Analyses of this model predict that consumers will differentiate only between resources also occurs and is mediated by their effects on specific ranges of environmental gradients (e.g., greater productivity, on and responses to the consumers (Holt 1977). However, weaker stressors, lower structural complexity), and where it occurs, the MacArthur’s original exploration of these issues recast all of magnitude of differentiation also depends on gradient position. In con- these indirect interactions into direct interactions between trastto“limitingsimilarity” expectations,greaterintraspecificphenotypic the consumers using the Lotka-Volterra competition frame- variance results in less differentiation among the consumers because of work (MacArthur 1969, 1970, 1972; Schoener 1974; Abrams fi how phenotypic variation alters the tness landscapes driving natural se- 1975; Case and Casten 1979; Chesson 1990; Kleinhesselink lection. In addition, the final structure of the community that results from the coevolution of these interacting species may be highly contin- and Adler 2015; Letten et al. 2017). This recasting remains gent on the initial properties of the species as the community is being as- the pervasive framework for interpreting the community sembled. These results highlight the fact that evolutionary conclusions structure of coexisting species (e.g., Chesson 2000; Adler about community structure cannot be based on ecological arguments et al. 2007), although many simplifying assumptions must of community stability or coexistence but rather must be explicitly based be made (MacArthur 1970, 1972; Schoener 1974). However, on the ecological dynamics of natural selection. a number of analyses have shown that these assumptions Keywords: adaptive evolution, apparent competition, character dis- greatly restrict the range of possible community outcomes placement, limiting similarity, resource competition. that can occur and completely remove the effects of apparent competition, which greatly distorts the effects of one con- sumer on another (Levene 1976; Chesson 1990; Abrams Introduction 1998; Abrams et al. 2008a; Abrams and Rueffler 2009; Klein- The idea that species must be different to coexist is embedded hesselink and Adler 2015). in the foundation of community ecology. The clearest initial If consumer species that compete for resources must be dif- articulations of this idea were made by Hutchinson in his ferent to coexist, how different must they be? Hutchinson elaboration of the “Volterra-Gause principle” to express his (1959) originally suggested that a lower limit to species sim- definition of the niche (Hutchinson 1958) and his hypothesis ilarity may exist, and MacArthur and Levins (1964, 1967) “ for why there are so many kinds of animals (Hutchinson began the theoretical search in earnest for such a limiting similarity.” This idea is best encapsulated in May and Mac- Arthur’s (1972) diagram of the degree of niche overlap * Email: [email protected]. ORCIDs: McPeek, http://orcid.org/0000-0001-7794-9466. among a set of consumers feeding on a spectrum of resources Am. Nat. 2019. Vol. 193, pp. E92–E115. q 2019 by The University of Chicago. and how these consumer feeding relationships are recast into 0003-0147/2019/19304-58163$15.00. All rights reserved. Lotka-Volterra competition. They argued that the ratio of the DOI: 10.1086/701629 difference between the peaks in the resource utilization curves Consumer and Resource Differentiation E93 of adjacent consumers relative to the widths of the utilization ing species to explore whether natural selection causes them curves—their d/w ratio—should have a minimum, limiting to differentiate. Many have utilized modified versions of May value that permits coexistence. The intuitive prediction from and MacArthur’s (1972) Lotka-Volterra competition frame- this is that if consumer species can utilize a broader spectrum work in which a continuous spectrum of resources is avail- of resources, for example, by having broader intraspecific able that determines the carrying capacities of genotypes or phenotypic distributions, adjacent consumers along the spec- phenotypes based on their utilization functions along that trum would have to be more differentiated to permit their co- spectrum (Roughgarden 1972; Bulmer 1974; Roughgarden existence (MacArthur and Levins 1967; May and MacArthur 1976; Slatkin 1980; Matessi and Jayakar 1981; Pacala and 1972; May 1973, 1974; Roughgarden 1974; Turelli 1978a, Roughgarden 1982; Milligan 1985; Taper and Case 1985, 1978b; Abrams et al. 2008a,2008b; Abrams and Rueffler 1992; Doebeli 1996; Ackermann and Doebeli 2004; Scheffer 2009; Barabás and D’Andrea 2016) or to decrease the sensitiv- and van Nes 2006; Vasseur et al. 2011; Barabás and D’Andrea ity of coexistence to perturbations in parameters (Meszéna 2016). Others have modeled both consumer and resource et al. 2006; Szabó and Meszéna 2006; Szilagyi and Meszéna species explicitly but used fitness set approaches to infer phe- 2009; Barabás et al. 2012a, 2012b, 2014). While no rigid limit notypic differences instead of modeling phenotypes directly of functional overlap between species has been identified (e.g., (Lawler and Maynard Smith 1976; Lundberg and Stenseth Abrams 1975; Turelli 1978a, 1981), greater overlap is ex- 1985; Abrams 1986, 1987a,1987b). Still others have explored pected to reduce the likelihood of coexistence (Meszéna how diet composition of the consumers may evolve when et al. 2006). The presumption underlying these ideas is that feeding on various types of resources (e.g., Abrams 1987a; natural selection should act to promote coexistence by caus- Vasseur and Fox 2011; Klauschies et al. 2016). Many of these ing species to differentiate in order to reduce competition via studies find that consumers will differentiate under some reducing niche overlap—character displacement (e.g., Brown circumstances and converge to have the same phenotypic dis- and Wilson 1956; Hutchinson 1959; MacArthur and Levins tributions under others. One disconcerting but recurring re- 1967; MacArthur 1970, 1972; Roughgarden 1974; Stuart sult is that consumer differentiation occurs when phenotypic and Losos 2013). variances (measured as the breadths of the utilization func- The other unstated presumption in this line of reasoning is tions) are small, but consumers converge when phenotypic that such differentiation should occur regardless of ecological variances are large (Bulmer 1974; Roughgarden 1976; Slatkin conditions, because reducing the strength of interspecificre- 1980; Taper and Case 1985; Ackermann and Doebeli 2004), source competition among the consumers is assumed to al- which would seem to contradict the ecological expectations. ways be beneficial. However, what will evolve depends on However, few of these studies have systematically explored how those ecological conditions shape the selection regime how phenotypic variance affects the likelihood or magnitude that each species experiences. In an unproductive ecosystem of differentiation (but see Taper and Case 1985; Barabás and where resources cannot achieve high abundances, the fitness D’Andrea 2016) or whether various ecological contexts may return to a consumer specializing on only one resource species promote or retard differentiation (for one example, see may be less than generalized feeding on multiple resource spe- Abrams 1986). cies, whereas resource specialization may be more profitable in In this article, I derive and analyze a model of the abun- a more productive ecosystem, even with the same array of re- dance and trait dynamics resulting from two consumer species source species. Additionally, the apparent competitive indirect feeding on two resource species (fig. 1). This is an elaboration effects among resource species will be shaped by their relative of MacArthur’s (1969, 1970, 1972) original mechanistic productivities, which may in turn skew how consumers dif- consumer-resource model and Tilman’s (1980, 1982) model ferentiate in response to them (Abrams 1986). Alternatively, of the abundance dynamics of two consumer species feeding other features of the ecosystem in which the species interact on two perfectly substitutable resource species. This is also an may limit consumer abundances (i.e., high intrinsic death extension of the model analyzed by Schreiber et al. (2011) of rates) or their abilities to exploit the resources (e.g., habitat apparent competition (i.e., one consumer feeding on two complexity), which might in turn limit their abilities to depress resources) in which only the consumer could evolve. In the resource abundances to levels that would favor differentiation model presented here, both consumers and resources evolve to reduce resource competition. These consequences would be in response to one another, and their ecological and evolu- apparent only when the ecological context that shapes the tionary dynamics are shaped by both the resource competi- strengths of both resource and apparent competition are con- tive indirect effects among the consumers and the apparent sidered, and the relative strengths of these indirect effects may competitive indirect effects among the resources (Levene be as important to determining whether consumer and re- 1976; Leibold 1995, 1998). The community ecologist should source species differentiate as the degree of niche overlap. see how these indirect effects generate natural selection A number of studies have addressed these presumptions among a set of interacting consumers and resources, and evo- more directly by building coevolutionary models of compet- lutionary biologists should see that these indirect effects are E94 The American Naturalist

Model Consider the interactions that occur in a community module with two consumer species and two resource species (fig. 1). Each consumer feeds on both resources, but the consumer species do not interact with one another directly. For exam- ple, one can imagine these as two bird species feeding on the seeds of two plant species or two fish species feeding on two zooplankton species. Following MacArthur’s(1969, 1970, 1972) and Tilman’s (1980, 1982) original approaches to this community module, the two resource species each fol- low logistic population growth in the absence of any con- sumers and so do not interact directly with one another, and each consumer has a linear functional response for feed- ing on each resource. Each consumer also has a density- dependent death rate in the analysis presented here. Each in- dividual of each species has one ecologically important trait that influences its performance in interactions both with in- Figure 1: Community module of two consumers feeding on two dividuals of its own species and with the other species that de- resources that is analyzed in this article. The double-headed arrows fi fi termine its overall tness: traits are identi ed as zR for each represent trophic interactions between the consumers and the i resource (i p 1, 2) and z for each consumer ( j p 1, 2). resources that underlie the consumers’ birth fitness components Nj ’ fi From these statements we can derive the equations de- and the resources death tness components, with a(zRi , zNj )identi- fying the attack coefficient associated with each. The arrow pointing scribing both the abundance and trait dynamics for the toward each resource identifies its birth fitness component underlain four species in this community module. First, assume that by c(z ), and the arrow pointing away from each consumer identifies Ri the ecologically important trait of each species is normally its death fitness component underlain by f (z ). The species identi- Nj fi ties are color coded as in the rest of the figures. distributed with a speci ed mean and variance: ! (z 2 z )2 central to how natural selection is generated among inter- exp 2 Ri Ri 2j2 acting species. zRi p(z ) p pffiffiffiffiffiffiffiffiffiffiffiffi , The analyses of the model presented here address three Ri 2 2pjzR questions. First, what ecological conditions retard or foster i the differentiation of resource and consumer species? In par- ! 2 2 ticular, I consider whether ecosystem features that shape the (zN z N ) exp 2 j j 2 productivity of the resources, the mortality of the consumers, 2jz fl p qffiffiffiffiffiffiffiffiffiffiffiffiffiNj : ð Þ or the abilities of consumers to harvest resources will in u- p(zNj ) 1 2 2pjz ence the likelihood and magnitude of differentiation. Second, Nj how do levels of phenotypic variance in consumers and re- sources influence the levels of phenotypic differentiation that Furthermore, the phenotypic variance of each species is com- occur? Intraspecific phenotypic variation defines variability posed of an additive genetic component (G and G ) that zRi zNj among conspecific consumers in their abilities to forage on determines the magnitude of evolutionary response to phe- the range of available resources and the degree of resource uti- notypic selection and an environmental component (E and zRi 2 p 1 2 p 1 lization overlap between the consumer populations. Likewise, Ez ); thus, jz Gz Ez and jzN Gz Ez (this Nj Ri Ri Ri j Nj Nj phenotypic variation in a resource defines the range of avail- assumes no nonadditive genetic effects and no genotype- able resource types to each consumer and so the scope of in- by-environment interaction effects). Throughout this analy- fluence for apparent competition among the resources. Fi- sis, I assume that the variance components underlying the nally, how do trade-offs among traits that influence multiple phenotypes of each species do not change, and their evolu- fitness components shape how consumers and resources will tionary dynamics are adequately described by change in the differentiate? A phenotypic trait may experience selection be- mean trait value of each species (Lande 1976, 1982, 2007). cause of its effect on multiple fitness components; how such The overall fitness of each resource individual is deter- traits will drive species differentiation depends on the fitness mined by the difference between two underlying fitness balances within each species that increase their fitness overall components: a density-dependent birth fitness component and not just in response to selection generated by resource or and a death fitness component determined solely by the apparent competition. two consumers feeding on it. The density-dependent birth Consumer and Resource Differentiation E95

fitness component of each resource is described by a gen- size of a bird or gill raker size of a fish) and some measure 2 ’ eralized logistic function, ci(zRi ) diRi. Each resource sin- of size of the resource (e.g., diameter of a plant seed or trinsic birthrate, ci(zRi ), is determined by its trait value, body length of a zooplankton species). If the trait values and di is the rate of decrease in this rate as resource i’s of the two species are identical, when each is measured 2 p fi overall abundance increases. The function ci(zRi )ismaxi- on an appropriate scale (zNj zRi 0), the attack coef - p ~c fi mized at zRi zRi and decreases as a quadratic function cient is maximized. However, the attack coef cient de- of the distance of the resource’s trait value away from this creases as the magnitude of the difference in trait values optimum, increases: for example, a bird may have the highest forag- À Á ing capability on a particular size of seed, but this foraging p 2 g 2 ~c 2 ð Þ ci(zRi ) c0i 1 i(zRi zRi ) , 2 capability decreases as seed size both decreases and in- creases away from this optimal size. g where c0i is the maximum birthrate and i scales the rate of From these assumptions, the expected absolute fitness ~c decrease away from zRi . In the absence of consumers, each fi of a resource individual is given by resource experiences stabilizing selection only on this t- ð ness component that will move the population’s trait mean X2 ∞ c p 2 2 to ~z . In the presence of consumers, the selection on this rRi (zRi ) ci(zRi ) diRi Nj p(zNj )aij(zRi , zNj )dzNj , Ri p 2∞ fitness component may create a fitness trade-off with the j 1 fitness components affected by consumer feeding if selec- ð4Þ fi tion on those other tness components to reduce death where the functional response determining the death rate rate from consumer feeding favors trait mean movement of the resource with this trait value is integrated over each away from ~zc . As in purely ecological models of this type, Ri consumer population. Substituting equations (1)–(3) into such a logistic growth term for a resource is often inter- (4) and integrating gives the absolute fitness of each re- “ ” fi preted as birthrate, but this tness component can also source individual based on its phenotypic trait value be interpreted as encapsulating all the demographic pro- cesses that impinge on the resource besides feeding by r (z ) p c (1 2 g (z 2 ~z c )2) 2 d R Ri Ri 0i i Ri Ri i i ! the consumers and not strictly birthrate (e.g., Slobodkin X2 2 2 a N b (z N zR ) ð Þ 2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi0j j j exp 2 j i : 5 1961; Rosenzweig and MacArthur 1963; Rosenzweig 1971; 2 2 2 2 2(j 1 b ) jp1 j 1 b zNj j Case 2000; Murdoch et al. 2003). Because I will consider zNj j situations only where this function has positive values within fi the scope of trait distributions, I will continue to refer to it as The average tness of each resource population is then fi the “birth fitness” component. found by integrating these individual tness values over its Each resource’sdeathfitness component is determined entire trait distribution: ð by linear functional responses of the consumers feeding on ∞ p fi rRi p(zRi )rRi (zRi )dzRi them. The value of the attack coef cient for an individual 2∞ consumer feeding on an individual resource is assumed to have a Gaussian form determined by the difference be- p c (1 2 g ((z 2 ~z c )2 1 j2 )) 2 d R 0i i Ri Ri zRi i i tween their trait values, ! X2 b 2 2  a0j jNj (z Nj z Ri ) 2 2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 : 2 exp 2 (zNj zRi ) 2 1 2 1 b p 2 ð Þ p 2 1 2 1 b2 2(jz jz j ) aij(zR , zN ) a0j exp , 3 j 1 jz jz j Ri Nj i j b2 Ri Nj 2 j ð Þ fi 6 where a0j is the maximum value of the attack coef cient for p b fi consumer j when zNj zRi and j scales the rate at which The rst two terms in equation (6) comprise the average the attack coefficient decreases away from this maximum birth fitness component (i.e., the population’s per capita for that consumer. Note that this formulation specifies birthrate), and the summation comprises the average death no trait value as best in these interactions: a given change fitness component (i.e., the population’s per capita death in the trait value of one species may either increase or de- rate) of the resource population. crease the attack coefficient depending on the trait value of Likewise, each consumer individual’s fitness is the sum the other species. Also, the direction of trait change that in- of a birth and a death fitness component. Each consumer’s creases the attack coefficient is different on either side of birth fitness component is determined solely by its con- the trait value of the other species. For example, the ability verting consumed resource individuals into its own off- of a consumer individual to catch and consume a given re- spring—that is, a linear numerical response for each re- source individual may depend on the match between some source. Each consumer also has a density-dependent death fi fi 1 metric of the trophic structure of the consumer (e.g., bill tness component de ned by f j(zNj ) gjNj (Gilpin 1975; E96 The American Naturalist

ð∞ Gatto 1991; Caswell and Neubert 1998; Neubert et al. 2004; p rNj p(zNj )rNj (zNj )dzNj Amarasekare 2008; McPeek 2012, 2014). Each consumer’s 2∞ ! intrinsic death rate, f j(zNj ), is a function of its trait value, X2 b 2 2 bja0j jRi (z Nj z Ri ) and gj is the rate of increase in its death rate with its overall p qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi exp 2 2 1 2 1 b2 2 2 2 2(jz jz j ) 1 ip1 j 1 j 1 b Ri Nj population size. When gj 0, the consumer population ex- zRi zNj j periences an additional source of direct density dependence 2 1 2 ~f 2 1 2 2 : ð Þ f 0j(1 vj((z N z N ) jz )) gjNj 10 from processes such as interference or cannibalism (Polis j j Nj 1981), physiological stress (Marraet al.1995; Lochmiller1996; The summation in equation (10) comprises the average McPeek 2004), or limitation due to territoriality (Pulliam and birth fitness component (i.e., per capita birthrate), and Danielson 1991; McPeek et al. 2001) or from other density- the last two terms comprise the average death fitness com- dependent features not being modeled, such as pathogens ponent (i.e., per capita death rate) of the consumer popu- and diseases (Janzen 1970; Holt and Pickering 1985; Grover lation. 1994; Terborgh 2012), that limit its population in addition to The average fitness of each species defines the dynamics the indirect density dependence that resource limitation of its abundance (Lande 1982; Charlesworth 1994; Lande imposes. f et al. 2009). From these, p ~z The function describing f j(zNj ) is minimized at zNj z Nj and increases as a quadratic away from this minimum: dRi p À Á RirRi p 1 2 ~ f 2 dt " f j(zN ) f 0j 1 vj(zN z ) , ð7Þ j zNj p R c (1 2 g ((z 2 ~z c )2 1 j2 )) 2 d R i 0i i Ri Ri zRi i i where f0j is the minimum intrinsic death rate and vj scales the rate of increase in death rate away from the optimum. X2 b a0j jNj Consequently, this fitness component always experiences 2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 1 2 1 b2 jp1 jz jz j ~f fi Ri Nj stabilizing selection toward zz , and so tness trade-offs Nj !# 2 2 may arise if feeding on resources imposes selection on (z N z R ) #exp 2 j i , fi 2 1 2 1 b2 the birth tness components to move the trait mean away 2(jz jz j ) f Ri Nj from ~z z . As with the resources, the evolutionary outcome Nj of natural selection on the consumer’s trait mean will typ- dN j p N r ically result from optimizing selection generated by various dt j Nj selection pressures acting to change the trait in different " ! X2 2 2 directions (Arnold and Wade 1984; Travis 1989). b a bR (z N z R ) p N qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffij 0j i exp 2 j i fi j 2 1 2 1 b2 From these assumptions, the tness of an individual 2 1 2 1 b2 2(jz jz j ) ip1 jz jz j Ri Nj consumer is found by integrating these individual fitness Ri Nj # values over the resource trait distributions: 2 2 f (1 1 v ((z 2 ~z f ) 1 j2 )) 2 g N : ð11Þ ð 0j j Nj Nj zNj j j X2 ∞ p 2 2 rNj (zNj ) Ri p(zRi )bja(zRi , zNj )dzRi f j(zNj ) gjNj, 2∞ ip1 This model is equivalent to the basic consumer-resource ð8Þ model assumed by MacArthur (1969, 1970, 1972) before being recast into Lotka-Volterra competition and to the fi fi where bj is the conversion ef ciency that de nes the num- model developed by Tilman (1980, 1982) for perfectly sub- ber of consumer offspring produced per resource killed stitutable resources, except that here the parameters of the and eaten (each consumer is assumed to have the same model are functions of the trait distributions of the inter- conversion efficiency for both resources, but they may dif- acting species. As in their models, the consumer abun- fer between consumers). Substituting equations (1), (3), dances are limited by the quantities of available resources, and (7) into (8) and integrating gives and the resource competitive interactions between con- ! sumers are indirect effects that are mediated by how each X2 2 2 b a b R (zN z R ) depletes resource abundances. Additionally, consumers may r (z ) p qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffij 0j j i exp 2 j i Nj Nj 2 1 b2 p 2 1 b2 2(jz j ) ð Þ also limit their own abundances directly. Likewise, the appar- i 1 jz j Ri 9 Ri ent competitive interactions between the resources are indi- 2 1 2 ~f 2 2 : fl f 0j(1 vj(zNj z Nj ) ) gjNj rect effects that are mediated by how each in ates consumer abundances. From this, the average fitness of each consumer popula- Because equations (6) and (10) describe the average fit- tion is ness of each species as a function of its trait distribution, Consumer and Resource Differentiation E97 this derivation also provides the machinery to follow the etc.), except to address issues about differences in specific coevolution of these species in response to one another. parameters. Also, alternative stable equilibria are apparent Following Lande (1976, 1982, 2007), I assume that the in some areas of parameter space—that is, alternative stable evolution of these species can be adequately described by outcomes result from different initial mean trait values. In changes in zRi and zNj over time, given the standard quan- general, I began the numerical simulations presented here titative genetic assumptions for the traits (see also Bulmer with the consumers near their intrinsic death optima (i.e., f 1980; Iwasa et al. 1991; Abrams et al. 1993; Barton et al. z ≈ ~z z ) and at very low abundances and with the resources Nj Nj ≈ ~c 2017). The change in the trait mean over time is then de- very near their intrinsic birth optima (i.e., zR zz )andat i Ri scribed by the product of the additive genetic variation in their equilibrium abundances for the absence of the con- the trait and the partial derivative of average fitness with sumers; this simulates invasion by the two consumers of a respect to the average trait value: community consisting of the two resources. However, I did ex- plore the effects of other sets of initial conditions, and I will dz ∂r Ri p Ri Gz note whether different initial mean trait values resulted in dt Ri ∂z " Ri the community approaching different locally stable equilibria. fi p G 22c g (z 2 ~z c ) To build intuition into the dynamics of differentiation, rst zRi 0i i Ri Ri !# consider the abundance and trait dynamics of a parameter X2 a b N (z 2 z ) (z 2 z )2 2 0j j j Nj Ri 2 Nj Ri combination that results in the differentiation of identically = exp 2 , 2 1 2 1 b2 3 2 2 1 2 1 b p (j j ) 2(jzR jzN j ) parameterized resources with a single consumer (see also j 1 zRi zNj j i j Schreiber et al. 2011). In this example, the phenotypic optima dz ∂r of the resources’ intrinsic birthrates and the consumer’sin- Nj p Nj ð Þ Gz 12 c c f Nj ∂ ~ p ~ p ~ dt z trinsic death rate are identical (i.e., zR1 zR2 z N ). For " Nj ! 1 X2 ba b R (z 2 z ) (z 2 z )2 the resources to differentiate, their initial trait means must p 2 0j j i Nj Ri 2 Nj Ri GzN = exp 2 straddle those of the consumer. The consumer imposes dis- j 2 1 2 1 b2 3 2 2 1 2 1 b p (jz jz j ) 2(jzR jzN j ) i 1 Ri Nj i j fi # ruptive selection on the death tness component of both resources, with the nadir at the mean trait value of the con- 2 2f v (z 2 ~z f ) : ð12Þ 0j j Nj Nj sumer. Thus, because the consumer’s trait mean is between those of the resources, the resources evolve to differentiate. Otherwise, if the trait means of the resources are both on Together, equations (11) and (12) describe an evolu- the same side of the consumer’s trait mean, both resources tionary elaboration of MacArthur’s (1969, 1970, 1972) ’ evolve away from the consumer in the same direction, and Tilman s (1980, 1982) mechanistic models of two con- resulting in the resources not differentiating. If the resources sumer species feeding on two resource species. Obviously, differentiate from one another, the consumer evolves to be a this system of eight differential equations describing their generalist with a trait mean that is intermediate between the joint abundance and mean trait dynamics is analytically two resources and so feeds equally on both (fig. 2). In this intractable, and an exhaustive analysis is beyond the scope case, the consumer occupies a stable fitness minimum of a single article. Therefore, I will analyze the resulting (Abrams et al. 1993) at the nadir between the two fitness dynamics numerically and present results from interesting peaks on its fitness topography, which are each near the phe- areas of parameter space to address the three questions notypic means of the two resources (fig. 2). This fitness min- expounded at the end of the introduction. (The code for imum is a stable equilibrium, because perturbations of the this numerical exploration was written in MATLAB and consumer’s trait distribution in either direction will cause fi 1 is available online in a zip le. ) changes in resource abundances that will alter the selection gradients on the consumer’s two birth fitness components Results to return it to this equilibrium. Specifically, if the consumer is perturbed toward one of the resources, it depresses the As in simpler models of consumer-resource coevolution, abundance of that resource, and the abundance of the other differences in most parameters among species on a specific resource increases because of the reduced feeding pressure. trophic level will foster differentiation (McPeek 2017b). Selection then favors the consumer to evolve toward the re- Therefore, I restrict the analyses presented here to situations source whose abundance increased and so back to the stable where the consumer species have identical underlying param- fi p p p 2 p 2 tness minimum. eter values (i.e., c01 c02, a01 a02, v1 v2, jz jz , N1 N2 Now consider the same situation but with an additional

1. Code that appears in The American Naturalist is provided as a conve- identically parameterized consumer (i.e., two consumers nience to the readers. It has not necessarily been tested as part of the peer re- and two resources). Again, the resources will differentiate view process. only if their initial trait means straddle those of the two E98 The American Naturalist

Figure 2: An example of the dynamics of phenotypic differentiation of the two resources and one consumer in which the consumer occupies fi fi astable tness minimum at equilibrium. The columns are the tness topographies for R1 (A; light green), R2 (B;darkgreen),andN1 (C;light blue). The top panel in each column is the topography of overall average fitness for the species, the middle panel is the topography for the average birth fitness component, and the bottom panel is the topography of the average death fitness component once the system reaches its abundance and trait mean equilibrium (i.e., graphing the components of eqq. [6] and [10]). The vertical dashed line in each panel identifies the equilibrium mean trait value for the species. Parameters were as follows: c p 3:0, d p 0:02, g p 0:01, ~zc p 25:0, G p E p 0:2, 0i i i Ri zRi zRi a p 0:5, b p 0:1, b p 5:0, f p 0:15, g p 0:0, v p 0:01, ~z f p 25:0, G p E p 0:2. 0j j j j j j Nj zNj zNj consumers. Once the resources differentiate, the fitness (fig. 3). At the joint ecological and evolutionary equilibrium surfaces of both consumers have two fitness peaks, because in this case, the resources and the consumers all occupy fit- their birth fitness components experience disruptive selec- ness peaks (fig. 3A–3D). (The changes in the trait means tion, and if their trait means are not identical, the fitness nadir and abundances of the species cause the shapes of the fitness is positioned between them because of the same density- and surfaces experienced by each species to change over the frequency-dependent selective forces due to resource deple- course of the simulation. An animation of figure 3 showing tion by the two consumers that caused the stable fitness min- these dynamics is available in the online appendix.) imum for only one consumer. However, with two consumers The phenotypic distributions of the four species at equi- present, selection then pushes the two consumers apart be- librium are substantially differentiated from one another cause each can increase its overall fitness by evolving toward (fig. 3E), but simply comparing the phenotypic distribu- the resource whose abundance is not being depressed by the tions is deceptive. The appropriate comparison is the func- other consumer. As a result, the two consumers will differen- tional phenotypic distributions that define their interactions tiate so that each has a much higher realized attack coefficient with the other species (Taper and Case 1985)—in this case, 2 1 b2 on one resource and so feeds primarily on that resource the distributions with variance parameters jzx j , where Functional zx E99 Frequency Frequency

Real zx

Figure 3: An example of the dynamics of phenotypic differentiation of the two resources and two consumers in which species at both trophic levels differentiate. The left four columns are

the fitness topographies at the abundance and trait equilibrium for R1 (A; light green), R2 (B; dark green), N1 (C; light blue), and N2 (D; dark blue). The top, middle, and bottom panels in each column are as in figure 2. The vertical dashed line in each panel identifies the equilibrium mean trait value for the species. E shows the real and functional phenotypic distributions for each species at equilibrium (colors as previously specified). Parameters were as follows: c p 3:0, d p 0:02, g p 0:01, ~zc p 25:0, G p E p 0:2, a p 0:5, b p 0:1, b p 5:0, 0i i i Ri zRi zRi 0j j j f p 0:15, g p 0:0, v p 0:01, ~z f p 25:0, G p E p 0:2. A video of the full dynamics of this example can be found in the online appendix. j j j Nj zNj zNj E100 The American Naturalist x identifies the species. The overlap of the consumers’ func- consumers differentiated from one another (e.g., fig. 4H). tional phenotypic distributions is much greater and more Moreover, the consumers differentiated to a greater extent fi fairly represented by what is being compared in ideas of at higher productivity levels (i.e., higher values of c0i; g. 4A). “limiting similarity.” A similar pattern of differentiation also emerged along gradients of the maximum attack coefficient. The maximum attack coefficient (a ) for consumers may depend on struc- What Ecological Conditions Retard or Foster the 0j tural features of the environment in which these interactions Differentiation of Resource and Consumer Species? take place. For example, fish feeding on their prey in lakes with The ecological context in which these species interactions turbid water may have lower maximum attack coefficients occur influences whether the resources and consumers will than the same fish feeding on the same prey species in other differentiate from one another to reduce apparent and re- lakes with clear water. Ecosystems with greater degrees of source competition. Specifically, the effects of various abiotic structural complexity will also reduce the maximum attack conditions are encapsulated in the parameters of this model. coefficients of consumers foraging for resource species. When For example, in the absence of the consumers, the resource the maximum attack coefficients were lower, the consumers * p = ! : fi species equilibrate at abundances of Ri c0i di. If the pro- did not differentiate (e.g., a0j 0 125 in g. 4C,4D), but both ductivity of the ecosystem in which this community is em- resources and consumers did differentiate when the maxi- fl fi 1 : bedded in uences the maximum intrinsic birthrates of the mum attack coef cients were higher (e.g., a0j 0 125 in fi resources (i.e., c0i), more resources will be available to con- g. 4C,4D). Again, the difference between these two regions sumers in more productive ecosystems that cause larger of parameter space is whether the consumers’ overall fitness values of c0i. Likewise, other types of environmental features, surfaces have one peak or two, and higher values of the attack such as water turbidity in aquatic systems or habitat struc- coefficients in the two-peak area cause the fitness peaks to be tural complexity in most systems, will cause different values farther apart at equilibrium. fi of the maximum attack coef cient (i.e., a0j)todifferamong Finally, ecosystems may differ in the minimum intrinsic communities found in different locations. Still other envi- death rates of the consumers ( f0j) because of varying levels ronmental features (e.g., stressors, pathogens) may cause of abiotic stressors or different types or abundances of differences in the consumers’ minimum intrinsic death rates their own enemies (e.g., pathogens, predators). Consumers

(i.e., f0j) across communities that develop in different loca- differentiated along the lower stress range of the gradient ! : fi tions. Thus, differentiation of identically parameterized spe- (e.g., f 0j 0 6in g. 4E,4F) but did not differentiate if the 1 : fi cies at each trophic level across ranges of these parameters f0j values were higher (e.g., f 0j 0 6in g. 4E,4F). With identifies ranges of environmental conditions that promote higher minimum intrinsic death rates, the shape of the or retard species differentiation. death fitness component dominates the shape of the over- Figure 4 shows the equilibrium trait means and popula- all fitness topography, which forces a single adaptive peak tion sizes for the four species over ranges of these three differ- for consumers. ent parameters that correspond to important environmental In all the communities illustrated in figure 4, the resources gradients. First, consider the coevolutionary outcomes in and consumers differentiated at each trophic level only if the ecosystems that differ in productivity (i.e., communities that initial resource trait means began straddling the trait means develop at different points along a gradient of c0i). In commu- of the consumers. Alternatively, if the resources both began ! : fi ’ nities with lower values of c0i (e.g., c0i 0 75 in g. 4A,4B), on the same side of the consumers phenotypes, the resources the resources differentiated because of the feeding pressures did not differentiate but rather evolved away from the of the consumers. However, the consumers did not differen- consumers in the same direction. In these latter cases, the tiate, because the resources were not abundant enough to pro- end point was two resources with identical trait means and vide sufficient fitness returns from feeding primarily on one: two consumers with identical trait means that were slightly fi ~f the overall tness surfaces for both consumers had only one offset from the resources in the direction of z Nj .Also,ifonly fitness peak (e.g., fig. 4G). Thus, in communities with one consumer species was present (as in fig. 2), the single con- productivities in this range, the consumers would be ecolog- sumer occupied a peak in the overall fitness landscape in the ically equivalent “neutral” generalists with identical pheno- gradient ranges where the two consumers would not differen- typic distributions that occupy the same functional position tiate and occupied a stable fitness minimum in the gradient in the community and thus have identical effects on the other ranges where the two consumers would differentiate. species in the community (Leibold and McPeek 2006; Differences in specific parameters between either the re- McPeek 2017b; fig. 4A,4B). If the resources’ maximum in- sources or consumers, which reflect differences in their eco- trinsic birthrates were above this range, the resources were logical performances or differences in other features of their abundant enough at equilibrium to generate two fitness biology, also shape how consumers evolve in response to peaks in the consumers’ overall fitness surfaces, and so the phenotypically differentiated resources. From a community Consumer and Resource Differentiation E101 ecology perspective, these differences cause differences in when the asymmetry in apparent competitive ability be- 1 : the strengths of the indirect interactions propagated from tween the resources was not substantial (e.g., c01 0 55 in each species in the community—for example, when the fig. 5A). consumers have fundamental differences in their resource The resource competitive ability of a consumer for a spe- fi fi = competitive abilities or when the resources have funda- ci c resource is de ned by the ratio f j(zNj ) (aj(zRi , zNj )bj): mental differences in their apparent competitive abilities. the consumer that has the lower value of this ratio is the better These examples thus illustrate how species will respond to competitor for that resource (i.e., the R* rule; Tilman 1980, asymmetries in the indirect effects from different species. 1982). Thus, if the two consumers differ in their f0j but have To better illustrate the main results here, I will consider all other parameters identical, the consumer with the lower the situation where the intrinsic birth optima of the re- f0j is the better resource competitor for both resources. Differ- sources straddle the intrinsic death optima of the con- ences in f0j may exist because of intrinsic physiological differ- sumers, but the consumers’ intrinsic death optima are the ences between the consumer or because they have different ~c ! ~f p ~ f ! ~c same (i.e., zR1 z N1 z N2 zR2 ). This relationship causes levels of enemies (e.g., specialized predators or pathogens) the resources to always differentiate from one another re- that cause their intrinsic death rates to differ. If the difference ! : 1 : fi gardless of initial trait means. In what follows in this section, in f0j was large (e.g., f 01 0 069 or f 01 0 306 in g. 5B), the I explore how a difference in one other parameter influences superior resource competitive consumer would drive the how the consumers evolve. other consumer extinct and adapt as a generalist feeding on In this model, the potential apparent competitive ability both resources at a stable fitness minimum. The poorer re- of a resource mediated through a specific consumer is de- source competitor, even though it adapted as best it could, fined by the ratio of its intrinsic birthrate to the attack co- was driven extinct because the superior resource competitor fi = ef cient from that consumer (i.e., ci(zRi ) aj(zRi , zNj )): the depressed the abundances of the resources below levels at resource with the higher ratio is the better apparent com- which the poorer resource competitor could maintain a pop- petitor mediated through that consumer, because it can ulation. Only when the difference in resource competitive : ! ! : fi maintain a population at a higher consumer abundance ability was not large (e.g., 0 069 f 01 0 306 in g. 5B)

(Holt 1977). If the two resource species differ in c0i but would both coexist as differentiated consumers. all other parameters (except their intrinsic birth optima) A difference in the attack coefficients affects both the re- ’ ’ are the same, the resource with the larger c0i is then the sources apparent competitive abilities and the consumers re- better potential apparent competitor mediated through source competitive abilities. Increasing the attack coefficient both consumers. Differences in c0i between the two re- of a consumer on one resource increases the resource com- sources would exist if they differ in their abilities to garner petitive ability of that consumer but decreases the apparent their own resources or if the resources that limit their competitive ability of that resource (see above). The maxi- abundances differ in availability. When this difference mum attack coefficients of the two consumers may differ ! : p : ( was extremely large (e.g., c01 0 06 while c02 3 0in (i.e., a01 a02) because of other traits that affect prey capture fig. 5A), the poorer apparent competitor—resource 1 in that are not being modeled. Because of the opposing effects this case—was driven extinct because the better apparent on resource and apparent competitive abilities of the inter- competitor inflated the consumers’ abundances above lev- acting species, a difference in the maximum attack coefficient els at which the poorer apparent competitor could main- between consumers had relatively little effect on the qualita- tain a population. If the initial consumer trait means both tive outcome of consumer evolution because of these opposite began between the resource trait means, the two con- effects on the resource competitive and apparent competitive sumers adapted to be specialists feeding primarily on the abilities (fig. 5C). Only when the maximum attack coefficient superior apparent competitive resource. If the consumer of one consumer was very near zero would the consumers not ! : trait means began outside the range of the resource trait differentiate to focus on different resources (e.g., a01 0 05 in means, the consumer that was initially closer to the better fig. 5C). When the consumers differentiated, the main differ- apparent competitive resource adapted faster and in so do- ence in the resulting community was in species abundances. ing typically drove the other consumer extinct, and this The consumer having the lower maximum attack coefficient surviving consumer evolved to the same trait mean feed- had a higher abundance because the resource on which it spe- ing primarily on the better apparent competitive resource. At cialized equilibrated at a higher abundance. : ! ! : intermediate levels of this difference (e.g., 0 06 c01 0 55 One prominent conclusion from analyses of models of in fig. 5A), the inferior apparent competitive resource could Lotka-Volterra competition is the importance of the strengths invade and coexist, but one or both consumers (depend- of intraspecific density dependence for the consumers rel- ing on their initial trait means) adapted to feed primarily ative to interspecific effects (e.g., MacArthur 1972; Chesson on the superior apparent competitive resource. The con- 2000; Adler et al. 2007). This general statement can be sumers differentiated to feed primarily on only one resource made about this formulation of resource competition as E102 The American Naturalist

Figure 4: Outcomes of coevolution at different points along parameter gradients that correspond to major environmental gradients of pro- ductivity (the resources’ intrinsic birthrate maxima; A, B), habitat complexity that affects the abilities of consumers to capture resources (the maximum attack coefficients; C, D), and stressors of the consumers that affect their death rates (the consumers’ intrinsic death rate minima; E, F). The equilibrium trait means and population sizes for the four species are presented. Each filled circle identifies the mean trait value (top panel) and population abundance (bottom panel) for that species in the four-species community with the corresponding value of the fi ~c parameter on the X-axis. In all simulations in this gure, the intrinsic birthrate optimal trait value for the resources (zRi ) and the intrinsic ~f fi death rate optimal trait value for the resources (z Nj ) were all 25.0. Symbols and lines for the different species are color coded as in gure 3. fi p : p : p : ~c p : Parameters were as follows except for the parameter being manipulated in the gure panel: c0i 3 0, di 0 02, gi 0 01, zRi 25 0, G p E p 0:2, a p 0:5, b p 0:1, b p 5:0, f p 0:15, g p 0:0, v p 0:01, ~z f p 25:0, G p E p 0:2. zRi zRi 0j j j j j j Nj zNj zNj well, but direct consumer intraspecific density dependence How Do Levels of Phenotypic Variance in Consumers 1 fl (i.e., gj 0) has very different effects in this model as com- and Resources In uence the Levels of Differentiation pared to Lotka-Volterra competition formulations. When That Occur? both consumers had identical strengths of direct density dependence for their death rates, they adapted symmetri- The theory of limiting similarity predicts that consumers p p cally to focus on the different resources (e.g., g1 g2 0 should be differentiated from one another to reduce com- in fig. 5D, but any low level of intraspecific density depen- petition for shared resources (MacArthur and Levins 1967; dence where they were equal gave comparable results). As MacArthur 1969, 1970; May and MacArthur 1972; Abrams the strength of density dependence was increased in only 1983; Meszéna et al. 2006; Abrams and Rueffler 2009; Szil- one consumer (consumer 1 in fig. 5D) but held constant agyi and Meszéna 2009). Because the degree of functional in the other, the consumer with the stronger intraspecific overlap between the consumers is the issue, consumers with density dependence had a much lower abundance (e.g., larger functional phenotypic variances are expected to have McPeek 2012) and adapted as a specialist on one resource, their mean trait values displaced farther apart to maintain while the other consumer had a much higher abundance the same level of overlap (May and MacArthur 1972). and adapted as a generalist feeding roughly equally on both Increasing the consumers’ phenotypic variances in this resources again at a stable fitness minimum (fig. 5D). Only model does not produce this result; it produced just the oppo- at extremely large differences would the consumer with site. First, consider how the equilibrium mean trait values of stronger direct intraspecific density dependence be driven the four species change with different levels of environmental extinct. variance (E ) for the two consumers (fig. 6). For the param- zNj Consumer and Resource Differentiation E103

Figure 4 (Continued) eters considered in figure 3, higher values of E caused the sumers co-occurred as ecologically identical “neutral” species zNj consumers to differentiate less from one another (fig. 6A). in an apparent competition community module. Moreover, above a specificvalueofE (i.e., E 1 1:8in This was also true when the resources’ intrinsic birth op- zNj zNj fig. 6A), the consumers did not differentiate at all: the con- tima straddled the consumers’ intrinsic death optima (fig. 6B): E104 The American Naturalist

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Figure 5: Equilibrium trait means that result in communities in which the resources have different intrinsic birth maxima (c0i; A)orthe fi consumers have different intrinsic death minima ( f0j; B), maximum attack coef cients (a0j; C), or strengths of density dependence in their fi death rates ( gj; D). In each panel, the value for one species is held constant (identi ed above the panel) and the value for the other species is manipulated (given on the X-axis). Symbols and lines for the different species are color coded as in figure 3. Parameters were as follows except for the parameter being manipulated in the figure panel: c p 3:0, d p 0:02, g p 0:01, ~zc p 20:0, ~zc p 30:0, G p 0:2, 0i i i R1 R2 zRi E p 4:0, a p 0:5, b p 0:1, b p 5:0, f p 0:15, g p 0:0, v p 0:01, ~z f p 25:0, G p 0:2, E p 4:0. zRi 0j j j j j j Nj zNj zNj in this case the resources differentiated from one another to shown for comparison in figure 6C–6E. The same was also a much greater degree, but higher values of E still caused true if the consumers’ E were held constant and the re- zNj zNj the consumers to differentiate less from one another. The sources’ E were varied (results not shown). I could find zRi equilibrium phenotypic distributions for three levels of E no area of parameter space where consumers differentiated zNj from figure 6B that result in consumer differentiation are more from one another as E or E were increased, and the zRi zNj Consumer and Resource Differentiation E105

~c ! ~f p ~f ! ~c convergence of their phenotypes always occurred smoothly ness components (i.e., zR1 z N1 z N2 zR2 ). All else being with increasing E or E . equal, these relationships favor the consumers differentiat- zRi zNj In the examples shown in figure 6, the species at each tro- ing symmetrically onto the different resources (e.g., figs. 3, phic level had identical phenotypic variances. The results 4, 6). However, consumers do not differentiate symmetri- were qualitatively identical when the species at each trophic cally if the resources’ intrinsic birth optima lie far enough level had very different levels of phenotypic variation. For away from the consumers’ intrinsic death optima (i.e., fi ~c ~c ≪ ~f ~f ~c ~c ≫ ~f ~f example, when all other parameters are as in gure 6B z R1 and z R2 z N1 and z N2 or z R1 and z R2 z N1 and z N2 ). and the environmental phenotypic variation for N1 is held Figure 7 presents instructive examples of this situation. In p : fi constant at EzN 4 0, the two consumers differentiated all the simulation results presented in gure 7, the initial trait 1 p : p : p to specialize on the different resources over the range of means of the four species were zR1 21 0, zR2 21 2, zN1 p : – : ’ : p : e e ! : Ez 0 0 62 1 (cf. Barabás and D Andrea 2016). 17 0, andzN 17 1. At low levels of V z (e.g., V z 1 5in N2 2 Nj Nj The consumers differentiated from one another because of fig. 7A), one consumer evolved to be a specialist feeding al- how all the direct and indirect interactions that propagate most exclusively on one resource and the other consumer through this community module determine the fitness topog- evolved to be a generalist feeding on both resources approx- raphy that shapes the evolution of each species (fig. 6F–6H). imately equally (fig. 7B). Each consumer occupied a different With little environmental variation in their phenotypes, the fitness peak in this range (fig. 7E). However, note that when consumers’ fitness surfaces had two well-defined peaks re- two peaks existed in the consumers’ overall fitness surfaces, sulting from the clear fitness advantages for specializing on the underlying birth fitness components were not two- one resource that were apparent in their birth fitness compo- peaked for a generalist and a specialist (fig. 7E). Even though nent surfaces (fig. 6F). With increasing E , the increasing both their birth and death fitness components experienced zNj breadth of the functional phenotypic distribution caused directional selection across their entire phenotypic range, the fitness gradients all along the consumers’ birth fitness the subtle curvature in both resulted in a two-peaked overall surfaces to become shallower (note the change in the con- fitness landscape that caused them to differentiate. Also, in sumers’ birth fitness component surfaces in fig. 6F–6H). this case, initial trait means had no effect on the outcome The result was that trait values where the selection gradients of selection. Because of the balances struck between their on birth and death fitness components balance (i.e., the over- two underlying fitness components, the resources evolved all fitness peaks) moved closer together and the fitness valley to match and then cross the phenotypic distributions of between them became shallower. This occurred until a level the consumers if need be to reach the single stable equilibri- of E was reached where the two peaks in overall fitness col- um configuration for a given parameter combination. At in- zNj e : ! e ! : fi lapsed into one, and selection moved the two consumers to termediate V z levels (e.g., 1 5 Vz 3 8in g. 7A), the Nj Nj this common fitness peak (fig. 6A,6B). consumers did not differentiate but rather converged to an intermediate generalist phenotype (fig. 7C). Interestingly, the consumers evolved to and occupied the stable fitness min- fi imum that ranged from 21.80 to 21.82 depending on the exact How Do Intraspeci c Trade-Offs among Fitness fi e level of phenotypic variance ( g. 7F). At high V z levels (e.g., fl Nj Components In uence How Consumers e 1 : fi V z 4 0in g. 7A), neither the consumers nor the and Resources Will Differentiate? Nj resources differentiated (fig. 7D). In this parameter range, The overall form that natural selection takes is defined by the consumers’ overall fitness surfaces finally had a single the balance that is struck among the selection gradients peak. However, the resources evolved to and occupied a of different underlying fitness components (Arnold and stable fitness saddle point, again resulting from the frequency- Wade 1984; Travis 1989; McPeek 1996). In the present and density-dependent feedbacks among the species abun- context, this means that how consumers and resources dances and mean trait values (fig. 7G). may adapt to one another will be influenced by the forms However, the outcomes for the various parameter combi- of selection gradients acting on the fitness components not nations considered in figure 7 were very different if the directly involved in predator evasion or prey capture, that resources began as differentiated species with trait means that is, the resources’ birth fitness components and the con- were far from their intrinsic birth optima. If the resources’ sumers’ death fitness components, respectively. To this trait means were initially far apart and straddled the con- point, I have considered situations where either the com- sumers’ trait means, the consumers differentiated as a gener- ponents of selection acting on these fitness components in alist and specialist for all the phenotypic variance values de- the resources and consumers all favor the same trait values picted in figure 7A. However, if the consumers’ initial trait ~c p ~c p ~ f p ~f ’ (i.e., zR1 zR2 z N1 z N2 ) or the traits favored by selec- means began outside of the range of the resources trait tion on the resources’ birth fitness components straddle means, the outcomes were again as depicted in figure 7A. the traits favored by selection on the consumers’ death fit- Here again, the initial trait distributions of the community ˜

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Figure 6: Effects of manipulating the magnitude of environmental phenotypic variance in the consumers on the equilibrium trait means of the four species. In A, all four species have the same optimal trait values for their intrinsic demographic rates, and in B, the resource intrinsic birth optima straddle the intrinsic death optima of the consumers. C–E show the equilibrium phenotypic distributions for the four species for three different values for the environmental variance component of the consumer’s phenotypic distribution from B (as in fig. 3E), and F–H show the average fitness surfaces for the four species at equilibrium in these same situations (as in fig. 2). Symbols and lines for the different species are color coded as in figure 3. Parameters were as follows in all simulations for this figure except for the parameter being manipulated in the figure panels: c p 3:0, d p 0:02, g p 0:01, G p 0:2, a p 0:5, b p 0:1, b p 5:0, f p 0:15, g p 0:0, v p 0:01, ~z f p 25:0, 0i i i zRi 0j j j j j j N j G p 0:2. In A, ~zc p ~zc p 25:0, E p 0:2; in B, unless otherwise specified, ~zc p 20:0, ~zc p 30:0, E p 4:0, E p 4:0. zNj R1 R2 zRi R1 R2 zRi zNj

E106 Figure 6 (Continued)

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Figure 7: An example of the dynamics of phenotypic differentiation of the two resources and two consumers when the resources’ intrinsic birth optimal trait values are much larger than the consumers’ intrinsic death optimal trait values. Equilibrium trait means for communities in which the consumers have different levels of environmental phenotypic variance are shown in A. B–D show the trait distributions (as in fig. 3E) for three values of the consumers’ environmental variation, and E–G show the average fitness surfaces for the four species at equi- librium for the same three values of the consumers’ environmental variation. Symbols and lines for the different species are color coded as in fi fi p : p : p : gure 3. Parameters were as follows except for the parameter being manipulated in the gure panel: c0i 3 0, di 0 02, gi 0 01, ~zc p 22:0, G p E p 0:2, a p 0:5, b p 0:1, b p 5:0, f p 0:15, g p 0:0, v p 0:01, ~z f p 10:0, G p 0:2. Ri zRi zRi 0j j j j j j Nj zNj

E108 Figure 7 (Continued)

E109 E110 The American Naturalist members as the community is assembled can strongly influ- feed primarily on one resource only in more productive ence the community structure that evolves. and more benign ecosystems and in ecosystems where the resources are easier to harvest, even if differentiated resources are available all along these gradients. Discussion The results of these analyses also strongly argue that a The analysis of this model clearly demonstrates that purely purely ecological analysis of consumer differentiation is ecological or purely evolutionary perspectives cannot ex- also insufficient. Schreiber et al. (2011) analyzed a compara- plain the rich set of possible coevolutionary outcomes for ble model with one consumer and two resources, and they the community structure of two consumers feeding on illustrated a rich set of consequences for both resources two resources. Their abundance and trait dynamics cannot and the consumer in the final community, including ap- be decomposed to be studied separately, and one does not parent competition, apparent facilitation, and “apparent have primacy over the other in effect. Ecologists have real- competitive” exclusion, depending on the level of the ized that the coevolution of interacting species can have pro- consumer’s phenotypic variance and initial trait distribu- found ramifications on the same magnitudes and on the tions. The original motivation for this work was to extend same timescales as abundance responses (e.g., Yoshida et al. their model to test whether the predictions of the theory of 2003; Fussmann et al. 2007; Kokko and López-Sepulcre limiting similarity are supported when consumers and 2007; Harmon et al. 2009; Schoener 2011; Bassar et al. resources can all evolve in response to one another. Eco- 2012; Urban et al. 2012; Travis et al. 2014; Urban and logical derivations of the idea of a limiting similarity Richardson 2015). However, the converse is also true that among resource competitors predict that coexistence is the coevolutionary dynamics of species depend critically on less likely with greater overlap of their phenotypic distri- how ecological context shapes the abundances of those inter- butions (MacArthur and Levins 1967; MacArthur 1970, acting species (Hutchinson 1965; Drossel et al. 2001; McPeek 1972; May and MacArthur 1972; May 1974; Roughgarden 2017b). 1974; Abrams 1975, 1983; Turelli 1978a; Meszéna et al. One area where the importance of ecological context is 2006; Abrams and Rueffler 2009). As a result, evolution clearest is consumer differentiation along parameter gra- is expected to push consumers apart to reduce interspecific dients that can be interpreted as environmental gradients competition—character displacement—and thus promote (fig. 4). Previous studies generally all noted that consumer dif- their coexistence (Brown and Wilson 1956; Hutchinson ferentiation was not inevitable, but few identified any ecolog- 1959; MacArthur and Levins 1967; MacArthur 1970, 1972; ical context to when differentiation may or may not be fa- Roughgarden 1974; Stuart and Losos 2013). vored (e.g., Lawler and Maynard Smith 1976; Roughgarden In contrast to this expectation based purely on ecological 1976; Slatkin 1980; Pacala and Roughgarden 1982; Taper considerations, increasing the phenotypic variances in this and Case 1985; Abrams 1986). Along a productivity gradient model decreased the degree to which consumers differenti-

(i.e., c0i), consumer differentiation occurred only when the re- ated, and above some level the two consumers converged to source species were at high enough abundances to provide a identical generalist trait distributions (fig. 6). Moreover, a sufficient overall fitness advantage for feeding primarily on stable community resulted no matter the level of phenotypic one over generalized feeding on both (fig. 4A,4B). Abrams variability in the species and no matter the degree of differ- (1986) found a similar relationship using a fitness set ap- entiation. Previous studies based on Lotka-Volterra compe- proach. Along a stressor gradient of consumer minimum tition dynamics also found that consumer differentiation oc- death rate (i.e., f0j; e.g., abiotic stressors or the abundances curred only at lower levels of phenotypic variance and or types of various enemies such as herbivores, predators, character convergence happened at high levels (Bulmer or diseases that are subsumed into the consumer’s death rate 1974; Roughgarden 1976; Slatkin 1980; Taper and Case in this model), consumers also showed a consistent pattern of 1985; Ackermann and Doebeli 2004). For example, in the differentiation or lack thereof (e.g., fig. 4E,4F). When a most detailed model constructed by Taper and Case consumer’s death rate is high, the shape of its death fitness (1985; i.e., their “Free WPNW Model”), they created a spec- component surface dominates the shape of the overall fitness trum of nonevolving resources that could be depleted in surface and so overrides any fitness advantages from feeding abundance, but the consumers had within- and between- specialization (McPeek 1996). Consumer differentiation is individual variances in resource exploitation abilities that also predicted to differ among communities that develop in could evolve, and the mean position of the entire consum- areas that differ in habitat structural complexity (e.g., a0j)that ers’ distributions could evolve. The genetic components of would affect the abilities of consumers to kill and consume phenotypic variance eventually evolved to zero, leaving only the resources (e.g., fig. 4C,4D). Thus, while phenotypically environmental components of phenotypic variation in the differentiated resource species are necessary for consumer consumers. Consumers differentiated less when the environ- differentiation, consumers are predicted to differentiate to mental components of their phenotypic variances were Consumer and Resource Differentiation E111 greater, and consumers converged to the same mean pheno- trait values near its trait mean most, and so each consumer’s type at high levels of environmental phenotypic variances birth fitness component has a fitness nadir between it and the (see fig. 8 in Taper and Case 1985), as was found for the pres- other consumer. Consequently, each consumer’soverallfit- ent model. I also explored whether temporal variation in the ness increases in the direction that is away from the other parameters (e.g., at each time step of a simulation drawing consumer because of higher resource abundances in that di- fi c0i randomly from a normal distribution with a speci ed mean rection. Consumer differentiation proceeds until the selection and variance) affected the degree of differentiation (May and gradients on their respective birth and death fitness compo- MacArthur 1972; May 1974; Turelli 1978a,1978b, 1981) and nents balance (i.e., the various terms in square brackets in ∂ =∂ p found that such temporal environmental variation had no ef- each equation of [12] sum to zero such that rx zx 0; fect on how species evolved (results not shown). Lande 1976; Felsenstein 1979; Lande 1982; Iwasa et al. If two consumers are present and they differentiate, the 1991; Abrams et al. 1993; McPeek 1996, 2017a,2017b). Inter- critical issue determining how much they will differentiate estingly, the same overall dynamics driving differentiation to from one another is how far the two fitness peaks are from different fitness peaks can occur when both consumers expe- one another (fig. 6F–6H). Increasing the phenotypic vari- rience overall directional selection on their birth fitness com- ance of a consumer decreases the strength of the selection ponents, if the curvatures of the underlying birth and death gradients on its birth fitness component (i.e., the feeding- fitness components will produce multiple peaks in the overall related fitness component) across the range of its pheno- fitness topography (e.g., fig. 7E). Thus, consumer differentia- type in two ways. First, a higher frequency of individuals tion is driven by the selection pressures that are generated by with lower fitnesses are included, which lowers average fit- the indirect effects caused by both resource and apparent ness, particularly near optimal trait values (e.g., note the competition that propagate through this community module decrease in the height of the average death fitness surface to shape the dynamics of the species’ overall fitness topog- e fi – with increasing levels of V z in g. 6F 6H). Second, a raphies (Abrams et al. 1993; McPeek 2017a,2017b). Nj broader phenotypic distribution will decrease the depth of The range of selection dynamics producing convergence the fitness valley between the two peaks because a greater of consumers to the same generalist phenotype can be just fraction of phenotypes that receive higher returns for forag- as diverse. In many cases, convergence results when the dis- ing on both resources will exist in the population (e.g., com- ruptive selection on each consumer’sbirthfitness compo- pare the consumers’ birth and overall fitness surfaces in nent is weaker than the stabilizing selection acting on their fig. 6F–6H); as a result, the selection gradients all along death fitness component, resulting in a single fitness peak the birth fitness component surface are shallower. Because for each at the same trait mean (e.g., fig. 4G). In other cases, the peaks in the overall fitness landscape occur where the se- the consumers converge to the same fitness maximum that lection gradients on the various fitness components balance results from optimizing selection caused by directional se- ∂ =∂ p fi (i.e., zx values where rx zx 0 in eqq. [12]), the overall lection pressures pushing different tness components in fitness peaks are also closer together with higher phenotypic opposing directions (e.g., fig. 7G; Travis 1989). In still other variance. cases, two consumers may evolve to and occupy the same The dynamics of consumer differentiation is driven by stable fitness minimum (e.g., fig. 7F). Thus, the ecological ecological dynamics analogous to what causes a single con- dynamics of natural selection can be just as complicated sumer to occupy a stable fitness minimum in figure 2 for both consumer divergence and convergence. (Abrams et al. 1993). If the trait mean of the single con- These same issues also explain why the initial mean trait sumer is perturbed away from this equilibrium toward one relationships among the species can push the system to alter- resource, the consumer depresses the abundance of that re- native equilibria. The shapes of these fitness surfaces change source, and the abundance of the other resource increases be- as the species abundances and trait distributions change in re- cause of the reduced feeding pressure on it. As a result, selec- sponse to one another (McPeek 2017a,2017b; and see the an- tion now favors the consumer evolving toward the resource imation of fig. 3 in the appendix). Without some intrinsic dif- with higher abundance and so back toward the equilibrium. ferences among the species, only the initial trait distributions These resource abundance responses to the change in the can cause more than one adaptive peak to exist or make selec- consumer’s mean trait value are what make this equilibrium tion move a species from one peak to another. For example, stable (fig. 2). When two consumers are present (e.g., the sce- consider the difference between the two parameter combina- nario illustrated in fig. 3), selection favors each consumer tions represented in figure 6A and 6B.Infigure 6A,because evolving away from the other consumer that is depleting the intrinsic birth and death optima are all at the same trait resources and so toward the resource with trait mean away value, the only way for the two resources to evolve in different from that of the other consumer that the competitor is not phenotypic directions is for them to begin straddling the depleting. When the differentiation process begins, each consumers’ trait means. Thus, the initial trait distributions consumer is depressing the abundances of the resources with are the only system feature that provides the impetus for E112 The American Naturalist the resources to differentiate. In contrast, initial trait distribu- produce two species in one local community. The scenarios I tions make no difference in figure 6B because the resources’ have modeled here represent situations where two ecologi- intrinsic birth optima already straddle the consumers’ intrin- cally nearly identical consumers come together in a commu- sic death optima. Here, selection always pulls the resources’ nity, for example, when Bateson-Dobzhansky-Muller incom- phenotypic distributions apart, regardless of where the re- patibilities develop in different parts of a consumer’srangeto sources or consumers start. These results and those of previ- generate reproductive isolation (Bateson 1909; Dobzhansky ous analyses of these types of models (e.g., Schreiber et al. 1937; Muller 1942; Coyne and Orr 2004) and then one 2011) highlight the fact that the structure of the final commu- invades the range of the other (McPeek 2017b also discusses nity can be highly contingent on the features of invading spe- other biological examples that may create these scenarios). cies as the community is assembled, because of the contingent In most cases, consumers that come together when both are nature of natural selection. at or near a stable fitness minimum will diverge (e.g., fig. 3), In considering the development of community struc- but a limited set of situations do exist where such con- ture, we typically consider the resource competitive abili- sumers will converge to the stable fitness minimum (e.g., ties of consumers only after differentiation has occurred, fig. 7A). Additionally, a central problem with splitting one instead of exploring potential intrinsic differences among species occupying a stable fitness minimum into two— consumers that would also foster or retard their differen- sympatric ecological speciation—is how to generate repro- tiation. Consumers may differ in fundamental features of ductive isolation in concert with this disruptive selection their resource competitive abilities that limit their scope (Kondrashov and Kondrashov 1999; Berlocher and Feder for evolving in response to the resources, and similarly dif- 2002; Kirkpatrick and Ravigné 2002; Gavrilets 2004; ferences in the fundamental capabilities of the apparent Bolnick and Fitzpatrick 2007). Evolutionary branching competitive abilities of the resources may also shape analyses in adaptive dynamics approaches to the problem how consumers differentiate in response to them. For ex- make the assumption that this will occur (Geritz et al. ample, a consumer’s resource competitive ability is not 1998; Doebeli and Dieckmann 2000; de Mazancourt and simply its ability to acquire a particular resource from Dieckmann 2004; Doebeli 2011). The analyses presented the environment but rather is the fitness balance between here suggest that the ecological component of such sympat- the benefits of feeding on that resource and the costs of ric ecological speciation could be driven by resource com- other demographic processes (i.e., the denominator and nu- petition only if the consumer began at a stable fitness min- = ’ merator, respectively, of f j(zNj ) (aj(zRi , zNj )bj) in Tilman s imum and had a trait distribution between those of two [1980, 1982] R* rule). Before differentiation, one consumer resource species onto which it would diversify. However, may be a poorer resource competitor on all available these two criteria are necessary but not sufficient in all cases resources because these demographic costs are higher for that to ensure that the process might proceed. species, but it is in every way identical to its resource The reciprocity of ecological and evolutionary dynamics in competitors in its intrinsic capabilities to utilize the resources this model illustrates how understanding of community (e.g., the scenarios depicted in fig. 5B). If it could not adapt, structure cannot be had without understanding how evolu- this consumer with higher demographic costs (higher fj) tion will shape interactions among the species. Inferences would be driven extinct by resource competition with the about the evolution of community structure cannot be based consumer having lower demographic costs. Adaptation on ecological arguments about community stability or likely resulting in differentiation allows the consumer with higher coexistence. Likewise, the adaptation of species cannot be un- demographic costs to also increase its benefits from feeding derstood in an ecological vacuum that ignores the ecological and thereby coexist in the community. Differences in other context in which they exist, the abundances of the species demographic processes that generate direct forms of intraspe- caused by that ecological context, or the ecological dynamics cific density dependence may be what fosters the evolution of of natural selection generated by various types of direct and coexisting generalist and specialist feeders, even though those indirect species interactions. Fitness is fundamentally an eco- species have identical underlying capacities for feeding on all logical metric, and so a truly predictive evolutionary theory available resources (fig. 5D). However, intrinsic differences must explicitly incorporate how the abiotic environment among consumers in their abilities to acquire all resources and the dynamics of species interactions shape the fitness (e.g., differences in the maximum attack coefficient) have lit- surfaces that drive natural selection. tle effect on the resulting community structure because they have countervailing effects resulting from apparent and re- Acknowledgments source competition. One important issue that is beyond the scope of this article I thank F. Fu and M. A. Kirkpatrick for helpful discussions is whether a single species that occupies a stable fitness min- about the model development and R. D. Holt for conver- imum (e.g., fig. 2) will differentiate and in so doing diversify to sations over the years on these topics. G. 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