EVOLUTION INTERNATIONAL JOURNAL OF ORGANIC EVOLUTION

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1 EVOLUTION INTERNATIONAL JOURNAL OF ORGANIC EVOLUTION PUBLISHED BY THE SOCIETY FOR THE STUDY OF EVOLUTION Vol. 57 Noveber 003 No. 11 Evolution, 57(11), 003, pp SEXUAL DIMORPHISM AND ADAPTIVE SPECIATION: TWO SIDES OF THE SAME ECOLOGICAL COIN DANIEL I. BOLNICK 1 * AND MICHAEL DOEBELI * 1 Section o Evolution and Ecology, Center or Population Biology, Storer Hall, University o Caliornia, Davis, Caliornia E-ail: dibolnick@ucdavis.edu Departent o Zoology, University o British Colubia, 670 University Boulevard, Vancouver, British Colubia V6T 1Z4, Canada E-ail: doebeli@zoology.ubc.ca Abstract. Models o adaptive speciation are typically concerned with deonstrating that it is possible or ecologically driven disruptive selection to lead to the evolution o assortative ating and hence speciation. However, disruptive selection could also lead to other ors o evolutionary diversiication, including ecological sexual diorphiss. Using a odel o requency-dependent intraspeciic copetition, we show analytically that adaptive speciation and diorphis require identical ecological conditions. Nuerical siulations o individual-based odels show that a single ecological odel can produce either evolutionary outcoe, depending on the genetic independence o ale and eale traits and the potential strength o assortative ating. Speciation is inhibited when the genetic basis o ale and eale ecological traits allows the sexes to diverge substantially. This is because sexual diorphis, which can evolve quickly, can eliinate the requency-dependent disruptive selection that would have provided the ipetus or speciation. Conversely, populations with strong assortative ating based on ecological traits are less likely to evolve a sexual diorphis because eales cannot siultaneously preer ales ore siilar to theselves while still allowing the ales to diverge. This conlict between speciation and diorphis can be circuvented in two ways. First, we ind a novel or o speciation via negative assortative ating, leading to two diorphic daughter species. Second, i assortative ating is based on a neutral arker trait, trophic diorphis and speciation by positive assortative ating can occur siultaneously. We conclude that while adaptive speciation and ecological sexual diorphis ay occur siultaneously, allowing or sexual diorphis restricts the likelihood o adaptive speciation. Thus, it is iportant to recognize that disruptive selection due to requency-dependent interactions can lead to ore than one or o adaptive splitting. Key words. Adaptive dynaics, disruptive selection, evolutionary branching, resource partitioning, stable itness inia, sypatric speciation. Traditionally, evolutionary biologists have thought that speciation is initiated by a phase o geographic isolation between subpopulations o an ancestral lineage (Mayr 1963). Over evolutionary tie, these allopatric populations diverge genetically, either in response to drit or dierent selection regies. As a by-product o the dierent evolutionary trajectories, the two eerging species becoe reproductively isolated. Even though adaptations ay be the cause o the dierentiation in such allopatric speciation scenarios, the initial process o splitting the gene pool is not itsel adaptive and instead is generated by external orces leading to geographic isolation. In contrast, the past years have seen a renewed interest in a process tered adaptive speciation, in which the split- * Both authors contributed equally to this paper. 003 The Society or the Study o Evolution. All rights reserved. Received October 9, 00. Accepted May 9, ting itsel is an adaptation (Dieckann et al. 003). This interest has been spurred on the one hand by a nuber o epirical studies suggesting that speciation can occur under nonallopatric conditions (e.g., Schliewen et al. 1994; Bernatchez et al. 1996; Shaw et al. 000; Wilson et al. 000; Schliewen et al. 001; Via 001), and on the other hand by theoretical advances showing that adaptive speciation is a theoretically plausible process (reviewed in Turelli et al. 001). Theoretical odels o adaptive speciation ust speciy the ecological echaniss generating the disruptive selection regie that renders the splitting adaptive. Under the classical view o static itness landscapes, disruptive selection (e.g., through biodal niches) is unlikely to be iportant or adaptive splitting because a population whose ean phenotype is close to a itness iniu will siply evolve directionally

2 434 D. I. BOLNICK AND M. DOEBELI away ro it, aking evolutionary diversiication unlikely. In contrast, requency-dependent interactions induce itness landscapes that change dynaically in response to changes in the phenotype distribution. In particular, i disruptive selection is generated by requency-dependent interactions, a perturbation to the ean phenotype away ro a itness iniu can induce changes in the itness landscape that drive the population back toward the state in which itness turns disruptive. Such evolutionary stability o itness inia has been ound in several dierent odels (e.g., Eshel 1983; Brown and Pavlovic 199; Abras et al. 1993; Christiansen 1991; Geritz et al. 1998; Doebeli and Dieckann 000; Doebeli and Dieckann 003). Consequently, odels o adaptive speciation typically involve requency-dependent intraspeciic interactions. In asexual odels, the process o convergence to a regie o disruptive selection is oten ollowed by adaptive splitting into separate lineages. This phenoenon is called evolutionary branching in the theoretical raework o adaptive dynaics, an analytic approxiation or the evolution o ean phenotypes (Metz 1996; Geritz et al. 1998). An iportant insight gained ro adaptive dynaics theory is that evolutionary branching is a generic and robust phenoenon in any dierent odels o evolution due to requency-dependent ecological interactions (e.g., Geritz et al. 1998; Kisdi 1999; Doebeli and Dieckann 000, 003). The ost coon ecological setting used to illustrate evolutionary branching entails requency-dependent copetition or a liiting resource. In the corresponding odels, populations typically evolve under directional selection toward the phenotype best suited to the ost abundant resource, the density-dependent optiu (Bolnick 001). Once there, this ost coon phenotype experiences disproportionately intense copetition, and hence has lowest itness. Accordingly, such odels readily exhibit evolutionary branching in clonal populations (Dieckann and Doebeli 1999; Kisdi and Geritz 1999; Doebeli and Dieckann 000). In sexual populations, however, adaptive splitting requires assortative ating echaniss that prevent the production o phenotypically interediate ospring. Consequently, a priary ai o recent odels o adaptive speciation has been to deonstrate that the eergence o disruptive selection can avor the evolution o assortative ating and subsequent evolutionary branching in sexual populations (Dieckann and Doebeli 1999; Doebeli and Dieckann 000, 003). However, adaptive speciation is not the only possible outcoe o convergence toward disruptive selection. Other evolutionary echaniss can widen the phenotypic distribution o the population, equalizing the eects o copetition (and hence equalizing itness) across all phenotypes (Roughgarden 197). In particular, adaptive splitting can occur intraspeciically, as seen in ontogenetic niche shits, resource polyorphiss, and ecological sexual diorphiss (Slatkin 1984). By lattening the itness unction, these alternative ors o phenotypic expansion ay eliinate the disruptive orce that would have driven speciation. It thus becoes iportant to understand the genetic conditions that ay give rise to alternative escape routes ro stable itness inia and the relative rates with which dierent alternatives ight evolve. In this paper we deonstrate that a single odel o intraspeciic copetition can give rise to ecological sexual diorphis and/or adaptive speciation, and we explore how ating behavior and genetic assuptions about trait deterination in ales and eales aect the relative likelihood o these two outcoes. Using an adaptive dynaics odel or quantitative traits in ales and eales deterining copetition or a liiting resource, we irst show that requencydependent copetition can avor an ecological sexual diorphis and that the ecological conditions or evolutionary branching and or sexual diorphis are identical. We then use individual-based odels incorporating explicit genetics and assortative ating to exaine the prerequisites or sexual diorphis and speciation. DETERMINISTIC MODEL OF SEXUAL DIMORPHISM In Slatkin s (1984) quantitative genetic odels sexual diorphis is a consequence o copetitive displaceent, and the ecological echaniss driving evolutionary change bear a striking reseblance to odels o adaptive speciation (e.g., Doebeli 1996; Dieckann and Doebeli 1999). Here we present a deterinistic odel o sexual diorphis using the sae underlying ecological dynaics as in Slatkin (1984) and Dieckann and Doebeli (1999). The resulting equations serve as the basis or the individual-based odels used in subsequent sections to exaine the interaction between diorphis and speciation. Males and eales are characterized by a quantitative character z (e.g., body size) that deterines ecological interactions, denoted by z in ales and by z in eales. To derive the deterinistic dynaics, we assue that there is no genetic covariance between z and z, or exaple, the ecological trait z is deterined by independent sets o loci in ales and eales. We assue that ales pass on their phenotype to sons and eales pass on their phenotype to daughters, so the value o a parent s trait is only iportant to progeny o the sae sex. Resources are ost abundant or individuals with soe interediate character value z 0, which we arbitrarily set at z 0 0. Speciically, we assue that populations that are onoorphic or character value z have carrying capacity [ ] (z z 0) K(z) K0exp. (1) k Here K 0 scales the axial carrying capacity, and k easures how ast resource availability decreases with increasing phenotypic distance ro the optial trait value z 0. To incorporate requency-dependence, the driving orce o copetitive displaceent, we assue that the strength o copetition between individuals with phenotypes z and z decreases with phenotypic distance and is given by [ ] (z z) c(z, z) exp, () c where c easures how ast copetitive ipacts decrease with an increase in the phenotypic distance between interacting individuals. Thus, c deterines the strength o requency dependence in the copetitive interactions, with sall c corresponding to a high degree o requency de-

3 SEXUAL DIMORPHISM AND ADAPTIVE SPECIATION 435 pendence. Note that we assue that the carrying capacity (eq. 1) and eects o copetition between two individuals (eq. ) are independent o the sex o the copeting individuals. Deterinistic adaptive dynaics odels assue that evolution is utation liited and that the phenotype distribution o a resident population deterines the invasion success o new utants (Dieckann and Law 1996; Metz et al. 1996; Geritz et al. 1998). We irst calculate the ecological equilibriu population sizes or a population in which eales and ales are each onoorphic or soe trait value z and z, respectively. Based on this equilibriu state, on the carrying capacity unction K(z), equation (1), and on the copetition unction c(z, z), equation (), we then calculate the per capita growth rate o any given rare utant phenotype in either ales or eales. In the liit o very sall utations, these growth rates yield selection gradients in both ales and eales, ro which the adaptive dynaics are deduced. Here we assue that the underlying odel or the ecological dynaics is a discrete-tie odel with nonoverlapping generations given by the Beverton-Holt equation, rn(t) n(t 1), (3) r 1 1 n(t) K where n(t) and n(t 1) are population densities in successive generations, r is the per capita nuber o ospring, and K is the carrying capacity. In the Appendix, we describe how this odel can be adopted to describe the dynaics o ale and eale population densities and calculate equilibriu population densities o onoorphic ales and eales. Using these equilibriu densities, one can calculate the growth rates o rare utant ales and eales in a resident population (z,z ), which are given by two unctions w ( z, z, z ) or utant ales z and w ( z, z, z ) or utant e- ales z (see Appendix). Fro these growth rates, one obtains the selection gradients or ale and eale traits in a resident population (z,z )as w g (z, z ) and (4a) dz z z w g (z, z ). (4b) dz z z These gradients describe the adaptive dynaics o the ale and eale traits z and z. In particular, equilibriu points o the adaptive dynaics are points z*, z* in phenotype space at which the gradients g and g vanish siultaneously. It is shown in the Appendix that the point ( z*, z* ) (0,0) is always an equilibriu point o the adaptive dynaics (recall that we assued that z 0 0 is the trait value axiizing the carrying capacity). This equilibriu (0, 0) is locally stable i and only i c k, where k and c are the paraeters deterining the width o the carrying capacity unction, equation (1), and the strength o requency dependence in the copetition unction, equation (), respectively. Thus, i the eect o requency dependence is weak relative to the stabilizing selection iposed by the uniodal resource distribution, both sexes will adapt to the odal resource and no diorphis will occur. We note that i the equilibriu ( z*, z* ) (0,0) is locally stable or the adaptive dynaics, then it is also evolutionarily stable in the sense that the invasion itness unctions w and w have a axiu with respect to the utant trait values at the equilibriu. Conversely, i requency dependence is relatively strong ( c k ), then the syetric equilibriu (0,0) is unstable, and instead there is a new equilibriu ( z*, z* ) o the adaptive dynaics given by 1 z* z* log k c 1. (5) This equilibriu represents a sexual diorphis, and it exists i and only i c k. (6) I the diorphic equilibriu exists, then so does the equilibriu with the ale and eale trait values reversed, and both equilibria are locally stable. Note that inequality (6) is essentially the sae condition as that ound by Slatkin (1984) or the evolution o sexual diorphis, naely V k c, where V is the phenotypic variance. In the present odel V 0 because o our assuption, necessary to derive the adaptive dynaics, that each sex is onoorphic. With V 0, Slatkin s (1984) condition and condition (6) above are identical. Our analysis also conirs Slatkin s (1984) conjecture that i the syetric equilibriu ( z*, z* ) (0,0) is unstable, then there is a stable asyetric equilibriu ( z*, z* ) given by equation (5), inducing convergence o the evo- lutionary dynaics toward a sexually diorphic state. It is iportant to note, however, that while this equilibriu is an attractor in the two-diensional phenotype space o ale and eale trait values, the equilibriu is not evolutionarily stable. This can be seen by considering the second derivatives o the itness unctions w and w with respect to utant trait values: one can show that both these unctions actually have a iniu at the equilibriu (5) whenever this equilibriu exists. In other words, the diorphic equilibria are theselves potential evolutionary branching points or urther niche partitioning. Nevertheless, the traits will not undergo evolutionary branching in randoly ating populations, or which the diorphic equilibriu (5) thereore represents the evolutionary end state. However, evolutionary branching could occur in principle when ating is assortative. This is exepliied by odels o adaptive speciation (Dieckann and Doebeli 1999). These speciation odels use the sae basic ecological assuptions as the diorphis odel above, but they are dierent in that ales and eales are assued to always have identical ecological phenotypes but ay exhibit nonrando ating. Thus, sexual diorphis and adaptive speciation are expected to occur under siilar ecological conditions, but or dierent genetic assuptions. There are two ain reasons why one ight expect that the two processes would be utually exclusive. First, whichever or o divergence evolves irst would tend to eliinate the disruptive selection necessary to drive the other. Second, positive assortative ating, which is generally deeed necessary or speciation, ight be incopatible with diorphis as long as it is based on ale and eale siilarity in ecological c

4 436 D. I. BOLNICK AND M. DOEBELI traits. Nevertheless, the act that the diorphic equilibriu (5) is an evolutionary branching point could lead to interesting interactions between sexual diorphis and assortative ating. To explore these issues we develop an individual-based nuerical odel with explicit genetics in which both processes can be studied siultaneously. STOCHASTIC MODEL OF SEXUAL DIMORPHISM We irst assue that ating is rando and concentrate on the dynaics o sexual diorphis using individual-based odels with explicit ultilocus genetics. As beore, the population is subject to the ecological dynaics in equations (1 3). Rather than siply assuing each sex is onoorphic, however, each individual is now assigned a genotype that in turn deterines its ecological trait value. In their nuerical odels o sypatric speciation, Dieckann and Doebeli (1999) assigned each diploid individual N loci o equal additive eect. Each locus had two alleles, with phenotypic value 1 or 1. An individual s phenotype value was the su o the additive values o all N alleles, ranging ro N to N. We reer to this as the basic ultilocus approach and use it later in this paper to odel the degree o assortative ating and an unlinked ating phenotype. However, this approach is insuicient or odeling sexual diorphis, because it does not allow one to vary the degree to which ale and eale phenotypes are genetically independent. To odel sexual diorphis, we used a siilar additive diploid ultilocus approach but incorporated loci that are only expressed in one sex or another. The total nuber o loci expressed by any one individual (N total ) can be divided into those loci that are expressed in both sexes (N shared ) and those that are only expressed in ales (N ale ) or eales (N eale ), so N total N shared N ale N shared N eale. This schee relects recent quantitative trait loci (QTL) studies o sexually diorphic quantitative traits that have revealed nuerous sex-speciic QTL (Mogil et al. 1997; Nuzhdin et al. 1997; Agulnik et al. 1998; Gurganus et al. 1999; Raos et al. 1999; Kopp et al. 003). We assue that N ale N eale so that N total is the sae or both sexes. As with the basic odel, each locus has two alleles, with allele j at locus i having two possible values: 1 locusij (7) 1. The value o an individual s ecological phenotype is then the su o the allele values at all the loci that the individual expresses (shared loci plus the loci or the relevant sex): Nshared Nale z locus locus and (8) i j ij i j ij Nshared Neale z locus locus. (9) i j ij i j ij Phenotypes ay range ro N total to N total. In the siulations we standardized the range o traits ro 1 to1, or exaple, we divided the values obtained ro equations (8) and (9) by N total. This schee or explicitly odeling ale and eale ecological character values allows us to anipulate a population s genetic capacity or sexual diorphis. When N shared N total, there are no sex-speciic loci, and hence ale and eale trait eans cannot possibly diverge. As N shared becoes saller the sexes can diverge ore, until their traits are copletely independent at N shared 0. Hence by anipulating the proportion o shared loci (N shared /N total )wecan control a population s potential or sexual diorphis. For the nuerical siulations, we initialize populations by assigning individuals a sex and a genotype, which in turn deterines the individuals ecological phenotype. The distribution o the ecological phenotypes then deterines individual survival probabilities, and hence the ecological dynaics o the population. At each tie step t, each individual survives with probability 1 P(z), (10) r 1 1 n e,z(t) K(z) where z is the individual s trait value, K(z) is the carrying capacity o the phenotype (eq. 1), and n e,z (t) is the eective population size that the individual experiences in the current population. Using the copetition unction c(z, z), equation (), this eective density is calculated as n (t) c(z, z)n (t), (11) e,z z where the su runs over all possible trait values z, and where n z (t) is the nuber o individuals with trait value z. Note that, in slight abuse o notation, we now use the sybol n to denote actual population size rather than population density, because in the individual-based odels we are dealing with actual nubers o individuals. Note also that n e,z (t) includes both ales and eales. Each o the surviving eales reproduces by randoly choosing one o the surviving ales as a ate and then producing a nuber o ospring drawn ro a Poisson distribution with ean r. The genotype o each ospring is deterined probabilistically ro the parent genotypes under the assuptions o Mendelian segregation within loci and ree recobination between loci. Each allele in the ospring has a probability o reversing its value due to utation. This unusually high utation rate was chosen to speed up the siulations. (We note that our genetic architecture can be understood ore generally as describing independent stretches o DNA o variable length that aect the trait under consideration additively and that recobine reely with other such stretches o DNA. In particular, such stretches ight be uch longer than a single locus, hence the utation rate per such stretch ight be quite high.) The ospring is randoly ade ale or eale with equal probability, which then deterines the subset o loci it will use to express its ecological trait z. The resulting population o ospring is then subjected again to ecological dynaics and ating, and this generational cycle is repeated iteratively. An exaple o the evolutionary dynaics o ale and eale trait values eerging ro this individual-based odel is shown in Figure 1 or a case when N shared /N total 0.4. The population was initialized with all individuals having an ecological phenotype o z 1 (all loci ixed with z

5 SEXUAL DIMORPHISM AND ADAPTIVE SPECIATION 437 FIG. 1. Siulation o the evolution o sexual diorphis as ale (A) and eale (B) phenotype distributions change over tie in response to resource copetition. Darker shading indicates a greater nuber o individuals o a given phenotype at a given tie. The horizontal line at 0.0 in (A) and (B) indicates the location o the axiu o the carrying capacity curve. Fitness unctions are shown or generation 10 (C), 00 (D), and 400 (E), with the ean phenotypes or ales ( ) and eales (). The dashed vertical line arks the onset o sexual diorphis. Both sexes were initially onoorphic or the ecological trait z 1.0. N shared /N total 0.4, s 10, K , k 1.0, c 0.5, r 5, 0.001, N total 10, N assort 5. allele values o 1), and both ales (Fig. 1A) and eales (Fig. 1B) quickly evolved under directional selection (Fig. 1C) toward the density-dependent phenotypic optiu o z 0. As the population ean approached this optiu, it cae under disruptive selection due to requency-dependent copetition (Fig. 1D). A sexual diorphis then evolved (Fig. 1A, B), lattening the itness unction so that all phenotypes had nearly equal itness (Fig. 1E). Siilar dynaics are seen or any run in which c k and N shared / N total is less than one. The direction o the resulting diorphis (z z or z z ) is arbitrary and varies between replicate siulations. The degree o sexual diorphis that results ro disruptive selection is sensitive to two sets o paraeters. The ecological paraeters k and c deterine the location o the diorphic equilibriu given by equation (5), to which ales and eales will evolve in the nongenetic, analytical odel o the previous section. However, in the genetic in-

6 438 D. I. BOLNICK AND M. DOEBELI FIG.. The agnitude o ecological sexual diorphis depends on the proportion o loci shared between ales and eales (N shared / N total ).The agnitude o diorphis is easured by the absolute value o Student s t-statistic. The horizontal line at t indicates the cut-o below which diorphis is not statistically signiicant. Paraeter values were: s 10, K , k 0.75, c 0.5, r 5, 0.001, N total 10, N assort 5, with 10 replicates or each value o N shared /N total, run or 1000 generations each. dividual-based odel, N shared /N total can constrain whether the sexes are able to evolve to these values, as illustrated in Figure. When between-sex covariance is high, the sexes are unable to diverge and so the population reains at the interediate phenotype value z 0, subject to a stable itness iniu. Such persistent disruptive selection is the starting point or adaptive speciation (Dieckann and Doebeli 1999). In the next section we incorporate assortative ating echaniss into our individual-based odel to illustrate that when N shared / N total 1 the population can escape ro the itness iniu via speciation. We then cobine the assortative ating odel with variable values o N shared /N total to investigate how speciation and sexual diorphis interact. STOCHASTIC MODEL OF ADAPTIVE SPECIATION As beore, all individuals possess an ecological phenotype deterined by the additive eect o N total diallelic loci. The ecological dynaics reain the sae, but in contrast to the preceding section, N shared N total so diorphis is ipossible, and eales ay choose their ate nonrandoly. Assortative ating is described by a ate-choice unction (Fig. 3) that deterines the probability o a given eale accepting a given ale as a ate. Feales vary with respect to a new quantitative genetic trait or assortability, a, which deterines the degree to which a eale ates assortatively. As with the ecological trait, the value o a represents the su o allele values o N assort independent diallelic loci, standardized to range ro 1 to 1. While the N assort loci are present in both ales and eales and inherited according to noral Mendelian rules, only eales express their assortability, in keeping with eale-liited ating (see Appendix). Negative values o a coner disassortative ating, positive values lead to positive assortative ating, and values near zero produce rando ating. The probability that a eale with assortative phenotype a and ecological trait z will ate with a ale with ecological trait z is described by the ollowing ate-choice unction (Fig. 3): P(a, z, z ) [ ] 1 a exp z z or a 0 s 1 or a 0 (1) [ 1 a ] exp ( z z ) or a 0. s Here s is a scaling paraeter that deterines the slope o the ate-choice unction. Large values o s latten the unction P(a, z,z ) or all a (Fig. 3B), so that all phenotypes are equally acceptable, in which case even eales with assortative trait values a close to 1 or 1 will ate randoly. As s decreases, the probability that a eale ates with a phenotypically dierent (phenotypically siilar) ale drops o ore and ore rapidly or eales with positive (negative) values o a (see Fig. 3A). In the nuerical siulations, we assued that every surviving eale ates, iplying that the ate-choice unction (1) only deterines the relative probabilities with which each ale is chosen by a particular eale. Thus, we assued that there is no cost to a eale or assortative ating (see Discussion), though ales with rare ecological phenotypes are penalized. Siulations in which diorphis was restricted (i.e., N shared /N total 1), and eales initially ated randoly, on average, conired that adding the potential or assortative ating allowed populations to escape their stable itness inia at z 0 via speciation. The results o one such siulation are illustrated in Figure 4. The population was initialized with equal probabilities o 1 and 1 alleles at all ating loci so trait a is polyorphic with ean zero. The population initially evolves toward the itness peak corresponding to the ost abundant resource (z 0) and the directional selection changes to disruptive selection as the population approaches z 0. Assortative ating then evolves in a process analogous to reinorceent (Fig. 4C). This allows the population to split into two ecologically distinct species, as shown by the branching in both ales and eales (Fig. 4A, B). Note that because o strong assortative ating, the two eerging species are reproductively isolated. The increase in phenotypic variation resulting ro evolutionary branching equalizes the itness across dierent phenotypes, lattening the itness unction (Fig. 4F). SIMULTANEOUS MODEL OF DIMORPHISM AND SPECIATION Given that disruptive selection can result in either sexual diorphis or sypatric speciation, we now turn to the question o which outcoe is ore likely when considered siultaneously. Because both ors o divergence have identical ecological prerequisites ( c k ), we ocus our attention on the potentially iportant genetic paraeters o this odel: N shared /N total and s. The orer paraeter puts an upper bound

7 SEXUAL DIMORPHISM AND ADAPTIVE SPECIATION 439 FIG. 3. The probability that a eale ates with a ale is given by the ating unction, equation (1), and depends on the dierence in their ecological (or arker) phenotypes, and on the eale s degree o assortative ating, a. In addition, the paraeter s in equation (1) deterines the shape o the ate choice unction. Lower values o s steepen the surace and correspond to a higher genetic potential or assortative ating (A), whereas higher values o s latten the surace and correspond to a lower genetic potential or assortative ating (B). on the extent o phenotypic divergence between the sexes, and the latter deterines how ast ating becoes strongly assortative when the ating trait changes ro 0 to 1 or 1. We investigated the relative robustness o each evolutionary outcoe by actorially varying each paraeter: (N shared /N total 0, 0.1, 0.,...,1.0; s 0.0, 0.05, 0.03,...,0.1). This was done or a ixed ecological scenario. Our extensive nuerical siulations showed that all the results reported below hold qualitatively or any ecological scenario avoring divergence. For each cobination o the two paraeters N shared / N total and s we ran 10 replicate nuerical siulations. All siulations started with populations that were phenotypically variable with a ean o zero (equal probability or each allele at all ecological and ating loci) or the evolving characters and were run or 000 generations. Three ain observations eerge ro these siulations. First, speciation is inhibited in populations with a high capacity or sexual diorphis (Fig. 5A). Second, diorphis is inhibited in populations with a high capacity or assortative ating (Fig. 5B). Third, contrary to our initial expectations it is possible to siultaneously achieve diorphis and speciation (Fig. 5C). We discuss each o these conclusions in turn. It is not surprising that speciation was ost coon in the area o paraeter space with the highest potential assortative ating (s 0.04, Fig. 5A). However, the requency o speciation declines as the population s potential or sexual diorphis increases (lower values o N shared /N total, Fig. 5A), even when s is very sall. This inhibition could relect either a direct conlict between assortative ating and diorphis or an indirect eect ediated via the itness unction. As noted above, diorphis eliinates disruptive selection (Fig. 1E), so i diorphis is aster, it ay reove the ipetus or speciation. Additional siulations conired that diorphis tends to evolve ore quickly than speciation. We ran 50 replicate siulations or each o three genetic systes, noting the tie to diorphis or speciation in each run. When diorphis was the only possible result (N shared /N total 0, s 10), it evolved aster than the ean tie to speciation when speciation was the only possibility (N shared /N total 1, s 0.05; c. Fig. 6A and 6B). Siilarly, when the two processes were allowed to copete within a single siulation (N shared /N total 0.4, s 0.05), the ean tie to diorphis was uch shorter than the tie to speciation (c. Fig. 6C and 6D). This dierence relects the act that disruptive selection can act directly on ale and eale ecological traits, but only indirectly on the level o assortative ating. Although the potential or diorphis reduces the probability o speciation, the reverse is also true. When the potential or assortative ating was weak (s 0.1), diorphis evolved or all values o N shared /N total except N shared /N total 1 (Fig. 5B), where diorphis is ipossible. However, as the potential or assortative ating increased (lower values o the ating paraeter s), diorphis becae less coon, restricted to situations where the sexes were largely independent (N shared /N total 0.5). Speciation can inhibit sexual diorphis in several ways. First, because both processes rely on stochastic eects, speciation occasionally occurs beore, and thus preepts, sexual diorphis (16 o 50 siulations or Fig. 6C, D). Second, there is a undaental antagonis between positive assortative ating and a sexual diorphis: eales cannot siultaneously preer ates that are ost like theselves ecologically and still aintain an ecological sexual diorphis. I soe degree o positive assortative ating (but not ull speciation) evolves beore a sexual diorphis, this will liit the degree to which the sexes ay partition resources, because ecologically divergent ales will be eliinated by sexual selection.

8 440 D. I. BOLNICK AND M. DOEBELI FIG. 4. Siulation o speciation in response to resource copetition. Male (A) and eale (B) phenotype distributions initially evolve toward the ode o the resource distribution, ater which the level o assortative ating increases (C) and branching occurs in both sexes, indicating speciation. Darker shading indicates a greater nuber o individuals o a given phenotype at a given tie. Fitness unctions are shown or generation 10 (D), 100 (E), and 190 (F). Dashed vertical lines indicate the points in tie corresponding to each itness unction. The ean phenotypes or ales ( ) and eales () are arked on the itness unctions. Both sexes were initially onoorphic or the ecological trait z 1.0 and polyorphic or assortativeness with ean a 0. Paraeter values were: N shared / N total 1.0, s 0.05, K , k 1.0, c 0.5, r 5, 0.001, N total 10, N assort 5. The third liit to sexual diorphis depends heavily on N shared /N total. I the axiu distance between the sexes is genetically constrained to be less than the distance between the two stable phenotypic optia, equation (5), sexual diorphis will be insuicient to eliinate the disruptive selection. Diorphis ight then evolve teporarily (because it is aster than speciation), but be replaced by speciation, which can ore eectively equalize itness across phenotypes. An exaple o this sequential sexual diorphis and speciation is shown in Figure 7. A population initially centered on the resource optiu (z 0) is subject to disruptive selection (Fig. 7D) in period a (generations 0 to 90), ater which a slight diorphis evolves (period b). The degree o diorphis is liited by genetic constraints (N shared /N total 0.7). Because phenotypic divergence is liited, the itness unction does not latten greatly and the total population size

9 SEXUAL DIMORPHISM AND ADAPTIVE SPECIATION 441 reains low, though arginally higher than in period a (Fig. 7F). This sexual diorphis then collapses, returning to a period o interediate ecological phenotypes, disruptive selection, low population size, but increasing assortative ating (period c). When assortative ating is strong enough speciation occurs (period d). With the advent o speciation, the phenotype distributions o both sexes biurcate, assortative ating reains consistently high, disruptive selection ceases (Fig. 7E), and population sizes increase draatically (Fig. 7F). This last eect is particularly noteworthy because it indicates that the higher phenotypic variance has increased the overall carrying capacity o the population an eect that was not achieved by the genetically constrained sexual diorphis. So ar we have shown that speciation and ecological sexual diorphis are utually antagonistic. Diorphis can preept speciation, whereas assortative ating can restrict or soeties replace diorphis. It was thereore surprising to ind soe siulations that resulted in both sexual diorphis and speciation (Fig. 5C). In contrast to previous odels o adaptive speciation, in this case speciation entails strong negative, rather than positive, assortative ating. The ecological phenotype distributions o both sexes becoe biodal, with the two ale odes toward the phenotype extrees, and the eale odes closer to the interior (Fig. 8). Thus, each group o eales is urthest ro a dierent group o ales. Due to strong negative assortative ating, each group o eales ates with the ales ecologically least like the, rejecting the ore phenotypically siilar ales. Note that the existence o our phenotypic clusters in this scenario is a relection o the act the diorphic equilibriu (5) in the analytical odel is an evolutionary branching point: with negative assortative ating and concoitant speciation into two sexually diorphic species, a iner partitioning o niche space is possible than with sexual diorphis alone. However, this particular outcoe is rare because it requires a inely balanced set o paraeters. Assortative ating ust be strong enough to aintain two species, while N shared /N total ust be sall enough to allow diorphis yet not so sall that diorphis preepts speciation. Assortative Mating Based on Marker Phenotypes In this section we investigate to what extent the conlict between diorphis and speciation carries over to cases in which assortative ating is not based on traits under ecological selection, but instead on ecologically neutral arker traits, such as coloration. For speciation to occur in this situation, a linkage disequilibriu between the arker trait and the ecological trait ust develop, so that assortative ating can indirectly latch onto the ecological trait. Classically, recobination between the arker and the ecological trait is expected to severely ipede speciation with this type o as- FIG. 5. Shaded contour plots indicate requency o speciation (A), sexual diorphis (B), and cases o siultaneous diorphis and speciation (C) as a unction o the potential or assortative ating (s) and the genetic independence o the sexes (N shared /N total ). For each cobination o paraeter values, we ran 10 siulations or 000 generations. The proportion o runs resulting in a particular outcoe is indicated by the shading, ranging ro white (0%) to black (100%). Populations were initially polyorphic or both ecological and ating traits with eans o zero. K , k 1.0, c 0.5, r 5, 0.001, N total 10, N assort 5.

10 44 D. I. BOLNICK AND M. DOEBELI FIG. 6. Box plots o the tie to diorphis (dark boxes) or speciation (light boxes), showing quartiles (boxes), 95% conidence intervals (horizontal lines), and outliers (dots) or 50 replicates o each o three scenarios (A, B, and C/D). (A) Diorphis only, due to rando ating (s 10) and coplete independence between ale and eale ecological phenotypes (N shared /N total 0). (B) Speciation only, due to potentially strong assortative ating (s 0.05) and sexes are not independent (N shared /N total 1). Speciation (B) occurs an order o agnitude ore slowly than sexual diorphis (A), t , P When both speciation (C) and diorphis (D) are possible outcoes o a single siulation (s 0.05, N shared /N total 0.4), diorphis still occurs ore rapidly (t , P ), although 16 o 50 replicate siulations led to speciation irst and ailed to evolve a sexual diorphis. Paraeter values K , k 0.75, c 0.5, r 5, 0.001, N total 10, N assort 5, with 5000 generations per siulation. sortative ating (Felsenstein 1981). However, Dieckann and Doebeli (1999) have shown that this expectation is in act unwarranted, and that speciation can easily occur even in this scenario, albeit or slightly ore restrictive ecological paraeters than in the case where assortative ating is based on the ecological trait. Following Dieckann and Doebeli (1999), we incorporate arker-based assortative ating by assuing that there is a third set o N arker diallelic loci deterining an ecologically neutral trait that is expressed in both sexes. As beore, ating depends on assortability trait a, and ay be disassortative, rando, or assortative to varying degrees, but now ate choice, equation (1), is based not on siilarity in the ecological trait, but in the neutral arker trait. Thus, in Figure 3 the x-axis now represents the dierence in the value o the arker trait between two potential ating partners, which varies between N arker and N arker. It is assued that the arker loci reely recobine with all the other loci. In accordance with the results o Dieckann and Doebeli (1999), adaptive speciation occurs in our odels with arker-based assortative ating i N shared N total, and i the paraeter s scaling the assortative ating unction is low enough.. However, i N shared N total, a new type o evolutionary dynaics can be seen, during which the ancestral population splits into two sexually diorphic descendant species with positive assortative ating (Fig. 9). Two clusters o individuals exist at opposite ends o the arker trait axis, representing two reproductively isolated species with high assortativeness. Within each species ale and eale ecological traits are diorphic. Thus, assortative ating based on a arker trait can alleviate the antagonis between sexual diorphis and positive assortative ating: as long as the sexes have the sae arker trait (and hence ate with each other), they or a species even i they are ecologically dierentiated. Note again that sexual diorphis together with speciation due to arker-based assortative ating allows or iner niche partitioning than either sexual diorphis or speciation would i they occurred alone. Although ating based on a arker trait alleviates one o the sources o conlict between diorphis and speciation, the region o paraeter space in which speciation occurs is ore liited than seen or ating based on ecological traits. This is illustrated in Figure 10, or which we used the sae nuerical procedure as or Figure 5, except that single runs were continued or 5000 generations (to allow or the potentially slow process o linkage disequilibriu build-up). Even or low values o the scaling paraeter s, speciation will not occur when N shared /N total is uch less than one. Instead it appears that sexual diorphis is acilitated, as it is no longer countered by any positive assortative ating. Dieckann and Doebeli (1999) noted that the tie to speciation was uch longer when assortative ating was based on a arker trait than when based on the ecological traits, a result also seen in our siulations. Consequently sexual diorphis will alost always occur beore speciation in this case and eliinate or reduce the disruptive selection needed to drive speciation. The exception is when N shared /N total restricts the degree o diorphis, so that the sexes cannot diverge all the way to the ecologically deterined optia. Disruptive selection is then aintained until speciation occurs in addition to the diorphis, ore eectively equalizing copetition across phenotypes. DISCUSSION Although it is now widely accepted that adaptive speciation is both theoretically plausible (Turelli et al. 001; Dieckann et al. 003) and has been established epirically in at least a ew cases (Schliewen et al 1994, 001; Berlocher and Feder 00; Dres and Mallet 00), its generality reains contentious (Barraclough and Vogler 000; Coyne and Price 000). We thereore eel that it is useul to ove theoretical work away ro showing that adaptive speciation is possible to ore directly considering the conditions under which it is ore and less likely. For exaple, the odel by Dieckann and Doebeli (1999) highlighted the iportance o withinpopulation niche variation ( c k ) in generating requencydependent disruptive selection. This acilitates epirical study because inoration about the degree and requency o within-population variation (Bolnick et al. 00, 003) then tells us about the range o species likely to experience the ecologically ediated disruptive selection necessary or adaptive speciation. In this paper we have illustrated one way in which theory can shit ro considering easibility o adaptive speciation toward considering its expected requency o occurrence. Previous studies lead one to believe that speciation is likely

11 SEXUAL DIMORPHISM AND ADAPTIVE SPECIATION 443 FIG. 7. A siulation resulting in successive sexual diorphis and speciation. The ale (A) and eale (B) ecological phenotype distributions, and assortative ating distributions (C) are divided into our teporal regions, a, b, c, and d. These regions correspond to a: a period o disruptive selection (D), b: a period o weak sexual diorphis. Note that the ale distribution (A) is below the dark horizontal reerence line, whereas the eale distribution (B) is above the reerence line. Assortative ating becoes negative (C), because eales ust choose ales with phenotype traits dierent ro their own. The diorphis is weak due to genetic constraints. c: sexual diorphis is lost, d: speciation, indicated by biurcation o both sexes ecological traits (A, B), and high assortative ating (C). Following speciation (in period d), the itness unction is lattened (E), and population sizes increase due to reduced intraspeciic copetition (F). Populations were initially polyorphic or both ecological and ating traits with eans o zero. N shared /N total 0.7, s 0.05, K , k 0.75, c 0.5, r 5, 0.001, N total 10, N assort 5. whenever the necessary ecological conditions are ulilled (e.g., when c k ). In contrast, we have taken the view here that once disruptive selection has eerged ro the ecological interactions, it can have ore than one outcoe. Speciically, we have studied the relative likelihood with which disruptive selection leads to sexual diorphis or adaptive speciation. In doing so we have ound that the genetic basis o ale and eale ecological traits greatly aects whether a population will undergo speciation even when the ecological dynaics are suicient. Under the assuptions o our odel, a population with a large capacity or sexual diorphis is less likely to undergo speciation. Our siulations suggest two ain reasons why sexual diorphis and speciation are utually antagonistic outcoes o requency-dependent disruptive selection. First, there is a undaental conlict between sexual diorphis and a e-

12 444 D. I. BOLNICK AND M. DOEBELI FIG. 8. Siultaneous speciation and sexual diorphis in which assortative ating is based on ecological traits. A histogra o ale ecological traits (A) shows two ecological groups at z 1 and z 1. Feales (B) express both ecological and assortative ating traits, so their phenotype distribution is shown as a density plot (darker shading indicates ore individuals). Feales have split into two ecological groups, each with strong negative assortative ating. Straight lines connect conspeciic ales and eales, whereas phenotypically siilar ales and eales ail to ate due to negative assortative ating. N shared /N total 0., s 0.05, K , k 1.0, c 0.5, r 5, 0.001, N total 10, N assort 5. FIG. 9. Siultaneous speciation and sexual diorphis in which assortative ating is based on a neutral arker trait. Joint ecological and ating arker phenotype distributions are shown or ales (A) and eales (B). Due to strong positive assortative ating, ales and eales with high arker values (connected by a line) constitute one species, and ales and eales with low arker values (connected by a line) constitute a second species. Each o these species is ildly sexually diorphic. N shared /N total 0.4, s 0.05, K , k 1.0, c 0.5, r 5, 0.001, N total 10, N assort 5, N arker 5. ale s ability to choose a ate phenotypically like hersel. This conlict can be resolved i eales ate preerences are based on independent arker cues (e.g., color), rather than ecologically iportant diorphic traits. Alternatively, it is possible or speciation and diorphis to occur siultaneously when the speciation is based on negative assortative ating. Such dual diversiication is consistent with our analytical and siulation observation that each two-species or diorphic equilibriu is itsel a slight itness iniu (see Figs. 1E, 4F) and hence ay lead to still iner niche partitioning through successive speciation events. Our genetic siulations are too coarse to observe iner partitioning than the cobined speciation and diorphis. The second reason or the antagonis is indirect, ediated by changes in the shape o the itness unction. Both ecological sexual diorphis and adaptive speciation reduce or eliinate disruptive selection by equalizing the eect o copetition across phenotypes. Consequently, the outcoe that occurs irst will eliinate the selective orce that is needed to drive the alternative evolutionary outcoe. Our siulations consistently ound that sexual diorphis evolved aster than speciation, presuably because selection acts directly on the ecological traits but only indirectly on ating behavior. Only i diorphis is insuicient to eliinate disruptive selection, such as when the sexes cannot diverge enough to reach the ecologically deterined optia due to genetic con-

13 SEXUAL DIMORPHISM AND ADAPTIVE SPECIATION 445 FIG. 10. Shaded contour plots indicate requency o speciation (A), sexual diorphis (B), and siultaneous speciation and diorphis (C), when ate choice is based on an independent arker trait such as color, as a unction o the potential or assortative ating (s), and the genetic independence o the sexes (N shared /N total ). For each cobination o paraeter values, we ran 10 siulations or 5000 generations. The proportion o runs resulting in a particular outcoe is indicated by the shading, ranging ro white (0%) to black (100%). Populations were initially polyorphic or both ecological and ating traits with eans o zero. K , k 1.0, c 0.5, r 5, 0.001, N total 10, N assort 5, N arker 5. straints, can speciation ollow, either replacing or copleenting the diorphis. As with any theoretical odel, it is iportant to bear in ind the underlying assuptions and their consequences. In the context o this odel, soe noteworthy assuptions include the choice o particular ecological equations, the syetrical resource distributions and copetition unctions, constant individual niche widths ( c ), the absence o resource population dynaics or evolution, the schee or siulating genetic independence o ale and eale traits, and the lack o any cost o assortative ating or eales. Our results are robust to changes in any o these assuptions. For exaple, we chose one o a nuber o alternative ways to odel genetic divergence between sexes. Alternative schees could include loci that have opposite sex-dependent eects, speciically control diorphis, or arrest growth earlier in one sex than another. While our choice appears to be biologically reasonable based on QTL studies o diorphic traits (Mogil et al. 1997; Nuzhdin et al. 1997; Agulnik et al. 1998; Gurganus et al. 1999; Raos et al. 1999; Kopp et al. 003), the particular choice o genetic odel is not likely to be critical. Slatkin s (1984) odel o ecological sexual diorphis concluded that a sexual diorphis is possible whenever the genetic correlation between sexes is less than one, so dierent approaches to incorporate explicit genetics should yield equivalent results. Siilarly, adding a (sall) cost to assortative ating does not qualitatively change our results (D. I. Bolnick and M. Doebeli, unpubl. siulations). Also, asyetrical copetition has been shown to induce evolutionary branching (Kisdi and Geritz 1999; Doebeli and Dieckann 000), and hence the ecological preconditions or sexual diorphis as well. However, with asyetrical copetition the evolutionary branching point is not located at the resource axiu K 0, and the eerging phenotypic clusters have dierent population sizes, which ay have quantitative eects on the evolution o sexual diorphis because one sex will tend to be rarer than the other. Other assuptions ay prove to be ore critical to our results. For instance, i individual niche widths ( c ) were allowed to evolve, niche expansion ight occur ost quickly through increased within-phenotype niche width rather than increased between-phenotype variation (Taper and Case 1985). However, it is epirically quite reasonable to assue an upper liit on c relecting unctional or cognitive tradeos that ipose liits on individual niche breadth. Such trade-os are known to aintain individual specialization in a wide range o taxa (Bolnick et al. 003). Our results ight also be sensitive to reoving our assuption that the resource distribution neither evolves nor shows a nuerical response to predation. The addition o interspeciic copetitors would also greatly change the dynaics, as rare phenotypes that would otherwise have been avored by disruptive selection are subject to copetitive exclusion by other species. Finally, we have assued that the ecological traits whose evolution we study aect viability, but not ertility, o individuals. This assuption is in line with any previous theoretical studies, and it ultiately originates in the observation that the ertility r has no qualitative eect on the dynaics o two-species Lotka-Volterra copetition odels.