Analysis of partial assortative mating and sexual selection models for a polygamous species involving a trait based on levels of heterozygosity

The consequences of preferential mating in the presence of partial assortative and sexual selection mechanisms are ascertained for a two-allele one-locus trait involving two phenotype classes C₁ = {all homozygotes} and C₂ = {heterozygotes}. Relevant biological cases may include Burley (1977, Proc. Nat. Acad. Sci. USA74, 3476–3479), Wilbur et al. (1978, Evolution32, 264–270), and Singh and Zouros (1978, Evolution32, 342–353). When the preference rate for the heterozygote exceeds that for homozygotes, it is established that the unique stable state is the central Hardy-Weinberg equilibrium. The rate of approach is faster with sexual selection than for the corresponding model of assortative mating. When the preference rates favor the homozygotes then in this symmetric model of sexual selection two asymmetric Hardy-Weinberg polymorphisms can evolve, and which succeeds depends on initial conditions. The models are also analyzed with natural selection acting on phenotypes superimposed on assortative mating. In this case we can have up to three coexisting stable states involving both fixation alternatives and a central polymorphism. The corresponding model with sexual selection maintains either the central equilibrium as in assortative mating or two asymmetric polymorphic equilibria.     

Sensory drive speciation and patterns of variation at selectively neutral genes

Speciation by sensory drive can occur if divergent adaptation of sensory systems causes rapid evolution of mating traits and the resulting development of assortative mating. Previous theoretical studies have shown that sensory drive can cause rapid divergent adaptive evolution from one to two phenotypes. In this study, we examined two topics: the possibility of adaptive radiation by sensory drive from one to more than two phenotypes and the relationships of patterns of variation at selectively neutral genes to levels of viability selection, habitat and mating preferences and migration. We conducted individual-based simulations assuming a sensory trait and a mating trait controlled by a small number of loci. We found that adaptive radiation is possible when the number of loci controlling the sensory trait is small; the levels of viability selection, habitat and mating preferences are intermediate; and the emigration rate is high. We also found that emigration rates as well as the levels of habitat and mating preferences are related to F _ST values at neutral loci, but F _ST proved to be insensitive to a small change in the number of loci controlling the mating trait. This suggests that an estimation of the past population history is possible without an accurate genetic model.     

Sexual dimorphism and adaptive speciation: two sides of the same ecological coin

Models of adaptive speciation are typically concerned with demonstrating that it is possible for ecologically driven disruptive selection to lead to the evolution of assortative mating and hence speciation. However, disruptive selection could also lead to other forms of evolutionary diversification, including ecological sexual dimorphisms. Using a model of frequency-dependent intraspecific competition, we show analytically that adaptive speciation and dimorphism require identical ecological conditions. Numerical simulations of individual-based models show that a single ecological model can produce either evolutionary outcome, depending on the genetic independence of male and female traits and the potential strength of assortative mating. Speciation is inhibited when the genetic basis of male and female ecological traits allows the sexes to diverge substantially. This is because sexual dimorphism, which can evolve quickly, can eliminate the frequency-dependent disruptive selection that would have provided the impetus for speciation. Conversely, populations with strong assortative mating based on ecological traits are less likely to evolve a sexual dimorphism because females cannot simultaneously prefer males more similar to themselves while still allowing the males to diverge. This conflict between speciation and dimorphism can be circumvented in two ways. First, we find a novel form of speciation via negative assortative mating, leading to two dimorphic daughter species. Second, if assortative mating is based on a neutral marker trait, trophic dimorphism and speciation by positive assortative mating can occur simultaneously. We conclude that while adaptive speciation and ecological sexual dimorphism may occur simultaneously, allowing for sexual dimorphism restricts the likelihood of adaptive speciation. Thus, it is important to recognize that disruptive selection due to frequency-dependent interactions can lead to more than one form of adaptive splitting.     

Revisiting santa rosalia to unfold a degeneracy of classic models of speciation

Abstract Many classic models of speciation incorporate assortative mating based on mating groups, such as plants with different flowering times, and they investigate whether an ecological trait under disruptive natural selection becomes genetically associated with the selectively neutral mating trait. It is well known that this genetic association is potently destroyed by recombination. In this note, we point out a more fundamental difficulty: if a "knife-edge" symmetry assumption of previous models is violated, then the mating trait is no longer neutral and sexual selection eliminates the polymorphism in the mating locus. This result strengthens the growing consensus that magic traits are the more likely route to nonallopatric speciation. We expand the model assuming also ecological selection on the mating trait and investigate the conditions for natural selection to overcome sexual selection and maintain mating polymorphism; we find that the combination of natural and sexual selection can cause also bistability of allele frequencies.     

Some multiallele partial assortative mating systems for a polygamous species

The consequences of preferential mating in the presence of partial assortative and sexual selection mechanisms are ascertained for a two-allele one-locus trait involving two phenotype classes C₁ = {all homozygotes} and C₂ = {heterozygotes}. Relevant biological cases may include Burley (1977, Proc. Nat. Acad. Sci. USA 74, 3476–3479), Wilbur et al. (1978, Evolution 32, 264–270), and Singh and Zouros (1978, Evolution 32, 342–353). When the preference rate for the heterozygote exceeds that for homozygotes, it is established that the unique stable state is the central Hardy-Weinberg equilibrium. The rate of approach is faster with sexual selection than for the corresponding model of assortative mating. When the preference rates favor the homozygotes then in this symmetric model of sexual selection two asymmetric Hardy-Weinberg polymorphisms can evolve, and which succeeds depends on initial conditions. The models are also analyzed with natural selection acting on phenotypes superimposed on assortative mating. In this case we can have up to three coexisting stable states involving both fixation alternatives and a central polymorphism. The corresponding model with sexual selection maintains either the central equilibrium as in assortative mating or two asymmetric polymorphic equilibria.     

Comparisons of positive assortative mating and sexual selection models

A series of theoretical models of positive assortative mating and sexual selection are contrasted. It is established that for a dominant trait partial positive assortative mating generally implies some fixation, whereas sexual selection exhibits a unique globally stable polymorphism exhibiting Hardy-Weinberg proportions. The effects of monogamy against polygamy do not qualitatively alter the equilibrium outcomes, although the rate of evolutionary change is generally slowed with monogamy vis-à-vis polygamy. For sexual selection the influence of timing of random mating as against preferential mating causes no change in the equilibrium states, although the rates of convergence can be slowed if sexual selection occurs late in the breeding season. Under assortative mating the timing can alter the equilibrium outcomes. The amount of heterozygosity is always deficient in cases of assortative mating, but always exhibits Hardy-Weinberg ratios under a sexual selection mechanism. This suggests that observations consistent with Hardy-Weinberg equilibrium states cannot preclude ipso facto certain forms of selection forces, including mating patterns and some natural selection structures.     

Effects of female preference intensity on the permissiveness of sexual trait polymorphisms

Recent developments in sexual selection theory suggest that on their own, mate preferences can promote the maintenance of sexual trait diversity. However, how mate preferences constrain the permissiveness of sexual trait diversity in different environmental regimes remains an open question. Here, we examine how a range of mate choice parameters affect the permissiveness of sexual trait polymorphism under several selection regimes. We use the null model of sexual selection and show that environments with strong assortative mating significantly increase the permissiveness of sexual trait polymorphism. We show that for a given change in mate choice parameters, the permissiveness of polymorphism changes more in environments with strong natural selection on sexual traits than in environments with weak selection. Sets of nearly stable polymorphic populations with weak assortative mating are more likely to show accidental divergence in sexual traits than sets of populations with strong assortative mating. The permissiveness of sexual trait polymorphism critically depends upon particular combinations of natural selection and mate choice parameters.     

A combination of sexual and ecological divergence contributes to rearrangement spread during initial stages of speciation

Chromosomal rearrangements between sympatric species often contain multiple loci contributing to assortative mating, local adaptation and hybrid sterility. When and how these associations arise during the process of speciation remains a subject of debate. Here, we address the relative roles of local adaptation and assortative mating on the dynamics of rearrangement evolution by studying how a rearrangement covaries with sexual and ecological trait divergence within a species. Previously, a chromosomal rearrangement that suppresses recombination on the Z (sex) chromosome was identified in European corn borer moths (Ostrinia nubilalis). We further characterize this recombination suppressor and explore its association with variation in sex pheromone communication and seasonal ecological adaptation in pairs of populations that are divergent in one or both of these characteristics. Direct estimates of recombination suppression in pedigree mapping families indicated that more than 39% of the Z chromosome (encompassing up to ~10 megabases and ~300 genes) resides within a nonrecombining unit, including pheromone olfactory receptor genes and a major quantitative trait locus that contributes to ecotype differences (Pdd). Combining direct and indirect estimates of recombination suppression, we found that the rearrangement was occasionally present between sexually isolated strains (E vs. Z) and between divergent ecotypes (univoltine vs. bivoltine). However, it was only consistently present when populations differed in both sexual and ecological traits. Our results suggest that independent of the forces that drove the initial establishment of the rearrangement, a combination of sexual and ecological divergence is required for rearrangement spread during speciation.     

Flexible mate choice may contribute to ecotype assortative mating in pumpkinseed sunfish (Lepomis gibbosus)

Gene flow is expected to limit adaptive divergence, but the ecological and behavioural factors that govern gene flow are still poorly understood, particularly at the earliest stages of population divergence. Reduced gene flow through mate choice (sexual isolation) can evolve even under conditions of subtle population divergence if intermediate phenotypes have reduced fitness. We indirectly tested the hypothesis that mate choice has evolved between coexisting littoral and pelagic ecotypes of polyphenic pumpkinseed sunfish (Lepomis gibbosus) that have diverged in morphology and resource use and where intermediate phenotypes have reduced performance. We assessed the ecotype of nesting males and females using stable isotope estimates of diet and a divergent male morphological trait, oral jaw width. We found positive assortative mating between ecotypes in a common spawning habitat along exposed lake shorelines, but contrary to expectations, assortative mating was variably expressed between two sampling years. Although the factors that influence variable assortative mating remain unclear, our results are consistent with mate choice being expressed by ecotypes. Despite being variably expressed, mate choice will reduce gene flow between ecotypes and could contribute to further adaptive divergence depending on its frequency and strength in the population. Our findings add to a growing body of evidence indicating mate choice behaviour can be a plastic trait, an idea that should be more explicitly considered in empirical studies of mate choice as well as conceptual frameworks of mate choice evolution and adaptive divergence.     

Frequency-dependent selection and the evolution of assortative mating

A long-standing goal in evolutionary biology is to identify the conditions that promote the evolution of reproductive isolation and speciation. The factors promoting sympatric speciation have been of particular interest, both because it is notoriously difficult to prove empirically and because theoretical models have generated conflicting results, depending on the assumptions made. Here, we analyze the conditions under which selection favors the evolution of assortative mating, thereby reducing gene flow between sympatric groups, using a general model of selection, which allows fitness to be frequency dependent. Our analytical results are based on a two-locus diploid model, with one locus altering the trait under selection and the other locus controlling the strength of assortment (a "one-allele" model). Examining both equilibrium and nonequilibrium scenarios, we demonstrate that whenever heterozygotes are less fit, on average, than homozygotes at the trait locus, indirect selection for assortative mating is generated. While costs of assortative mating hinder the evolution of reproductive isolation, they do not prevent it unless they are sufficiently great. Assortative mating that arises because individuals mate within groups (formed in time or space) is most conducive to the evolution of complete assortative mating from random mating. Assortative mating based on female preferences is more restrictive, because the resulting sexual selection can lead to loss of the trait polymorphism and cause the relative fitness of heterozygotes to rise above homozygotes, eliminating the force favoring assortment. When assortative mating is already prevalent, however, sexual selection can itself cause low heterozygous fitness, promoting the evolution of complete reproductive isolation (akin to "reinforcement") regardless of the form of natural selection.     

The scale‐of‐choice effect and how estimates of assortative mating in the wild can be biased due to heterogeneous samples

The mode in which sexual organisms choose mates is a key evolutionary process, as it can have a profound impact on fitness and speciation. One way to study mate choice in the wild is by measuring trait correlation between mates. Positive assortative mating is inferred when individuals of a mating pair display traits that are more similar than those expected under random mating while negative assortative mating is the opposite. A recent review of 1134 trait correlations found that positive estimates of assortative mating were more frequent and larger in magnitude than negative estimates. Here, we describe the scale‐of‐choice effect (SCE), which occurs when mate choice exists at a smaller scale than that of the investigator's sampling, while simultaneously the trait is heterogeneously distributed at the true scale‐of‐choice. We demonstrate the SCE by Monte Carlo simulations and estimate it in two organisms showing positive (Littorina saxatilis) and negative (L. fabalis) assortative mating. Our results show that both positive and negative estimates are biased by the SCE by different magnitudes, typically toward positive values. Therefore, the low frequency of negative assortative mating observed in the literature may be due to the SCE's impact on correlation estimates, which demands new experimental evaluation.     

Limits to the evolution of assortative mating by female choice under restricted gene flow

The evolution of assortative mating is a key component of the process of speciation with gene flow. Several recent theoretical studies have pointed out, however, that sexual selection which can result from assortative mating may cause it to plateau at an intermediate level; this is primarily owing to search costs of individuals with extreme phenotypes and to assortative preferences developed by individuals with intermediate phenotypes. I explore the limitations of assortative mating further by analysing a simple model in which these factors have been removed. Specifically, I use a haploid two-population model to ask whether the existence of assortative mating is sufficient to drive the further evolution of assortative mating. I find that a weakening in the effective strength of sexual selection with strong assortment leads to the existence of both a peak level of trait differentiation and the evolution of an intermediate level of assortative mating that will cause that peak. This result is robust to the inclusion of local adaptation and different genetic architecture of the trait. The results imply the existence of fundamental limits to the evolution of assortment via sexual selection in this situation, with which other factors, such as search costs, may interact.     

Assortative pairing and divergent evolution in Darwin’s Small Tree Finch, Camarhynchus parvulus

Size assortative mating has received increasing attention due to its potential to drive divergence and perhaps speciation. In this study, we examined assortative pairing at 17 nests of Darwin’s Small Tree Finches, Camarhynchus parvulus. We found positive assortative pairing for two traits: bill length and tarsus length, and these traits showed a significant positive correlation to each other. Assortative pairing could be driven by female choice for similar phenotypes because male–male competition has rarely been observed in the Small Tree Finch, nor have males been observed to reject potential mates. Given the high heritability of bill morphology in Darwin’s finches, it is possible that female preference for male bill length, a trait that is known to be important for foraging, will influence offspring bill size to maximise efficient exploitation of resources. The finding of size assortative pairing on the basis of tarsus length requires more research, but suggests different trait utilities for different foraging niches. Interestingly, the highland distribution of tarsus length across the population showed a unimodal distribution, but a bimodal distribution after pairing. While not significant, we found comparatively large differences across study plots in tarsus length, which suggests the possibility of phenotype–habitat matching at a small spatial scale in this species. Our findings are significant in the context of the adaptive radiation of Darwin’s finches as they are consistent with the allopatric model of speciation but also show potential for adaptive divergence in sympatry in Darwin’s tree finches.     

Sympatric Speciation: When Is It Possible in Bacteria?

According to theory, sympatric speciation in sexual eukaryotes is favored when relatively few loci in the genome are sufficient for reproductive isolation and adaptation to different niches. Here we show a similar result for clonally reproducing bacteria, but which comes about for different reasons. In simulated microbial populations, there is an evolutionary tradeoff between early and late stages of niche adaptation, which is resolved when relatively few loci are required for adaptation. At early stages, recombination accelerates adaptation to new niches (ecological speciation) by combining multiple adaptive alleles into a single genome. Later on, without assortative mating or other barriers to gene flow, recombination generates unfit intermediate genotypes and homogenizes incipient species. The solution to this tradeoff may be simply to reduce the number of loci required for speciation, or to reduce recombination between species over time. Both solutions appear to be relevant in natural microbial populations, allowing them to diverge into ecological species under similar constraints as sexual eukaryotes, despite differences in their life histories.     

Substrate selection and assortative mating in Gammarus pulex L.

We reject the published proposition that assortative mating for size in Gammarus is brought about purely as a result of spatial heterogeneity in substrate particle size. We confirm that, in general, large Gammarus prefer substrates with larger particle size than small Gammarus. However, in artificial streams in the laboratory, in choice experiments Gammarus males and females showed positive assortative mating for size in each of three substrates differing in mean particle size. We propose an explanation for assortative mating based on sexual selection.     

Effect of genetic heterogeneity and assortative mating on linkage analysis: a simulation study.

Linkage studies of complex genetic traits raise questions about the effects of genetic heterogeneity and assortative mating on linkage analysis. To further understand these problems, I have simulated and analyzed family data for a complex genetic disease in which disease phenotype is determined by two unlinked disease loci. Two models were studied, a two-locus threshold model and a two-locus heterogeneity model. Information was generated for a marker locus linked to one of the disease-defining loci. Random-mating and assortative-mating samples were generated. Linkage analysis was then carried out by use of standard methods, under the assumptions of a single-locus disease trait and a random-mating population. Results were compared with those from analysis of a single-locus homogeneous trait in samples with the same levels of assortative mating as those considered for the two-locus traits. The results show that (1) introduction of assortative mating does not, in itself, markedly affect the estimate of the recombination fraction; (2) the power of the analysis, reflected in the LOD scores, is somewhat lower with assortative rather than random mating. Loss of power is greater with increasing levels of assortative mating; and (3) for a heterogeneous genetic disease, regardless of mating type, heterogeneity analysis permits more accurate estimate of the recombination fraction but may be of limited use in distinguishing which families belong to each homogeneous subset. These simulations also confirmed earlier observations that linkage to a disease "locus" can be detected even if the disease is incorrectly defined as a single-locus (homogeneous) trait, although the estimated recombination fraction will be significantly greater than the true recombination fraction between the linked disease-defining locus and the marker locus.     

The evolution of sexual imprinting through reinforcement*

Reinforcement is the process whereby assortative mating evolves due to selection against costly hybridization. Sexual imprinting could evolve as a mechanism of reinforcement, decreasing hybridization, or it could potentially increase hybridization in genetically purebred offspring of heterospecific social pairs. We use deterministic population genetic simulations to explore conditions under which sexual imprinting can evolve through reinforcement. We demonstrate that a sexual imprinting component of female preference can evolve as a one‐allele assortative mating mechanism by reducing the risk of hybridization, and is generally effective at causing trait divergence. However, imprinting often evolves to be a component rather than the sole determinant of female preference. The evolution of imprinting has the unexpected side effect of homogenizing existing innate preference, because the imprinted preference neutralizes any innate preference. We also find that the weight of the imprinting component may evolve to a lower value when migration and divergent selection are strong and the cost of hybridization is low; these conditions render hybridization adaptive for immigrant females because they can acquire locally adaptive genes by mating with local males. Together, these results suggest that sexual imprinting can itself evolve as part of the speciation process, and in doing so has the capacity to promote or retard divergence through complex interactions.     

Assortative mating by diet in a phenotypically unimodal but ecologically variable population of stickleback

Speciation with gene flow may be driven by a combination of positive assortative mating and disruptive selection, particularly if selection and assortative mating act on the same trait, eliminating recombination between ecotype and mating type. Phenotypically unimodal populations of threespine stickleback (Gasterosteus aculeatus) are commonly subject to disruptive selection due to competition for alternate prey. Here we present evidence that stickleback also exhibit assortative mating by diet. Among-individual diet variation leads to variation in stable isotopes, which reflect prey use. We find a significant correlation between the isotopes of males and eggs within their nests. Because egg isotopes are derived from females, this correlation reflects assortative mating between males and females by diet. In concert with disruptive selection, this assortative mating should facilitate divergence. However, the stickleback population remains phenotypically unimodal, highlighting the fact that assortative mating and disruptive selection do not guarantee evolutionary divergence and speciation.     

Assortative mating,sexual selection,and their consequences for gene flow in Littorina

When divergent populations are connected by gene flow, the establishment of complete reproductive isolation usually requires the joint action of multiple barrier effects. One example where multiple barrier effects are coupled consists of a single trait that is under divergent natural selection and also mediates assortative mating. Such multiple-effect traits can strongly reduce gene flow. However, there are few cases where patterns of assortative mating have been described quantitatively and their impact on gene flow has been determined. Two ecotypes of the coastal marine snail, Littorina saxatilis, occur in North Atlantic rocky-shore habitats dominated by either crab predation or wave action. There is evidence for divergent natural selection acting on size, and size-assortative mating has previously been documented. Here, we analyze the mating pattern in L. saxatilis with respect to size in intensively sampled transects across boundaries between the habitats. We show that the mating pattern is mostly conserved between ecotypes and that it generates both assortment and directional sexual selection for small male size. Using simulations, we show that the mating pattern can contribute to reproductive isolation between ecotypes but the barrier to gene flow is likely strengthened more by sexual selection than by assortment.     

Revealing the mechanisms of sexual isolation in a case of sympatric and parallel ecological divergence

Two ecotypes of a marine intertidal snail (Littorina saxatilis), living at different microhabitats and shore levels, have evolved in sympatry and in parallel across the Galician rocky shore. These ecotypes differ in many traits (including size) due to differential adaptation. They meet, mate assortatively, and partially hybridize at the mid shore where the two microhabitats overlap. The partial sexual isolation observed is claimed to be a side‐effect of the size differences between ecotypes combined with a size assortative mating found in most populations of this species. We investigated this hypothesis using three complementary experimental approaches. First, we investigated which of the different shell variables contributed most to the variation in individual sexual isolation in the field by using two new statistics developed for that purpose: (1) pair sexual isolation and (2) r_i, which is based on the Pearson correlation coefficient. We found that size is the most important trait explaining the sexual isolation and, in particular, the males appear to be the key sex contributing to sexual isolation. Second, we compared the size assortative mating between regions: exposed rocky shore populations from north‐westwern Spain (showing incomplete reproductive isolation due to size assortative mating) and protected Spanish and Swedish populations (showing size assortative mating but not reproductive isolation between ecomorphs). Most of the variation in size assortative mating between localities was significantly explained by the within‐population level of variation on size. Third, we performed a laboratory male choice experiment, which further suggested that the choice is made predominantly on the basis of size. These results confirm the mechanism proposed to explain the sexual isolation in the Galician hybrid zone and thus support this case as a putative example of parallel incipient speciation. © 2008 The Linnean Society of London, Biological Journal of the Linnean Society, 2008, 94 , 513–526.