Negative Coupling: The Coincidence of Premating Isolating Barriers Can Reduce Reproductive Isolation

Speciation can be mediated by a variety of reproductive barriers, and the interaction among different barriers has often been shown to enhance overall reproductive isolation, a process referred to as "coupling." Here, we analyze a population genetics model to study the establishment of linkage disequilibrium (LD) among loci involved in multiple premating barriers, an aspect that has received little theoretical attention to date. We consider a simple genetic framework underlying two distinct premating barriers, each encoded by a preference locus and its associated mating trait locus. We show that their interaction can lead to a decrease in overall reproductive isolation relative to a situation with a single barrier, a process we call "negative coupling." More specifically, in our model, negative coupling results either from sexual selection that reduces divergence at all loci, or from reduced LD that occurs because the presence of many females with "mismatched" preferences causes the mating success of recombinant males to become high. Interestingly, the latter effect may even cause LD among preference loci to become negative when recombination rates among loci are low. We conclude that coincident reproductive barriers may not necessarily reinforce each other, and that the underlying loci may not necessarily develop a positive association.

Coupling of Barriers to Gene Exchange: Causes and Consequences

Coupling has emerged as a concept to describe the transition from differentiated populations to newly evolved species through the strengthening of reproductive isolation. However, the term has been used in multiple ways, and relevant processes have sometimes not been clearly distinguished. Here, we synthesize existing uses of the concept of coupling and find three main perspectives: (1) coupling as the build-up of linkage disequilibrium among loci underlying barriers to gene exchange, (2) coupling as the build-up of genome-wide linkage disequilibrium, and (3) coupling as the process generating a coincidence of distinct barrier effects. We compare and contrast these views, show the diverse processes involved and the complexity of the relationships among recombination, linkage disequilibrium, and reproductive isolation, and, finally, we emphasize how each perspective can guide new directions in speciation research. Although the importance of coupling for evolutionary divergence and speciation is well established, many theoretical and empirical questions remain unanswered.

Host learning selects for the coevolution of greater egg mimicry and narrower antiparasitic egg-rejection thresholds

Egg rejection is an effective and widespread antiparasitic defense to eliminate foreign eggs from the nests of hosts of brood parasitic birds. Several lines of observational and critical experimental evidence support a role for learning by hosts in the recognition of parasitic versus own eggs; specifically, individual hosts that have had prior or current experience with brood parasitism are more likely to reject foreign eggs. Here we confirm experimentally the role of prior experience in altering subsequent egg-rejection decisions in the American robin Turdus migratorius, a free-living host species of an obligate brood parasite, the brown-headed cowbird Molothrus ater. We then model the coevolutionary trajectory of both the extent of mimicry of host eggs by parasitic eggs and the host's egg rejection thresholds in response to an increasing role of learning in egg recognition. Critically, with more learning, we see the evolution of both narrower (more discriminating) rejection thresholds in hosts and greater egg mimicry in parasites. Increasing host clutch size (number of eggs/nest) and increasing parasite load (parasitism rate) also have narrowing effects on the egg-rejection threshold. Together, these results suggest that learning from prior experience with egg rejection may play an important role in the coevolution of egg-mimetic lineages of brood parasites and the refined egg rejection defenses of hosts.

Evolutionary rescue under demographic and environmental stochasticity

Populations suffer two types of stochasticity: demographic stochasticity, from sampling error in offspring number, and environmental stochasticity, from temporal variation in the growth rate. By modelling evolution through phenotypic selection following an abrupt environmental change, we investigate how genetic and demographic dynamics, as well as effects on population survival of the genetic variance and of the strength of stabilizing selection, differ under the two types of stochasticity. We show that population survival probability declines sharply with stronger stabilizing selection under demographic stochasticity, but declines more continuously when environmental stochasticity is strengthened. However, the genetic variance that confers the highest population survival probability differs little under demographic and environmental stochasticity. Since the influence of demographic stochasticity is stronger when population size is smaller, a slow initial decline of genetic variance, which allows quicker evolution, is important for population persistence. In contrast, the influence of environmental stochasticity is population-size-independent, so higher initial fitness becomes important for survival under strong environmental stochasticity. The two types of stochasticity interact in a more than multiplicative way in reducing the population survival probability. Our work suggests the importance of explicitly distinguishing and measuring the forms of stochasticity during evolutionary rescue.

Inferred Attractiveness: A generalized mechanism for sexual selection that can maintain variation in traits and preferences over time

Sexual selection by mate choice is a powerful force that can lead to evolutionary change, and models of why females choose particular mates are central to understanding its effects. Predominant mate choice theories assume preferences are determined solely by genetic inheritance, an assumption still lacking widespread support. Moreover, preferences often vary among individuals or populations, fail to correspond with conspicuous male traits, or change with context, patterns not predicted by dominant models. Here, we propose a new model that explains this mate choice complexity with one general hypothesized mechanism, "Inferred Attractiveness." In this model, females acquire mating preferences by observing others' choices and use context-dependent information to infer which traits are attractive. They learn to prefer the feature of a chosen male that most distinguishes him from other available males. Over generations, this process produces repeated population-level switches in preference and maintains male trait variation. When viability selection is strong, Inferred Attractiveness produces population-wide adaptive preferences superficially resembling "good genes." However, it results in widespread preference variation or nonadaptive preferences under other predictable circumstances. By casting the female brain as the central selective agent, Inferred Attractiveness captures novel and dynamic aspects of sexual selection and reconciles inconsistencies between mate choice theory and observed behavior.

Predation drives complex eco-evolutionary dynamics in sexually selected traits

Predation plays a role in preventing the evolution of ever more complicated sexual displays, because such displays often increase an individual's predation risk. Sexual selection theory, however, omits a key feature of predation in modeling costs to sexually selected traits: Predation is density dependent. As a result of this density dependence, predator-prey dynamics should feed back into the evolution of sexual displays, which, in turn, feeds back into predator-prey dynamics. Here, we develop both population and quantitative genetic models of sexual selection that explicitly link the evolution of sexual displays with predator-prey dynamics. Our primary result is that predation can drive eco-evolutionary cycles in sexually selected traits. We also show that mechanistically modeling the cost to sexual displays as predation leads to novel outcomes such as the maintenance of polymorphism in sexual displays and alters ecological dynamics by muting prey cycles. These results suggest predation as a potential mechanism to maintain variation in sexual displays and underscore that short-term studies of sexual display evolution may not accurately predict long-run dynamics. Further, they demonstrate that a common verbal model (that predation limits sexual displays) with widespread empirical support can result in unappreciated, complex dynamics due to the density-dependent nature of predation.

Indiscriminate Mating and the Coevolution of Sex Discrimination and Sexual Signals

AbstractThe presence of same-sex sexual behavior across the animal kingdom is often viewed as unexpected. One explanation for its prevalence in some taxa is indiscriminate mating-a strategy wherein an individual does not attempt to determine the sex of its potential partner before attempting copulation. Indiscriminate mating has been argued to be the ancestral mode of sexual reproduction and can also be an optimal strategy given search costs of choosiness. Less attention has been paid to the fact that sex discrimination requires not just the attempt to differentiate between the sexes but also some discernible difference (a signal or cue) that can be detected. To address this, we extend models of mating behavior to consider the coevolution of sex discrimination and sexual signals. We find that under a wide range of parameters, including some with relatively minor costs, indiscriminate mating and the absence of sexual signals will be an evolutionary end point. Furthermore, the absence of both sex discrimination and sexual signals is always evolutionarily stable. These results suggest that an observable difference between the sexes likely arose as a by-product of the evolution of different sexes, allowing discrimination to evolve.

The effectiveness of pseudomagic traits in promoting premating isolation

Upon the secondary contact of populations, speciation with gene flow is greatly facilitated when the same pleiotropic loci are both subject to divergent ecological selection and induce non-random mating, leading to loci with this fortuitous combination of functions being referred to as 'magic trait' loci. We use a population genetics model to examine whether 'pseudomagic trait' complexes, composed of physically linked loci fulfilling these two functions, are as efficient in promoting premating isolation as magic traits. We specifically measure the evolution of choosiness, which controls the strength of assortative mating. We show that, surprisingly, pseudomagic trait complexes, and to a lesser extent also physically unlinked loci, can lead to the evolution of considerably stronger assortative mating preferences than do magic traits, provided polymorphism at the involved loci is maintained. This is because assortative mating preferences are generally favoured when there is a risk of producing maladapted recombinants, as occurs with non-magic trait complexes but not with magic traits (since pleiotropy precludes recombination). Contrary to current belief, magic traits may not be the most effective genetic architecture for promoting strong premating isolation. Therefore, distinguishing between magic traits and pseudomagic trait complexes is important when inferring their role in premating isolation. This calls for further fine-scale genomic research on speciation genes.

The Fisher process of sexual selection with the coevolution of preference strength

Sexual selection has a rich history of mathematical models that consider why preferences favor one trait phenotype over another (for population genetic models) or what specific trait value is preferred (for quantitative genetic models). Less common is exploration of the evolution of choosiness or preference strength: that is, by how much a trait is preferred. We examine both population and quantitative genetic models of the evolution of preferences, specifically developing "baseline models" of the evolution of preference strength during the Fisher process. Using a population genetic approach based on the classic model of Kirkpatrick (1982), we find selection for stronger and stronger preferences when trait variation is maintained by mutation. However, this force is quite weak and likely to be swamped by drift in moderately-sized populations. In a quantitative genetic model based on Lande (1981), unimodal preferences will generally not evolve to be increasingly strong without bounds when male traits are under stabilizing viability selection, but evolve to extreme values when viability selection is directional. Our results highlight that different shapes of fitness and preference functions lead to qualitatively different trajectories for preference strength evolution ranging from no evolution to extreme evolution of preference strength.

The evolution of age-specific choosiness and reproductive isolation in a model with overlapping generations

The strength of mate choice (choosiness) often varies with age, but theory to understand this variation is scarce. Additionally, theory has investigated the evolution of choosiness in speciation scenarios but has ignored that most organisms have overlapping generations. We investigate whether speciation can result in variation of choosiness with age, and whether such variation can in turn affect speciation. We develop a population-genetic model of the evolution of choosiness in organisms with overlapping generations in the context of secondary contact between two divergent populations. We assume that females choose males that match their phenotype, such that choosiness evolves by sexual selection. We demonstrate that speciation can result in the evolution of age-specific choosiness when the mating trait is under divergent ecological selection and age is not used as a mating cue. The cause of this result is that allele frequencies differ between choosy females and males. However, we find that the evolution of age-specific choosiness does not affect the overall level of reproductive isolation compared to a case without age-structure, supporting previous speciation theory. Overall, our results connect life history and speciation theory, and the mechanisms that we highlight have implications for the understanding of the role of sex-specific selection in the evolution of choosiness.

The evolution of flower longevity in unpredictable pollination environments

Pollination requires a flower to remain open for long enough to allow for the arrival of pollinators. However, maintaining flowers costs energy and resources. Therefore, flower longevity, the length of time a flower remains viable, is critical for the outcome of plant reproduction. Although previous studies showed that the evolution of flower longevity depends on the rates of pollen deposition and removal, whether plants should increase or decrease flower life span when the pollination environment is unpredictable has not been explored. Moreover, the common hypothesis that an unpredictable pollination environment should select for increased flower longevity may be too simplistic since there is no distinction drawn between the effects of spatial and temporal variation. Adopting evolutionary game theory, we investigate the evolution of flower longevity under three types of variation: spatial heterogeneity, daily fluctuations within a flowering season and yearly fluctuations between flowering seasons. We find that spatial heterogeneity often selects for a shorter flower lifespan, while temporal fluctuations of fitness accrual rates at both daily and yearly time scales tends to favour greater longevity, although daily and yearly fluctuations have somewhat different effects. However, the presence of correlation between female and male fitness accrual rates seems to have no effect on flower longevity. Our work suggests that explicit measurements of spatial and temporal variation in both female and male functions may provide a better understanding of the evolution of flower longevity and reproduction.

Homage to Felsenstein 1981, or why are there so few/many species?

If there are no constraints on the process of speciation, then the number of species might be expected to match the number of available niches and this number might be indefinitely large. One possible constraint is the opportunity for allopatric divergence. In 1981, Felsenstein used a simple and elegant model to ask if there might also be genetic constraints. He showed that progress towards speciation could be described by the build-up of linkage disequilibrium among divergently selected loci and between these loci and those contributing to other forms of reproductive isolation. Therefore, speciation is opposed by recombination, because it tends to break down linkage disequilibria. Felsenstein then introduced a crucial distinction between "two-allele" models, which are subject to this effect, and "one-allele" models, which are free from the recombination constraint. These fundamentally important insights have been the foundation for both empirical and theoretical studies of speciation ever since.

The effectiveness of pseudomagic traits in promoting divergence and enhancing local adaptation

"Magic traits," in which the same trait is both under divergent ecological selection and forms the basis of assortative mating, have been sought after due to their supposed unique ability to promote divergence with gene flow. Here, we ask how unique magic traits are, by exploring whether a tightly linked complex of a locus under divergent selection and a locus that acts as a mating cue can mimic a magic trait in its divergence. We find that these "pseudomagic traits" can be very effective in promoting divergence; with tight linkage they are essentially as effective as a magic trait and with loose linkage, and even no linkage, divergence can still be enhanced. Distinguishing between magic and pseudomagic traits in empirical cases may thus not be important when inferring their role in divergence. The ability of divergence in the mating trait to drive divergence in the ecological trait by lowering the effective migration rate, which occurs somewhat even without linkage, is particularly striking; magic traits are typically considered to have the other direction of causality. Our results thus suggest that divergence in a mating trait can at least modestly increase local adaption by allowing more ecological divergence, particularly with tighter linkage.

An Effective Mutualism? The Role of Theoretical Studies in Ecology and Evolution

Theoretical models often have fundamentally different goals than do empirical studies of the same topic. Models can test the logic of existing hypotheses, explore the plausibility of new hypotheses, provide expectations that can be tested with data, and address aspects of topics that are currently inaccessible empirically. Theoretical models are common in ecology and evolution and are generally well cited, but I show that many citations appearing in nontheoretical studies are general to topic and that a substantial proportion are incorrect. One potential cause of this pattern is that some functions of models are rather abstract, leading to miscommunication between theoreticians and empiricists. Such misunderstandings are often triggered by simplifying logistical assumptions that modelers make. The 2018 Vice Presidential Symposium of the American Society of Naturalists included a variety of mathematical models in ecology and evolution from across several topics. Common threads that appear in the use of the models are identified, highlighting the power of a theoretical approach and the role of the assumptions that such models make.

Grey zones of sexual selection: why is finding a modern definition so hard?

Sexual selection has long been acknowledged as an important evolutionary force, capable of shaping phenotypes ranging from fascinating and unusual displays to cryptic traits whose function is only uncovered by careful study. Yet, despite decades of research, reaching a consensus definition of the term 'sexual selection' has proved difficult. Here we explore why arriving at a unifying definition of sexual selection is so hard. While some researchers have argued about whether sexual selection should be considered a form of natural selection, we concentrate on where the line between sexual selection and other forms of selection falls. We focus on identifying the 'grey zones' of sexual selection by illustrating cases in which application of the term 'sexual selection' would be considered controversial or ambiguous. We believe that clarifying why sexual selection is so difficult to define is an essential first step forward towards greater clarity, and if possible towards reaching a consensus definition. We suggest that a more nuanced perspective may be necessary, particularly one that specifies for cases of 'sexual selection' why the term is used or whether they fall into a grey zone.

Searching for Sympatric Speciation in the Genomic Era

Sympatric speciation illustrates how natural and sexual selection may create new species in isolation without geographic barriers. However, recent genomic reanalyses of classic examples of sympatric speciation reveal complex histories of secondary gene flow from outgroups into the radiation. In contrast, the rich theoretical literature on this process distinguishes among a diverse range of models based on simple genetic histories and different types of reproductive isolating barriers. Thus, there is a need to revisit how to connect theoretical models of sympatric speciation and their predictions to empirical case studies in the face of widespread gene flow. Here, theoretical differences among different types of sympatric speciation and speciation-with-gene-flow models are reviewed and summarized, and genomic analyses are proposed for distinguishing which models apply to case studies based on the timing and function of adaptive introgression. Investigating whether secondary gene flow contributed to reproductive isolation is necessary to test whether predictions of theory are ultimately borne out in nature.

Female resistance to sexual coercion can evolve to preserve the indirect benefits of mate choice

Sexual conflict over the indirect benefits of mate choice may arise when traits in one sex limit the ability of the other sex to freely choose mates but when these coercive traits are not necessarily directly harmful (i.e. forced fertilization per se). Although we might hypothesize that females can evolve resistance in order to retain the indirect, genetic benefits (reflected in offspring attractiveness) of mating with attractive males, up to now it has been difficult to evaluate potential underlying mechanisms. Traditional theoretical approaches do not usually conceptually distinguish between female preference for male mating display and female resistance to forced fertilization, yet sexual conflict over indirect benefits implies the simultaneous action of all of these traits. Here, we present an integrative theoretical framework that draws together concepts from both sexual selection and sexual conflict traditions, allowing for the simultaneous coevolution of displays and preferences, and of coercion and resistance. We demonstrate that it is possible for resistance to coercion to evolve in the absence of direct costs of mating to preserve the indirect benefits of mate choice. We find that resistance traits that improve the efficacy of female mating preference can evolve as long as females are able to attain some indirect benefits of mating with attractive males, even when both attractive and unattractive males can coerce. These results reveal new evolutionary outcomes that were not predicted by prior theories of indirect benefits or sexual conflict.

Theory Meets Empiry: A Citation Network Analysis

According to a recent survey, ecologists and evolutionary biologists feel that theoretical and empirical research should coexist in a tight feedback loop but believe that the two domains actually interact very little. We evaluate this perception using a citation network analysis for two data sets, representing the literature on sexual selection and speciation. Overall, 54%-60% of citations come from a paper's own category, whereas 17%-23% are citations across categories. These cross-citations tend to focus on highly cited papers, and we observe a positive correlation between the numbers of citations a study receives within and across categories. We find evidence that reviews can function as integrators between the two literatures, argue that theoretical models are analogous to specific empirical study systems, and complement our analyses by studying a cocitation network. We conclude that theoretical and empirical research are more tightly connected than generally thought but that avenues exist to further increase this integration.

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.

The evolution of male mate choice and female ornamentation: a review of mathematical models

The evolution of male preferences and of female ornaments in species with traditional sex roles (i.e., polygyny) have been highlighted as areas in need of more active research by an accumulation of recent findings. The theoretical literature on these topics is relatively small and has centered on the evolution of male choice. Mathematical models have emphasized that, under polygyny, the evolution of male preferences faces much greater competition costs than does the evolution of female preferences. We discuss ways in which costly male choice can nonetheless evolve, via (1) direct selection that favors preferences, primarily through mating with highly fecund females, (2) mechanisms that rely on indirect selection, which weakly counters competitive costs of male preferences, and (3) genetic constraints, primarily in the form of pleiotropy of male and female preferences and traits. We also review a variety of mathematical models that have elucidated how costs to male preferences can be avoided. Finally, we turn our attention to the relatively scant theoretical literature on the effects of male mate choice on the evolution of female traits. We emphasize the finding that the presence of male preferences cannot be assumed to lead to the evolution of female ornaments during polygyny, and point out situations where models have elucidated ways in which female ornaments can nevertheless evolve.

The Effects on Parapatric Divergence of Linkage between Preference and Trait Loci versus Pleiotropy

Attempts to uncover the genetic basis of female mating preferences and male signals involved in reproductive isolation have discovered intriguing cases in which loci contributing to these traits co-localize in their chromosomal positions. Such discoveries raise the question of whether alleles at certain loci contribute pleiotropically to male and female components of premating reproductive isolation, versus whether these loci are merely tightly linked. Here we use population genetic models to assess the degree to which these alternatives affect both short term and equilibrium patterns of trait (signal) and preference divergence. We take advantage of the fact that in the case of secondary contact between populations exchanging migrants, patterns of divergence across the range of preference strengths differ markedly when preferences and traits are controlled by the same locus (the case of phenotype matching) versus when they are on separate chromosomes. We find that tight linkage between preference and trait loci can mimic the pleiotropic pattern for many generations (roughly the reciprocal of the recombination rate), but that any recombination ultimately results in equilibrium patterns of divergence far more similar to those found when preferences and traits are on separate chromosomes. In general, our finding that pleiotropy results in quite different long-term patterns from tight linkage highlights the importance of distinguishing between these possibilities in empirical systems.

Direct detection of male quality can facilitate the evolution of female choosiness and indicators of good genes: Evolution across a continuum of indicator mechanisms

The evolution of mating displays as indicators of male quality has been the subject of extensive theoretical and empirical research for over four decades. Research has also addressed the evolution of female mate choice favoring such indicators. Yet, much debate still exists about whether displays can evolve through the indirect benefits of female mate choice. Here, we use a population genetic model to investigate how the extent to which females can directly detect male quality influences the evolution of female choosiness and male displays. We use a continuum framework that incorporates indicator mechanisms that are traditionally modeled separately. Counter to intuition, we find that intermediate levels of direct detection of male quality can facilitate, rather than impede, the evolution of female choosiness and male displays in broad regions of this continuum. We examine how this evolution is driven by selective forces on genetic quality and on the display, and find that direct detection of male quality results in stronger indirect selection favoring female choosiness. Our results imply that displays maybe more likely to evolve when female choosiness has already evolved to discriminate perceptible forms of male quality. They also highlight the importance of considering general female choosiness, as well as preference, in studies of "good genes."

Nonadaptive female pursuit of extrapair copulations can evolve through hitchhiking

Mounting evidence has indicated that engaging in extrapair copulations (EPCs) might be maladaptive or detrimental to females. It is unclear why such nonadaptive female behavior evolves. In this study, we test two hypotheses about the evolution of female EPC behavior using population genetic models. First, we find that both male preference for allocating extra effort to seek EPCs and female pursuit behavior without costs can be maintained and remain polymorphic in a population via frequency‐dependent selection. However, both behaviors cannot evolve when females with pursuit behavior suffer from a decline in male parental care. Second, we present another novel way in which female pursuit behavior can evolve; indirect selection can act on this behavior through a ratchet‐like mechanism involving oscillating linkage disequilibria between the target EPC pursuit locus and two other loci determining male mate choice and a female sexual signal. Although the overall positive force of such indirect selection is relatively weak, our results suggest that it may still play a role in promoting the evolution of female EPC behavior when this behavior is nonadaptive (i.e., it is neutral) or only somewhat maladaptive (e.g., males only occasionally lower parental care when their mates pursue EPCs).

The Role of Sexual Selection in Local Adaptation and Speciation

Sexual selection plays several intricate and complex roles in the related processes of local adaptation and speciation. In some cases sexual selection can promote these processes, but in others it can be inhibitory. We present theoretical and empirical evidence supporting these dual effects of sexual selection during local adaptation, allopatric speciation, and speciation with gene flow. Much of the empirical evidence for sexual selection promoting speciation is suggestive rather than conclusive; we present what would constitute strong evidence for sexual selection driving speciation. We conclude that although there is ample evidence that sexual selection contributes to the speciation process, it is very likely to do so only in concert with natural selection.

Evolution of a mating preference for a dual-utility trait used in intrasexual competition in genetically monogamous populations

The selection pressures by which mating preferences for ornamental traits can evolve in genetically monogamous mating systems remain understudied. Empirical evidence from several taxa supports the prevalence of dual-utility traits, defined as traits used both as armaments in intersexual selection and ornaments in intrasexual selection, as well as the importance of intrasexual resource competition for the evolution of female ornamentation. Here, we study whether mating preferences for traits used in intrasexual resource competition can evolve under genetic monogamy. We find that a mating preference for a competitive trait can evolve and affect the evolution of the trait. The preference is more likely to persist when the fecundity benefit for mates of successful competitors is large and the aversion to unornamented potential mates is strong. The preference can persist for long periods or potentially permanently even when it incurs slight costs. Our results suggest that, when females use ornaments as signals in intrasexual resource competition, males can evolve mating preferences for those ornaments, illuminating both the evolution of female ornamentation and the evolution of male preferences for female ornaments in monogamous species.

The evolution of postpairing male mate choice

An increasing number of empirical studies in animals have demonstrated male mate choice. However, little is known about the evolution of postpairing male choice, specifically which occurs by differential allocation of male parental care in response to female signals. We use a population genetic model to examine whether such postpairing male mate choice can evolve when males face a trade-off between parental care and extra-pair copulations (EPCs). Specifically, we assume that males allocate more effort to providing parental care when mated to preferred (signaling) females, but they are then unable to allocate additional effort to seek EPCs. We find that both male preference and female signaling can evolve in this situation, under certain conditions. First, this evolution requires a relatively large difference in parental investment between males mated to preferred versus nonpreferred females. Second, whether male choice and female signaling alleles become fixed in a population versus cycle in their frequencies depends on the additional fecundity benefits from EPCs that are gained by choosy males. Third, less costly female signals enable both signaling and choice alleles to evolve under more relaxed conditions. Our results also provide a new insight into the evolution of sexual conflict over parental care.

Speciation in peripheral populations: effects of drift load and mating systems

Speciation in peripheral populations has long been considered one of the most plausible scenarios for speciation with gene flow. In this study, however we identify two additional problems of peripatric speciation, as compared to the parapatric case, that may impede the completion of the speciation process for most parameter regions. First, with (predominantly) unidirectional gene flow, there is no selection pressure to evolve assortative mating on the continent. We discuss the implications of this for different mating schemes. Second, genetic load can build up in small populations. This can lead to extinction of the peripheral species, or generate selection pressure for lower assortative mating to avoid inbreeding. In this case, either a stable equilibrium with intermediate assortment evolves or there is cycling between phases of hybridization and phases of complete isolation.

Geography, assortative mating, and the effects of sexual selection on speciation with gene flow

Theoretical and empirical research on the evolution of reproductive isolation have both indicated that the effects of sexual selection on speciation with gene flow are quite complex. As part of this special issue on the contributions of women to basic and applied evolutionary biology, I discuss my work on this question in the context of a broader assessment of the patterns of sexual selection that lead to, versus inhibit, the speciation process, as derived from theoretical research. In particular, I focus on how two factors, the geographic context of speciation and the mechanism leading to assortative mating, interact to alter the effect that sexual selection through mate choice has on speciation. I concentrate on two geographic contexts: sympatry and secondary contact between two geographically separated populations that are exchanging migrants and two mechanisms of assortative mating: phenotype matching and separate preferences and traits. I show that both of these factors must be considered for the effects of sexual selection on speciation to be inferred.

Reproductive isolation with a learned trait in a structured population

Assortative mating displays and/or preferences can be affected by learning across a wide range of animal taxa, but the specifics of how this learning affects speciation with gene flow are not well understood. We use population genetic models with trait learning to investigate how the identity of the tutor affects the divergence of a self-referent phenotype-matching trait. We find that oblique learning (learning from unrelated individual of the previous generation) and maternal learning mask sexual selection and therefore do not allow the maintenance of divergence. In contrast, by enhancing positive frequency-dependent sexual selection, paternal learning can maintain more divergence than genetic inheritance, but leads to the loss of polymorphism more easily. Furthermore, paternal learning inhibits the invasion of a novel self-referent phenotype-matching trait, especially in a large population.

The interpretation of selection coefficients

Evolutionary biologists have an array of powerful theoretical techniques that can accurately predict changes in the genetic composition of populations. Changes in gene frequencies and genetic associations between loci can be tracked as they respond to a wide variety of evolutionary forces. However, it is often less clear how to decompose these various forces into components that accurately reflect the underlying biology. Here, we present several issues that arise in the definition and interpretation of selection and selection coefficients, focusing on insights gained through the examination of selection coefficients in multilocus notation. Using this notation, we discuss how its flexibility-which allows different biological units to be identified as targets of selection-is reflected in the interpretation of the coefficients that the notation generates. In many situations, it can be difficult to agree on whether loci can be considered to be under "direct" versus "indirect" selection, or to quantify this selection. We present arguments for what the terms direct and indirect selection might best encompass, considering a range of issues, from viability and sexual selection to kin selection. We show how multilocus notation can discriminate between direct and indirect selection, and describe when it can do so.

Not just a theory--the utility of mathematical models in evolutionary biology

Models have made numerous contributions to evolutionary biology, but misunderstandings persist regarding their purpose. By formally testing the logic of verbal hypotheses, proof-of-concept models clarify thinking, uncover hidden assumptions, and spur new directions of study. thumbnail image credit: modified from the Biodiversity Heritage Library

Effects on population divergence of within-generational learning about prospective mates

Although learned mate preferences are suspected to have important effects during speciation, theoretical models have largely neglected the effects on speciation and population divergence of within-generational learning, that is, learning based upon prior experience with potential mates. Here, we use population genetic models to address this deficit. Focusing on the situation of secondary contact between populations that still hybridize, we consider models of learning by females and by males under polygyny. We assess the effects of learning to prefer conspecifics from previous conspecific encounters, learning to avoid heterospecifics from previous heterospecific encounters, and learning to prefer familiar types. We examine the amount of population divergence that results from learning in these models. We also assess the effect of learning on the spread of an allele that strengthens assortative mating in both models. We find that learning can have counterintuitive, but logical and understandable effects that differ with the version of the model assessed. In general, population divergence is expected to increase most consistently when females learn to strengthen their preferences for conspecifics from previous encounters with conspecifics. Our results also suggest that within-generational learning will generally inhibit the spread of alleles strengthening assortative mating.

Evolution of displays within the pair bond

Although sexual selection is an important cause of display evolution, in socially monogamous species (e.g. many birds), displays continue after formation of the pair bond. Here, we consider that these displays evolve because they stimulate the partner to increase investment in offspring. Our study is motivated by elaborate mutual displays in species that are largely monomorphic and have long-term pair bonds (e.g. the great crested grebe, Podiceps cristatus) and by many empirical results evidencing that display manipulation affects parental investment. Using population genetic models, we show that a necessary condition for the permanent establishment of mutual displays in the pair bond is that the benefit of investment by the pair is more than twice that resulting from investment by a single individual. Pre-existing biases to respond to displays by increased investment are a necessary component of display evolution. We also consider examples where one sex (e.g. males) stimulates increased investment in offspring by the other sex. Here, display and additional investment cannot evolve permanently, but can increase and linger at high frequency for a long time before loss. We discuss how such transient effects may lead to the evolution of permanent displays as a result of evolution at additional loci.

The evolution of preference strength under sensory bias: a role for indirect selection?

Evidence suggests that female preferences may sometimes arise through sensory bias, and that males may subsequently evolve traits that increase their conspicuousness to females. Here, we ask whether indirect selection, arising through genetic associations (linkage disequilibrium) during the sexual selection that sensory bias imposes, can itself influence the evolution of preference strength. Specifically, we use population genetic models to consider whether or not modifiers of preference strength can spread under different ecological conditions when female mate choice is driven by sensory bias. We focus on male traits that make a male more conspicuous in certain habitats-and thus both more visible to predators and more attractive to females-and examine modifiers of the strength of preference for conspicuous males. We first solve for the rate of spread of a modifier that strengthens preference within an environmentally uniform population; we illustrate that this spread will be extremely slow. Second, we used a series of simulations to consider the role of habitat structure and movement on the evolution of a modifier of preference strength, using male color polymorphisms as a case study. We find that in most cases, indirect selection does not allow the evolution of stronger or weaker preferences for sensory bias. Only in a "two-island" model, where there is restricted migration between different patches that favor different male phenotypes, did we find that preference strength could evolve. The role of indirect selection in the evolution of sensory bias is of particular interest because of ongoing speculation regarding the role of sensory bias in the evolution of reproductive isolation.

Sexual selection and magic traits in speciation with gene flow

The extent to which sexual selection is involved in speciation with gene flow remains an open question and the subject of much research. Here, we propose that some insight can be gained from considering the concept of magic traits (i.e., traits involved in both reproductive isolation and ecological divergence). Both magic traits and other, “non-magic”, traits can contribute to speciation via a number of specific mechanisms. We argue that many of these mechanisms are likely to differ widely in the extent to which they involve sexual selection. Furthermore, in some cases where sexual selection is present, it may be prone to inhibit rather than drive speciation. Finally, there are a priori reasons to believe that certain categories of traits are much more effective than others in driving speciation. The combination of these points suggests a classification of traits that may shed light on the broader role of sexual selection in speciation with gene flow. In particular, we suggest that sexual selection can act as a driver of speciation in some scenarios, but may play a negligible role in potentially common categories of magic traits, and may be likely to inhibit speciation in common categories of non-magic traits.