Mate‐sampling costs and sexy sons

Costly female mating preferences for purely Fisherian male traits (i.e. sexual ornaments that are genetically uncorrelated with inherent viability) are not expected to persist at equilibrium. The indirect benefit of producing ‘sexy sons’ (Fisher process) disappears: in some models, the male trait becomes fixed; in others, a range of male trait values persist, but a larger trait confers no net fitness advantage because it lowers survival. Insufficient indirect selection to counter the direct cost of producing fewer offspring means that preferences are lost. The only well‐cited exception assumes biased mutation on male traits. The above findings generally assume constant direct selection against female preferences (i.e. fixed costs). We show that if mate‐sampling costs are instead derived based on an explicit account of how females acquire mates, an initially costly mating preference can coevolve with a male trait so that both persist in the presence or absence of biased mutation. Our models predict that empirically detecting selection at equilibrium will be difficult, even if selection was responsible for the location of the current equilibrium. In general, it appears useful to integrate mate sampling theory with models of genetic consequences of mating preferences: being explicit about the process by which individuals select mates can alter equilibria.     

Sexual selection and the evolution of costly female preferences: spatial effects

Abstract.— Models of Fisher's runaway process show that if there is a cost to female preference, no preference or male trait exaggeration will evolve. Surprisingly, this is true no matter how small the cost, which reveals that these models of Fisher's process are structurally unstable (Bulmer 1989). Here a model of Fisher's runaway process is presented to demonstrate that costly female preference evolves very easily when space is explicitly included in the model. The only requirement is that the optimal male phenotype changes across the species' range. The model shows that the spatial average of the female preference and male trait reach an evolutionary equilibrium that is identical to those of nonspatial models, but that the preference and male trait can deviate greatly from these averages at any point in space. For example, if random mating results in the lowest cost to females, then at equilibrium the spatial average preference will be zero. Nevertheless, there will be some locations at which females prefer males with larger ornaments and others where they prefer males with smaller ornaments. Results also show that the structural instability of nonspatial models of Fisher's process is less of a problem in spatial models. In particular, many of the main qualitative features of cost-free spatial models of Fisher's process remain valid even when there are small costs of female preference. Finally, the model shows that abrupt changes in the optimal male phenotype across space can result in an amplification of this pattern when preference has a small cost, but it can also result in a pattern similar to reproductive character displacement. Which of these occurs depends on the magnitude of the cost of female preference. This suggests that some patterns of reproductive character displacement in nature might be explained simply by sexual selection rather than by hybrid dysgenesis and reinforcement.     

The evolutionary significance of sexual selection

A model for the joint evolution of a secondary sexual male trait Z and a female mating preference Y is discussed. Recurrence relations for the moments of (Z, Y) are given under the assumption that the traits are binormally distributed. It is shown that female preference for a male character can lead to an equilibrium distribution of the male trait with non-zero variances. The conditions under which the distribution is stable, are given. Unstable situations, in which a continued exaggeration of the male trait occurs, are described. It is demonstrated that the effect of sexual selection on the evolution of the male trait depends on the intensity of natural selection, i.e. the effect of the sexual selection increases when the intensity of natural selection is reduced. The effect of the female preference on the male trait also increases with increasing availability of males. This provides a link to several ecological conditions which have generally been known to be correlated with the degree of sexual selection. Furthermore, it is demonstrated that perturbations away from the equilibrium may cause rapid evolution of the male character, eventually leading to speciation.     

Reinforcement of mate preference among hybridizing Heliconius butterflies

Recent models of mate preference evolution suggest that direct selection on alleles at preference loci and correlated evolution of preference with locally adapted mating cues are more likely to drive the evolution of assortative mate preference than reinforcement. Mate preference evolution in mimetic Heliconius butterflies has been attributed to all three forms of selection, but here we show that reinforcement has been critical. By examining geographical variation in assortative mating and male mate preference among seven populations of three hybridizing Heliconius species from Costa Rica, we found pronounced character displacement of preference such that sexual isolation was enhanced in areas of interspecific contact. Of the different explanations for the evolution of assortative mate preference, only reinforcement is dependent on interspecific contact in this system. Thus, the observed pattern of reproductive character displacement of mate preference is best explained as a product of indirect selection generated by natural selection against nonmimetic hybrids.     

THE LANDE–KIRKPATRICK MECHANISM IS THE NULL MODEL OF EVOLUTION BY INTERSEXUAL SELECTION: IMPLICATIONS FOR MEANING,HONESTY, AND DESIGN IN INTERSEXUAL SIGNALS

The Fisher‐inspired, arbitrary intersexual selection models of Lande (1981) and Kirkpatrick (1982) , including both stable and unstable equilibrium conditions, provide the appropriate null model for the evolution of traits and preferences by intersexual selection. Like the Hardy–Weinberg equilibrium, the Lande–Kirkpatrick (LK) mechanism arises as an intrinsic consequence of genetic variation in trait and preference in the absence of other evolutionary forces. The LK mechanism is equivalent to other intersexual selection mechanisms in the absence of additional selection on preference and with additional trait‐viability and preference‐viability correlations equal to zero. The LK null model predicts the evolution of arbitrary display traits that are neither honest nor dishonest, indicate nothing other than mating availability, and lack any meaning or design other than their potential to correspond to mating preferences. The current standard for demonstrating an arbitrary trait is impossible to meet because it requires proof of the null hypothesis. The LK null model makes distinct predictions about the evolvability of traits and preferences. Examples of recent intersexual selection research document the confirmationist pitfalls of lacking a null model. Incorporation of the LK null into intersexual selection will contribute to serious examination of the extent to which natural selection on preferences shapes signals.     

Aspects of variance and covariance analysis with cultural inheritance

Linear Gaussian models of genotypic, phenotypic, and environmental transmission are studied. The nature of equilibrium assumptions under various modes of assortative mating are discussed with particular emphasis on expected correlations between relatives. Assorting models based only on phenotype, or only on environment, are compared with those in which the mating correlation structure is more complex. Explicit values in terms of transmission parameters and within individual covariances are given for the usual correlations between relatives. The possibility of decomposing these in terms of correlations involving adoptive families is indicated.     

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.     

Models of selective mating and the initiation of the Fisherian process.

The effects of various rules of selective mating on the initial stages of Fisherian sexual selection are investigated. A comparison of three models of selective mating, fixed relative preference, best of N males and absolute preference is provided, with a special emphasis on their mathematical properties. Using a two-locus haploid model of sexual selection in a polygamous population, I show that the absolute preference rule of selective mating may lower the threshold frequency of the preference trait, required for the initiation of the Fisherian process, as low as zero. This was not observed in the previous analyses with fixed relative preference or best of N male rules. It is then argued that absolute preference may cause the initiations of the Fisherian process more easily without introducing additional assumptions such as pleiotropy or random genetic drift. Some problems associated with the mating rule are also discussed.     

Reinforcement and the genetics of nonrandom mating

Abstract.— The occurrence of reinforcement is compared when premating isolation is caused by the spread of a gene causing females to prefer to mate with males carrying a population-specific trait (a "preference" model) and by a gene that causes females to prefer to mate with males that share their own trait phenotype (an "assortative mating" model). Both two-island models, which have symmetric gene flow, and continent-island models, which have one-way gene flow, are explored. Reinforcement is found to occur much more easily in a two-island assortative mating model than in any of the other three models. This is due primarily to the fact that in this model the assortative mating allele will automatically become genetically associated in each population with the trait allele that is favored by natural selection on that island. In contrast, natural selection on the trait both favors and opposes the evolution of premating isolation in the two-island preference model, depending on the particular population. These results imply that species recognition in the context of mating may evolve particularly easily when it targets cues that are favored by natural selection in each population. In the continent-island models, reinforcement is found to occur more often under the preference model than the assortative mating model, thus reversing the trend from the two-island models. Patterns of population subdivision may therefore play a role in determining what types of premating isolation may evolve.     

The population genetics of assortative mating based on imprinting

This paper is concerned with the population effects of mating preferences for inherited traits. We suppose that the trait is determined by a pair of alleles and concentrate on the autosomal case with complete dominance. We are interested in the case when the mating preferences are determined by the phenotype of relatives, such as parents or sibs. This is a possible consequence of imprinting, a kind of learning process which occurs early after birth in warmblooded vertebrates. In spite of the greater analytical complexity of these models, their results are very similar to those found when the preference is determined by the phenotype of the mating individual itself. In particular the preference for the same phenotype as that of relatives usually leads to the fixation of either morph, depending on the initial frequency. Polymorphism, on the other hand, always results when the preference is for a phenotype which differs from that of relatives.     

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.     

Female mate preferences in Drosophila simulans: evolution and costs

Female mate preference is central to sexual selection, and all indirect benefit models require that there is genetic variation in female preference. This has rarely been tested however, with relatively few studies documenting heritable variation in female preference and even fewer that have directly selected on mate preference to unequivocally show that it can evolve. Additionally, costs of mate preference are poorly understood even though these have implications for preference evolution. We selected on female preference for ebony‐males in replicate Drosophila simulans lines, and generated a rapid evolutionary response in both replicates, with the proportion of females mating with ebony‐males increasing from approximately 5% to 30% after five generations of selection. This increase was independent of changes in ebony‐males as only females were included in our selection regime. We could detect no cost to mate preference itself other than that associated with the fitness consequences of mating with ebony males.     

The Evolutionary Consequences of Disrupted Male Mating Signals: An Agent-Based Modelling Exploration of Endocrine Disrupting Chemicals in the Guppy

Females may select a mate based on signalling traits that are believed to accurately correlate with heritable aspects of male quality. Anthropogenic actions, in particular chemicals released into the environment, are now disrupting the accuracy of mating signals to convey information about male quality. The long-term prediction for disrupted mating signals is most commonly loss of female preference. Yet, this prediction has rarely been tested using quantitative models. We use agent-based models to explore the effects of rapid disruption of mating signals. In our model, a gene determines survival. Males signal their level of genetic quality via a signal trait, which females use to select a mate. We allowed this system of sexual selection to become established, before introducing a disruption between the male signal trait and quality, which was similar in nature to that induced by exogenous chemicals. Finally, we assessed the capacity of the system to recover from this disruption. We found that within a relatively short time frame, disruption of mating signals led to a lasting loss of female preference. Decreases in mean viability at the population-level were also observed, because sexual-selection acting against newly arising deleterious mutations was relaxed. The ability of the population to recover from disrupted mating signals was strongly influenced by the mechanisms that promoted or maintained genetic diversity in traits under sexual selection. Our simple model demonstrates that environmental perturbations to the accuracy of male mating signals can result in a long-term loss of female preference for those signals within a few generations. What is more, the loss of this preference can have knock-on consequences for mean population fitness.     

CAN REINFORCEMENT OCCUR WITH A LEARNED TRAIT?

We use birdsong as a case study to ask whether reinforcement can occur via the spread of a genetically determined female preference for a socially inherited (learned) male trait. We envision secondary contact between two neighboring populations with different song dialects. An individual's ability to learn song is confined by a genetic predisposition: if predispositions are strong, there will be no phenotypic overlap in song between populations, whereas weak predispositions allow phenotypic overlap, or "mixed" song. To determine if reinforcement has occurred, we consider if an allele for within-population female mating preference, based on song, can spread, and whether population specific songs can concurrently be maintained at equilibrium. We model several scenarios, including costs to mating preferences, mating preferences in hybrids, and hybrids having the ability to learn pure songs. We find that when weak predispositions are fixed within a population reinforcement based on song cannot occur. However, when some individuals have strong predispositions, restricting phenotypic overlap between populations in the trait, reinforcement is only slightly inhibited from a purely genetic model. Generalizing beyond the example of song, we conclude that socially learned signals will tend to prohibit reinforcement, but it may still occur if some individuals acquire trait phenotypes genetically.     

Can Preference for Oviposition Sites Initiate Reproductive Isolation in Callosobruchus maculatus?

Theory has identified a variety of evolutionary processes that may lead to speciation. Our study includes selection experiments using different host plants and test key predictions concerning models of speciation based on host plant choice, such as the evolution of host use (preference and performance) and assortative mating. This study shows that after only ten generations of selection on different resources/hosts in allopatry, strains of the seed beetle Callosobruchus maculatus develop new resource preferences and show resource-dependent assortative mating when given the possibility to choose mates and resources during secondary contact. The resulting reduced gene flow between the different strains remained for two generations after contact before being overrun by disassortative mating. We show that reduced gene flow can evolve in a population due to a link between host preference and assortative mating, although this result was not found in all lines. However, consistent with models of speciation, assortative mating alone is not sufficient to maintain reproductive isolation when individuals disperse freely between hosts. We conclude that the evolution of reproductive isolation in this system cannot proceed without selection against hybrids. Other possible factors facilitating the evolution of isolation would be longer periods of allopatry, the build up of local adaptation or reduced migration upon secondary contact.     

Studies on assortative mating. III. The effects of incomplete penetrance in assortative mating systems

Four models of positive and negative assortative mating systems, exclusive or partial, in relation to phenotypes determined by a pair of autosomal alleles with dominance but with incomplete penetrance of the dominant allele in heterozygous state, are presented. By introducing the parameter of incomplete penetrance in the models of assortative matings, matings between individuals with identical genotypes will occur within the negative systems, as well as matings between individuals with different genotypes within the positive assortative mating systems. Thus, incomplete penetrance has the effect of retarding equilibrium on an assortative mating system, making this equilibrium equivalent to a system with a lower degree of assortative mating, where the penetrance equals 1 or 0. Another conclusion of biological interest drawn from the mathematical analysis presented in this paper is that for any value of the penetrance, the frequency of 0.5 for recessive individuals is also typical of exclusive or partial negative assortative mating systems at equilibrium.     

Two locus models of selection and mutation within and among full-sib lines

Summary General models for continued full-sib mating with two diallelic autosomal loci taking account of linkage, mutation and selection within and among lines are considered. The problems are first approached by deriving the full probability transition matrix, taking account of linkage, mutation and within-line selection. Exact solutions to the equilibrium system are possible, but the computational effort is prohibitive, and this is exacerbated by the introduction of between-line selection. A second approach is based on decomposing the transition matrix into blocks whose properties suggest approximations that lead to a rapid iterative solution of the equilibrium system. Extensive numerical analysis of models of within-line selection and of combined within- and between-line selection were made. The results show that equilibrium values are essentially independent of the degree of linkage under models of within-line selection. This is because mutation plays a dominant role in determining equilibrium structure. Results from models of combined within- and between-line selection show that between-line selection has the dominant influence on gene frequency equilibrium. Both within-line and between-line selection produce appreciable linkage disequilibrium only when selection is disruptive. The results also suggest that much of the twolocus equilibrium structure can be predicted from a knowledge of single-locus equilibria.     

The Classical Assortative Mating Process when more than one Continuous Characteristic is Considered

In this article we give a general proof for the existence of the equilibrium position for the joint phenotypic distribution of several continuous characteristics, in a population which reproduces assortatively, and wherein generations are overlapping. This model is a more realistic one for human populations, compared with models arising from consideration of a single characteristic. By placing realistic conditions on the assortation process in the equilibrium position it is found that the consequences are even less realistic and less satisfactory compared with conclusions from single (continuous) characteristic models involving assortative mating. This suggests that a different approach to modelling the assortation process may be required, and this is discussed alsewhere (WILSON, 1981).     

FEMALE PREFERENCE FOR MALE COURTSHIP EFFORT CAN DRIVE THE EVOLUTION OF MALE MATE CHOICE

The evolution of male mate choice is constrained by costs of choice in species with a male‐biased operational sex ratio (OSR). Previous theoretical studies have shown that significant benefits of male choice are required, for example, by mating with more fecund females, in order for these costs to be offset and a male preference to spread. In a series of population genetic models we show the novel effect that male mating preference, expressed as a bias in courtship, can spread when females prefer, and thus are more likely to mate with, males who court more. We explore two female preference functions for levels of male courtship, one representing a threshold and the other a weighted female preference. The basic finding generally holds for both preference functions. However, the preference function greatly affects the spread of a male preference allele after the addition of competing males who can court more in total. Our results thus stress that a thorough understanding of the response of females to male courtship is a critical component to understanding male preference evolution in polygynous species.     

Runaway sexual selection with paternal transmission of the male trait and gene-culture determination of the female preference

Sexual selection is modeled with a male viability-reducing trait and a female mating preference for that trait both of which are culturally transmitted. Both the male trait and the female preference are transmitted only between same-sex individuals, so that non-random association between the trait and the preference, which would give rise to a Fisherian runaway process, cannot arise. Inclusion of an autosomal gene that confers a female predisposition to acquire a certain preference is shown to allow the coevolution of the male trait and the female preference by a Fisherian process. This holds true even when the female preference has a slight viability cost, provided the male cultural transmission is not perfect. It is also suggested that a Fisherian process can be more easily initiated in these models than in the conventional genetic models. Furthermore, a Fisherian process may cause cultural transmission of female preference to evolve. Additionally, polymorphism can be maintained at the predisposition locus if heterozygous females have a stronger predisposition to acquire the preference than homozygotes. Our models may be applicable to the case when the male trait is a Y-linked genetic or environmentally determined trait.