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.     

The role of amplifiers in sexual selection: An integration of the amplifying and the Fisherian mechanisms

Summary In a non-Fisherian genetic model I have shown that sexual displays can evolve even if displays are not directly and unconditionally preferred by females (a basic requirement in any Fisherian model), provided that they amplify previously recognized differences in male quality. Here I show how this amplifying mechanism interacts with the traditional Fisherian mechanism of sexual selection. The theory that integrates these two mechanisms provides a more robust, entirely selective scenario of the evolution of mating preferences and sexual displays.     

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.     

The costs of choice in sexual selection

In Fisher's model of sexual selection female mating preferences are not subject to direct selection but evolve purely because they are genetically correlated with the favoured male trait. But when female choice is costly relative to random mating, for example in energy, time or predation risks, the evolution of female mating preference is subject also to direct selection. With costly female choice the set or line of equilibria found in models of Fisher's process no longer exists. On the line the male trait is under zero net selection, and there is no advantage for a female choosing a male with a more exaggerated character. Therefore any cost to choice causes choosiness to decline. In turn this lowers the strength of sexual selection and the male trait declines as well. So when Fisher's process is the sole force of sexual selection and female choice is costly, only transitory increases in female choice and the preferred male trait are possible. It has often been claimed that exaggerated male characters act as markers or revealers of the genetic quality of potential mates. If females choose their mates using traits that correlate with heritable viability differences then stable exaggeration of both female choice and the preferred male character is possible, even when female choice is costly. The offspring of choosy females have not only a Fisherian reproductive advantage but also greater viability. This suggests that in species with exaggerated male ornamentation, in which female choice is costly, it is likely that female mate choice will be for traits that correlate with male genetic quality.     

SEXUAL SELECTION,SPACE, AND SPECIATION

A Fisherian model of sexual selection is combined with a diffusion model of mate dispersal to investigate the evolution of assortative mating in a sympatric population. Females mate with one of two types of polygynous males according to a male's display of one of two sex-limited, autosomal traits; these male traits may be associated with differential phenotypic mortalities. Through a Fisherian runaway process, female preferences and male traits can become associated in linkage disequilibrium, leading to patterns of assortative mating. Dispersing males, whose rate of movement is dependent on mating success, carry female preference genes with them, and displaced males thereby produce daughters with preference genes for their respective traits in locally higher than average frequencies. The reduced diffusion of the more preferred males permits the success of other male types in adjacent areas. Thus, mating-success dependent diffusion, when coupled with the rapid divergence in phenotypes possible under the Fisher process, can lead to the coexistence of two female preferences and two male traits in sympatry. We argue that many existing approaches to sympatric speciation fail to explain observed male polymorphisms because they exclude explicit spatial structure from their speciation models.     

EVOLUTION OF CONDITION-DEPENDENT SEX ORNAMENTS AND MATING PREFERENCES: SEXUAL SELECTION BASED ON VIABILITY DIFFERENCES

The possibility that the evolution of mating preferences and secondary sex traits can be based on heritable differences in viability is examined with a three-locus model. Earlier genetic models suggested that viability-based processes alone cannot explain the evolution of mate choice and sex ornaments that reduce survival; a Fisherian mating advantage seemed necessary. The present model is based on a monogamous mating system that precludes such a mating advantage. A key assumption is that ornament development depends on the phenotypic condition and overall genotype of the possessor; there is evidence that secondary sex traits often mirror nutritional status and health, sometimes through hormonal mediation. Ornament and preference can then hitchhike slowly to high frequency with alleles that confer a slight survival advantage, provided that such alleles become available often enough. The evolution of mating preferences and secondary sex traits that reflect overall genotypic constitution therefore can be based solely on viability differences, no Fisherian mating advantage being required. In practice, these and several other mechanisms of sexual selection may occur together.     

Z LINKAGE OF FEMALE PROMISCUITY GENES IN THE MOTH UTETHEISA ORNATRIX: SUPPORT FOR THE SEXY‐SPERM HYPOTHESIS?

Female preference genes for large males in the highly promiscuous moth Utetheisa ornatrix (Lepidoptera: Arctiidae) have previously been shown to be mostly Z‐linked, in accordance with the hypothesis that ZZ–ZW sex chromosome systems should facilitate Fisherian sexual selection. We determined the heritability of both female and male promiscuity in the highly promiscuous moth U. ornatrix (Lepidoptera: Arctiidae) through parent–offspring and grandparent–offspring regression analyses. Our data show that male promiscuity is not sex‐limited and either autosomal or sex‐linked whereas female promiscuity is primarily determined by sex‐limited, Z‐linked genes. These data are consistent with the “sexy‐sperm hypothesis,” which posits that multiple‐mating and sperm competitiveness coevolve through a Fisherian‐like process in which female promiscuity is a kind of mate choice in which sperm‐competitiveness is the trait favored in males. Such a Fisherian process should also be more potent when female preferences are Z‐linked and sex‐limited than when autosomal or not limited.     

DYNAMICS OF SEXUAL SELECTION IN DIPLOID POPULATIONS

We describe results for a diploid, two-locus model for the evolution of a female mating preference directed at an attractive male trait that is subject to viability and/or fertility selection. Using computer simulation, we studied a large, random sample of parameter values, assuming additivity of alleles at the preference locus and partial dominance at the trait locus. Simulation results were classifiable into nine types of parameter sets, each differing in equilibria, evolutionary trajectories, and rates of evolution. For many parameters, evolutionary trajectories converged on curves within the allelic frequency plane and subsequently evolved along the curves toward fixation. Neutrally stable curves of equilibria did not occur in Fisherian models that assume only viability and sexual selection unless there is complete dominance at the trait locus. The Fisherian models also exhibited oscillation of allelic frequencies and unique polymorphic equilibria. “Sexy son” models in which attractive males had reduced fertility were much less likely to lead to increase in traits and preferences than were the Fisherian models. However, if less fertile males had increased viability, trait polymorphisms and fixation of rare “sexy” alleles occurred. In general, the behavior of the diploid model was much more complex than that of analogous haploid or polygenic models.     

PLOIDY AND EVOLUTION BY SEXUAL SELECTION: A COMPARISON OF HAPLOID AND DIPLOID FEMALE CHOICE MODELS NEAR FIXATION EQUILIBRIA

We compare the stability properties of haploid and diploid models of Fisherian sexual selection (with male contribution limited to sperm) by examining both models at equilibria for which a male trait is fixed or absent. Haploid and diploid two locus diallelic models share the property that the stability of such fixation equilibria is determined by the relationship between the harmonic mean of relative preference values for the common male trait, weighted by the frequency of the preferences, and the relative viability associated with the common male trait. When diploid females with heterozygotic-based preferences express preference strengths intermediate between homozygote-based preferences, then boundary equilibria of haploid and diploid models share many stability properties. However, even with intermediate heterozygote preferences, haploid and diploid models do differ: (1) for a particular frequency of the preference allele, both fixation boundaries can be stable for the diploid model, and (2) with over- or underdominance at the preference locus (a possibility precluded in the haploid model), a fixation boundary in the diploid model may show two switches in its stability state for increasing frequencies of one of the preference alleles. These differences are due not just to the impossibility of dominance in haploid models, but also to the larger number of diploid genotypes.     

Sympatric speciation by sexual selection: a critical reevaluation

Several empirical studies put forward sexual selection as an important driving force of sympatric speciation. This idea agrees with recent models suggesting that speciation may proceed by means of divergent Fisherian runaway processes within a single population. Notwithstanding this, the models so far have not been able to demonstrate that sympatric speciation can unfold as a fully adaptive process driven by sexual selection alone. Implicitly or explicitly, most models rely on nonselective factors to initiate speciation. In fact, they do not provide a selective explanation for the considerable variation in female preferences required to trigger divergent runaway processes. We argue that such variation can arise by disruptive selection but only when selection on female preferences is frequency dependent. Adaptive speciation is therefore unattainable in traditional female choice models, which assume selection on female preferences to be frequency independent. However, when frequency-dependent sexual selection processes act alongside mate choice, truly adaptive sympatric speciation becomes feasible. Speciation is then initiated independently of nonadaptive processes and does not suffer from the theoretical weaknesses associated with the current Fisherian runaway model of speciation. However, adaptive speciation requires the simultaneous action of multiple mechanisms, and therefore it occurs under conditions far more restrictive than earlier models of sympatric speciation by sexual selection appear to suggest.     

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.     

Sexual selection in genetic colour-polymorphic species: a review of experimental studies and perspectives

Sexual selection theory has primarily focussed on the role of mating preferences for the best individuals in the evolution of condition-dependent ornaments, traits that signal absolute quality. Because the most suitable mate for one individual is not always the best for others, however, we argue that non-directional mate choice can promote the evolution of alternative morphs that are not condition-dependent in their expression (i.e. genetic polymorphism). We list the different mate-choice rules (i.e. all individuals have the same preference; preference depends on the chooser’s morph; individuals mate preferentially with conspecifics displaying an uncommon or the most frequent morph) and review experimental studies that investigated mate choice in natural populations of colour-polymorphic animals. Our review emphasises that although the experimental data support the idea that sexual selection plays an important role in the evolution of genetic colour polymorphism in many different ways, little is known about the adaptive value of each mate-choice strategy and about their implication in the evolutionary stability of colour polymorphism. One way of solving this problem is to determine the adaptive function of colour morphs, a worthwhile objective, because better understanding of mate-choice rules in polymorphic species should provide important insights into sexual-selection processes and, in turn, into the maintenance of genetic variation.     

Runaway sexual selection without genetic correlations: social environments and flexible mate choice initiate and enhance the fisher process

Female mating preferences are often flexible, reflecting the social environment in which they are expressed. Associated indirect genetic effects (IGEs) can affect the rate and direction of evolutionary change, but sexual selection models do not capture these dynamics. We incorporate IGEs into quantitative genetic models to explore how variation in social environments and mate choice flexibility influence Fisherian sexual selection. The importance of IGEs is that runaway sexual selection can occur in the absence of a genetic correlation between male traits and female preferences. Social influences can facilitate the initiation of the runaway process and increase the rate of trait elaboration. Incorporating costs to choice do not alter the main findings. Our model provides testable predictions: (1) genetic covariances between male traits and female preferences may not exist, (2) social flexibility in female choice will be common in populations experiencing strong sexual selection, (3) variation in social environments should be associated with rapid sexual trait divergence, and (4) secondary sexual traits will be more elaborate than previously predicted. Allowing feedback from the social environment resolves discrepancies between theoretical predictions and empirical data, such as why indirect selection on female preferences, theoretically weak, might be sufficient for preferences to become elaborated.     

Female mating preferences determine system-level evolution in a gene network model

Environmental patterns of directional, stabilizing and fluctuating selection can influence the evolution of system-level properties like evolvability and mutational robustness. Intersexual selection produces strong phenotypic selection and these dynamics may also affect the response to mutation and the potential for future adaptation. In order to to assess the influence of mating preferences on these evolutionary properties, I modeled a male trait and female preference determined by separate gene regulatory networks. I studied three sexual selection scenarios: sexual conflict, a Gaussian model of the Fisher process described in Lande (in Proc Natl Acad Sci 78(6):3721–3725, 1981) and a good genes model in which the male trait signalled his mutational condition. I measured the effects these mating preferences had on the potential for traits and preferences to evolve towards new states, and mutational robustness of both the phenotype and the individual’s overall viability. All types of sexual selection increased male phenotypic robustness relative to a randomly mating population. The Fisher model also reduced male evolvability and mutational robustness for viability. Under good genes sexual selection, males evolved an increased mutational robustness for viability. Females choosing their mates is a scenario that is sufficient to create selective forces that impact genetic evolution and shape the evolutionary response to mutation and environmental selection. These dynamics will inevitably develop in any population where sexual selection is operating, and affect the potential for future adaptation.     

Sexually selected traits and adult survival: a meta-analysis

Traits correlated with male mating success are likely to be subject to sexual selection. Sexually selected characters are thought to be costly to develop and maintain. If males do not vary their investment in sexual traits in relation to their ability to bear the costs, there should be a negative relationship between male longevity or survival and the expression of sexual traits. In particular, a negative relationship is predicted by pure Fisherian models for the evolution of sexual ornaments. The same should also be true for traits that evolve via pleiotropy (e.g., due to sensory exploitation or bias) with no subsequent evolution of condition dependent modification. We collected information on the relationship between traits correlated with male mating rate and estimates of adult male survivorship or life span. In total we obtained 122 samples from 69 studies of 40 species of bird, spider, insect, and fish. In a meta-analysis we calculated the average sample size weighted correlation between trait expression and adult survival. Analyses at the level of samples, studies, and species revealed significant positive relationships (r = 0.08, 0.10, and 0.13, respectively; all P < 0.001). The unweighted correlation at the species level was r = 0.24. In general, males with larger ornaments or weapons, greater body size, or higher rates of courtship showed greater survivorship or longevity. This finding is inconsistent with pure Fisherian models or other models that do not incorporate condition or quality dependent trait expression. It suggests that male investment in sexually selected traits is not fixed but varies in relation to the ability to pay the underlying costs of expressing these characters. Hence, many secondary sexual characters are likely to be condition dependent in their expression.     

On the logic of Fisherian sexual selection*

In Fisher's model of sexual selection, a female preference for a male trait spreads together with the trait because their genetic bases become correlated. This can be interpreted as a “greenbeard” system: a preference gene, by inducing a female to mate with a trait-bearing male, favors itself because the male is disproportionately likely also to carry the preference gene. Here, we use this logic to argue that Fisherian sexual selection in diploids proceeds via two channels: (i) trait-bearing males are disproportionately the product of matings between preference-bearing mothers and trait-bearing fathers, and thus trait and preference genes are correlated “in trans”; (ii) trait and preference genes come into gametic phase disequilibrium, and thus are correlated “in cis.” Gametic phase disequilibrium is generated by three distinct mechanisms that we identify. The trans channel does not operate when sexual selection is restricted to the haploid phase, and therefore represents a fundamental difference between haploid and diploid models of sexual selection. We show that the cis and trans channels contribute equally to the spread of the preference when recombination between the preference and trait loci is free, but that the trans channel is substantially more important when linkage is tight.     

SEXUAL SELECTION BY THE HANDICAP MECHANISM

The handicap mechanism of sexual selection by female choice has been strongly criticized because it does not cause sexual selection to reinforce viability selection and it cannot account for the origin of mating preferences. However, several models indicate that the handicap mechanism can have important effects when operating in conjunction with Fisher's mechanism in polygynous populations. These models have been criticized because they require that fitness remains heritable indefinitely. I develop a simple haploid model of the handicap mechanism based on nonheritable variation in paternal investment, thus eliminating the problem of heritable fitness. This model produces the same evolutonary dynamics as both simple and quantitative genetic models of the handicap mechanism based on heritable fitness. If the parameters are such that Fisherian runaway selection does not occur in the null model (i.e., the polymorphic equilibria, which lie along the “Fisher line,” are stable), then the handicap mechanism turns the Fisher line into an evolutionary trajectory upon which all other trajectories converge. This occurs because Fisher's mechanism generates no net selection on female preference when the population is on the Fisher line, so that any additional source of selection (direct or indirect) on female choice causes the population to evolve deterministically along the Fisher line. This change in the evolutionary dynamics has the important consequence of eliminating the potential for rapid population divergence for mating systems via genetic drift along the Fisher line.     

Heterospecific mating preferences for a feather ornament in least auklets

Auklets (Alddae, Aethiini) include five species of small, sociallymonogamous, sexually monomorphic seabirds that display a varietyof feather and bare-part ornaments during the breeding season.Previous experimental work on two auklet species has demonstratedthat some ornaments are likely to be favored by sexual selectionbecause mutual male and female mating preferences benefit individualswith the most elaborate expression of these traits. In thisstudy we experimentally investigated whether naturally crestlessleast auklets Aethia pusilla have a maring preference for foreheadcrests similar to the most prominent ornament of two other species,crested A. cristatella and whiskered auklets A. pygmaea. Ourobjective was to investigate the function of this ornament asa species-recognition mechanism or as a product of one or moreof three proposed sexual selection models that address the originof elaborate traits and preferences. During the experiment,least auklets reacted to realistic models equipped with artificialforehead crests with approximately an order of magnitude morefrequent sexual displays and greater interest, consistent withthe idea that they have a mating preference for crests, eventhough they do not naturally express this ornament This heterospecificpreference also favored large crest size. These results refutethe possibility that least auklet forehead ornamentation alonedetermines species recognition at present Among models of sexualselection considered, the results are consistent with the sensoryexploitation model, although this could not be established unequivocallybecause a viability indicator or Fisherian mechanism could havebeen involved if least auklets had an ancestor with a foreheadcrest.     

GOOD GENES AND DIRECT SELECTION IN THE EVOLUTION OF MATING PREFERENCES

A model is used to study quantitatively the impact of a good genes process and direct natural selection on the evolution of a mating preference. The expression of a male display trait is proportional to genetic quality, which is determined by the number of deleterious mutations a male carries throughout his genome. Genetic variances and covariances, including the covariance between the preference and male trait that drives the good genes process, are allowed to evolve under an infinitesimal model. Results suggest that the good genes process generates only weak indirect selection on preferences, with an effective selection intensity of a few percent or less. If preferences are subject to direct natural selection of the intensity observed for other characters, the good genes process alone is not expected to exaggerate the male trait by more than a few phenotypic standard deviations, contrary to what is observed in highly sexually selected species. Good genes can, however, cause substantial exaggeration if preference genes are nearly selectively neutral. Alternatively, direct selection on preference genes, acting on mating behavior itself or on the genes' pleiotropic effects, can cause mating preferences and male display traits to be exaggerated by any degree. Direct selection of preference genes may therefore play an important role in species that show extreme sexual selection.