Sexual Dimorphism Increases Evolvability in a Genetic Regulatory Network

The majority of work on genetic regulatory networks has focused on environmental and mutational robustness, and much less attention has been paid to the conditions under which a network may produce an evolvable phenotype. Sexually dimorphic characters often show rapid rates of change over short evolutionary time scales and while this is thought to be due to the strength of sexual selection acting on the trait, a dimorphic character with an underlying pleiotropic architecture may also influence the evolution of the regulatory network that controls the character and affect evolvability. As evolvability indicates a capacity for phenotypic change and mutational robustness refers to a capacity for phenotypic stasis, increases in evolvability may show a negative relationship with mutational robustness. I tested this with a computational model of a genetic regulatory network and found that, contrary to expectation, sexually dimorphic characters exhibited both higher mutational robustness and higher evolvability. Decomposition of the results revealed that linkage disequilibrium within sex and linkage disequilibrium between sexes, two of the three primary components of additive genetic variance and evolvability in quantitative genetics models, contributed to the differences in evolvability between sexually dimorphic and monomorphic populations. These results indicate that producing two pleiotropically linked characters did not constrain either the production of a robust phenotype or adaptive potential. Instead, the genetic system evolved to maximize both quantities.     

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.     

Environmental Noise,Genetic Diversity and the Evolution of Evolvability and Robustness in Model Gene Networks

The ability of organisms to adapt and persist in the face of environmental change is accepted as a fundamental feature of natural systems. More contentious is whether the capacity of organisms to adapt (or “evolvability”) can itself evolve and the mechanisms underlying such responses. Using model gene networks, I provide evidence that evolvability emerges more readily when populations experience positively autocorrelated environmental noise (red noise) compared to populations in stable or randomly varying (white noise) environments. Evolvability was correlated with increasing genetic robustness to effects on network viability and decreasing robustness to effects on phenotypic expression; populations whose networks displayed greater viability robustness and lower phenotypic robustness produced more additive genetic variation and adapted more rapidly in novel environments. Patterns of selection for robustness varied antagonistically with epistatic effects of mutations on viability and phenotypic expression, suggesting that trade-offs between these properties may constrain their evolutionary responses. Evolution of evolvability and robustness was stronger in sexual populations compared to asexual populations indicating that enhanced genetic variation under fluctuating selection combined with recombination load is a primary driver of the emergence of evolvability. These results provide insight into the mechanisms potentially underlying rapid adaptation as well as the environmental conditions that drive the evolution of genetic interactions.     

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.     

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.     

Reducing mutation load through sexual selection on males

Mutation load is a key parameter in evolutionary theories, but relatively little empirical information exists on the mutation load of populations, or the elimination of this load through selection. We manipulated the opportunity for sexual selection within a mutation accumulation divergence experiment to determine how sexual selection on males affected the accumulation of mutations contributing to sexual and nonsexual fitness. Sexual selection prevented the accumulation of mutations affecting male mating success, the target trait, as well as reducing mutation load on productivity, a nonsexual fitness component. Mutational correlations between mating success and productivity (estimated in the absence of sexual selection) were positive. Sexual selection significantly reduced these fitness component correlations. Male mating success significantly diverged between sexual selection treatments, consistent with the fixation of genetic differences. However, the rank of the treatments was not consistent across assays, indicating that the mutational effects on mating success were conditional on biotic and abiotic context. Our experiment suggests that greater insight into the genetic targets of natural and sexual selection can be gained by focusing on mutational rather than standing genetic variation, and on the behavior of trait variances rather than means.     

Limits to runaway sexual selection: The wallflower paradox

In his mathematical treatment of Fisher's ideas on sexual selection (so-called runaway selection) Lande (1981) predicted that males may evolve increasingly elaborate sexual characters despite opposing viability selection as a consequence of the associated costs. Lande thereby assumed that female mate preferences are not subject to selection since (1) females are all inseminated and (2) the quantity and quality of their offspring are independent of the female's mate preferences. Kirkpatrick (1985) removed the latter assumption and investigated the consequences for the mean phenotype with respect to both female and male traits. He also explored the dynamics of the (co)-variance matrix by numerical methods. In this paper we consider a simpler model with just two multi-allelic loci. This enables us to derive explicit expressions for (co)-variances under steady state conditions. Rather than assume natural selection through differential fertility (as in Kirkpatrick, 1985), we take sexual selection on females into account by modelling the preference-dependent risk that females remain unmated. We argue that this wallflower effect is a realistic feature of any mating system, since it merely depends on the existence of (1) variation in mating preferences and (2) a finite mating season. Our approach provided an insight into the dynamic behaviour of the means of the phenotypes. This is because the dynamics of the means depend on the steady state (co)-variance matrix. Thus, an insight into the former requires explicit expressions for the latter. Whereas Lande and Kirkpatrick predicted runaway processes, despite opposing viability selection, our model predicts a globally stable steady state, i.e. no runaway, even without opposing viability selection (under the assumption of an asymptotically stable steady state of the (co)-variances. Admittedly, we have no analytic proof of this stability but only support for it, based on simulations.) The absence of the runaway processes in our model is caused by the wallflower effect, since it imposes constraints on the steady state of the (co)-variance matrix. When mutational input applies to female traits but not to male traits, explicit expressions for the (co)-variances under steady state conditions can be derived, and these show that: (1) both the genetic covariance and the variance of male traits are equal to zero, but (2) the variance of the female trait exceeds to zero. Should there be mutational input influencing the male trait, then these results would suggest that the male-to-female ratio of variances is much smaller than unity. This prediction is of tremendous importance for speciation through founding events.     

Phenotypic variability can promote the evolution of adaptive plasticity by reducing the stringency of natural selection

Adaptive phenotypic plasticity is a potent but not ubiquitous solution to environmental heterogeneity, driving interest in what factors promote and limit its evolution. Here, a novel computational model representing stochastic information flow in development is used to explore evolution from a constitutive phenotype to an adaptively plastic response. Results show that populations tend to evolve robustness to developmental stochasticity, but that this evolved robustness limits evolvability; specifically, robust genotypes have less ability to evolve adaptive plasticity when presented with a mix of both the ancestral environment and a new environment. Analytic calculations and computational experiments confirm that this constraint occurs when the initial mutational steps towards plasticity are pleiotropic, such that mutant fitnesses decline in the environment to which their parents are well‐adapted. Greater phenotypic variability improves evolvability in the model by lessening this decline as well as by improving the fitness of partial adaptations to the new environment. By making initial plastic mutations more palatable to natural selection, phenotypic variability can increase the evolvability of an innovative, plastic response without improving evolvability to simpler challenges such as a shifted optimum in a single environment. Populations that evolved robustness by negative feedback between the trait and its rate of change show a particularly strong constraining effect on the evolvability of plasticity, revealing another mechanism by which evolutionary history can limit later innovation. These results document a novel mechanism by which weakening selection could actually stimulate the evolution of a major innovation.     

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.     

THE DARWIN-FISHER THEORY OF SEXUAL SELECTION IN MONOGAMOUS BIRDS

Males of monogamous birds often show secondary sexual traits that are conspicuous but considerably less extreme than those of polygynous species. We develop a quantitative-genetic model for the joint evolution of a male secondary sexual trait, a female mating preference, and female breeding date, following a theory proposed by Darwin and Fisher. Good nutritional condition is postulated to cause females to breed early and to have high fecundity. The most-preferred males are mated by early-breeding females and receive a sexual-selection advantage from those females' greater reproductive success. Results show that conspicuous male traits that decrease survival can evolve but suggest that the extent of maladaptive evolution is greatly limited relative to what is possible in a polygynous mating system for two reasons. First, in the absence of direct fitness effects of mate choice on the female, the equilibria for the male trait and female preference form a curve whose shape shows that the maximum possible strength of sexual selection on males (and hence the potential for maladaptive evolution) is constrained. Under certain conditions, a segment of the equilibrium curve may become unstable, leading to two alternative stable states for the male trait. Second, male parental care will often favor the evolution of mating preferences for less conspicuous males. We also find that sexual selection can appear in the absence of the nutritional effects emphasized by Darwin and Fisher. A review of the literature suggests that the assumptions of the Darwin-Fisher mechanism may often be met in monogamous birds and that other mechanisms may often reinforce it by producing additional components of sexual selection.     

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.     

Divergence and evolution of assortative mating in a polygenic trait model of speciation with gene flow

Assortative mating is an important driver of speciation in populations with gene flow and is predicted to evolve under certain conditions in few‐locus models. However, the evolution of assortment is less understood for mating based on quantitative traits, which are often characterized by high genetic variability and extensive linkage disequilibrium between trait loci. We explore this scenario for a two‐deme model with migration, by considering a single polygenic trait subject to divergent viability selection across demes, as well as assortative mating and sexual selection within demes, and investigate how trait divergence is shaped by various evolutionary forces. Our analysis reveals the existence of sharp thresholds of assortment strength, at which divergence increases dramatically. We also study the evolution of assortment via invasion of modifiers of mate discrimination and show that the ES assortment strength has an intermediate value under a range of migration‐selection parameters, even in diverged populations, due to subtle effects which depend sensitively on the extent of phenotypic variation within these populations. The evolutionary dynamics of the polygenic trait is studied using the hypergeometric and infinitesimal models. We further investigate the sensitivity of our results to the assumptions of the hypergeometric model, using individual‐based simulations.     

The emotion system promotes diversity and evolvability

Studies on the relationship between the optimal phenotype and its environment have had limited focus on genotype-to-phenotype pathways and their evolutionary consequences. Here, we study how multi-layered trait architecture and its associated constraints prescribe diversity. Using an idealized model of the emotion system in fish, we find that trait architecture yields genetic and phenotypic diversity even in absence of frequency-dependent selection or environmental variation. That is, for a given environment, phenotype frequency distributions are predictable while gene pools are not. The conservation of phenotypic traits among these genetically different populations is due to the multi-layered trait architecture, in which one adaptation at a higher architectural level can be achieved by several different adaptations at a lower level. Our results emphasize the role of convergent evolution and the organismal level of selection. While trait architecture makes individuals more constrained than what has been assumed in optimization theory, the resulting populations are genetically more diverse and adaptable. The emotion system in animals may thus have evolved by natural selection because it simultaneously enhances three important functions, the behavioural robustness of individuals, the evolvability of gene pools and the rate of evolutionary innovation at several architectural levels.     

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.     

THE EVOLUTION OF MATE PREFERENCES FOR MULTIPLE SEXUAL ORNAMENTS

Males of many species use multiple sexual ornaments in their courtship display. We investigate the evolution of female sexual preferences for more than a single male trait by the handicap process. The handicap process assumes that ornaments are indicators of male quality, and a female benefits from mate choice by her offspring inheriting “good genes” that increase survival chances. A new handicap model is developed that allows equilibria to be given in terms of selection pressures, independent of genetic parameters. Multiple sexual preferences evolve if the overall cost of choice is not greatly increased by a female using additional male traits in her assessment of potential mates. However, only a single preference is evolutionarily stable if assessment of additional male traits greatly increases the overall cost of choice (more than expected by combining the cost of each preference independently). Any single preference can evolve, the outcome being determined by initial conditions. The evolution of one preference effectively blocks the evolution of others, even for traits that are better indicators of male quality. Comparison is made with sexual selection caused by Fisher's runaway process in which male traits are purely attractive characters. This shows that sexual preferences for multiple Fisher traits are likely to evolve alongside preference for a single handicap trait that indicates male quality. This is a general difference in the evolutionary outcome of these two causes of sexual selection.     

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.     

The evolutionary dynamics of evolvability in a gene network model

Evolvability, the ability of populations to adapt, has recently emerged as a major unifying concept in biology. Although the study of evolvability offers new insights into many important biological questions, the conceptual bases of evolvability, and the mechanisms of its evolution, remain controversial. We used simulated evolution of a model of gene network dynamics to test the contentious hypothesis that natural selection can favour high evolvability, in particular in sexual populations. Our results conclusively demonstrate that fluctuating natural selection can increase the capacity of model gene networks to adapt to new environments. Detailed studies of the evolutionary dynamics of these networks establish a broad range of validity for this result and quantify the evolutionary forces responsible for changes in evolvability. Analysis of the genotype–phenotype map of these networks also reveals mechanisms connecting evolvability, genetic architecture and robustness. Our results suggest that the evolution of evolvability can have a pervasive influence on many aspects of organisms.     

An evolutionary limit to male mating success

The well-known phenotypic diversity of male sexual displays, and the high levels of genetic variation reported for individual display traits have generated the expectation that male display traits, and consequently male mating success, are highly evolvable. It has not been shown however that selection for male mating success, exerted by female preferences in an unmanipulated population, results in evolutionary change. Here, we tested the expectation that male mating success is highly evolvable in Drosophila bunnanda using an experimental evolution approach. Female D. bunnanda exhibit a strong, consistent preference for a specific combination of male cuticular hydrocarbons (CHCs). We used female preference to select for male mating success by propagating replicate populations from either attractive or unattractive males over 10 generations. Neither the combination of CHCs under sexual selection (the sexual signal) nor male mating success itself evolved. The lack of a response to selection was consistent with previous quantitative genetic experiments in D. bunnanda that demonstrated the virtual absence of genetic variance in the combination of CHCs under sexual selection. Persistent directional selection, such as applied by female mate choice, may erode genetic variance, resulting in multitrait evolutionary limits.     

Models of sexual selection on a quantitative genetic trait when preference is acquired by sexual imprinting

The evolution of a quantitative genetic trait under stabilizing viability selection and sexual selection is modeled for a polygynous species in which female mating preferences are acquired by sexual imprinting on the parents and by exposure to the surviving population at large. Stabilizing viability selection acts equally on both sexes in the case of a sexually monomorphic trait and on males only in the case of a dimorphic trait. A genetically fixed sensory or perceptual bias defines the origin of the scale on which the trait is measured, and the possibility is incorporated that female preferences may deviate asymmetrically from the familiar-either toward or away from this origin. When viability selection is strong relative to sexual selection, the models predict that the mean trait value will evolve to the viability optimum. With intermediate ratios of the strength of viability to sexual selection, a stable equilibrium can occur on either side of this viability optimum, depending on the direction of asymmetry in female preferences. When viability selection is relatively weak and certain other conditions are also satisfied, runaway selection is predicted.