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.     

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.     

Why do females care more than males?

Females tend to provide more parental care than males. Previous efforts to account for this have been confused because it is difficult to express the costs of care for males and females in the same currency. Here I propose a null model that does so, using the Fisherian constraint that total male and female reproduction must be equal. The model shows that, contrary to a number of recent analyses, lower probability of parentage for males does tend to make males less likely than females to provide care. It also shows how sexual selection stemming from premating asymmetries in investment promotes similar post-mating asymmetries.     

An experimental demonstration of Fisher's principle: evolution of sexual proportion by natural selection.

Most sexually reproducing species have sexual proportions around 1:1. This major biological phenomenon remained unexplained until 1930, when FISHER proposed that it results from a mechanism of natural selection. Here we report the first experimental test of his model that obeys all its assumptions. We used a naturally occurring X-Y meiotic drive system--the sex-ratio trait of Drosophila mediopunctat--to generate female-biased experimental populations. As predicted by FISHER, these populations evolved toward equal sex proportions due to natural selection, by accumulation of autosomal alleles that direct the parental reproductive effort toward the rare sex. Classical Fisherian evolution is a rather slow mechanism: despite a very large amount of genetic variability, the experimental populations evolved from 16% of males to 32% of males in 49 generations and would take 330 generations (29 years) to reach 49%. This slowness has important implications for species potentially endangered by skewed sexual proportions, such as reptiles with temperature sex determination.     

Digest: Differentiating Fisherian sexual selection dynamics between haploids and diploids*

Female mate preference for males displaying costly traits is a puzzling phenomenon found in nature. Fisher was the first to propose a formal model describing this paradoxical system of sexual selection. Despite the many models constructed from his theory, much remains unknown about its mechanics, especially in different genetic settings. Through simulations, Veller et al. compared population dynamics between haploids and diploids and found that Fisherian sexual selection acts differently on diploids compared to haploids due to linkage mechanisms.     

Numerical non-identifiability regions of the minimal model of glucose kinetics: superiority of Bayesian estimation

The so-called minimal model (MM) of glucose kinetics is widely employed to estimate insulin sensitivity (S(I)) both in clinical and epidemiological studies. Usually, MM is numerically identified by resorting to Fisherian parameter estimation techniques, such as maximum likelihood (ML). However, unsatisfactory parameter estimates are sometimes obtained, e.g. S(I) estimates virtually zero or unrealistically high and affected by very large uncertainty, making the practical use of MM difficult. The first result of this paper concerns the mathematical demonstration that these estimation difficulties are inherent to MM structure which can expose S(I) estimation to the risk of numerical non-identifiability. The second result is based on simulation studies and shows that Bayesian parameter estimation techniques are less sensitive, in terms of both accuracy and precision, than the Fisherian ones with respect to these difficulties. In conclusion, Bayesian parameter estimation can successfully deal with difficulties of MM identification inherently due to its structure.     

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.     

Sympatric speciation and extinction driven by environment dependent sexual selection

A theoretical model is studied to investigate the possibility of sympatric speciation driven by sexual selection and ecological diversification. In particular we focus on the rock-dwelling haplochromine cichlid species in Lake Victoria. The high speciation rate in these cichlids has been explained by their apparent ability to specialize rapidly to a large diversity of feeding niches. Seehausen and colleagues however, demonstrated the importance of sexual selection in maintaining reproductive barriers between species. Our individual-orientated model integrates both niche differentiation and a Fisherian runaway process, which is limited by visibility constraints. The model shows rapid sympatric speciation or extinction of species, depending on the strength of sexual selection.     

Long-term persistence of exaggerated ornaments under Fisherian runaway despite costly mate search

Exaggerated ornaments often evolve due to the mating preferences of the opposite sex. Genetic correlations between preferences and ornaments can lead both traits to elaborate dramatically in tandem, in a process known as ‘Fisherian runaway’. However, in most previous models of Fisherian runaway, elaborate ornaments are not expected to persist when preferences are consistently costly to the choosing sex. In contrast, we show here that exaggerated male ornaments can be maintained long term even when females must pay a cost to choose their mates. Preferences per se are not costly in our model, but females can only act on their preferences by investing resources in mate search. We predict that mate search effort should decrease with the cost of sampling additional mates and increase with the number of possible ornaments that females can choose from. The potential for multiple exaggerated ornaments to coexist depends on subtleties of their cost structure: strict trade-offs (additive costs) favour sequential ornament evolution, whereas looser trade-offs (multiplicative costs) allow for coexistence. Lastly, we show that pleiotropy affecting both ornaments and preferences makes it difficult for Fisherian runaway to initiate, increasing the evolutionary time until ornamentation. Our model highlights the important but neglected role of mate search effort in sexual selection.     

Genetic variation in male attractiveness: It is time to see the forest for the trees

Female choice based on multiple male traits, rather than on any single one, has been reported in many species and may well be a rule rather than an exception. However, the implications this has for selection acting on choosiness itself remain underappreciated. We argue that this constitutes one of the important impediments to our understanding of the evolution of mate choice. We discuss this issue primarily in the context of the Fisherian model of sexual selection. We review theory and empirical data, showing how the crucial parameter of the model—genetic variation in male attractiveness—can be estimated when attractiveness is a function of multiple traits. Based on the reviewed theory, we show how relying on individual male traits, instead of overall attractiveness, can produce biased estimates of Fisherian benefits of female choice. This bias can be substantial, especially when many traits contribute to male attractiveness. We discuss a number of methodological issues that, we hope, will stimulate future studies and help resolving the long‐standing mystery of mate choice.     

EVOLUTION BY FISHERIAN SEXUAL SELECTION IN DIPLOIDS

Most models of Fisherian sexual selection assume haploidy. However, analytical models that focus on dynamics near fixation boundaries and simulations show that the resulting behavior depends on ploidy. Here we model sexual selection in a diploid to characterize behaviour away from fixation boundaries. The model assumes two di-allelic loci, a male-limited trait locus subject to viability selection, and a preference locus that determines a female's tendency to mate with males based on their genotype at the trait locus. Using a quasi-linkage equilibrium (QLE) approach, we find a general equation for the curves of quasi-neutral equilibria, and the conditions under which they are attracting or repelling. Unlike in the haploid model, the system can move away from the internal curve of equilibria in the diploid model. We show that this is the case when the combined forces of natural and sexual selection induce underdominance at the trait locus.     

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.     

Maintenance of genetic variation in sexual ornaments: a review of the mechanisms

Female preferences for elaborate male sexual traits have been documented in a number of species in which males contribute only genes to the next generation. In such systems, mate choice has been hypothesised to benefit females genetically. For the genetic benefits to be possible there must be additive genetic variation (V(A)) for sexual ornaments, such that highly ornamented males can pass fitter genes on to the progeny of choosy females. Here, I review the mechanisms that can contribute to the maintenance of this variation. The variation may be limited to sexual ornaments, resulting in Fisherian benefits in terms of the increased reproductive success of male progeny produced by choosy females. Alternatively, ornaments may capture V(A) in other life-history traits. In the latter case, "good genes" benefits may apply in terms of improved performance of the progeny of either sex. Some mechanisms, however, such as negative pleiotropy, sexually antagonistic variation or overdominance, can maintain V(A )in ornaments and other life-history traits with little variation in total fitness, leaving little room for any genetic benefits of mate choice. Distinguishing between these mechanisms has consequences not only for the theory of sexual selection, but also for evolution of sex and for biological conservation. I discuss how the traditional ways of testing for genetic benefits can usefully be supplemented by tests detecting benefits resulting from specific mechanisms maintaining V(A )in sexual ornaments.     

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.     

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.     

Ecology and evolution of extravagant feather ornaments

The ancestral conditions that permit the evolution of extravagant secondary sexual characters are of considerable theoretical and empirical interest because they allow identification of necessary ecological conditions, but also allow empirical tests of models of female mate preferences. We investigated the ancestral and derived state of a range of ecological and evolutionary variables that might have been implicated in the evolution of secondary sexual characters. Extravagant feather ornaments have evolved independently at least 70 times in birds, and the context of these evolutionary events was investigated statistically. The acquisition of feather ornaments was significantly associated with a change in social mating system from monogamy to polygyny or lekking. This association is consistent with the Fisherian mechanism of sexual selection. However, very often also the acquisition of feather ornaments occurred without change in mating system. Therefore, ornamentation can develop for reasons other than polygyny. We did not find any indication of male parental care, kind of food, foraging mode, coloniality, nest site, migration or body mass being significantly associated with a change in the state of ornamentation.     

The evolution of female preferences for multiple indicators of quality

In a variety of species, females exhibit preferences for multiple male ornaments. Several hypotheses have been proposed to explain this phenomenon. Which, if any, of these hypotheses is the most plausible in general remains largely unresolved based on the available empirical data. Yet theoretical studies conclude that the evolution of preferences for multiple signals of male quality is unlikely, especially when the use of an additional cue in mate choice strongly increases the overall cost of choice. This would imply that most male courtship characters do not reflect the male's genetic quality but instead evolved through Fisherian sexual selection. However, the existing models focus on ornaments that signal overall genetic quality and do not address the possibility that different ornaments provide information about different aspects of quality. Therefore, we develop a model in which the ornaments act as signals for distinct quality components. When the ornaments provide overlapping information about these quality components, we retrieve the results of earlier models. However, when the ornaments provide independent information, preferences for multiple ornaments may evolve, even when exhibiting multiple preferences is costly. We discuss our results in relation to the multiple-message and redundant-signal hypotheses for ornament diversity and identify parallels between Fisherian and good-genes mechanisms for the evolution of multiple ornaments.     

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.     

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.