General analysis of frequency-dependent sexual selection at a multi-allelic locus

A general model is analyzed in which arbitrarily frequency-dependent selection acts on one sex of a diploid population with several alleles at one locus, as a result of viability or mating-success differences. The existence of boundary and polymorphic equilibria is examined, and conditions for local stability, internal and external, are obtained. The status of Hardy-Weinberg approximations in studying stability and approach to equilibria is also considered. The general principles are then applied to two specific models: one where genotypes fall into two phenotypic classes; and one with a hierarchy of dominance where viability and sexual selection are opposed. In the latter case it is found that, of all the equilibria present, there is one and only one which could possibly be stable: the existence of a unique globally stable equilibrium might then be inferred.     

Nonlinear frequency-dependent selection at a single locus with two alleles and two phenotypes

 The paper investigates the discrete frequency dynamics of two phenotype diploid models where genotypic fitness is an exponential function of the expected payoff in the matrix game. Phenotypic and genotypic equilibria are defined and their stability compared to frequency-dependent selection models based on linear fitness when there are two possible phenotypes in the population. In particular, it is shown that stable equilibria of both types can exist in the same nonlinear model. It is also shown that period-doubling bifurcations emerge when there is sufficient selection in favor of interactions between different phenotypes. Received: 22 October 1998     

Optimization under frequency-dependent selection

We consider a model of frequency-dependent selection, which we refer to as the Wildcard Model. A variety of more specific models, representing quite diverse biological situations, are covered by the Wildcard Model as particular cases. Two very different particular models that are subsumed by the Wildcard Model are the game theoretically motivated two-phenotype model of Lessard [Lessard, S.,1984. Evolutionary dynamics in frequency-dependent two-phenotype models, Theor. Popul. Biol. 25, 210-234], and the model of selection on a continuous trait due to intraspecific competition of Bürger [Bürger, R., 2005. A multilocus analysis of intraspecific competition and stabilizing selection on a quantitative trait. J. Math. Biol. 50 (4), 355-396] and Schneider [Schneider, K.A., 2006. A multilocus-multiallele analysis of frequency-dependent selection induced by intraspecific competition. J. Math. Biol. 52 (4), 483-523]. Both these models have been shown in the past to have a global Lyapunov function (LF) under appropriate genetic assumptions. We show that (i) the Wildcard Model in continuous time for a single multiallelic locus, or for multiple multiallelic loci in linkage equilibrium, has a global LF, of which the Lessard and Bürger-Scheneider LF are special cases in spite of their widely different biological interpretations; (ii) the LF of the Wildcard Model can be derived from an LF previously identified for a model of density- and frequency-dependent selection due to Lotka-Volterra competition, with one locus, multiple alleles, multiple species and continuous-time dynamics [Matessi, C., Jayakar, S.D., 1981. Coevolution of species in competition: A theoretical study. Proc. Natl. Acad. Sci. USA, 78 (2, part2), 1081-1084]. We extend the LF with density and frequency dependence to the multilocus case with linkage-equilibrium dynamics. As a possible application of our results, the optimization principle we established can be used as a tool in the study of long-term evolution of various models subsumed by the Wildcard Model based on explicit short-term dynamics.     

Facultative sexual reproduction in the parthenogenetic ant Platythyrea punctata

Summary. In a few, scattered species of social Hymenoptera, unmated workers are capable of producing female offspring from unfertilized eggs through thelytokous parthenogenesis. Regular thelytoky has previously been demonstrated in a number of populations of the neotropical ant Platythyrea punctata. Nevertheless, the finding of males and inseminated queens and workers suggested the sporadic occurrence of sex. In this study we investigated the genetic structure of colonies from Puerto Rico and Costa Rica in order to detect traces of occasional sexual reproduction. Most Puerto Rican colonies had a clonal structure with all nestmates sharing the same multilocus genotype, indicating that thelytoky is the predominant mode of reproduction. Genetic variability was detected in six of 18 colonies and might have arisen from adoption of alien workers in one colony and from the adoption of alien workers, recombination during parthenogenesis, or sexual reproduction in the other colonies. The reproductive of one of these latter colonies was found to be an inseminated worker (gamergate), and the genotypes of its nestmates definitively suggested recombination and sexual reproduction. Three gamergates were found in a single colony collected in Costa Rica, and all produced offspring from fertilized eggs, while uninseminated workers were apparently incapable of reproducing by thelytoky.Received 10 August 2004; revised 20 October 2004; accepted 3 November 2004.     

Polymorphism of melanic ladybirds maintained by frequency-dependent sexual selection

Sexual selection, whether by female preference or male competition, is almost inevitably frequency-dependent. Female preference gives rise to a 'rare male effect', by which the rarer male phenotypes gain a relatively greater selective advantage. In addition to this effect, the proportion of females expressing a preference may also be frequency-dependent.
Frequency-dependent expression of mating preference can arise in at least two ways: (1) when females encounter a succession of courting males while searching for a male they prefer; (2) when females chose a male from within a lek. Models of mating behaviour reveal a clear distinction between the frequency dependence in the expression of female preference and the frequency dependence in the consequent selection of the males. When expression of preference is highly dependent on frequency, the selection of males is constant or only slightly frequency-dependent: constant expression of preference produces high frequency dependence of selection. Analysis of general models shows that genetic polymorphisms can be maintained under a wide range of conditions.
The ladybird, Adalia bipunctata , is polymorphic for several melanic and non-melanic phenotypes. Females have a genetically determined preference for melanic males. Non-melanic phenotypes mate assortatively. By estimating the parameters of a detailed model of natural selection, sexual selection and assortative mating, it has been shown that the Adalia bipunctata polymorphism will be maintained at frequencies observed in the wild.     

The evolution of genetic architecture under frequency-dependent disruptive selection

We propose a model to analyze a quantitative trait under frequency-dependent disruptive selection. Selection on the trait is a combination of stabilizing selection and intraspecific competition, where competition is maximal between individuals with equal phenotypes. In addition, there is a density-dependent component induced by population regulation. The trait is determined additively by a number of biallelic loci, which can have different effects on the trait value. In contrast to most previous models, we assume that the allelic effects at the loci can evolve due to epistatic interactions with the genetic background. Using a modifier approach, we derive analytical results under the assumption of weak selection and constant population size, and we investigate the full model by numerical simulations. We find that frequency-dependent disruptive selection favors the evolution of a highly asymmetric genetic architecture, where most of the genetic variation is concentrated on a small number of loci. We show that the evolution of genetic architecture can be understood in terms of the ecological niches created by competition. The phenotypic distribution of a population with an adapted genetic architecture closely matches this niche structure. Thus, evolution of the genetic architecture seems to be a plausible way for populations to adapt to regimes of frequency-dependent disruptive selection. As such, it should be seen as a potential evolutionary pathway to discrete polymorphisms and as a potential alternative to other evolutionary responses, such as the evolution of sexual dimorphism or assortative mating.     

A model of quantitative traits under frequency-dependent balancing selection

We describe a computer model that stimulates a combination of stabilizing and frequency-dependent selection acting on a quantitative character determined by several loci. The results correspond to many features of natural variations at both the phenotypic and genotypic levels. The model is robust, and its results are not strongly dependent either on the nature and shape of the function describing the stabilizing selection, or on the precise form of frequency dependence, except near the extrema. It suggests a mechanism for the maintenance of large amounts of variability, and shows a relation between population size and heterozygosity roughly corresponding to that found in nature. In this respect it is unlike the purely neutral model.     

The ancestral graph and gene genealogy under frequency-dependent selection.

Minority-advantage frequency-dependent selection has been proposed as the cause for the high level of observed polymorphism in some self/nonself-recognition systems. We present a mathematically rigorous derivation of the ancestral graph for a sample of genes that evolved according to a haploid infinite-alleles model of minority-advantage frequency-dependent selection. In the case of sufficiently weak selection, the gene genealogy can be extracted from the ancestral graph. We demonstrate that the gene genealogy under this model is identical to that obtained for a diploid model with heterozygote advantage. The case of strong selection is exemplified by a one-locus haploid self-incompatibility system; in this context, we investigate the number of alleles that can be maintained in a spatial versus a non-spatial habitat. Finally, we compare gametophytic self-incompatibility to the haploid self-incompatibility model.     

The long-term evolution of multilocus traits under frequency-dependent disruptive selection

Frequency-dependent disruptive selection is widely recognized as an important source of genetic variation. Its evolutionary consequences have been extensively studied using phenotypic evolutionary models, based on quantitative genetics, game theory, or adaptive dynamics. However, the genetic assumptions underlying these approaches are highly idealized and, even worse, predict different consequences of frequency-dependent disruptive selection. Population genetic models, by contrast, enable genotypic evolutionary models, but traditionally assume constant fitness values. Only a minority of these models thus addresses frequency-dependent selection, and only a few of these do so in a multilocus context. An inherent limitation of these remaining studies is that they only investigate the short-term maintenance of genetic variation. Consequently, the long-term evolution of multilocus characters under frequency-dependent disruptive selection remains poorly understood. We aim to bridge this gap between phenotypic and genotypic models by studying a multilocus version of Levene's soft-selection model. Individual-based simulations and deterministic approximations based on adaptive dynamics theory provide insights into the underlying evolutionary dynamics. Our analysis uncovers a general pattern of polymorphism formation and collapse, likely to apply to a wide variety of genetic systems: after convergence to a fitness minimum and the subsequent establishment of genetic polymorphism at multiple loci, genetic variation becomes increasingly concentrated on a few loci, until eventually only a single polymorphic locus remains. This evolutionary process combines features observed in quantitative genetics and adaptive dynamics models, and it can be explained as a consequence of changes in the selection regime that are inherent to frequency-dependent disruptive selection. Our findings demonstrate that the potential of frequency-dependent disruptive selection to maintain polygenic variation is considerably smaller than previously expected.     

European hair and eye color: A case of frequency-dependent sexual selection?

Human hair and eye color is unusually diverse in northern and eastern Europe. The many alleles involved (at least seven for hair color) and their independent origin over a short span of evolutionary time indicate some kind of selection. Sexual selection is particularly indicated because it is known to favor color traits and color polymorphisms. In addition, hair and eye color is most diverse in what used to be, when first peopled by hunter-gatherers, a unique ecozone of low-latitude continental tundra. This type of environment skews the operational sex ratio (OSR) of hunter-gatherers toward a male shortage in two ways: (1) men have to hunt highly mobile and spatially concentrated herbivores over longer distances, with no alternate food sources in case of failure, the result being more deaths among young men; (2) women have fewer opportunities for food gathering and thus require more male provisioning, the result being less polygyny. These two factors combine to leave more women than men unmated at any one time. Such an OSR imbalance would have increased the pressures of sexual selection on early European women, one possible outcome being an unusual complex of color traits: hair- and eye-color diversity and, possibly, extreme skin depigmentation.     

Migration rates, frequency-dependent selection and the self-incompatibility locus in Leavenworthia (brassicaceae)

Loci subject to negative frequency-dependent selection are expected to exhibit higher effective migration rates compared to reference loci. Although the number of gene copies transferred between populations by migration is the same for all genes, those subject to negative frequency-dependent selection are more likely to be retained in the immigrant population because rare alleles are selectively favored. So far, evidence for this prediction has been indirect, based on summary statistics rather than on migration rate estimates. Here, we introduce an approximate Bayesian procedure to jointly estimate migration rates at two predefined sets of loci between two populations. We applied the procedure to compare migration rate estimates at the self-incompatibility locus (S-locus) with that at 10 reference loci in two plant species, Leavenworthia alabamica and L. crassa (Brassicaceae). The maximum likelihood estimate for the proportion of migrants (m) was four times higher at the S-locus than at reference loci, but the difference was not statistically significant. Lack of significance might be due to insufficient data, but perhaps also to the recent divergence of the two species (311 ka), because we also show using simulations that the effective migration rate at the S-locus is expected to increase with increasing divergence time. These findings aid in understanding the evolutionary dynamics of negative frequency-dependent selection and they suggest that divergence time should be accounted for when employing migration rates to help detect negative frequency-dependent selection.     

Orchestration of sexual reproduction and virulence by the fungal mating-type locus

The mating-type locus (MAT) orchestrates sexual reproduction in fungi. Sexual reproduction is related not only to fitness of an organism, but also correlated with virulence in certain pathogens. In the dandruff-associated fungus Malassesia globosa, although the sexual cycle remains to be discovered, whole genome analysis has led to the hypothesis that mating may occur on host skin. Furthermore, the MAT locus of M. globosa and U. hordei provides evidence that transitions between tetrapolar and bipolar systems have independently occurred. These results, together with studies recapitulating the ancestral tetrapolar mating system in Cryptococcus and the structure of MAT in related smut fungi, have furthered understanding on transitions between different mating systems and the evolution of MAT in the Basidiomycota.     

The locus of sexual selection: moving sexual selection studies into the post‐genomics era

Sexual selection drives fundamental evolutionary processes such as trait elaboration and speciation. Despite this importance, there are surprisingly few examples of genes unequivocally responsible for variation in sexually selected phenotypes. This lack of information inhibits our ability to predict phenotypic change due to universal behaviours, such as fighting over mates and mate choice. Here, we discuss reasons for this apparent gap and provide recommendations for how it can be overcome by adopting contemporary genomic methods, exploiting underutilized taxa that may be ideal for detecting the effects of sexual selection and adopting appropriate experimental paradigms. Identifying genes that determine variation in sexually selected traits has the potential to improve theoretical models and reveal whether the genetic changes underlying phenotypic novelty utilize common or unique molecular mechanisms. Such a genomic approach to sexual selection will help answer questions in the evolution of sexually selected phenotypes that were first asked by Darwin and can furthermore serve as a model for the application of genomics in all areas of evolutionary biology.     

Evolution of cyclic sexual reproduction under host-parasite interactions

Alternate changes of sexual and asexual generations was studied theoretically by numerical analyses, from the viewpoint of host-parasite infective interactions. The host species was considered a diploid organism, characterized by two loci determining parasite resistance type and sexual strategy, between which a linkage exists to a certain degree. The sexual reproductive strategy was assumed to be determined by three alleles: asexual, complete sexual and cyclic sexual alleles. The effect of the parasites was represented by decreasing fitness functions of each host-type frequency. Numerical analyses of various linkages between genes and frequency dependence of host fitness revealed that the dynamics varied depending on whether the cyclic sexual allele was dominant or recessive against the complete sexual allele. When the cyclic sexual allele was dominant, the cyclic sexual strain persisted under intermediate frequency dependence of host fitness. On the other hand, when the cyclic sexual allele was recessive, it always tended to spread and to be maintained in the population. In such situations, both complete and cyclic sexual strains coexist, but the asexual strain is lost.     

桦纤孔菌有性生殖相关特征及交配型位点分析

对桦纤孔菌菌株MDJCBS88的显微形态、菌丝及担孢子核相进行了观察。采用棉籽壳培养基对担孢子萌发形成的菌株进行栽培试验,筛选出不形成子实体或子实体发育不完整的菌株,将这些菌株在平板上进行了亲和试验,分析桦纤孔菌的有性生殖方式;并基于基因组序列进行交配型基因克隆验证,分析桦纤孔菌的交配型位点结构。显微观察发现,桦纤孔菌菌丝没有锁状联合结构,菌丝细胞无核到多核;子实层担孢子可含0-4个不等的细胞核,不同时期弹射的担孢子含有的细胞核数量不同。桦纤孔菌担孢子萌发率极低,能萌发的担孢子多为早期弹射的担孢子;培养基也影响担孢子的萌发率,与PDA培养基和CYM培养基相比,桦木屑培养基最适合桦纤孔菌担孢子萌发,萌发率为4.55%。从担孢子萌发的96个菌株中获得了2个不结实菌株和9个结实不产孢菌株,占11.5%,这些菌株间亲和试验出现不同的表现特征,包括形成产孢子实体,产生菌丝纽结,相互融合和相互拮抗等现象,认为桦纤孔菌的有性生殖以次级同宗结合为主,并受交配型基因控制。交配型位点克隆测序后分析发现,桦纤孔菌交配型A位点共14 034 bp,含有一个MIP基因和两组HD1和HD2基因;交配型B位点包含3个疑似信息素受体基因和1个信息素前体编码基因。     

Evolution at a multiallelic locus under migration and uniform selection

The semilinear parabolic system that describes the evolution of the gene frequencies in the diffusion approximation for migration and selection at a multiallelic locus is investigated. The population occupies a finite habitat of arbitrary dimensionality and shape. The drift and diffusion coefficients may depend on position, but the selection coefficients do not. It is established that if p is a uniform equilibrium point under pure selection, then p is a migration-selection equilibrium, and that generically the introduction of migration does not change the stability of p. It is also proved that if p is a uniform, globally asymptotically stable, internal equilibrium point under pure selection, then the gene frequencies converge to p when both migration and selection are present. Thus, in this case, after a sufficiently long time, there is no genetic indication of the spatial distribution of the population.