Facultative sexual reproduction under frequency-dependent selection on a single locus

The evolution of a facultative sexual strategy that simultaneously produced sexual and asexual individuals was studied theoretically, under negative frequency-dependence of fitness. The organism was considered to be diploid, characterized by two loci concerning fitness and determining sexual strategy, between which a certain degree of linkage existed. The locus concerning fitness was assumed to involve two alleles, resulting in three genotypes, the relative fitness of an individual being defined by a decreasing function of frequency of its own genotype on this locus in the population. The sexual reproductive strategy was considered to be determined by three alleles; asexual, obligate sexual and facultative sexual. Simulations under various linkages between loci and level of frequency dependence of fitness showed that a facultative sexual strategy was generally able to invade and increase in the population. In particular, when the level of frequency dependence was high to some degree, the facultative strain producing many sexual individuals tended to exclusively occupy the population. Namely, the frequency-dependent selection resulted in a predominance of obligate sexual strategy over asexual strategy, simultaneously causing a subordination of the former to the facultative sexual strategy. This indicated that the evolution of sex should be considered carefully with respect to the possibility of invasion of facultative sex.     

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     

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 effect of subdivision on variation at multi-allelic loci under balancing selection

Simulations are used to investigate the expected pattern of variation at loci under different forms of multi-allelic balancing selection in a finite island model of a subdivided population. The objective is to evaluate the effect of restricted migration among demes on the distribution of polymorphism at the selected loci at equilibrium, and to compare the results with those expected for a neutral locus. The results show that the expected number of alleles maintained, and numbers of nucleotide differences between alleles, are relatively insensitive to the migration rate, and differentiation remains low even under very restricted migration. However, nucleotide divergence between copies of functionally identical alleles increases sharply when migration decreases. These results are discussed in relation to published surveys of allelic diversity in MHC and plant self-incompatibility systems, and to the possibility of inferring ancient population genetic events and processes. In addition, it is shown that, for sporophytic self-incompatibility systems, it is not necessarily true in a subdivided population that recessive alleles are more frequent than dominant ones.     

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.     

An analysis of multi-allelic data

Some multi-allelic data obtained by Coyne (1976) and by Singh, Lewontin and Felton (1976) are analyzed for their compatibility with the neutral alleles theory. It is found that strict neutrality appears not to be the case, but that if further alleles were to be distinguished in the samples, neutrality could become a possible explanation.     

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.     

The enigma of frequency-dependent selection

Frequency-dependent selection is so fundamental to modern evolutionary thinking that everyone `knows' the concept. Yet the term is used to refer to different types of selection. The concept is well defined in the original context of population genetics theory, which focuses on short-term evolutionary change. The original concept becomes ambiguous, however, when used in the context of long-term evolution, where density dependence becomes essential. Weak and strong frequency dependence, as distinguished in this article, refer to two very different forms of selection.     

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.     

A multilocus-multiallele analysis of frequency-dependent selection induced by intraspecific competition

The study of the mechanisms that maintain genetic variation has a long history in population genetics. We analyze a multilocus-multiallele model of frequency- and density-dependent selection in a large randomly mating population. The number of loci and the number of alleles per locus are arbitrary. The n loci are assumed to contribute additively to a quantitative character under stabilizing or directional selection as well as under frequency-dependent selection caused by intraspecific competition. We assume the strength of stabilizing selection to be weak, whereas the strength of frequency dependence may be arbitrary. Density-dependence is induced by population regulation. Our main result is a characterization of the equilibrium structure and its stability properties in terms of all parameters. It turns out that no equilibrium exists with more than two alleles segregating per locus. We give necessary and sufficient conditions on the strength of frequency dependence to ensure the maintenance of multilocus polymorphism. We also give explicit formulas on the number of polymorphic loci maintained at equilibrium. These results are based on the assumption that selection is sufficiently weak compared with recombination, so that linkage equilibrium can be assumed. If additionally the population size is assumed to be constant, we prove that the dynamics of the model form a generalized gradient system. For the model in its general form we are able to derive necessary and sufficient conditions for the stability of the monomorphic equilibria. Furthermore, we briefly analyze a special symmetric two-locus two-allele model for a constant population size but allowing for linkage disequilibrium. Finally, we analyze a single diallelic locus with dominance to illustrate the complications that can occur if the assumption of additivity is relaxed.     

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.     

Computer simulation analysis suggests weak balancing selection operative at the MICA locus

A high degree of polymorphism has been reported at the major histocompatibility class I chain-related gene A (MICA) locus, which is located 46 kb away from HLA-Bin the human major histocompatibility complex (MHC) class I region. Although it is known that the polymorphisms at the conventional MHC class I loci have been maintained by balancing selection, it is unclear whether positive natural selection is also operative in maintaining the polymorphism at the MICA locus. In order to explain the degree of polymorphism at the MICA locus, a computer simulation study was carried out. The high degree of polymorphism at the MICA locus (heterozygosity and number of polymorphic residues) could not be explained solely by balancing selection at the HLA-B locus even if no recombination was assumed between MICA and HLA-B. Although there is no definite evidence indicating that balancing selection is operative at the MICA locus, our results suggest that the MICA gene is subject to weak balancing selection.     

Assessing frequency-dependent seed size selection: a field experiment

Seed size is a life history attribute that affects the probability of seed predation, and therefore affects plant fitness. Compared with smaller seeds, those with large size should be more attractive to predators, as they constitute a more profitable food item because of higher energetic and/or nutrient content. However, predator preferences may be frequency-dependent in the sense that they may be modulated by the relative abundance of alternative seeds of different sizes. We set up a field experiment to evaluate frequency-dependent seed predation using seeds of Cryptocarya alba (Lauraceae), at La Campana National Park in central Chile. Predators (rodents and birds) preferentially consumed large seeds in an antiapostatic manner. These selective responses were maintained throughout the experiment and seed selection by predators was not affected by previous seed consumption. Our results suggest that (a) large seeds are very profitable food items actively sought by seed predators even at low relative abundance, (b) seed selection is expressed in a short time scale and (c) seed predators, by consuming large seeds consistently, have the potential to modify significantly the quality of plant progeny.  © 2004 The Linnean Society of London, Biological Journal of the Linnean Society , 2004, 81 , 307–312.     

Fundamental theorem of natural selection and frequency-dependent selection: analysis of the matrix game diploid model

Following Ewens' interpretation about Fisher's fundamental theorem of natural selection, the matrix game model for diploid populations undergoing non-overlapping, discrete generations is investigated. The total genetic variance is decomposed and it is shown that the partial change in the mean fitness, which is equal to the additive genetic variance over the mean fitness, can be thought of as a change due only to the partial changes in the phenotypic frequencies.     

Negative frequency-dependent selection is intensified at higher population densities in protist populations

Natural populations of free-living protists often exhibit high-levels of intraspecific diversity, yet this is puzzling as classic evolutionary theory predicts dominance by genotypes with high fitness, particularly in large populations where selection is efficient. Here, we test whether negative frequency-dependent selection (NFDS) plays a role in the maintenance of diversity in the marine flagellate Oxyrrhis marina using competition experiments between multiple pairs of strains. We observed strain-specific responses to frequency and density, but an overall signature of NFDS that was intensified at higher population densities. Because our strains were not selected a priori on the basis of particular traits expected to exhibit NFDS, these data represent a relatively unbiased estimate of the role for NFDS in maintaining diversity in protist populations. These findings could help to explain how bloom-forming plankton, which periodically achieve exceptionally high population densities, maintain substantial intraspecific diversity.