A comprehensive test for negative frequency-dependent selection

Understanding the mechanisms that maintain genetic diversity within a population remains a primary challenge for evolutionary biology. Of the processes capable of maintaining variation, negative frequency-dependent selection (NFDS), under which rare phenotypes (or alleles) enjoy a high fitness advantage, is suggested to be the most powerful. However, few experimental studies have confirmed that this process operates in nature. Although a lot of suggestive evidence has separately been provided in various polymorphic systems, these are not enough to prove the existence of NFDS in each system. Here we present a general review of NFDS and point out some problems with previous works to develop reasonable alternative research strategies for testing NFDS. In the second half of this paper, we focused on NFDS in the common bluetail damselfly, Ischnura senegalensis, that shows female-limited genetic polymorphism. We show (1) the proximate causal mechanisms of the frequency-dependent process, (2) frequency-dependent inter-morph interaction, (3) rare morph advantage and (4) morph frequency oscillations in a natural population. These results provide unequivocal empirical support for NFDS in a natural system.     

Partial protection from cyclical selection generates a high level of polymorphism at multiple non‐neutral sites

Temporally varying selection is known to maintain genetic polymorphism under certain restricted conditions. However, if part of a population can escape from selective pressure, a condition called the “storage effect” is produced, which greatly promotes balanced polymorphism. We investigate whether seasonally fluctuating selection can maintain polymorphism at multiple loci, if cyclically fluctuating selection is not acting on a subpopulation called a “refuge.” A phenotype with a seasonally oscillating optimum is determined by alleles at multiple sites, across which the effects of mutations on phenotype are distributed randomly. This model resulted in long‐term polymorphism at multiple sites, during which allele frequencies oscillate heavily, greatly increasing the level of nonneutral polymorphism. The level of polymorphism at linked neutral sites was either higher or lower than expected for unlinked neutral loci. Overall, these results suggest that for a protein‐coding sequence, the nonsynonymous‐to‐synonymous ratio of polymorphism may exceed one. In addition, under randomly perturbed environmental oscillation, different sets of sites may take turns harboring long‐term polymorphism, thus making trans‐species polymorphism (which has been predicted as a classical signature of balancing selection) less likely.     

Balancing selection on a floral polymorphism

Abstract.— The common morning glory, Ipomoea purpurea , exhibits a flower color polymorphism at the W locus throughout the southeastern North America. The W locus controls whether flowers will be darkly pigmented ( WW ), lightly pigmented ( Ww ), or white with pigmented rays ( ww ). In this report, we describe results of a perturbation, or convergence, experiment using five plots designed to determine whether balancing selection operates on the W locus. The pattern of gene frequency changes obtained are indicative of balancing selection operating at the W locus, providing direct evidence that both the alleles are actively maintained by selection.     

Lifetime selection on adult body size and components of body size in a waterstrider: opposing selection and maintenance of sexual size dimorphism

Abstract.— Sexual size dimorphism (SSD), the difference in body size between males and females, is common in almost all taxa of animals and is generally assumed to be adaptive. Although sexual selection and fecundity selection alone have often been invoked to explain the evolution of SSD, more recent views indicate that the sexes must experience different lifetime selection pressures for SSD to evolve and be maintained. We estimated selection acting on male and female adult body size (total length) and components of body size in the waterstrider Aquarius remigis during three phases of life history. Opposing selection pressures for overall body size occurred in separate episodes of fitness for females in both years and for males in one year. Specific components of body size were often the targets of the selection on overall body size. When net adult fitness was estimated by combining each individual's fitnesses from all episodes, we found stabilizing selection in both sexes. In addition, the net optimum overall body size of males was smaller than that of females. However, even when components of body size had experienced opposing selection pressures in individual episodes, no components appeared to be under lifetime stabilizing selection. This is the first evidence that contemporary selection in a natural population acts to maintain female size larger than male size, the most common pattern of SSD in nature.     

Inference on the strength of balancing selection for epistatically interacting loci

Existing inference methods for estimating the strength of balancing selection in multi-locus genotypes rely on the assumption that there are no epistatic interactions between loci. Complex systems in which balancing selection is prevalent, such as sets of human immune system genes, are known to contain components that interact epistatically. Therefore, current methods may not produce reliable inference on the strength of selection at these loci. In this paper, we address this problem by presenting statistical methods that can account for epistatic interactions in making inference about balancing selection. A theoretical result due to Fearnhead (2006) is used to build a multi-locus Wright-Fisher model of balancing selection, allowing for epistatic interactions among loci. Antagonistic and synergistic types of interactions are examined. The joint posterior distribution of the selection and mutation parameters is sampled by Markov chain Monte Carlo methods, and the plausibility of models is assessed via Bayes factors. As a component of the inference process, an algorithm to generate multi-locus allele frequencies under balancing selection models with epistasis is also presented. Recent evidence on interactions among a set of human immune system genes is introduced as a motivating biological system for the epistatic model, and data on these genes are used to demonstrate the methods.     

Fixation probability with multiple alleles and projected average allelic effect on selection

The first-order effect of selection on the probability of fixation of an allele, with respect to an intensity of selection s>0 in a diploid population of fixed finite size N, undergoing discrete, non-overlapping generations, is shown to be given by the sum of the average effects of that allele on the coefficient of selection in the current generation and all future generations, given the population state in the current generation. This projected average allelic effect is a weighted sum of average allelic effects in allozygous and autozygous offspring in the initial generation, with weights given in terms of expected coalescence times, under neutrality, for the lineages of two or three gametes chosen at random in the same generation. This is shown in the framework of multiple alleles at one locus, with genotypic values determining either viability or fertility differences, and with either multinomial or exchangeable reproduction schemes. In the limit of weak selection in a large population such that Ns tends to zero, the initial average allelic effects in allozygous offspring and autozygous offspring have the same weight on the fixation probability only in the domain of application of the Kingman coalescent. With frequency-dependent selection in a linear-game-theoretic context with two phenotypes determined by additive gene action, the first-order effect on the fixation probability is a combination of two effects of frequency-independent selection, one in a haploid population, the other in a diploid population. In the domain of application of the Kingman coalescent as the population size goes to infinity and Ns to zero, the first effect is three times more important than the second effect. This explains the one-third law of evolutionary dynamics in this domain, and shows how this law can be extended beyond this domain.     

The transient properties of balancing selection in large finite populations

The transient properties of balancing selection in large, but finite, populations are described by means of an asymptotic analysis. Heterotic selection is shown to retard the rate of loss of genetic variation while random environment selection is shown to retard the rate of loss of variation when the initial variant is a rare mutant. Otherwise random environment selection can speed up the loss of variation for certain parametric cases. The asymptotic analysis leads to a particularly simple conceptualization of the selection process which allows the computation of asymptotic forms of the dominant eigenvalue of the process.     

A method to optimize selection on multiple identified quantitative trait loci

A mathematical approach was developed to model and optimize selection on multiple known quantitative trait loci (QTL) and polygenic estimated breeding values in order to maximize a weighted sum of responses to selection over multiple generations. The model allows for linkage between QTL with multiple alleles and arbitrary genetic effects, including dominance, epistasis, and gametic imprinting. Gametic phase disequilibrium between the QTL and between the QTL and polygenes is modeled but polygenic variance is assumed constant. Breeding programs with discrete generations, differential selection of males and females and random mating of selected parents are modeled. Polygenic EBV obtained from best linear unbiased prediction models can be accommodated. The problem was formulated as a multiple-stage optimal control problem and an iterative approach was developed for its solution. The method can be used to develop and evaluate optimal strategies for selection on multiple QTL for a wide range of situations and genetic models.     

Learning rules for optimal selection in a varying environment: mate choice revisited

The quality of a chosen partner can be one of the most significantfactors affecting an animal's long-term reproductive success.We investigate optimal mate choice rules in an environment wherethere is both local variation in the quality of potential mateswithin each local mating pool and spatial (or temporal) variationin the average quality of the pools themselves. In such a situation,a robust rule that works well across a variety of environmentswill confer a significant reproductive advantage. We formulatea full Bayesian model for updating information in such a varyingenvironment and derive the form of the rule that maximizes expectedreward in a spatially varying environment. We compare the theoreticalperformance of our optimal learning rule against both fixedthreshold rules and simpler near-optimal learning rules andshow that learning is most advantageous when both the localand environmental variances are large. We consider how optimalsimple learning rules might evolve and compare their evolutionwith that of fixed threshold rules using genetic algorithmsas minimal models of the relevant genetics. Our analysis pointsup the variety of ways in which a near-optimal rule can be expressed.Finally, we describe how our results extend to the case of temporallyvarying environments.     

A model of weak selection in the infinite alleles framework

Ewens (1972) proposed a model in the infinite allele framework for populations with neutrality of all alleles at a particular locus. This paper proposes a generalisation of Ewens' result for situations where there is a form of weak selection. The models considered here are continuous time, discrete state space Markov processes.     

Structure and Evolution of a New Avian MHC Class II B Gene in a Sub-Antarctic Seabird,the Thin-Billed Prion (Procellariiformes: <Emphasis Type="Italic">Pachyptila belcheri</Emphasis>)

The major histocompatibility complex encodes molecules that present foreign peptides to T cells of the immune system. The peptide binding region (PBR) of these molecules is among the most polymorphic regions found in vertebrate taxa. Genomic cloning approaches are improving our understanding of the evolution of this multigene family in nonmodel avian groups. By building a cosmid library, a new MHC class II B gene, Pabe-DAB1, was isolated and characterized at the genomic level in a sub-Antarctic seabird, the thin-billed prion (Pachyptila belcheri). Pabe-DAB1 exhibits the hallmark structural features of functional MHC class II loci. Direct sequencing of the PBR encoding exon in a panel of prions revealed significantly higher levels of genetic diversity compared to two noncoding neutral loci, with most alleles differing by at least one replacement substitution in the peptide binding codons. We estimated evolutionary dynamics for Pabe-DAB1 using a variety of Bayesian and other approaches. Evidence for balancing selection comes from a spatially variable ratio of nonsynonymous-to-synonymous substitutions (mean d _N/d _S = 2.87) in the PBR, with sites predicted to be functionally relevant exhibiting the highest ω values. We estimate the population recombination rate to be approximately 0.3 per site per generation, indicating an important role for recombination in generating polymorphism at this locus. Pabe-DAB1 is among the few avian class II loci characterized at the genomic level and with a known intron-exon structure, a feature that greatly facilitated the amplification and sequencing of a single MHC locus in this species.     

A comparative analysis of experimental selection on the stickleback pelvis

Mechanisms of natural selection can be identified using experimental approaches. However, such experiments often yield nonsignificant effects and imprecise estimates of selection due to low power and small sample sizes. Combining results from multiple experimental studies might produce an aggregate estimate of selection that is more revealing than individual studies. For example, bony pelvic armour varies conspicuously among stickleback populations, and predation by vertebrate and insect predators has been hypothesized to be the main driver of this variation. Yet experimental selection studies testing these hypotheses frequently fail to find a significant effect. We experimentally manipulated length of threespine stickleback (Gasterosteus aculeatus) pelvic spines in a mesocosm experiment to test whether prickly sculpin (Cottus asper), an intraguild predator of stickleback, favours longer spines. The probability of survival was greater for stickleback with unclipped pelvic spines, but this effect was noisy and not significant. We used meta‐analysis to combine the results of our mesocosm experiment with previously published experimental studies of selection on pelvic armour. We found evidence that fish predation indeed favours increased pelvic armour, with a moderate effect size. The same approach found little evidence that insect predation favours reduced pelvic armour. The causes of reduced pelvic armour in many stickleback populations remain uncertain.     

Coloniality and migration are related to selection on MHC genes in birds

The major histocompatibility complex (MHC) plays a key role in pathogen recognition as a part of the vertebrate adaptive immune system. The great diversity of MHC genes in natural populations is maintained by different forms of balancing selection and its strength should correlate with the diversity of pathogens to which a population is exposed and the rate of exposure. Despite this prediction, little is known about how life‐history characteristics affect selection at the MHC. Here, we examined whether the strength of balancing selection on MHC class II genes in birds (as measured with nonsynonymous nucleotide substitutions, dN) was related to their social or migratory behavior, two life‐history characteristics correlated with pathogen exposure. Our comparative analysis indicated that the rate of nonsynonymous substitutions was higher in colonial and migratory species than solitary and resident species, suggesting that the strength of balancing selection increases with coloniality and migratory status. These patterns could be attributed to: (1) elevated transmission rates of pathogens in species that breed in dense aggregations, or (2) exposure to a more diverse fauna of pathogens and parasites in migratory species. Our study suggests that differences in social structure and basic ecological traits influence MHC diversity in natural vertebrate populations.     

The effect of variable environments on polymorphism at loci with several alleles I. A symmetric model

Much of the extant polymorphism has been attributed to spatial and temporal variation among selection regimes. Analysis of models entailing two alleles at a single locus has demonstrated that polymorphism may result from variation among selection regimes which prescribe monomorphism if constant. This relationship is studied in the context of several alleles at a locus.One result which is not valid with only two alleles is that variation among selection regimes which specify polymorphic equilibria may lead to a stable monomorphic equilibrium. The analyses of temporal variation and total panmixia spatial variation among environments show that temporal variation allows the simultaneous stability of equilibrium configurations which cannot be simultaneously stable under total panmixia spatial variation (hard or soft selection). The principle that polymorphism is more readily maintained with spatial than temporal variation is invalidated.Supported in part by Purdue Research Foundation and National Science Foundation (USA) grant MCS-8002227     

Consequences of population structure on genes under balancing selection

This paper describes a new approach to modeling population structure for genes under strong balancing selection of the type seen in plant self-incompatibility systems and the major histocompatibility complex (MHC) system of vertebrates. Simple analytic solutions for the number of alleles maintained at equilibrium and the expected proportion of alleles shared between demes at various levels are derived and checked against simulation results. The theory accurately captures the dynamics of allele number in a subdivided population and identifies important values of m (migration rate) at which allele number and distribution change qualitatively. Starting from a panmictic population, as migration among demes decreases a qualitative change in dynamics is seen at approximately m(crit) approximately equal to the square root of(s/4piNT) where NT is the total population size and s is a measure of the strength of selection. At this point, demes can no longer maintain their panmictic allele number, due to increasing isolation from the total population. Another qualitative change occurs at a migration rate on the same order of magnitude as the mutation rate, mu. At this point, the demes are highly differentiated for allele complement, and the total number of alleles in the population is increased. Because in general u < m<(crit) at intermediate migration rates slightly fewer alleles may be maintained in the total population than are maintained at panmixia. Within this range, total allele number may not be the best indicator of whether a population is effectively panmictic, and some caution should be used when interpreting samples from such populations. The theory presented here can help to analyze data from genes under balancing selection in subdivided populations.     

Index selection on seed traits under direct, cytoplasmic and maternal effects in multiple environments

Crop seeds are important sources of protein, oil, and carbohydrates for food, animal feeds, and industrial products. Recently, much attention has been paid to quality and functional properties of crop seeds. However, seed traits possess some distinct genetic characteristics in comparison with plant traits, which increase the difficulty of genetically improving these traits. In this study, diallel analysis for seed models with genotype by environment interaction （GE） effect was applied to estimate the variance-covariance components of seed traits. Mixed linear model approaches were used to estimate the genetic covariances between pair-wise seed and plant traits. The breeding values （BV） were divided into two categories for the seed models. The first category of BV was defined as the combination of direct additive, cytoplasmic, and maternal additive effects, which should be utilized for selecting stable cultivars over multi-environments. The three genetic effects, together with their GE interaction, were included in the second category of BV for selecting special lines to be grown in specific ecosystems. Accordingly, two types of selection indices for seed traits, i.e., general selection index and interaction selection index, were developed and constructed on the first and the second category BV, respectively. These proposed selection indices can be applied to solve the difficult task of simultaneously improving multiple seed traits in various environments. Data of crop seeds with regard to four seed traits and four yield traits based on the modified diallel crosses in Upland cotton （Gossypium hirsutum L.） were used as an example for demonstrating the proposed methodology.     

A multilocus analysis of intraspecific competition and stabilizing selection on a quantitative trait

The equilibrium structure of an additive, diallelic multilocus model of a quantitative trait under frequency- and density-dependent selection is derived. The trait is under stabilizing selection and mediates intraspecific competition as induced, for instance, by differential resource utilization. It is assumed that stabilizing selection is weak, but the strength of competition may be arbitrary relative to it. Density dependence is caused by population regulation, which may be of a very general kind. The number and effects of loci are arbitrary, and stabilizing selection is not necessarily symmetric with respect to the range of phenotypic values. All previously studied models of intraspecific competition for a continuum of resources known to the author reduce to a special case of the present model if overall selection is weak. Therefore, in this case our results are applicable as approximations to all these models. Our central result is the (nearly) complete characterization of the equilibrium and stability structure in terms of all parameters. It is derived under the sole assumption that selection is weak enough relative to recombination to ignore linkage disequilibrium. In particular, necessary and sufficient conditions on the strength of competition relative to stabilizing selection are found that ensure the maintenance of multilocus polymorphism and the occurrence of disruptive selection. In this case, explicit formulas for the number of polymorphic loci at equilibrium, the allele frequencies, the genetic variance, and the strength of disruptive selection are obtained. For two loci, the effects of linkage are investigated analytically; for several loci, they are studied numerically.     

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.     

A genomic selection component analysis characterizes migration‐selection balance

The genetic differentiation of populations in response to local selection pressures has long been studied by evolutionary biologists, but key details about the process remain obscure. How rapidly can local adaptation evolve, how extensive is the process across the genome, and how strong are the opposing forces of natural selection and gene flow? Here, we combine direct measurement of survival and reproduction with whole‐genome genotyping of a plant species (Mimulus guttatus) that has recently invaded a novel habitat (the Quarry population). We renovate the classic selection component method to accommodate genomic data and observe selection at SNPs throughout the genome. SNPs showing viability selection in Quarry exhibit elevated divergence from neighboring populations relative to neutral SNPs. We also find that nonsignificant SNPs exhibit a subtle, but still significant, change in allele frequency toward neighboring populations, a predicted effect of gene flow. Given that the Quarry population is most probably only 30–40 generations old, the alleles conferring local advantage are almost certainly older than the population itself. Thus, local adaptation owes to the recruitment of standing genetic variation.     

A microbial modified prisoner's dilemma game: how frequency-dependent selection can lead to random phase variation

Random phase variation (RPV) is a control strategy in which the expression of a cell state or phenotype randomly alternates between discrete 'on' and 'off' states. Though this mode of control is common for bacterial virulence factors like pili and toxins, precise conditions under which RPV confers an advantage have not been well defined. In Part I of this study, we predicted that fluctuating environments select for RPV if transitions between different selective environments cannot be reliably sensed (J. Theor. Biol. (2005)). However, selective forces both inside and outside of human hosts are also likely to be frequency dependent in the sense that the fitnesses of some bacterial states are greatest when rare. Here we show that RPV at slow rates can provide a survival advantage in such a frequency-dependent environment by generating population heterogeneity, essentially mimicking a polymorphism. More surprisingly, RPV at a faster 'optimal' rate can shift the population composition toward an optimal growth rate that exceeds that possible for polymorphic populations, but this optimal strategy is not evolutionarily stable. The population would be most fit if all cells randomly phase varied at the optimal rate, but individual cells have a growth-rate incentive to defect (mutate) to other switching rates or non-phase variable phenotype expression, leading to an overall loss of fitness of the individual and the population. This scenario describes a modified Prisoner's Dilemma game (Evolution and the Theory of Games, Cambridge University Press, Cambridge, New York, 1982, viii, 224pp.; Nature 398 (6726) (1999) 367), with random phase variation at optimal switching rates serving as the cooperation strategy.