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.     

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.     

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     

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 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.     

Fixation of new alleles and the extinction of small populations: drift load, beneficial alleles, and sexual selection

With a small effective population size, random genetic drift is more important than selection in determining the fate of new alleles. Small populations therefore accumulate deleterious mutations. Left unchecked, the effect of these fixed alleles is to reduce the reproductive capacity of a species, eventually to the point of extinction. New beneficial mutations, if fixed by selection, can restore some of this lost fitness. This paper derives the overall change in fitness due to fixation of new deleterious and beneficial alleles, as a function of the distribution of effects of new mutations and the effective population size. There is a critical effective size below which a population will on average decline in fitness, but above which beneficial mutations allow the population to persist. With reasonable estimates of the relevant parameters, this critical effective size is likely to be a few hundred. Furthermore, sexual selection can act to reduce the fixation probability of deleterious new mutations and increase the probability of fixing new beneficial mutations. Sexual selection can therefore reduce the risk of extinction of small populations.     

Index of intensity of sexual selection: A comment on Nishida's article

An index of intensity of sexual selection proposed by Nishida (1992: Res. Popul. Ecol. 34: 373–382) was examined. Two examples were presented to show that Nishida's index was not free from confounding effect of mortality schedule. Importance of removing the phylogenetic effects in comparative analyses was also discussed.     

Positive selection on multiple antique allelic lineages of transferrin in the polyploid Carassius auratus

Transferrin polymorphism has been studied in the polyploid Carassius auratus by cloning and sequence analysis of cDNAs from its three subspecies C. auratus gibelio, C. auratus auratus, and C. auratus cuvieri. DNA polymorphism of extremely high extent was shown for the transferrin gene by the 248 segregation sites among coding region sequences of its alleles. The deduced amino acid sequences of the transferrin alleles showed variable theoretical physicochemical parameters, which might constitute molecular basis for their electrophoretic heterogeneity. Positive selection was inferred by the replacement/synonymous ratios larger than 1 in partial allelic lineages which was subsequently confirmed by likelihood simulation under neutral or selection models. Furthermore, the correspondent sites to these selected codons were collectively located at two planes in the crystallographic structure of rabbit transferrin, which suggested that the rapid evolution of C. auratus transferrin might correlate to its adaptation to variable environmental elements such as oxygen pressure. The minimal 26 recombination events were detected among coding sequences of C. auratus transferrin, with partial mosaic sequences and breakpoints identified by identity scanning and information site analyses. Phylogenetic analyses revealed multiple antique allelic lineages of transferrin, which was estimated to diverge fifteen to twenty MYA. All these features strongly suggested the role of balancing selection in long persistence of high transferrin polymorphism in C. auratus. Furthermore, owing to its particular evolutionary backgrounds, the silver crucian carp might possess a distinctive balancing selection mechanism.     

Sexual selection in genetic colour-polymorphic species: a review of experimental studies and perspectives

Sexual selection theory has primarily focussed on the role of mating preferences for the best individuals in the evolution of condition-dependent ornaments, traits that signal absolute quality. Because the most suitable mate for one individual is not always the best for others, however, we argue that non-directional mate choice can promote the evolution of alternative morphs that are not condition-dependent in their expression (i.e. genetic polymorphism). We list the different mate-choice rules (i.e. all individuals have the same preference; preference depends on the chooser’s morph; individuals mate preferentially with conspecifics displaying an uncommon or the most frequent morph) and review experimental studies that investigated mate choice in natural populations of colour-polymorphic animals. Our review emphasises that although the experimental data support the idea that sexual selection plays an important role in the evolution of genetic colour polymorphism in many different ways, little is known about the adaptive value of each mate-choice strategy and about their implication in the evolutionary stability of colour polymorphism. One way of solving this problem is to determine the adaptive function of colour morphs, a worthwhile objective, because better understanding of mate-choice rules in polymorphic species should provide important insights into sexual-selection processes and, in turn, into the maintenance of genetic variation.     

A graphical method for the analysis of anisotropic rotational diffusion in proteins

A graphical method for the analysis of relaxation data is presented. It allows a fast estimation of the range of values of the components of the axially symmetric rotational diffusion tensor that are compatible with the experimental relaxation data. The graphical method clearly shows the contribution of different experimental relaxation parameters to the measured anisotropy. In particular, for proteins with moderate anisotropy, data from at least two N-H bonds forming angles close to 0° and 90° with respect to the principal axis of the rotational diffusional tensor are needed. For very anisotropic systems, combination of different relaxation parameters from a single residue is enough to characterize the local anisotropy.     

Natural selection on body size is mediated by multiple interacting factors: a comparison of beetle populations varying naturally and experimentally in body size

Body size varies considerably among species and among populations within species, exhibiting many repeatable patterns. However, which sources of selection generate geographic patterns, and which components of fitness mediate evolution of body size, are not well understood. For many animals, resource quality and intraspecific competition may mediate selection on body size producing large-scale geographic patterns. In two sequential experiments, we examine how variation in larval competition and resource quality (seed size) affects the fitness consequences of variation in body size in a scramble-competing seed-feeding beetle, Stator limbatus. Specifically, we compared fitness components among three natural populations of S. limbatus that vary in body size, and then among three lineages of beetles derived from a single base population artificially selected to vary in size, all reared on three sizes of seeds at variable larval density. The effects of larval competition and seed size on larval survival and development time were similar for larger versus smaller beetles. However, larger-bodied beetles suffered a greater reduction in adult body mass with decreasing seed size and increasing larval density; the relative advantage of being large decreased with decreasing seed size and increasing larval density. There were highly significant interactions between the effects of seed size and larval density on body size, and a significant three-way interaction (population-by-density-by-seed size), indicating that environmental effects on the fitness consequences of being large are nonadditive. Our study demonstrates how multiple ecological variables (resource availability and resource competition) interact to affect organismal fitness components, and that such interactions can mediate natural selection on body size. Studying individual factors influencing selection on body size may lead to misleading results given the potential for nonlinear interactions among selective agents.     

Marker-assisted introgression using non-unique marker alleles I: selection on the presence of linked marker alleles

This paper investigates marker-assisted introgression of a major gene into an outbred line, where identification of the introgressed gene is incomplete because marker alleles are not unique to the base populations (the same marker allele can occur in both donor and recipient population). Those markers are used to identify the introgressed allele as well as the background genotype. The effect of using those markers, as if they were completely informative on the retention of the introgressed allele, was examined over five generations of backcrossing by using a single marker or a marker bracket for different starting frequencies of the marker alleles. Results were calculated by using both a deterministic approach, where selection is only for the desired allele, and by a stochastic approach, where selection is also on background genotype. When marker allele frequencies in donor and recipient population diverged from 1 and 0 (using a diallelic marker), the ability to retain the desired allele rapidly declined. Marker brackets performed notably better than single markers. If selection on background marker genotype was applied, the desired allele could be lost even more quickly than expected at random because the chance that the allele, which is common in the donor line, is present on the locus identifying the introgressed allele and is surrounded by alleles common in the recipient line on the background marker loci, will descend from the donor line (double recombination has taken place), is a lot smaller than the chance that this allele will stem from the recipient line (in which the allele occurs in low frequency). Marker brackets again performed better. Preselection against marker homozygotes (producing uninformative gametes) gave a slightly better retention of the introgressed allele.     

A genetic analysis of quantitative resistance to late blight in potato: towards marker-assisted selection

Late blight caused by the oomycete Phytophthora infestans is the most important fungal disease in potato cultivation worldwide. Resistance to late blight is controlled by a few major genes (R genes) which can be easily overcome by new races of P. infestans and/or by an unknown number of genes expressing a quantitative type of resistance which may be more durable. Quantitative resistance of foliage to late blight was evaluated in five F₁ hybrid families originating from crosses among seven different diploid potato clones. Tuber resistance was evaluated in four of the families. Two of the families were scored for both foliage maturity and vigour. The five families were genotyped with DNA-based markers and tested for linkage with the traits analysed. QTL (quantitative trait locus) analysis identified at least twelve segments on ten chromosomes of potato having genes that affect reproducibly foliage resistance. Two of those segments also have major R genes for resistance to late blight. The segments are tagged by 21 markers that can be analyzed based on PCR (polymerase chain reaction) with specific oligonucleotide primers. One QTL was detected for tuber resistance and one for foliage vigour. Two QTLs were mapped for foliage maturity. Major QTL effects on foliage and tuber resistance to late blight and on foliage maturity and vigour were all linked with marker GP179 on linkage group V of potato. Plants having alleles at this QTL, which increased foliage resistance, exhibited decreased tuber resistance, later maturity and more vigour.