The conditional ancestral selection graph with strong balancing selection

Using a heuristic separation-of-time-scales argument, we describe the behavior of the conditional ancestral selection graph with very strong balancing selection between a pair of alleles. In the limit as the strength of selection tends to infinity, we find that the ancestral process converges to a neutral structured coalescent, with two subpopulations representing the two alleles and mutation playing the role of migration. This agrees with a previous result of Kaplan et al., obtained using a different approach. We present the results of computer simulations to support our heuristic mathematical results. We also present a more rigorous demonstration that the neutral conditional ancestral process converges to the Kingman coalescent in the limit as the mutation rate tends to infinity.     

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.     

Biotic interaction strength and the intensity of selection

Although the ecological and evolutionary impacts of species interactions have been the foci of much research, the relationship between the strength of species interactions and the intensity of selection has been investigated only rarely. I develop a simple model demonstrating how the opportunity for selection varies with interaction strength, and then use the relationship between the maximum value of the selection differential and the opportunity for selection (Arnold & Wade 1984) to evaluate how selection differentials vary in relation to species interaction strength. This model predicts an initial deceleration and then an accelerating increase in the intensity of selection with increasing strength of antagonistic interactions and with decreasing strength of mutualistic interactions. Empirical data from several studies provide support for this model. These results further support an evolutionary mechanism for some striking patterns of evolutionary diversification including the latitudinal species gradient, and should be relevant to studies of eco‐evolutionary dynamics.     

A general framework for marker-assisted selection

Early simulation studies have showed that the inclusion of epistatic components (especially the additive-by-additive effects) into marker-assisted selection (MAS) can improve selection efficiency for a short-term breeding program. In this study I extend Lande and Thompson's theory to incorporate both additive and non-additive effects into MAS with reference to the mass selection case. Four different indices are analytically examined in terms of the type of genetic components involved in the marker scores: phenotype-, general combining ability (GCA)-, and GCA and reciprocal effects-based marker scores. The phenotype-based marker index is applicable to any population of non-random mating, while the other three indices are applicable to the synthetic population derived from diallel crosses. All these indices may have higher selection efficiencies than the index with solely additive effects-associated markers as long as the detectable transient non-additive effects are present. The improvement in selection efficiency depends on the magnitude of non-additive variances and the proportion of them explained by markers. The index with the phenotype-based marker scores operates on the whole of the additive and non-additive effects, and has the largest selection efficiency. The indices with the GCA-based marker scores operate only on additive and additive-by-additive genetic variation and have relatively small selection efficiencies. Inclusion of the markers from organelle genomes can also increase selection efficiency, depending upon the proportion of the total genetic variation attributable to organelle genomes and the proportion of them explained by organelle genomic markers. Sharing of markers among different marker scores does not facilitate the improvement of selection efficiency.     

Different mechanisms drive the maintenance of polymorphism at loci subject to strong versus weak fluctuating selection

The long‐running debate about the role of selection in maintaining genetic variation has been given new impetus by the discovery of hundreds of seasonally oscillating polymorphisms in wild Drosophila, possibly stabilized by an alternating summer‐winter selection regime. Historically, there has been skepticism about the potential of temporal variation to balance polymorphism, because selection must be strong to have a meaningful stabilizing effect—unless dominance also varies over time (“reversal of dominance”). Here, we develop a simplified model of seasonally variable selection that simultaneously incorporates four different stabilizing mechanisms, including two genetic mechanisms (“cumulative overdominance” and reversal of dominance), as well as ecological “storage” (“protection from selection” and boom‐bust demography). We use our model to compare the stabilizing effects of these mechanisms. Although reversal of dominance has by far the greatest stabilizing effect, we argue that the three other mechanisms could also stabilize polymorphism under plausible conditions, particularly when all three are present. With many loci subject to diminishing returns epistasis, reversal of dominance stabilizes many alleles of small effect. This makes the combination of the other three mechanisms, which are incapable of stabilizing small effect alleles, a better candidate for stabilizing the detectable frequency oscillations of large effect alleles.     

Multiple loci mapping via model-free variable selection

Despite recent flourish of proposals on variable selection, genome-wide multiple loci mapping remains to be challenging. The majority of existing variable selection methods impose a model, and often the homoscedastic linear model, prior to selection. However, the true association between the phenotypical trait and the genetic markers is rarely known a priori, and the presence of epistatic interactions makes the association more complex than a linear relation. Model-free variable selection offers a useful alternative in this context, but the fact that the number of markers p often far exceeds the number of experimental units n renders all the existing model-free solutions that require n > p inapplicable. In this article, we examine a number of model-free variable selection methods for small-n-large-p regressions in the context of genome-wide multiple loci mapping. We propose and advocate a multivariate group-wise adaptive penalization solution, which requires no model prespecification and thus works for complex trait-marker association, and handles one variable at a time so that works for n < p. Effectiveness of the new method is demonstrated through both intensive simulations and a comprehensive real data analysis across 6100 gene expression traits.     

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.     

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.     

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.     

Temporally varying selection on multiple alleles: A diffusion analysis

A generalization of Gillespie's SAS-CFF model for natural selection acting on multiple alleles in a randomly fluctuating environment is presented that relaxes symmetry assumptions concerning the variances and covariances of allelic effects. The stationary density for a multidimensional diffusion approximation of the model is obtained and provides approximate necessary and sufficient conditions for the existence of stable polymorphisms. These conditions have exactly the same form as those derived by Kimura and Mandel for polymorphism under multiple allele selection in a constant environment, except that the time-invariant fitnesses are replaced by the approximate geometric mean fitnesses of the genotypes over time. An example illustrates that this simple relationship between random environment and constant environment conditions for polymorphism does not hold for more general selection schemes. The implications of these results for the maintenance of multiple alleles by balancing selection are discussed.     

The generalized multiplicative model for viability selection at multiple loci

Selection due to differential viability is studied in an n-locus two-allele model using a set indexation that allows the simplicity of the one-locus two-allele model to be carried to multi-locus models. The existence condition is analyzed for polymorphic equilibria with linkage equilibrium: Robbins' equilibria. The local stability condition is given for the Robbins' equilibria on the boundaries in the generalized non-epistatic selection regimes of Karlin and Liberman (1979). These generalized non-epistatic regimes include the additive selection model, the multiplicative selection model and the multiplicative interaction model, and their symmetric versions cover all the symmetric viability models.Research supported by grant no. 11-7805 from the Danish Natural Science Research Council, by NIH grant GM 28016, by a fellowship from the Research Foundation of Aarhus University, and by a visiting fellowship from the University of New England, N.S.W.     

Optimal selection on two quantitative trait loci with linkage

A mathematical approach to optimize selection on multiple quantitative trait loci (QTL) and an estimate of residual polygenic effects was applied to selection on two linked or unlinked additive QTL. Strategies to maximize total or cumulative discounted response over ten generations were compared to standard QTL selection on the sum of breeding values for the QTL and an estimated breeding value for polygenes, and to phenotypic selection. Optimal selection resulted in greater response to selection than standard QTL or phenotypic selection. Tight linkage between the QTL (recombination rate 0.05) resulted in a slightly lower response for standard QTL and phenotypic selection but in a greater response for optimal selection. Optimal selection capitalized on linkage by emphasizing selection on favorable haplotypes. When the objective was to maximize total response after ten generations and QTL were unlinked, optimal selection increased QTL frequencies to fixation in a near linear manner. When starting frequencies were equal for the two QTL, equal emphasis was given to each QTL, regardless of the difference in effects of the QTL and regardless of the linkage, but the emphasis given to each of the two QTL was not additive. These results demonstrate the ability of optimal selection to capitalize on information on the complex genetic basis of quantitative traits that is forthcoming.     

Efficiency of direct selection on quantitative trait loci for a two-trait breeding objective

Selection on known loci affecting quantitative traits (DSQ) was compared to phenotypic selection index for a single and a two-trait selection objective. Two situations were simulated; a single known quantitative locus, and ten identified loci accounting for all the additive genetic variance. Selection efficiency of DSQ relative to traitbased selection was higher for two-trait selection, than was selection on a single trait with the same heritability. The advantage of DSQ was greater when the traits were negatively correlated. Relative selection efficiency (RSE) for a single locus responsible for 0.1 of the genetic variance was 1.11 with heritabilities of 0.45 and 0.2 and zero genetic and phenotypic correlations between the traits. RSE of DSQ for ten known loci was 1.5 to 1.8 in the first 3 generations of selection, but declined in each subsequent generation. With DSQ most loci reached fixation after 7 generations. Response to trait-based selection continued through generation 15 and approached the response obtained with DSQ after 10 generations. The cumulative genetic response after 10 generations of DSQ was only 93% to 97% of the economically optimum genotype because the less favorable allele reached fixation for some loci, generally those with effects in opposite directions on the two traits.     

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.     

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.     

Footprints of intragenic recombination at HLA loci

 To evaluate the effect of balancing selection and intragenic recombination (or gene conversion) at six individual HLA loci, synonymous nucleotide diversity in different exon groups is examined within (π_w) and between (π_b) allelic lineages that may be defined by either serological or DNA sequence differences. Both π values are high in exons which encode for the peptide binding region (PBR) and tend to decrease in other exons. The value of π_w is significantly smaller than that of π_b in any exon of any locus. However, even π_w is much greater than nucleotide diversity at non-HLA loci. These observations provide additional strong evidence for the operation of balancing selection in PBR-encoding exons and its indirect effects on polymorphism at linked neighboring regions. It appears that allelic lineages have generally evolved in isolation but the linkage relationships within and between exons are incomplete throughout the long evolutionary history. To quantify intragenic recombination and account for the large discrepancy between the HLA and non-HLA diversity, a population genetics model is analyzed with special reference to the evolution of modern humans. The analysis suggests that the recombination rate between two sites 1000 base pairs apart is about 10^–5 per generation and that the effective size of human populations (equivalent roughly to the number of breeding individuals in a randomly mating population) has dropped from 10⁵ to 10⁴ in most of the Quaternary. One possibility for this reduction is discussed. Received: 11 August 1997 / Revised: 8 October 1997     

Evidence for overdominant selection maintaining X-linked fitness variation in Drosophila melanogaster

The role of balancing selection in maintaining genetic variation for fitness is largely unresolved. This reflects the inherent difficulty in distinguishing between models of recurrent mutation versus selection, which produce similar patterns of inbreeding depression, as well as the limitations of testing such hypotheses when fitness variation is averaged across the genome. Signatures of X-linked overdominant selection are less likely to be obscured by mutational variation because X-linked mutations are rapidly eliminated by purifying selection in males. Although models maintaining genetic variation for fitness are not necessarily mutually exclusive, a series of predictions for identifying X-linked overdominant selection can be used to separate its contribution from other underlying processes. We consider the role of overdominant selection in maintaining fitness variation in a sample of 12 X chromosomes from a population of Drosophila melanogaster. Substantial variation was observed for male reproductive success and female fecundity, with heterozygous-X genotypes exhibiting the greatest degree of variance, a finding that agrees well with predictions of the overdominance model. The importance of X-linked overdominant selection is discussed along with models of recurrent mutation and sexually antagonistic selection.     

In silico two-hybrid system for the selection of physically interacting protein pairs

Deciphering the interaction links between proteins has become one of the main tasks of experimental and bioinformatic methodologies. Reconstruction of complex networks of interactions in simple cellular systems by integrating predicted interaction networks with available experimental data is becoming one of the most demanding needs in the postgenomic era. On the basis of the study of correlated mutations in multiple sequence alignments, we propose a new method (in silico two-hybrid, i2h) that directly addresses the detection of physically interacting protein pairs and identifies the most likely sequence regions involved in the interactions. We have applied the system to several test sets, showing that it can discriminate between true and false interactions in a significant number of cases. We have also analyzed a large collection of E. coli protein pairs as a first step toward the virtual reconstruction of its complete interaction network.     

Emergence of long‐term balanced polymorphism under cyclic selection of spatially variable magnitude

A fundamental question in evolutionary biology is what promotes genetic variation at nonneutral loci, a major precursor to adaptation in changing environments. In particular, balanced polymorphism under realistic evolutionary models of temporally varying environments in finite natural populations remains to be demonstrated. Here, we propose a novel mechanism of balancing selection under temporally varying fitnesses. Using forward‐in‐time computer simulations and mathematical analysis, we show that cyclic selection that spatially varies in magnitude, such as along an environmental gradient, can lead to elevated levels of nonneutral genetic polymorphism in finite populations. Balanced polymorphism is more likely with an increase in gene flow, magnitude and period of fitness oscillations, and spatial heterogeneity. This polymorphism‐promoting effect is robust to small systematic fitness differences between competing alleles or to random environmental perturbation. Furthermore, we demonstrate analytically that protected polymorphism arises as spatially heterogeneous cyclic fitness oscillations generate a type of storage effect that leads to negative frequency dependent selection. Our findings imply that spatially variable cyclic environments can promote elevated levels of nonneutral genetic variation in natural populations.     

A new criterion for confounder selection

Summary We propose a new criterion for confounder selection when the underlying causal structure is unknown and only limited knowledge is available. We assume all covariates being considered are pretreatment variables and that for each covariate it is known (i) whether the covariate is a cause of treatment, and (ii) whether the covariate is a cause of the outcome. The causal relationships the covariates have with one another is assumed unknown. We propose that control be made for any covariate that is either a cause of treatment or of the outcome or both. We show that irrespective of the actual underlying causal structure, if any subset of the observed covariates suffices to control for confounding then the set of covariates chosen by our criterion will also suffice. We show that other, commonly used, criteria for confounding control do not have this property. We use formal theory concerning causal diagrams to prove our result but the application of the result does not rely on familiarity with causal diagrams. An investigator simply need ask, “Is the covariate a cause of the treatment?” and “Is the covariate a cause of the outcome?” If the answer to either question is “yes” then the covariate is included for confounder control. We discuss some additional covariate selection results that preserve unconfoundedness and that may be of interest when used with our criterion.