Convergence of multilocus systems under weak epistasis or weak selection

Nagylaki, Thomas; Hofbauer, Josef; Brunovský, Pavol

doi:10.1007/s002850050143

Cited by 119 publications

(168 citation statements)

References 39 publications

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“…In one generation, the allele frequencies change by approximately f, which can be sustained over ϳf Ϫ1 generations. The mean fitness increases by V A per generation, consistent with Fisher's theorem (23,26). Our results show, that epistasis causes the breakdown of the infinitesimal model for r Ͻ r c .…”

Section: Resultssupporting

confidence: 74%

“…1C. The QLE dynamics was first described by Kimura (21) in the limit of weak selection/fast recombination for a pair of biallelic loci and subsequently generalized to multiloci systems (22,23). The possibility of a collective behavior involving linkage disequilibrium among many loci and selection effectively acting on the whole chromosome as a unit has been pointed out before in the context of overdominance by Franklin and Lewontin (24) in the strong selection limit.…”

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confidence: 99%

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Competition between recombination and epistasis can cause a transition from allele to genotype selection

Neher

Shraiman

2009

Proc. Natl. Acad. Sci. U.S.A.

113

129

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Biochemical and regulatory interactions central to biological networks are expected to cause extensive genetic interactions or epistasis affecting the heritability of complex traits and the distribution of genotypes in populations. However, the inference of epistasis from the observed phenotype-genotype correlation is impeded by statistical difficulties, while the theoretical understanding of the effects of epistasis remains limited, in turn limiting our ability to interpret data. Of particular interest is the biologically relevant situation of numerous interacting genetic loci with small individual contributions to fitness. Here, we present a computational model of selection dynamics involving many epistatic loci in a recombining population. We demonstrate that a large number of polymorphic interacting loci can, despite frequent recombination, exhibit cooperative behavior that locks alleles into favorable genotypes leading to a population consisting of a set of competing clones. When the recombination rate exceeds a certain critical value that depends on the strength of epistasis, this ''genotype selection'' regime disappears in an abrupt transition, giving way to ''allele selection''-the regime where different loci are only weakly correlated as expected in sexually reproducing populations. We show that large populations attain highest fitness at a recombination rate just below critical. Clustering of interacting sets of genes on a chromosome leads to the emergence of an intermediate regime, where blocks of cooperating alleles lock into genetic modules. These haplotype blocks disappear in a second transition to pure allele selection. Our results demonstrate that the collective effect of many weak epistatic interactions can have dramatic effects on the population structure.gene interactions ͉ population genetics S election acting on genetic polymorphisms in populations is a major force of evolution (1-4) and it is possible to identify specific loci under positive selection, e.g., the Adh locus in Drosophila (4). However, the attribution of fitness differentials to specific allelic variants and combinations remains a great challenge (5). Efforts to correlate quantitative phenotypes with genetic polymorphisms typically identify a small number of loci with a significant contribution to the observed phenotypic variance, but leave much of the variance unaccounted for (6). This unaccounted variance is believed to arise from a large number of loci with small individual contributions, or be due to epistasis and quite likely involves both effects. New studies accumulate evidence that epistasis is widespread and accounts for a significant fraction of phenotypic variation, e.g., in yeast (7-9). Additional evidence for epistasis comes from crosses of mildly diverged strains, where the recombinant progeny often has reduced average fitness, i.e., displays outbreeding depression. The reduction in fitness is attributed to the breakdown of favorable combinations of alleles in the ancestral strains (10). Outbreeding depression is...

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Section: Resultssupporting

confidence: 74%

mentioning

confidence: 99%

Competition between recombination and epistasis can cause a transition from allele to genotype selection

Neher

Shraiman

2009

Proc. Natl. Acad. Sci. U.S.A.

113

129

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“…In the selection-dominated regime, however, LD should be generated consistently in a directional fashion. Nagylaki's theorem (31) states that, under weak selection, as we assume here, the population is guaranteed to approach and remain close to linkage equilibrium. Furthermore, the fact that we assume that interactions have no preferred direction should further hinder the buildup of LD.…”

Section: Discussionmentioning

confidence: 99%

The effect of gene interactions on the long-term response to selection

Paixão

Barton

2016

Proc. Natl. Acad. Sci. U.S.A.

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The role of gene interactions in the evolutionary process has long been controversial. Although some argue that they are not of importance, because most variation is additive, others claim that their effect in the long term can be substantial. Here, we focus on the long-term effects of genetic interactions under directional selection assuming no mutation or dominance, and that epistasis is symmetrical overall. We ask by how much the mean of a complex trait can be increased by selection and analyze two extreme regimes, in which either drift or selection dominate the dynamics of allele frequencies. In both scenarios, epistatic interactions affect the long-term response to selection by modulating the additive genetic variance. When drift dominates, we extend Robertson's [Robertson A (1960) Proc R Soc Lond B Biol Sci 153(951):234−249] argument to show that, for any form of epistasis, the total response of a haploid population is proportional to the initial total genotypic variance. In contrast, the total response of a diploid population is increased by epistasis, for a given initial genotypic variance. When selection dominates, we show that the total selection response can only be increased by epistasis when some initially deleterious alleles become favored as the genetic background changes. We find a simple approximation for this effect and show that, in this regime, it is the structure of the genotype−phenotype map that matters and not the variance components of the population.T he relation between an organism's genotype and its phenotype is immensely complicated, yet quantitative genetics predicts the correlations between relatives, and the response to selection over tens of generations, based primarily on an additive model. How do interactions between genes affect the response to selection? This question is not easy to answer: Although the additive model can be represented by a few parameters, there are an enormous number of possible relationships between genotype and phenotype. Some insight may come from studying specific well-understood systems, for example, regulation of gene expression by binding of transcription factors, or folding of RNA molecules. Here, we take the alternative approach, seeking statistical regularities, while making minimal assumptions about the nature of epistasis.There has been a long-standing debate about the effect of genetic interactions on adaptation (1-7). Although some claim that they are unimportant because they contribute very little to the total genetic variance of a population, and consequently to its short-term response, others claim that their long-term effects can be substantial. At the heart of the debate is the distinction between what has been called physiological and statistical epistasis. The former is independent of the state of the population, whereas the latter is the statistical contribution of gene interactions to the trait variance, which depends on the allele frequencies (8, 9).In the absence of new mutations, the total response to selection is limited by the in...

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“…For example, many current evolutionary rates depend on additive genetic rather than epistatic components, and Kimura's analysis of pseudo-linkage equilibrium shows that even in the presence of epistasis, rates of evolution stabilize to those described by additive variances (Kimura 1965;Nagylaki 1993;Crow 2010).…”

Section: (C) Epistatic Interactions Between Mutational Effectsmentioning

confidence: 99%

The population genetics of mutations: good, bad and indifferent

Loewe

Hill

2010

Phil. Trans. R. Soc. B

202

129

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Population genetics is fundamental to our understanding of evolution, and mutations are essential raw materials for evolution. In this introduction to more detailed papers that follow, we aim to provide an oversight of the field. We review current knowledge on mutation rates and their harmful and beneficial effects on fitness and then consider theories that predict the fate of individual mutations or the consequences of mutation accumulation for quantitative traits. Many advances in the past built on models that treat the evolution of mutations at each DNA site independently, neglecting linkage of sites on chromosomes and interactions of effects between sites (epistasis). We review work that addresses these limitations, to predict how mutations interfere with each other. An understanding of the population genetics of mutations of individual loci and of traits affected by many loci helps in addressing many fundamental and applied questions: for example, how do organisms adapt to changing environments, how did sex evolve, which DNA sequences are medically important, why do we age, which genetic processes can generate new species or drive endangered species to extinction, and how should policy on levels of potentially harmful mutagens introduced into the environment by humans be determined?

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Convergence of multilocus systems under weak epistasis or weak selection

Cited by 119 publications

References 39 publications

Competition between recombination and epistasis can cause a transition from allele to genotype selection

Competition between recombination and epistasis can cause a transition from allele to genotype selection

The effect of gene interactions on the long-term response to selection

The population genetics of mutations: good, bad and indifferent

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