Fluctuating selection models and Mcdonald-Kreitman type analyses

It is likely that the strength of selection acting upon a mutation varies through time due to changes in the environment. However, most population genetic theory assumes that the strength of selection remains constant. Here we investigate the consequences of fluctuating selection pressures on the quantification of adaptive evolution using McDonald-Kreitman (MK) style approaches. In agreement with previous work, we show that fluctuating selection can generate evidence of adaptive evolution even when the expected strength of selection on a mutation is zero. However, we also find that the mutations, which contribute to both polymorphism and divergence tend, on average, to be positively selected during their lifetime, under fluctuating selection models. This is because mutations that fluctuate, by chance, to positive selected values, tend to reach higher frequencies in the population than those that fluctuate towards negative values. Hence the evidence of positive adaptive evolution detected under a fluctuating selection model by MK type approaches is genuine since fixed mutations tend to be advantageous on average during their lifetime. Never-the-less we show that methods tend to underestimate the rate of adaptive evolution when selection fluctuates

Evolutionary control: Targeted change of allele frequencies in natural populations using externally directed evolution

© 2017 Elsevier LtdRandom processes in biology, in particular random genetic drift, often make it difficult to predict the fate of a particular mutation in a population. Using principles of theoretical population genetics, we present a form of biological control that ensures a focal allele's frequency, at a given locus, achieves a prescribed probability distribution at a given time. This control is in the form of an additional evolutionary force that acts on a population. We provide the mathematical framework that determines the additional force. Our analysis indicates that generally the additional force depends on the frequency of the focal allele, and it may also depend on the time. We argue that translating this additional force into an externally controlled process, which has the possibility of being implemented in a number of different ways corresponding to selection, migration, mutation, or a combination of these, may provide a flexible instrument for targeted change of traits of interest in natural populations. This framework may be applied, or used as an informed form of guidance, in a variety of different biological scenarios including: yield and pesticide optimisation in crop production, biofermentation, the local regulation of human-associated natural populations, such as parasitic animals, or bacterial communities in hospitals

A modified Wright-Fisher model that incorporates Ne: A variant of the standard model with increased biological realism and reduced computational complexity.

The Wright-Fisher model is an important model in evolutionary biology and population genetics. It has been applied in numerous analyses of finite populations with discrete generations. It is recognised that real populations can behave, in some key aspects, as though their size that is not the census size, N, but rather a smaller size, namely the effective population size, Ne. However, in the Wright-Fisher model, there is no distinction between the effective and census population sizes. Equivalently, we can say that in this model, Ne coincides with N. The Wright-Fisher model therefore lacks an important aspect of biological realism. Here, we present a method that allows Ne to be directly incorporated into the Wright-Fisher model. The modified model involves matrices whose size is determined by Ne. Thus apart from increased biological realism, the modified model also has reduced computational complexity, particularly so when Ne⪡N. For complex problems, it may be hard or impossible to numerically analyse the most commonly-used approximation of the Wright-Fisher model that incorporates Ne, namely the diffusion approximation. An alternative approach is simulation. However, the simulations need to be sufficiently detailed that they yield an effective size that is different to the census size. Simulations may also be time consuming and have attendant statistical errors. The method presented in this work may then be the only alternative to simulations, when Ne differs from N. We illustrate the straightforward application of the method to some problems involving allele fixation and the determination of the equilibrium site frequency spectrum. We then apply the method to the problem of fixation when three alleles are segregating in a population. This latter problem is significantly more complex than a two allele problem and since the diffusion equation cannot be numerically solved, the only other way Ne can be incorporated into the analysis is by simulation. We have achieved good accuracy in all cases considered. In summary, the present work extends the realism and tractability of an important model of evolutionary biology and population genetics

The Effect of Variation in the Effective Population Size on the Rate of Adaptive Molecular Evolution in Eukaryotes

The role of adaptation is a fundamental question in molecular evolution. Theory predicts that species with large effective population sizes should undergo a higher rate of adaptive evolution than species with low effective population sizes if adaptation is limited by the supply of mutations. Previous analyses have appeared to support this conjecture because estimates of the proportion of nonsynonymous substitutions fixed by adaptive evolution, α, tend to be higher in species with large N(e). However, α is a function of both the number of advantageous and effectively neutral substitutions, either of which might depend on N(e). Here, we investigate the relationship between N(e) and ω(a), the rate of adaptive evolution relative to the rate of neutral evolution, using nucleotide polymorphism and divergence data from 13 independent pairs of eukaryotic species. We find a highly significant positive correlation between ω(a) and N(e). We also find some evidence that the rate of adaptive evolution varies between groups of organisms for a given N(e). The correlation between ω(a) and N(e) does not appear to be an artifact of demographic change or selection on synonymous codon use. Our results suggest that adaptation is to some extent limited by the supply of mutations and that at least some adaptation depends on newly occurring mutations rather than on standing genetic variation. Finally, we show that the proportion of nearly neutral nonadaptive substitutions declines with increasing N(e). The low rate of adaptive evolution and the high proportion of effectively neutral substitution in species with small N(e) are expected to combine to make it difficult to detect adaptive molecular evolution in species with small N(e)

Determinants of the efficacy of natural selection on coding and noncoding variability in two passerine species

Population genetic theory predicts that selection should be more effective when the effective population size (Ne) is larger, and that the efficacy of selection should correlate positively with recombination rate. Here, we analyzed the genomes of ten great tits and ten zebra finches. Nucleotide diversity at 4-fold degenerate sites indicates that zebra finches have a 2.83-fold larger Ne. We obtained clear evidence that purifying selection is more effective in zebra finches. The proportion of substitutions at 0-fold degenerate sites fixed by positive selection (α) is high in both species (great tit 48%; zebra finch 64%) and is significantly higher in zebra finches. When α was estimated on GC-conservative changes (i.e., between A and T and between G and C), the estimates reduced in both species (great tit 22%; zebra finch 53%). A theoretical model presented herein suggests that failing to control for the effects of GC-biased gene conversion (gBGC) is potentially a contributor to the overestimation of α, and that this effect cannot be alleviated by first fitting a demographic model to neutral variants. We present the first estimates in birds for α in the untranslated regions, and found evidence for substantial adaptive changes. Finally, although purifying selection is stronger in high-recombination regions, we obtained mixed evidence for α increasing with recombination rate, especially after accounting for gBGC. These results highlight that it is important to consider the potential confounding effects of gBGC when quantifying selection and that our understanding of what determines the efficacy of selection is incomplete

Ice-Age Climate Adaptations Trap the Alpine Marmot in a State of Low Genetic Diversity.

Some species responded successfully to prehistoric changes in climate [1, 2], while others failed to adapt and became extinct [3]. The factors that determine successful climate adaptation remain poorly understood. We constructed a reference genome and studied physiological adaptations in the Alpine marmot (Marmota marmota), a large ground-dwelling squirrel exquisitely adapted to the "ice-age" climate of the Pleistocene steppe [4, 5]. Since the disappearance of this habitat, the rodent persists in large numbers in the high-altitude Alpine meadow [6, 7]. Genome and metabolome showed evidence of adaptation consistent with cold climate, affecting white adipose tissue. Conversely, however, we found that the Alpine marmot has levels of genetic variation that are among the lowest for mammals, such that deleterious mutations are less effectively purged. Our data rule out typical explanations for low diversity, such as high levels of consanguineous mating, or a very recent bottleneck. Instead, ancient demographic reconstruction revealed that genetic diversity was lost during the climate shifts of the Pleistocene and has not recovered, despite the current high population size. We attribute this slow recovery to the marmot's adaptive life history. The case of the Alpine marmot reveals a complicated relationship between climatic changes, genetic diversity, and conservation status. It shows that species of extremely low genetic diversity can be very successful and persist over thousands of years, but also that climate-adapted life history can trap a species in a persistent state of low genetic diversity.This work was supported by the Francis Crick Institute which receives its core funding from Cancer Research UK (FC001134), the UK Medical Research Council (FC001134), and the Wellcome Trust (FC001134). CB and AC are supported by the Agence Nationale de la Recherche (project ANR-13-JSV7-0005) and the Centre National de la Recherche Scientifique (CNRS), CB is supported by the Rhône-Alpes region (Grant 15.005146.01). LD is supported by Agence Nationale de la Recherche (project ANR-12-ADAP-0009). TIG is supported by a Leverhulme Early Career Fellowship (Grant ECF-2015-453) and a NERC grant (NE/N013832/1). JMG is supported by a Hertha Finberg Fellowship (FWF T703). LDR is supported by the Diabetes UK RD Lawrence Fellowship (16/0005382)

Quantifying the variation in the effective population size within a genome

The effective population size (Ne) is one of the most fundamental parameters in population genetics. It is thought to vary across the genome as a consequence of differences in the rate of recombination and the density of selected sites due to the processes of genetic hitchhiking and background selection. Although it is known that there is intragenomic variation in the effective population size in some species, it is not known whether this is widespread or how much variation in the effective population size there is. Here, we test whether the effective population size varies across the genome, between protein-coding genes, in 10 eukaryotic species by considering whether there is significant variation in neutral diversity, taking into account differences in the mutation rate between loci by using the divergence between species. In most species we find significant evidence of variation. We investigate whether the variation in Ne is correlated to recombination rate and the density of selected sites in four species, for which these data are available. We find that Ne is positively correlated to recombination rate in one species, Drosophila melanogaster, and negatively correlated to a measure of the density of selected sites in two others, humans and Arabidopsis thaliana. However, much of the variation remains unexplained. We use a hierarchical Bayesian analysis to quantify the amount of variation in the effective population size and show that it is quite modest in all species—most genes have an Ne that is within a few fold of all other genes. Nonetheless we show that this modest variation in Ne is sufficient to cause significant differences in the efficiency of natural selection across the genome, by demonstrating that the ratio of the number of nonsynonymous to synonymous polymorphisms is significantly correlated to synonymous diversity and estimates of Ne, even taking into account the obvious nonindependence between these measures

Distributions of mean fitness effects of mutations at the time of fixation for fluctuating conditions (, and ) with mean selective effect for all mutations of zero.

<p>Distributions of mean fitness effects of mutations at the time of fixation for fluctuating conditions (, and ) with mean selective effect for all mutations of zero.</p

estimates for different fluctuating conditions with a expected mean fitness of zero.

<p><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0084540#pone.0084540-Fay1" target="_blank">[2]</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0084540#pone.0084540-EyreWalker1" target="_blank">[5]</a>,<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0084540#pone.0084540-Schneider1" target="_blank">[26]</a>.</p><p>Estimates of adaptive divergence, , for polymorphism and divergence simulated under varying random fluctuating selection. Three different MK type tests were used. The intensity of the fluctuation is denoted by .</p