scholarly journals Polygenic adaptation after a sudden change in environment

2019 ◽  
Author(s):  
Laura K. Hayward ◽  
Guy Sella
Keyword(s):  
Genetic Variance ◽  
Sudden Change ◽  
Directional Selection ◽  
Stabilizing Selection ◽  
Effective Population ◽  
Short Term ◽  
Exponential Process ◽  
Optimal Value ◽  
Polygenic Adaptation ◽  
The Mean

AbstractPolygenic adaptation in response to selection on quantitative traits is thought to be ubiquitous in humans and other species, yet this mode of adaptation remains poorly understood. We investigate the dynamics of this process, assuming that a sudden change in environment shifts the optimal value of a highly polygenic quantitative trait. We find that when the shift is not too large relative to the genetic variance in the trait and this variance arises from segregating loci with small to moderate effect sizes (defined in terms of the selection acting on them before the shift), the mean phenotype’s approach to the new optimum is well approximated by a rapid exponential process first described by Lande (1976). In contrast, when the shift is larger or large effect loci contribute substantially to genetic variance, the initially rapid approach is succeeded by a much slower one. In either case, the underlying changes to allele frequencies exhibit different behaviors short and long-term. Over the short term, strong directional selection on the trait introduces small differences between the frequencies of minor alleles whose effects are aligned with the shift in optimum versus those with effects in the opposite direction. The phenotypic effects of these differences are dominated by contributions from alleles with moderate and large effects, and cumulatively, these effects push the mean phenotype close to the new optimum. Over the longer term, weak directional selection on the trait can amplify the expected frequency differences between opposite alleles; however, since the mean phenotype is close to the new optimum, alleles are mainly affected by stabilizing selection on the trait. Consequently, the frequency differences between opposite alleles translate into small differences in their probabilities of fixation, and the short-term phenotypic contributions of large effect alleles are largely supplanted by contributions of fixed, moderate ones. This process takes on the order of ~4Ne generations (where Ne is the effective population size), after which the steady state architecture of genetic variation around the new optimum is restored.

scholarly journals Polygenic Adaptation in a Population of Finite Size

Entropy ◽  
2020 ◽  
Vol 22 (8) ◽  
pp. 907
Author(s):  
Wolfgang Stephan ◽  
Sona John
Keyword(s):  
Genetic Drift ◽  
Evolutionary Biology ◽  
Genetic Variance ◽  
Finite Size ◽  
Stabilizing Selection ◽  
Rapid Phase ◽  
Exponential Process ◽  
Polygenic Adaptation ◽  
The Mean ◽  
High Equilibrium

Polygenic adaptation in response to selection on quantitative traits has become an important topic in evolutionary biology. Here we review the recent literature on models of polygenic adaptation. In particular, we focus on a model that includes mutation and both directional and stabilizing selection on a highly polygenic trait in a population of finite size (thus experiencing random genetic drift). Assuming that a sudden environmental shift of the fitness optimum occurs while the population is in a stochastic equilibrium, we analyze the adaptation of the trait to the new optimum. When the shift is not too large relative to the equilibrium genetic variance and this variance is determined by loci with mostly small effects, the approach of the mean phenotype to the optimum can be approximated by a rapid exponential process (whose rate is proportional to the genetic variance). During this rapid phase the underlying changes to allele frequencies, however, may depend strongly on genetic drift. While trait-increasing alleles with intermediate equilibrium frequencies are dominated by selection and contribute positively to changes of the trait mean (i.e., are aligned with the direction of the optimum shift), alleles with low or high equilibrium frequencies show more of a random dynamics, which is expected when drift is dominating. A strong effect of drift is also predicted for population size bottlenecks. Our simulations show that the presence of a bottleneck results in a larger deviation of the population mean of the trait from the fitness optimum, which suggests that more loci experience the influence of drift.

scholarly journals Quantitative genetic variability maintained by mutation-stabilizing selection balance: sampling variation and response to subsequent directional selection

1989 ◽  
Vol 54 (1) ◽  
pp. 45-58 ◽  
Author(s):  
Peter D. Keightley ◽  
William G. Hill
Keyword(s):  
Genetic Variance ◽  
Directional Selection ◽  
Quantitative Character ◽  
Stabilizing Selection ◽  
Effective Population ◽  
Selection Responses ◽  
Quantitative Genetic ◽  
Before And After ◽  
Cage Population ◽  
Selection Of

SummaryA model of genetic variation of a quantitative character subject to the simultaneous effects of mutation, selection and drift is investigated. Predictions are obtained for the variance of the genetic variance among independent lines at equilibrium with stabilizing selection. These indicate that the coefficient of variation of the genetic variance among lines is relatively insensitive to the strength of stabilizing selection on the character. The effects on the genetic variance of a change of mode of selection from stabilizing to directional selection are investigated. This is intended to model directional selection of a character in a sample of individuals from a natural or long-established cage population. The pattern of change of variance from directional selection is strongly influenced by the strengths of selection at individual loci in relation to effective population size before and after the change of regime. Patterns of change of variance and selection responses from Monte Carlo simulation are compared to selection responses observed in experiments. These indicate that changes in variance with directional selection are not very different from those due to drift alone in the experiments, and do not necessarily give information on the presence of stabilizing selection or its strength.

Short-term Changes in the Variance: 1. Changes in the Additive Variance

2018 ◽  
Author(s):  
Bruce Walsh ◽  
Michael Lynch
Keyword(s):  
Linkage Disequilibrium ◽  
Assortative Mating ◽  
Genetic Variance ◽  
Additive Genetic Variance ◽  
Allele Frequencies ◽  
Disruptive Selection ◽  
Stabilizing Selection ◽  
Short Term ◽  
Additive Variance ◽  
The Mean

Selection changes the additive-genetic variance (and hence the response in the mean) by both changing allele frequencies and by generating correlations among alleles at different loci (linkage disequilibrium). Such selection-induced correlations can be generated even between unlinked loci, and (generally) are negative, such that alleles increasing trait values tend to become increasingly negative correlated under direction or stabilizing selection, and positively correlated under disruptive selection. Such changes in the additive-genetic variance from disequilibrium is called the Bulmer effects. For a large number of loci, the amount of change can be predicted from the Bulmer equation, the analog of the breeder's equation, but now for the change in the variance. Upon cessation of selection, any disequilibrium decays away, and the variances revert back to their additive-genic variances (the additive variance in the absence of disequilibrium). Assortative mating also generates such disequilibrium.

scholarly journals Selection Response in Finite Populations

Genetics ◽  
1996 ◽  
Vol 144 (4) ◽  
pp. 1961-1974 ◽  
Author(s):  
Ming Wei ◽  
Armando Caballero ◽  
William G Hill
Keyword(s):  
Linkage Disequilibrium ◽  
Inbreeding Depression ◽  
Genetic Variance ◽  
Relative Rate ◽  
Selection Response ◽  
Rate Of Change ◽  
Effective Population ◽  
Short Term ◽  
Model Account

Formulae were derived to predict genetic response under various selection schemes assuming an infinitesimal model. Account was taken of genetic drift, gametic (linkage) disequilibrium (Bulmer effect), inbreeding depression, common environmental variance, and both initial segregating variance within families (σAW02) and mutational (σM2) variance. The cumulative response to selection until generation t(CRt) can be approximated asCRt≈R0[t−β(1−σAW∞2σAW02)t24Ne]−Dt2Ne,where Ne is the effective population size, σAW∞2=NeσM2 is the genetic variance within families at the steady state (or one-half the genic variance, which is unaffected by selection), and D is the inbreeding depression per unit of inbreeding. R  0 is the selection response at generation 0 assuming preselection so that the linkage disequilibrium effect has stabilized. β is the derivative of the logarithm of the asymptotic response with respect to the logarithm of the within-family genetic variance, i.e., their relative rate of change. R  0 is the major determinant of the short term selection response, but σM2, Ne and β are also important for the long term. A selection method of high accuracy using family information gives a small Ne and will lead to a larger response in the short term and a smaller response in the long term, utilizing mutation less efficiently.

scholarly journals Learning from your mistakes: a novel method to predict the response to directional selection

2021 ◽  
Author(s):  
Lisandro Milocco ◽  
Isaac Salazar-Ciudad
Keyword(s):  
Evolutionary Biology ◽  
Genetic Variance ◽  
Learning Algorithm ◽  
Additive Genetic Variance ◽  
Fruit Fly ◽  
Directional Selection ◽  
Prediction Errors ◽  
Evolution Experiment ◽  
Novel Method ◽  
The Mean

Predicting how populations respond to selection is a key goal of evolutionary biology. The field of quantitative genetics provides predictions for the response to directional selection through the breeder’s equation. However, differences between the observed responses to selection and those predicted by the breeder’s equation occur. The sources of these errors include omission of traits under selection, inaccurate estimates of genetic variance, and nonlinearities in the relationship between genetic and phenotypic variation. A key insight from previous research is that the expected value of these prediction errors is often not zero, in which case the predictions are systematically biased. Here, we propose that this prediction bias, rather than being a nuisance, can be used to improve the predictions. We use this to develop a novel method to predict the response to selection, which is built on three key innovations. First, the method predicts change as the breeder’s equation plus a bias term. Second, the method combines information from the breeder’s equation and from the record of past changes in the mean, to estimate the bias and predict change using a Kalman filter. Third, the parameters of the filter are fitted in each generation using a machine-learning algorithm on the record of past changes. We apply the method to data of an artificial selection experiment of the wing of the fruit fly, as well as to an in silico evolution experiment for teeth. We find that the method outperforms the breeder’s equation, and notably provides good predictions even when traits under selection are omitted from the analysis and when additive genetic variance is estimated inaccurately. The proposed method is easy to apply since it only requires recording the mean of the traits over past generations.

scholarly journals The statistical mechanics of a polygenic character under stabilizing selection, mutation and drift

2010 ◽  
Vol 8 (58) ◽  
pp. 720-739 ◽  
Author(s):  
Harold P. de Vladar ◽  
Nick H. Barton
Keyword(s):  
Population Genetics ◽  
Statistical Mechanics ◽  
Generating Function ◽  
Genetic Drift ◽  
Infinite Series ◽  
Genetic Variance ◽  
Directional Selection ◽  
Entropy Measure ◽  
Stabilizing Selection ◽  
Approximation Procedure

By exploiting an analogy between population genetics and statistical mechanics, we study the evolution of a polygenic trait under stabilizing selection, mutation and genetic drift. This requires us to track only four macroscopic variables, instead of the distribution of all the allele frequencies that influence the trait. These macroscopic variables are the expectations of: the trait mean and its square, the genetic variance, and of a measure of heterozygosity, and are derived from a generating function that is in turn derived by maximizing an entropy measure. These four macroscopics are enough to accurately describe the dynamics of the trait mean and of its genetic variance (and in principle of any other quantity). Unlike previous approaches that were based on an infinite series of moments or cumulants, which had to be truncated arbitrarily, our calculations provide a well-defined approximation procedure. We apply the framework to abrupt and gradual changes in the optimum, as well as to changes in the strength of stabilizing selection. Our approximations are surprisingly accurate, even for systems with as few as five loci. We find that when the effects of drift are included, the expected genetic variance is hardly altered by directional selection, even though it fluctuates in any particular instance. We also find hysteresis, showing that even after averaging over the microscopic variables, the macroscopic trajectories retain a memory of the underlying genetic states.

scholarly journals Evolution of amphimixis and recombination under fluctuating selection in one and many traits

1996 ◽  
Vol 68 (2) ◽  
pp. 165-173 ◽  
Author(s):  
Alexey S. Kondrashov ◽  
Lev Yu. Yampolsky
Keyword(s):  
Genetic Variance ◽  
Genetic Load ◽  
Short Term ◽  
Fluctuating Selection ◽  
Total Load ◽  
Mean Values ◽  
Individual Traits ◽  
The Mean ◽  
One And Many ◽  
Frequent Allele

SummaryBoth stabilizing and directional selection acting on one or many quantitative traits usually reduce the genetic variance in a polymorphic population. Amphimixis and recombination restore the variance, pushing it closer to its value under linkage equilibrium. They thus increase the response of the population to fluctuating selection and decrease the genetic load when the mean phenotype is far from optimum. Amphimixis can have a short-term advantage over apomixis if selection fluctuates frequently and widely, so that every genotype often has a low fitness. Such selection causes high genetic variance due to frequent allele substitutions, and a high load even with amphimixis. Recombination in an amphimictic population is maintained only if selection is usually strong and effectively directional. A modifier allele causing free recombination can have a significant advantage only if fluctuations of selection are such that the load is substantial. With smaller fluctuations, an intermediate recombination rate can be established, either due to fixation of alleles that cause such a rate or due to the stable coexistence of alleles causing high and low recombination. If many traits simultaneously are under fluctuating selection, amphimixis and recombination can be maintained when selection associated with individual traits is weaker and the changes in their mean values are smaller than with a single trait. Still, the range of changes of the fitness optima in each trait must be at least of the order of the trait's standard deviation, and the total load must be high.

scholarly journals On the distribution of the mean and variance of a quantitative trait under mutation-selection-drift balance.

Genetics ◽  
1994 ◽  
Vol 138 (3) ◽  
pp. 901-912 ◽  
Author(s):  
R Bürger ◽  
R Lande
Keyword(s):  
Genetic Drift ◽  
Quantitative Trait ◽  
Quantitative Traits ◽  
Genetic Variance ◽  
Stochastic Simulations ◽  
Stabilizing Selection ◽  
Phenotypic Evolution ◽  
Theoretical Predictions ◽  
Mean And Variance ◽  
The Mean

Abstract The distributions of the mean phenotype and of the genetic variance of a polygenic trait under a balance between mutation, stabilizing selection and genetic drift are investigated. This is done by stochastic simulations in which each individual and each gene are represented. The results are compared with theoretical predictions. Some aspects of the existing theories for the evolution of quantitative traits are discussed. The maintenance of genetic variance and the average dynamics of phenotypic evolution in finite populations (with Ne < 1000) are generally simpler than those suggested by some recent deterministic theories for infinite populations.

scholarly journals THE SELECTIVE VALUE OF ALLELES UNDERLYING POLYGENIC TRAITS

Genetics ◽  
1984 ◽  
Vol 108 (4) ◽  
pp. 1021-1033
Author(s):  
Michael Lynch
Keyword(s):  
Molecular Evolution ◽  
Genetic Drift ◽  
Genetic Variance ◽  
Neutral Theory ◽  
Mechanistic Explanation ◽  
Neutral Evolution ◽  
Stabilizing Selection ◽  
Average Effect ◽  
Absolute Value ◽  
The Mean

ABSTRACT To define the genetic and ecological circumstances that are conductive to evolution via genetic drift at the allelic level, the selection coefficient for a constituent allele of arbitrary effect is derived for a polygenic character exposed to stabilizing selection. Under virtually all possible conditions, alleles within the class for which the absolute value of the average effect is <10-2 phenotypic standard deviations are neutral with respect to each other. In addition, when the mean phenotype is at the optimum and the genetic variance is in selection-drift-mutation equilibrium, a considerable amount of neutral evolution is expected in the class of alleles with intermediate effects on the phenotype. These results help clarify how molecular evolution via genetic drift may occur at a locus despite intense selection and provide a potential mechanistic explanation for the neutral theory of molecular evolution.

scholarly journals Linkage and the maintenance of variation for quantitative traits by mutation–selection balance: an infinitesimal model

1998 ◽  
Vol 71 (2) ◽  
pp. 161-170 ◽  
Author(s):  
ENRIQUE SANTIAGO
Keyword(s):  
Quantitative Traits ◽  
Genetic Variance ◽  
Chromosome Length ◽  
Stabilizing Selection ◽  
Effective Population ◽  
Environmental Variance ◽  
Homologous Chromosomes ◽  
Quadratic Equations ◽  
Mutational Variance ◽  
The Continuum

The infinitesimal model is extended to cover linkage in finite populations. General equations to predict the dynamics of the genetic variation under the joint effects of mutation, selection and drift are derived. Under truncation and stabilizing selection, the quadratic equations for the asymptotic genetic variance (VG) are respectivelyV2G(1+kS)+VG (Ve−2NeVm) −2NeVmVe=0andV2G(1+S)+VG (Ve+γ−2NeVm) −2NeVm(Ve+γ)=0,where Ne is the effective population size, Vm is the mutational variance, Ve is the environmental variance, γ is the parameter that measures the spread of fitness around the optimum under stabilizing selection, k is equal to i(i−x) where i is the selection intensity and x is the cut-off point under truncation selection. The term S is a function of the number of chromosomes (v) and the average chromosome length (l):formula hereThese predictions are accurate when compared with results of simulations of small populations unless the number of genes is small. The infinitesimal model reduces to the continuum of alleles model if there is no recombination between homologous chromosomes.

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