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 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 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.

Combinatorics of Genotype-Phenotype Maps: An RNA Case Study

2005 ◽  
Author(s):  
Christian M. Reidys
Keyword(s):  
Natural Selection ◽  
Genetic Drift ◽  
Optimization Problem ◽  
Neutral Theory ◽  
Biological Evolution ◽  
Neutral Evolution ◽  
Evolutionary Search ◽  
Random Drift ◽  
Molecular Change ◽  
Biological Phenomena

The fundamental mechanisms of biological evolution have fascinated generations of researchers and remain popular to this day. The formulation of such a theory goes back to Darwin (1859), who in the The Origin of Species presented two fundamental principles: genetic variability caused by mutation, and natural selection. The first principle leads to diversity and the second one to the concept of survival of the fittest, where fitness is an inherited characteristic property of an individual and can basically be identified with its reproduction rate. Wright [530, 531] first recognized the importance of genetic drift in evolution in improving the evolutionary search capacity of the whole population. He viewed genetic drift merely as a process that could improve evolutionary search. About a decade later, Kimura proposed [317] that the majority of changes that are observed in evolution at the molecular level are the results of random drift of genotypes. The neutral theory of Kimura does not deny that selection plays a role, but claims that no appreciable fraction of observable molecular change can be caused by selective forces: mutations are either a disadvantage or, at best, neutral in present day organisms. Only negative selection plays a major role in the neutral evolution, in that deleterious mutants die out due to their lower fitness. Over the last few decades, there has been a shift of emphasis in the study of evolution. Instead of focusing on the differences in the selective value of mutants and on population genetics, interest has moved to evolution through natural selection as an abstract optimization problem. Given the tremendous opportunities that computer science and the physical sciences now have for contributing to the study of biological phenomena, it is fitting to study the evolutionary optimization problem in the present volume. In this chapter, we adopt the following framework: assuming that selection acts exclusively upon isolated phenotypes, we introduce the following compositum of mappings . . . Genotypes→ Phenotypes →Fitness . . . . We will refer to the first map as to the genotype-phenotype map and call the preimage of a given phenotype its neutral network. Clearly, the main ingredients here are the phenotypes and genotypes and their respective organization. In the following we will study various combinatorial properties of phenotypes and genotypes for RNA folding maps.

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.

Isolation by distance in a quantitative trait.

Genetics ◽  
1991 ◽  
Vol 128 (2) ◽  
pp. 443-452 ◽  
Author(s):  
R Lande
Keyword(s):  
Genetic Drift ◽  
Genetic Variance ◽  
Two Dimensions ◽  
Quantitative Character ◽  
Stabilizing Selection ◽  
Neighborhood Size ◽  
Phenotypic Variance ◽  
Two Dimensional ◽  
Random Genetic Drift ◽  
Dispersal Function

Abstract Random genetic drift in a quantitative character is modeled for a population with a continuous spatial distribution in an infinite habitat of one or two dimensions. The analysis extends Wright's concept of neighborhood size to spatially autocorrelated sampling variation in the expected phenotype at different locations. Weak stabilizing selection is assumed to operate toward the same optimum phenotype in every locality, and the distribution of dispersal distances from parent to offspring is a (radially) symmetric function. The equilibrium pattern of geographic variation in the expected local phenotype depends on the neighborhood size, the genetic variance within neighborhoods, and the strength of selection, but is nearly independent of the form of the dispersal function. With all else equal, geographic variance is smaller in a two-dimensional habitat than in one dimension, and the covariance between expected local phenotypes decreases more rapidly with the distance separating them in two dimensions than in one. The equilibrium geographic variance is less than the phenotypic variance within localities, unless the neighborhood size is small and selection is extremely weak, especially in two dimensions. Nevertheless, dispersal of geographic variance created by random genetic drift is an important mechanism maintaining genetic variance within local populations. For a Gaussian dispersal function it is shown that, even with a small neighborhood size, a population in a two-dimensional habitat can maintain within neighborhoods most of the genetic variance that would occur in an infinite panmictic population.

Frequency-dependent selection, metrical characters and molecular evolution

1988 ◽  
Vol 319 (1196) ◽  
pp. 631-640 ◽  
Keyword(s):  
Molecular Evolution ◽  
Genetic Drift ◽  
Random Order ◽  
Quantitative Character ◽  
Stabilizing Selection ◽  
Molecular Clocks ◽  
Random Genetic Drift ◽  
Stochastic Effects ◽  
Frequency Dependent ◽  
Frequency Dependent Selection

Computer models of selection acting on a quantitative character show that a combination of frequency-dependent and stabilizing selection can maintain many polymorphisms among the genes that determine the character. The models also show that the random order of mutations can give rise to selectively driven stochastic effects that are sometimes more important than random genetic drift. They suggest simple explanations for patterns of divergence between populations and species, and for apparent discrepancies between the rates of morphological and molecular evolution. They point towards a selective theory of ‘molecular clocks’

scholarly journals Genetic differentiation of quantitative characters between populations or species: I. Mutation and random genetic drift

1982 ◽  
Vol 39 (3) ◽  
pp. 303-314 ◽  
Author(s):  
Ranajit Chakraborty ◽  
Masatoshi Nei
Keyword(s):  
Population Size ◽  
Effective Population Size ◽  
Genetic Drift ◽  
Genetic Variance ◽  
Genetic Model ◽  
Neutral Evolution ◽  
Random Genetic Drift ◽  
Effective Population ◽  
Quantitative Characters ◽  
Allelic State

SummaryIntroducing a new genetic model called the discrete allelic-state model, the evolutionary change of genetic variation of quantitative characters within and between populations is studied under the assumption of no selection. This model allows us to study the effects of mutation and random genetic drift in detail. It is shown that when the allelic effects on phenotype are additive, the rate of approach of the genetic variance within populations to the equilibrium value depends only on the effective population size. It is also shown that the distribution of genotypic value often deviates from normality particularly when the effective population size and the number of loci concerned are small. On the other hand, the interpopulational variance increases linearly with time, if the intrapopu-lational variance remains constant. Therefore, the ratio of interpopulational variance to intrapopulational variance can be used for testing the hypothesis of neutral evolution of quantitative characters.

scholarly journals The Rate of Molecular Evolution When Mutation May Not Be Weak

2018 ◽  
Author(s):  
A.P. Jason de Koning ◽  
Bianca D. De Sanctis
Keyword(s):  
Natural Selection ◽  
Molecular Evolution ◽  
Population Size ◽  
Mutation Rate ◽  
Molecular Clock ◽  
Neutral Theory ◽  
Neutral Evolution ◽  
Systematic Bias ◽  
Effective Population ◽  
Sequence Comparisons

AbstractOne of the most fundamental rules of molecular evolution is that the rate of neutral evolution equals the mutation rate and is independent of effective population size. This result lies at the heart of the Neutral Theory, and is the basis for numerous analytic approaches that are widely applied to infer the action of natural selection across the genome and through time, and for dating divergence events using the molecular clock. However, this result was derived under the assumption that evolution is strongly mutation-limited, and it has not been known whether it generalizes across the range of mutation pressures or the spectrum of mutation types observed in natural populations. Validated by both simulations and exact computational analyses, we present a direct and transparent theoretical analysis of the Wright-Fisher model of population genetics, which shows that some of the most important rules of molecular evolution are fundamentally changed by considering recurrent mutation’s full effect. Surprisingly, the rate of the neutral molecular clock is found to have population-size dependence and to not equal the mutation rate in general. This is because, for increasing values of the population mutation rate parameter (θ), the time spent waiting for mutations quickly becomes smaller than the cumulative time mutants spend segregating before a substitution, resulting in a net deceleration compared to classical theory that depends on the population mutation rate. Furthermore, selection exacerbates this effect such that more adaptive alleles experience a greater deceleration than less adaptive alleles, introducing systematic bias in a wide variety of methods for inferring the strength and direction of natural selection from across-species sequence comparisons. Critically, the classical weak mutation approximation performs well only when θ< 0.1, a threshold that many biological populations seem to exceed.

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.

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.

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