REDUCED GENETIC VARIANCE AMONG HIGH FITNESS INDIVIDUALS: INFERRING STABILIZING SELECTION ON MALE SEXUAL DISPLAYS INDROSOPHILA SERRATA

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.

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Genetic constraints predict evolutionary divergence in Dalechampia blossoms

Philosophical Transactions of the Royal Society B Biological Sciences ◽

10.1098/rstb.2013.0255 ◽

2014 ◽

Vol 369 (1649) ◽

pp. 20130255 ◽

Cited By ~ 52

Author(s):

Geir H. Bolstad ◽

Thomas F. Hansen ◽

Christophe Pélabon ◽

Mohsen Falahati-Anbaran ◽

Rocío Pérez-Barrales ◽

...

Keyword(s):

Genetic Variance ◽

Floral Morphology ◽

Additive Genetic Variance ◽

Genetic Data ◽

Stabilizing Selection ◽

Evolutionary Divergence ◽

Genetic Constraints ◽

Quantitative Genetic ◽

Rates Of Evolution ◽

Genetic Constraint

If genetic constraints are important, then rates and direction of evolution should be related to trait evolvability. Here we use recently developed measures of evolvability to test the genetic constraint hypothesis with quantitative genetic data on floral morphology from the Neotropical vine Dalechampia scandens (Euphorbiaceae). These measures were compared against rates of evolution and patterns of divergence among 24 populations in two species in the D. scandens species complex. We found clear evidence for genetic constraints, particularly among traits that were tightly phenotypically integrated. This relationship between evolvability and evolutionary divergence is puzzling, because the estimated evolvabilities seem too large to constitute real constraints. We suggest that this paradox can be explained by a combination of weak stabilizing selection around moving adaptive optima and small realized evolvabilities relative to the observed additive genetic variance.

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Deleterious mutations, apparent stabilizing selection and the maintenance of quantitative variation.

Genetics ◽

10.1093/genetics/132.2.603 ◽

1992 ◽

Vol 132 (2) ◽

pp. 603-618 ◽

Cited By ~ 7

Author(s):

A S Kondrashov ◽

M Turelli

Keyword(s):

Quantitative Trait ◽

Genetic Variance ◽

Additive Genetic Variance ◽

Pleiotropic Effects ◽

Direct Selection ◽

Selection Function ◽

Stabilizing Selection ◽

Deleterious Mutations ◽

Additive Variance ◽

Deleterious Alleles

Abstract Apparent stabilizing selection on a quantitative trait that is not causally connected to fitness can result from the pleiotropic effects of unconditionally deleterious mutations, because as N. Barton noted, "...individuals with extreme values of the trait will tend to carry more deleterious alleles...." We use a simple model to investigate the dependence of this apparent selection on the genomic deleterious mutation rate, U; the equilibrium distribution of K, the number of deleterious mutations per genome; and the parameters describing directional selection against deleterious mutations. Unlike previous analyses, we allow for epistatic selection against deleterious alleles. For various selection functions and realistic parameter values, the distribution of K, the distribution of breeding values for a pleiotropically affected trait, and the apparent stabilizing selection function are all nearly Gaussian. The additive genetic variance for the quantitative trait is kQa2, where k is the average number of deleterious mutations per genome, Q is the proportion of deleterious mutations that affect the trait, and a2 is the variance of pleiotropic effects for individual mutations that do affect the trait. In contrast, when the trait is measured in units of its additive standard deviation, the apparent fitness function is essentially independent of Q and a2; and beta, the intensity of selection, measured as the ratio of additive genetic variance to the "variance" of the fitness curve, is very close to s = U/k, the selection coefficient against individual deleterious mutations at equilibrium. Therefore, this model predicts appreciable apparent stabilizing selection if s exceeds about 0.03, which is consistent with various data. However, the model also predicts that beta must equal Vm/VG, the ratio of new additive variance for the trait introduced each generation by mutation to the standing additive variance. Most, although not all, estimates of this ratio imply apparent stabilizing selection weaker than generally observed. A qualitative argument suggests that even when direct selection is responsible for most of the selection observed on a character, it may be essentially irrelevant to the maintenance of variation for the character by mutation-selection balance. Simple experiments can indicate the fraction of observed stabilizing selection attributable to the pleiotropic effects of deleterious mutations.

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Response of Regulatory Genetic Variation in Gene Expression to Environmental Change in Drosophila melanogaster

10.1101/2020.06.23.163501 ◽

2020 ◽

Author(s):

Wen Huang ◽

Mary Anna Carbone ◽

Richard F. Lyman ◽

Robert H. H. Anholt ◽

Trudy F. C. Mackay

Keyword(s):

Gene Expression ◽

Drosophila Melanogaster ◽

Genetic Architecture ◽

Genetic Variance ◽

Network Connectivity ◽

Genotype By Environment Interaction ◽

Stabilizing Selection ◽

Environment Interaction ◽

Genotype By Environment ◽

Phenotypic Responses

AbstractThe genetics of phenotypic responses to changing environments remains elusive. Using whole genome quantitative gene expression as a model, we studied how the genetic architecture of regulatory variation in gene expression changed in a population of fully sequenced inbred Drosophila melanogaster strains when flies developed at different environments (25 °C and 18 °C). We found a substantial fraction of the transcriptome exhibited genotype by environment interaction, implicating environmentally plastic genetic architecture of gene expression. Genetic variance in expression increased at 18 °C relative to 25 °C for most genes that had a change in genetic variance. Although the majority of expression quantitative trait loci (eQTLs) for the gene expression traits in the two environments were shared and had similar effects, analysis of the environment-specific eQTLs revealed enrichment of binding sites for two transcription factors. Finally, although genotype by environment interaction in gene expression could potentially disrupt genetic networks, the co-expression networks were highly conserved across environments. Genes with higher network connectivity were under stronger stabilizing selection, suggesting that stabilizing selection on expression plays an important role in promoting network robustness.

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

Journal of The Royal Society Interface ◽

10.1098/rsif.2010.0438 ◽

2010 ◽

Vol 8 (58) ◽

pp. 720-739 ◽

Cited By ~ 15

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.

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Isolation by distance in a quantitative trait.

Genetics ◽

10.1093/genetics/128.2.443 ◽

1991 ◽

Vol 128 (2) ◽

pp. 443-452 ◽

Cited By ~ 1

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.

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Joint Effects of Pleiotropic Selection and Stabilizing Selection on the Maintenance of Quantitative Genetic Variation at Mutation-Selection Balance

Genetics ◽

10.1093/genetics/162.1.459 ◽

2002 ◽

Vol 162 (1) ◽

pp. 459-471 ◽

Cited By ~ 7

Author(s):

Xu-Sheng Zhang ◽

William G Hill

Keyword(s):

Genetic Variation ◽

Genetic Variance ◽

Stabilizing Selection ◽

Limited Impact ◽

Quantitative Genetic ◽

High Heritability ◽

Selection For ◽

Selection Parameters ◽

Mutation And Selection ◽

Polygenic Variation

AbstractIn quantitative genetics, there are two basic “conflicting” observations: abundant polygenic variation and strong stabilizing selection that should rapidly deplete that variation. This conflict, although having attracted much theoretical attention, still stands open. Two classes of model have been proposed: real stabilizing selection directly on the metric trait under study and apparent stabilizing selection caused solely by the deleterious pleiotropic side effects of mutations on fitness. Here these models are combined and the total stabilizing selection observed is assumed to derive simultaneously through these two different mechanisms. Mutations have effects on a metric trait and on fitness, and both effects vary continuously. The genetic variance (VG) and the observed strength of total stabilizing selection (Vs,t) are analyzed with a rare-alleles model. Both kinds of selection reduce VG but their roles in depleting it are not independent: The magnitude of pleiotropic selection depends on real stabilizing selection and such dependence is subject to the shape of the distributions of mutational effects. The genetic variation maintained thus depends on the kurtosis as well as the variance of mutational effects: All else being equal, VG increases with increasing leptokurtosis of mutational effects on fitness, while for a given distribution of mutational effects on fitness, VG decreases with increasing leptokurtosis of mutational effects on the trait. The VG and Vs,t are determined primarily by real stabilizing selection while pleiotropic effects, which can be large, have only a limited impact. This finding provides some promise that a high heritability can be explained under strong total stabilizing selection for what are regarded as typical values of mutation and selection parameters.

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Genotype by environment interaction for gene expression in Drosophila melanogaster

Nature Communications ◽

10.1038/s41467-020-19131-y ◽

2020 ◽

Vol 11 (1) ◽

Author(s):

Wen Huang ◽

Mary Anna Carbone ◽

Richard F. Lyman ◽

Robert R. H. Anholt ◽

Trudy F. C. Mackay

Keyword(s):

Gene Expression ◽

Drosophila Melanogaster ◽

Genetic Architecture ◽

Genetic Variance ◽

Network Connectivity ◽

Genotype By Environment Interaction ◽

Stabilizing Selection ◽

Environment Interaction ◽

Genotype By Environment ◽

Phenotypic Responses

Abstract The genetics of phenotypic responses to changing environments remains elusive. Using whole-genome quantitative gene expression as a model, here we study how the genetic architecture of regulatory variation in gene expression changed in a population of fully sequenced inbred Drosophila melanogaster strains when flies developed in different environments (25 °C and 18 °C). We find a substantial fraction of the transcriptome exhibited genotype by environment interaction, implicating environmentally plastic genetic architecture of gene expression. Genetic variance in expression increases at 18 °C relative to 25 °C for most genes that have a change in genetic variance. Although the majority of expression quantitative trait loci (eQTLs) for the gene expression traits in the two environments are shared and have similar effects, analysis of the environment-specific eQTLs reveals enrichment of binding sites for two transcription factors. Finally, although genotype by environment interaction in gene expression could potentially disrupt genetic networks, the co-expression networks are highly conserved across environments. Genes with higher network connectivity are under stronger stabilizing selection, suggesting that stabilizing selection on expression plays an important role in promoting network robustness.

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Pleiotropic models of polygenic variation, stabilizing selection, and epistasis.

Genetics ◽

10.1093/genetics/134.2.609 ◽

1993 ◽

Vol 134 (2) ◽

pp. 609-625 ◽

Cited By ~ 2

Author(s):

S Gavrilets ◽

G de Jong

Keyword(s):

Genetic Variance ◽

Genetic Load ◽

Genetic System ◽

Stabilizing Selection ◽

Selection System ◽

Genotypic Variance ◽

Epistatic Model ◽

Polygenic System ◽

Polygenic Variation ◽

Total Selection

Abstract We show that in polymorphic populations many polygenic traits pleiotropically related to fitness are expected to be under apparent "stabilizing selection" independently of the real selection acting on the population. This occurs, for example, if the genetic system is at a stable polymorphic equilibrium determined by selection and the nonadditive contributions of the loci to the trait value either are absent, or are random and independent of those to fitness. Stabilizing selection is also observed if the polygenic system is at an equilibrium determined by a balance between selection and mutation (or migration) when both additive and nonadditive contributions of the loci to the trait value are random and independent of those to fitness. We also compare different viability models that can maintain genetic variability at many loci with respect to their ability to account for the strong stabilizing selection on an additive trait. Let Vm be the genetic variance supplied by mutation (or migration) each generation, Vg be the genotypic variance maintained in the population, and n be the number of the loci influencing fitness. We demonstrate that in mutation (migration)-selection balance models the strength of apparent stabilizing selection is order Vm/Vg. In the overdominant model and in the symmetric viability model the strength of apparent stabilizing selection is approximately 1/(2n) that of total selection on the whole phenotype. We show that a selection system that involves pairwise additive by additive epistasis in maintaining variability can lead to a lower genetic load and genetic variance in fitness (approximately 1/(2n) times) than an equivalent selection system that involves overdominance. We show that, in the epistatic model, the apparent stabilizing selection on an additive trait can be as strong as the total selection on the whole phenotype.

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

Genetics ◽

10.1093/genetics/138.3.901 ◽

1994 ◽

Vol 138 (3) ◽

pp. 901-912 ◽

Cited By ~ 4

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.

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