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.

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 Genetic constraints predict evolutionary divergence in Dalechampia blossoms

2014 ◽  
Vol 369 (1649) ◽  
pp. 20130255 ◽  
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.

scholarly journals The quantitative genetic consequences of pleiotropy under stabilizing and directional selection.

Genetics ◽  
1990 ◽  
Vol 125 (1) ◽  
pp. 207-213 ◽  
Author(s):  
M Slatkin ◽  
S A Frank
Keyword(s):  
Directional Selection ◽  
Stabilizing Selection ◽  
Normal Model ◽  
Multivariate Normal ◽  
Genetic Covariance ◽  
Phenotypic Characters ◽  
House Of Cards ◽  
Quantitative Genetic ◽  
Stepwise Mutation ◽  
Multivariate Normal Model

Abstract The independence of two phenotypic characters affected by both pleiotropic and nonpleiotropic mutations is investigated using a generalization of M. Slatkin's stepwise mutation model of 1987. The model is used to determine whether predictions of either the multivariate normal model introduced in 1980 by R. Lande or the house-of-cards model introduced in 1985 by M. Turelli can be regarded as typical of models that are intermediate between them. We found that, under stabilizing selection, the variance of one character at equilibrium may depend on the strength of stabilizing selection on the other character (as in the house-of-cards model) or not (as in the multivariate normal model) depending on the types of mutations that can occur. Similarly, under directional selection, the genetic covariance between two characters may increase substantially (as in the house-of-cards model) or not (as in the multivariate normal model) depending on the kinds of mutations that are assumed to occur. Hence, even for the simple model we consider, neither the house-of-cards nor the multivariate normal model can be used to make predictions, making it unlikely that either could be used to draw general conclusions about more complex and realistic models.

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.

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

Genetics ◽  
2002 ◽  
Vol 162 (1) ◽  
pp. 459-471 ◽  
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.

scholarly journals Variance of neutral genetic variances within and between populations for a quantitative character.

Genetics ◽  
1991 ◽  
Vol 129 (2) ◽  
pp. 535-553
Author(s):  
Z B Zeng ◽  
C C Cockerham
Keyword(s):  
Linkage Disequilibrium ◽  
Coefficient Of Variation ◽  
Genetic Variance ◽  
Quantitative Character ◽  
Sampling Variance ◽  
Effective Population ◽  
Identity By Descent ◽  
Multiple Allele ◽  
Genetic Variances ◽  
Parameter Variance

Abstract The variances of genetic variances within and between finite populations were systematically studied using a general multiple allele model with mutation in terms of identity by descent measures. We partitioned the genetic variances into components corresponding to genetic variances and covariances within and between loci. We also analyzed the sampling variance. Both transient and equilibrium results were derived exactly and the results can be used in diverse applications. For the genetic variance within populations, sigma 2 omega, the coefficient of variation can be very well approximated as [formula: see text] for a normal distribution of allelic effects, ignoring recurrent mutation in the absence of linkage, where m is the number of loci, N is the effective population size, theta 1(0) is the initial identity by descent measure of two genes within populations and t is the generation number. The first term is due to genic variance, the second due to linkage disequilibrium, and third due to sampling. In the short term, the variation is predominantly due to linkage disequilibrium and sampling; but in the long term it can be largely due to genic variance. At equilibrium with mutation [formula: see text] where u is the mutation rate. The genetic variance between populations is a parameter. Variance arises only among sample estimates due to finite sampling of populations and individuals. The coefficient of variation for sample gentic variance between populations, sigma 2b, can be generally approximated as [formula: see text] when the number of loci is large where S is the number of sampling populations.

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.

Is Function of the Drosophila Homeotic Gene Ultrabithorax Canalized?

Genetics ◽  
1997 ◽  
Vol 147 (3) ◽  
pp. 1155-1168 ◽  
Author(s):  
Greg Gibson ◽  
Sylvie van Helden
Keyword(s):  
Genetic Variance ◽  
Population Level ◽  
Homeotic Gene ◽  
Stabilizing Selection ◽  
Homeotic Genes ◽  
Wild Type ◽  
Isofemale Lines ◽  
Environmental Variance ◽  
Quantitative Genetic ◽  
Genetic Contributions

Genetic variation affecting the expressivity of an amorphic allele of the homeotic gene Ultrabithorax, (Ubx1) was characterized after 11 generations of introgression into 29 different isofemale lines. Heterozygotes display a range of haploinsufficient phenotypes, from overlap with wild-type halteres to dramatic transformations such as a 50% increase in area and the presence of over 20 bristles on the anterior margin of each haltere. In both the wild-type and mutant genetic backgrounds, there is moderate genetic variance and low environmental variance/developmental asymmetry, as expected of a trait under stabilizing selection pressure. Surprisingly, there is little evidence that mutant halteres are more variable than wild-type ones, so it is unclear that haltere development is also canalized. The correlation between wild-type and Ubx haltere size is very low, indicating that interactions among modifiers of Ubx are complex, and in some cases sex-specific. The potential quantitative genetic contributions of homeotic genes to appendage morphology are discussed, noting that population-level effects of variation in key regulatory genes may be prevalent and complex but cannot be readily extrapolated to macroevolutionary diversification.

scholarly journals Neutral additive genetic variance in a metapopulation

1999 ◽  
Vol 74 (3) ◽  
pp. 215-221 ◽  
Author(s):  
MICHAEL C. WHITLOCK
Keyword(s):  
Genetic Variance ◽  
Additive Genetic Variance ◽  
Additive Model ◽  
Divergent Evolution ◽  
Fixation Index ◽  
Effective Population ◽  
Quantitative Genetic ◽  
Population Structures ◽  
Diploid Individual ◽  
Mutational Variance

For neutral, additive quantitative characters, the amount of additive genetic variance within and among populations is predictable from Wright's FST, the effective population size and the mutational variance. The structure of quantitative genetic variance in a subdivided metapopulation can be predicted from results from coalescent theory, thereby allowing single-locus results to predict quantitative genetic processes. The expected total amount of additive genetic variance in a metapopulation of diploid individual is given by 2Neσ2m (1 + FST), where FST is Wright's among-population fixation index, Ne is the eigenvalue effective size of the metapopulation, and σ2m is the mutational variance. The expected additive genetic variance within populations is given by 2Neσ2e(1 − FST), and the variance among demes is given by 4FSTNeσ2m. These results are general with respect to the types of population structure involved. Furthermore, the dimensionless measure of the quantitative genetic variance among populations, QST, is shown to be generally equal to FST for the neutral additive model. Thus, for all population structures, a value of QST greater than FST for neutral loci is evidence for spatially divergent evolution by natural selection.

Sign in / Sign up

Export Citation Format

Share Document