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 The effects of stabilizing selection on the time of development in Drosophila melanogaster

1962 ◽  
Vol 3 (3) ◽  
pp. 364-382 ◽  
Author(s):  
Timothy Prout
Keyword(s):  
Drosophila Melanogaster ◽  
Development Time ◽  
Genetic Variance ◽  
Additive Genetic Variance ◽  
Parallel Line ◽  
Total Variance ◽  
Disruptive Selection ◽  
Stabilizing Selection ◽  
Environmental Component ◽  
The Mean

The length of time of development, from oviposition to emergence in Drosophila melanogaster was subjected to stabilizing selection. In each generation only the individuals emerging close to the mean development time were used as parents of the next generation. This line was designated the ‘S’ line. In a parallel line disruptive selection was practised; where in each generation the earliest flies to emerge were mated to the flies last to emerge; those emerging at intermediate times were discarded. This line was designated the ‘D’ line. Two control lines were also carried, where the flies were mated at random with respect to time of emergence. The experiment extended for 40 generations and produced the following results:(1) The variance of development time decreased in the S line and increased in the D line, relative to the control lines.(2) The mean development time decreased in the S line and increased in the D line.(3) The coefficients of variation decreased in the S line and increased in the D line.(4) The viability, measured as per cent flies emerging, decreased in the D line.Toward the end of the experiment the amount of additive genetic variance in the selected lines and in the control lines was estimated from the response to directional selection. The estimates showed that (i) the loss of total variance in the S line can be accounted for completely by a loss in additive genetic variance, and (ii) the increase in the total variance of the D line cannot be ascribed to an increase in the additive genetic variance. It was probably due to an increase in the environmental component of variance, i.e. to a loss of ‘buffering capacity’.

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

Genetics ◽  
1992 ◽  
Vol 132 (2) ◽  
pp. 603-618 ◽  
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.

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 Hidden genetic variance contributes to increase the short-term adaptive potential of selfing populations

2019 ◽  
Author(s):  
Josselin Clo ◽  
Joëlle Ronfort ◽  
Diala Abu Awad
Keyword(s):  
Genetic Variation ◽  
Mutation Rate ◽  
Genetic Variance ◽  
Purifying Selection ◽  
Stabilizing Selection ◽  
Genetic Associations ◽  
Adaptive Potential ◽  
Short Term ◽  
Additive Variance ◽  
Standing Variation

Standing genetic variation is considered a major contributor to the adaptive potential of species. The low heritable genetic variation observed in self-fertilising populations has led to the hypothesis that species with this mating system would be less likely to adapt. However, a non-negligible amount of cryptic genetic variation for polygenic traits, accumulated through negative linkage disequilibrium, could prove to be an important source of standing variation in self-fertilising species. To test this hypothesis we simulated populations under stabilizing selection subjected to an environmental change. We demonstrate that, when the mutation rate is high (but realistic), selfing populations are better able to store genetic variance than outcrossing populations through genetic associations, notably due to the reduced effective recombination rate associated with predominant selfing. Following an environmental shift, this diversity can be partially remobilized, which increases the additive variance and adaptive potential of predominantly (but not completely) selfing populations. In such conditions, despite initially lower observed genetic variance, selfing populations adapt as readily as outcrossing ones within a few generations. For low mutation rates, purifying selection impedes the storage of diversity through genetic associations, in which case, as previously predicted, the lower genetic variance of selfing populations results in lower adaptability compared to their outcrossing counterparts. The population size and the mutation rate are the main parameters to consider, as they are the best predictors of the amount of stored diversity in selfing populations. Our results and their impact on our knowledge of adaptation under high selfing rates are discussed.

scholarly journals Quantitative genetic models for the balance between migration and stabilizing selection

2000 ◽  
Vol 76 (3) ◽  
pp. 285-293 ◽  
Author(s):  
JARLE TUFTO
Keyword(s):  
Linkage Disequilibrium ◽  
Genetic Basis ◽  
Genetic Variance ◽  
Approximate Model ◽  
Allele Frequencies ◽  
Stabilizing Selection ◽  
Local Optimum ◽  
Symmetric Model ◽  
The Difference ◽  
And Migration

The evolution of a quantitative trait subject to stabilizing selection and immigration, with the immigrants deviating from the local optimum, is considered under a number of different models of the underlying genetic basis of the trait. By comparing exact predictions under the infinitesimal model obtained using numerical methods with predictions of a simplified approximate model based on ignoring linkage disequilibrium, the increase in the expressed genetic variance as a result of linkage disequilibrium generated by migration is shown to be relatively small and negligible, provided that the genetic variance relative to the squared deviation of immigrants from the local optimum is sufficiently large or selection and migration is sufficiently weak. Deviation from normality is shown to be less important by comparing predictions of the infinitesimal model with a model presupposing normality. For a more realistic symmetric model, involving a finite number of loci only, no linkage and equal effects and frequencies across loci, additional changes in the genetic variance arise as a result of changes in underlying allele frequencies. Again, provided that the genetic variance relative to the squared deviation of the immigrants from the local optimum is small, the difference between the predictions of infinitesimal and the symmetric model are small unless the number of loci is very small. However, if the genetic variance relative to the squared deviation of the immigrants from the local optimum is large, or if selection and migration are strong, both linkage disequilibrium and changes in the genetic variance as a result of changes in underlying allele frequencies become important.

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 How does parental environment influence the potential for adaptation to global change?

2018 ◽  
Vol 285 (1886) ◽  
pp. 20181374 ◽  
Author(s):  
Evatt Chirgwin ◽  
Dustin J. Marshall ◽  
Carla M. Sgrò ◽  
Keyne Monro
Keyword(s):  
Genetic Variation ◽  
Global Change ◽  
Adaptive Capacity ◽  
Genetic Variance ◽  
Life Stage ◽  
Additive Genetic Variance ◽  
Parental Exposure ◽  
Future Warming ◽  
The Mean ◽  
Negative Impacts

Parental environments are regularly shown to alter the mean fitness of offspring, but their impacts on the genetic variation for fitness, which predicts adaptive capacity and is also measured on offspring, are unclear. Consequently, how parental environments mediate adaptation to environmental stressors, like those accompanying global change, is largely unknown. Here, using an ecologically important marine tubeworm in a quantitative-genetic breeding design, we tested how parental exposure to projected ocean warming alters the mean survival, and genetic variation for survival, of offspring during their most vulnerable life stage under current and projected temperatures. Offspring survival was higher when parent and offspring temperatures matched. Across offspring temperatures, parental exposure to warming altered the distribution of additive genetic variance for survival, making it covary across current and projected temperatures in a way that may aid adaptation to future warming. Parental exposure to warming also amplified nonadditive genetic variance for survival, suggesting that compatibilities between parental genomes may grow increasingly important under future warming. Our study shows that parental environments potentially have broader-ranging effects on adaptive capacity than currently appreciated, not only mitigating the negative impacts of global change but also reshaping the raw fuel for evolutionary responses to it.

Genetic and statistical analyses of strong selection on polygenic traits: what, me normal?

Genetics ◽  
1994 ◽  
Vol 138 (3) ◽  
pp. 913-941 ◽  
Author(s):  
M Turelli ◽  
N H Barton
Keyword(s):  
Allele Frequency ◽  
Genetic Variance ◽  
Gaussian Approximation ◽  
Selection Response ◽  
Disruptive Selection ◽  
Breeding Values ◽  
Central Moments ◽  
Linkage Disequilibria ◽  
The Mean ◽  
Frequency Changes

Abstract We develop a general population genetic framework for analyzing selection on many loci, and apply it to strong truncation and disruptive selection on an additive polygenic trait. We first present statistical methods for analyzing the infinitesimal model, in which offspring breeding values are normally distributed around the mean of the parents, with fixed variance. These show that the usual assumption of a Gaussian distribution of breeding values in the population gives remarkably accurate predictions for the mean and the variance, even when disruptive selection generates substantial deviations from normality. We then set out a general genetic analysis of selection and recombination. The population is represented by multilocus cumulants describing the distribution of haploid genotypes, and selection is described by the relation between mean fitness and these cumulants. We provide exact recursions in terms of generating functions for the effects of selection on non-central moments. The effects of recombination are simply calculated as a weighted sum over all the permutations produced by meiosis. Finally, the new cumulants that describe the next generation are computed from the non-central moments. Although this scheme is applied here in detail only to selection on an additive trait, it is quite general. For arbitrary epistasis and linkage, we describe a consistent infinitesimal limit in which the short-term selection response is dominated by infinitesimal allele frequency changes and linkage disequilibria. Numerical multilocus results show that the standard Gaussian approximation gives accurate predictions for the dynamics of the mean and genetic variance in this limit. Even with intense truncation selection, linkage disequilibria of order three and higher never cause much deviation from normality. Thus, the empirical deviations frequently found between predicted and observed responses to artificial selection are not caused by linkage-disequilibrium-induced departures from normality. Disruptive selection can generate substantial four-way disequilibria, and hence kurtosis; but even then, the Gaussian assumption predicts the variance accurately. In contrast to the apparent simplicity of the infinitesimal limit, data suggest that changes in genetic variance after 10 or more generations of selection are likely to be dominated by allele frequency dynamics that depend on genetic details.

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 role of epistasis in the increase in the additive genetic variance after population bottlenecks

1999 ◽  
Vol 73 (1) ◽  
pp. 45-59 ◽  
Author(s):  
C. LÓPEZ-FANJUL ◽  
A. FERNÁNDEZ ◽  
M. A. TORO
Keyword(s):  
Additive Genetic Variance ◽  
Allele Frequencies ◽  
Environment Interaction ◽  
Genotypic Frequency ◽  
Population Bottlenecks ◽  
Ancestral Allele ◽  
Additive Variance ◽  
Low Frequencies ◽  
Multiple Loci ◽  
Genotype Environment Interaction

The effect of population bottlenecks on the additive variance generated by two neutral independent epistatic loci has been studied theoretically. Three kinds of epistasis were considered: (1) additive×additive, (2) multiple dominant genotype favoured, and (3) Dobzhansky–Muller type. The additive variance in an infinitely large panmictic population (ancestral variance) was compared with its expected value at equilibrium, after t consecutive bottlenecks of equal size N (derived variance). Formulae were derived in terms of allele frequencies and effects at each locus and the corresponding epistatic effects. An increase in the additive variance after bottlenecks will occur only if its ancestral value is minimal or very small. This has been detected only for: (1) intermediate ancestral allele frequencies at both loci ; (2) extreme ancestral allele frequencies at one or both loci. The magnitude of the excess was inversely related to N and t. With dominance gene action, enhanced additive variance after bottlenecks implies a rise in the genotypic frequency of homozygous deleterious recessives, resulting in inbreeding depression. Considering multiple loci, simultaneous segregation of unfavourable alleles at intermediate frequencies, or of favourable recessives at low frequencies, cannot easily be conceived of unless there is strong genotype–environment interaction. With this possible exception, it is unlikely that the rate of evolution may be accelerated after population bottlenecks, in spite of occasional increments of the derived additive variance over its ancestral value.

Sign in / Sign up

Export Citation Format

Share Document