Neutral additive genetic variance in a metapopulation

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.

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

Genetics Research ◽

10.1017/s0016672300028366 ◽

1989 ◽

Vol 54 (1) ◽

pp. 45-58 ◽

Cited By ~ 17

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.

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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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Quantitative genetics of postponed aging in Drosophila melanogaster. II. Analysis of selected lines.

Genetics ◽

10.1093/genetics/127.4.729 ◽

1991 ◽

Vol 127 (4) ◽

pp. 729-737

Author(s):

E W Hutchinson ◽

A J Shaw ◽

M R Rose

Keyword(s):

Drosophila Melanogaster ◽

Maternal Effects ◽

Genetic Variance ◽

Additive Genetic Variance ◽

Starvation Resistance ◽

Selected Lines ◽

Quantitative Genetic ◽

Degree Of Differentiation ◽

Postponed Aging ◽

Allelic Differentiation

Abstract Quantitative genetic analyses of Drosophila melanogaster stocks with postponed aging have suffered from the problem of a lack of certainty concerning patterns of allelic differentiation. The present experiments were designed to alleviate this difficulty by selecting for enhanced levels of characters known to be related to postponed aging. Selection successfully increased the degree of differentiation of postponed aging stocks with respect to starvation resistance and fecundity, but persistent additive genetic variance suggested that selection did not result in fixation of alleles. The artificially selected stocks were subjected to crosses to test for patterns of dominance and maternal effects. There was little evidence for these effects in the inheritance of the characters underlying postponed aging, even with the increased differentiation of the selected stocks.

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F statistics in Drosophila buzzatii: selection, population size and inbreeding.

Genetics ◽

10.1093/genetics/134.1.369 ◽

1993 ◽

Vol 134 (1) ◽

pp. 369-375 ◽

Cited By ~ 2

Author(s):

T Prout ◽

J S Barker

Keyword(s):

Body Size ◽

Population Size ◽

Genetic Variance ◽

Additive Genetic Variance ◽

Effective Population ◽

Allozyme Data ◽

Drosophila Buzzatii ◽

Sib Mating ◽

Selective Differentiation ◽

F Statistics

Abstract Drosophila buzzatii is confined to reproducing in a well defined patchy environment consisting of rotting cactus cladodes which are ephemeral, permitting at most three generations. Flies emerging from such rots were used to estimate the additive genetic variance within rots and the genetic variance between rots for body size and also were electrophoresed to determine their genotypes at six polymorphic loci. F statistics were estimated from body size and allozyme data. The FST derived from body size was significantly larger than the allozyme FST. It is proposed this is due to selective differentiation of body size. The allozyme FST is used to estimate effective population size: 10 < N < 50. It is suggested that the regularly observed positive FIS's could be due to partial sib mating, S. If so, the estimated lower bound is S = 0.258. Experiments are identified which could support or contradict these interpretations.

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THE GENETIC STRUCTURE OF NATURAL POPULATIONS OF DROSOPHILA MELANOGASTER. XVIII. CLINAL AND UNIFORM GENETIC VARIATION OVER POPULATIONS

Genetics ◽

10.1093/genetics/108.3.617 ◽

1984 ◽

Vol 108 (3) ◽

pp. 617-632

Author(s):

Shinichi Kusakabe ◽

Terumi Mukai

Keyword(s):

Genetic Variation ◽

Population Size ◽

Mutation Rate ◽

Genetic Variance ◽

Balancing Selection ◽

Additive Genetic Variance ◽

Southern Population ◽

Effective Population ◽

Northern Population ◽

The Difference

ABSTRACT It has been reported in the previous papers of this series that in the eastern United States and Japan there is a north-to-south cline of additive genetic variance of viability and that the amount of the additive genetic variance in the northern population can be explained by mutation-selection balance. To determine whether or not the difference in the genetic variation in northern and southern populations can be explained by the differences in mutation rate and/or effective population size, numerical calculations were made using population genetic parameters. In addition, the average heterozygosities of the northern and southern populations at ten of 19 polymorphic structural loci surveyed were estimated in relation to the cline of additive genetic variance of viability, and the following findings were obtained. (1) The changes in mutation rate and population size cannot simultaneously explain the difference in additive genetic variance and inbreeding decline between the northern and southern populations. Thus, the operation of some kind of balancing selection, most likely diversifying selection, was suggested to explain the observed excess of additive genetic variance. (2) Estimates of the average heterozygosities of the southern population were not significantly different from those of the northern population. Thus, it was strongly suggested that the excess of additive genetic variance in the southern population cannot be caused by structural loci, but by factors outside the structural loci, and that protein polymorphisms are selectively neutral or nearly neutral.

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Linkage and the limits to natural selection.

Genetics ◽

10.1093/genetics/140.2.821 ◽

1995 ◽

Vol 140 (2) ◽

pp. 821-841 ◽

Cited By ~ 27

Author(s):

N H Barton

Keyword(s):

Genetic Variance ◽

Additive Genetic Variance ◽

Large Population ◽

Substantial Effect ◽

Relative Fitness ◽

Fixation Probability ◽

Deleterious Mutations ◽

Effective Population ◽

Probability Of Fixation ◽

General Method

Abstract The probability of fixation of a favorable mutation is reduced if selection at other loci causes inherited variation in fitness. A general method for calculating the fixation probability of an allele that can find itself in a variety of genetic backgrounds is applied to find the effect of substitutions, fluctuating polymorphisms, and deleterious mutations in a large population. With loose linkage, r, the effects depend on the additive genetic variance in relative fitness, var(W), and act by reducing effective population size by (N/Ne) = 1 + var(W)/2r2. However, tightly linked loci can have a substantial effect not predictable from Ne. Linked deleterious mutations reduce the fixation probability of weakly favored alleles by exp (-2U/R), where U is the total mutation rate and R is the map length in Morgans. Substitutions can cause a greater reduction: an allele with advantage s < scrit = (pi 2/6) loge (S/s) [var(W)/R] is very unlikely to be fixed. (S is the advantage of the substitution impeding fixation.) Fluctuating polymorphisms at many (n) linked loci can also have a substantial effect, reducing fixation probability by exp [square root of 2Kn var(W)/R] [K = -1/E((u-u)2/uv) depending on the frequencies (u,v) at the selected polymorphisms]. Hitchhiking due to all three kinds of selection may substantially impede adaptation that depends on weakly favored alleles.

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

Genetics Research ◽

10.1017/s0016672398003231 ◽

1998 ◽

Vol 71 (2) ◽

pp. 161-170 ◽

Cited By ~ 14

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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Effects of bottlenecks on quantitative genetic variation in the butterfly Bicyclus anynana

Genetics Research ◽

10.1017/s0016672301004906 ◽

2001 ◽

Vol 77 (2) ◽

pp. 167-181 ◽

Cited By ~ 29

Author(s):

ILIK J. SACCHERI ◽

RICHARD A. NICHOLS ◽

PAUL M. BRAKEFIELD

Keyword(s):

Genetic Variance ◽

Additive Genetic Variance ◽

Additive Model ◽

Morphological Characters ◽

Hatching Rate ◽

Phenotypic Variance ◽

Bicyclus Anynana ◽

Single Population ◽

Egg Hatching ◽

And Control

The effects of a single population bottleneck of differing severity on heritability and additive genetic variance was investigated experimentally using a butterfly. An outbred laboratory stock was used to found replicate lines with one pair, three pairs and 10 pairs of adults, as well as control lines with approximately 75 effective pairs. Heritability and additive genetic variance of eight wing pattern characters and wing size were estimated using parent–offspring covariances in the base population and in all daughter lines. Individual morphological characters and principal components of the nine characters showed a consistent pattern of treatment effects in which average heritability and additive genetic variance was lower in one pair and three pair lines than in 10 pair and control lines. Observed losses in heritability and additive genetic variance were significantly greater than predicted by the neutral additive model when calculated with coefficients of inbreeding estimated from demographic parameters alone. However, use of molecular markers revealed substantially more inbreeding, generated by increased variance in family size and background selection. Conservative interpretation of a statistical analysis incorporating this previously undetected inbreeding led to the conclusion that the response to inbreeding of the morphological traits studied showed no significant departure from the neutral additive model. This result is consistent with the evidence for minimal directional dominance for these traits. In contrast, egg hatching rate in the same experimental lines showed strong inbreeding depression, increased phenotypic variance and rapid response to selection, highly indicative of an increase in additive genetic variance due to dominance variance conversion.

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THE EFFECT OF AN EXPERIMENTAL BOTTLENECK UPON QUANTITATIVE GENETIC VARIATION IN THE HOUSEFLY

Genetics ◽

10.1093/genetics/114.4.1191 ◽

1986 ◽

Vol 114 (4) ◽

pp. 1191-1211 ◽

Cited By ~ 3

Author(s):

Edwin H Bryant ◽

Steven A McCommas ◽

Lisa M Combs

Keyword(s):

Genetic Variation ◽

Body Size ◽

Genetic Variance ◽

Additive Genetic Variance ◽

Control Line ◽

Additive Effects ◽

Morphometric Traits ◽

Complete Dominance ◽

Quantitative Genetic ◽

Principal Axes

ABSTRACT Effects of a population bottleneck (founder-flush cycle) upon quantitative genetic variation of morphometric traits were examined in replicated experimental lines of the housefly founded with one, four or 16 pairs of flies. Heritability and additive genetic variances for eight morphometric traits generally increased as a result of the bottleneck, but the pattern of increase among bottleneck sizes differed among traits. Principal axes of the additive genetic correlation matrix for the control line yielded two suites of traits, one associated with general body size and another set largely independent of body size. In the former set containing five of the traits, additive genetic variance was greatest in the bottleneck size of four pairs, whereas in the latter set of two traits the largest additive genetic variance occurred in the smallest bottleneck size of one pair. One trait exhibited changes in additive genetic variance intermediate between these two major responses. These results were inconsistent with models of additive effects of alleles within loci or of additive effects among loci. An observed decline in viability measures and body size in the bottleneck lines also indicated that there was nonadditivity of allelic effects for these traits. Several possible nonadditive models were explored that increased additive genetic variance as a result of a bottleneck. These included a model with complete dominance, a model with overdominance and a model incorporating multiplicative epistasis.

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Pleiotropic Model of Maintenance of Quantitative Genetic Variation at Mutation-Selection Balance

Genetics ◽

10.1093/genetics/161.1.419 ◽

2002 ◽

Vol 161 (1) ◽

pp. 419-433 ◽

Cited By ~ 6

Author(s):

Xu-Sheng Zhang ◽

Jinliang Wang ◽

William G Hill

Keyword(s):

Genetic Variation ◽

Genetic Variance ◽

Large Population ◽

Stabilizing Selection ◽

Fitness Effect ◽

Environmental Variance ◽

Quantitative Genetic ◽

Phenotypic Standard Deviation ◽

Bivariate Gamma Distribution ◽

Mutational Variance

AbstractA pleiotropic model of maintenance of quantitative genetic variation at mutation-selection balance is investigated. Mutations have effects on a metric trait and deleterious effects on fitness, for which a bivariate gamma distribution is assumed. Equations for calculating the strength of apparent stabilizing selection (Vs) and the genetic variance maintained in segregating populations (VG) were derived. A large population can hold a high genetic variance but the apparent stabilizing selection may or may not be relatively strong, depending on other properties such as the distribution of mutation effects. If the distribution of mutation effects on fitness is continuous such that there are few nearly neutral mutants, or a minimum fitness effect is assumed if most mutations are nearly neutral, VG increases to an asymptote as the population size increases. Both VG and Vs are strongly affected by the shape of the distribution of mutation effects. Compared with mutants of equal effect, allowing their effects on fitness to vary across loci can produce a much higher VG but also a high Vs (Vs in phenotypic standard deviation units, which is always larger than the ratio VP/Vm), implying weak apparent stabilizing selection. If the mutational variance Vm is ∼10-3 Ve (Ve, environmental variance), the model can explain typical values of heritability and also apparent stabilizing selection, provided the latter is quite weak as suggested by a recent review.

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