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

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.

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Linkage disequilibrium and genetic variances under mutation-selection balance.

Genetics ◽

10.1093/genetics/121.4.857 ◽

1989 ◽

Vol 121 (4) ◽

pp. 857-860 ◽

Cited By ~ 1

Author(s):

A Hastings

Keyword(s):

Linkage Disequilibrium ◽

Mutation Rate ◽

Genetic Variance ◽

Harmonic Mean ◽

Recombination Rates ◽

Genetic Variances ◽

Locus Selection

Abstract I determine the contribution of linkage disequilibrium to genetic variances using results for two loci and for induced or marginal systems. The analysis allows epistasis and dominance, but assumes that mutation is weak relative to selection. The linkage disequilibrium component of genetic variance is shown to be unimportant for unlinked loci if the gametic mutation rate divided by the harmonic mean of the pairwise recombination rates is much less than one. For tightly linked loci, linkage disequilibrium is unimportant if the gametic mutation rate divided by the (induced) per locus selection is much less than one.

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Selection Response in Finite Populations

Genetics ◽

10.1093/genetics/144.4.1961 ◽

1996 ◽

Vol 144 (4) ◽

pp. 1961-1974 ◽

Cited By ~ 2

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.

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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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Segregation variance after hybridization of isolated populations

Genetics Research ◽

10.1017/s0016672300032547 ◽

1994 ◽

Vol 64 (1) ◽

pp. 51-56 ◽

Cited By ~ 28

Author(s):

Montgomery Slatkin ◽

Russell Lande

Keyword(s):

Genetic Variance ◽

Low Frequency ◽

Quantitative Character ◽

Hybrid Population ◽

Effective Population ◽

Isolated Populations ◽

Average Value ◽

House Of Cards ◽

Deleterious Alleles ◽

Two Populations

SummaryWe develop a model to predict the increase in genetic variance of a quantitative character in a hybrid population produced by crossing two previously isolated populations of the same species. The increase in variance in the F2 hybrids, the ‘segregation variance’, is caused by differences in the average allelic effects at each locus and by linkage disequilibrium among loci. We focus on the case in which the character is additively based and the average value of the character does not differ in the two populations. In that case the predicted segregation variance depends strongly on what is assumed about the genetic basis of the character. If the genetic variance of the character in each population is attributable to loci with numerous alleles of small effect that are in moderate frequency, as in Lande's (1975) model, the segregation variance should increase linearly with time since the populations were isolated, at a rate determined by the inverse of the effective population size. If the genetic variance is attributable to loci with alleles in very low frequency, as in Turelli's (1984) house-of-cards model or in Barton's (1990) model of pleiotropic, deleterious alleles, then the segregation variance in the hybrid population increases at a much lower rate.

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Animal models with group-specific additive genetic variances: extending genetic group models

10.1101/331157 ◽

2018 ◽

Author(s):

Stefanie Muff ◽

Alina K. Niskanen ◽

Dilan Saatoglu ◽

Lukas F. Keller ◽

Henrik Jensen

Keyword(s):

Animal Model ◽

Animal Models ◽

Genetic Variance ◽

Additive Genetic Variance ◽

Genetic Group ◽

Breeding Value ◽

Sampling Variance ◽

Implicit Assumption ◽

Genetic Variances ◽

Genetic Groups

Abstract1. The animal model is a key tool in quantitative genetics and has been used extensively to estimate fundamental parameters, such as additive genetic variance, heritability, or inbreeding effects. An implicit assumption of animal models is that all founder individuals derive from a single population. This assumption is commonly violated, for instance in cross-bred livestock breeds, when an observed population receive immigrants, or when a meta-population is split into genetically differentiated subpopulations. Ignoring genetic differences among different source populations of founders may lead to biased parameter estimates, in particular for the additive genetic variance.2. To avoid such biases, genetic group models, extensions to the animal model that account for the presence of more than one genetic group, have been proposed. As a key limitation, the method to date only allows that the breeding values differ in their means, but not in their variances among the groups. Methodology previously proposed to account for group-specific variances included terms for segregation variance, which rendered the models infeasibly complex for application to most real study systems.3. Here we explain why segregation variances are often negligible when analyzing the complex polygenic traits that are frequently the focus of evolutionary ecologists and animal breeders. Based on this we suggest an extension of the animal model that permits estimation of group-specific additive genetic variances. This is achieved by employing group-specific relatedness matrices for the breeding value components attributable to different genetic groups. We derive these matrices by decomposing the full relatedness matrix via the generalized Cholesky decomposition, and by scaling the respective matrix components for each group. To this end, we propose a computationally convenient approximation for the matrix component that encodes for the Mendelian sampling variance. Although convenient, this approximation is not critical.4. Simulations and an example from an insular meta-population of house sparrows in Norway with three genetic groups illustrate that the method is successful in estimating group-specific additive genetic variances and that segregation variances are indeed negligible in the empirical example.5. Quantifying differences in additive genetic variance within and among populations is of major biological interest in ecology, evolution, and animal and plant breeding. The proposed method allows to estimate such differences for subpopulations that form a connected meta-population, which may also be useful to study temporal or spatial variation of additive genetic variance.

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Chinese Holstein Cattle effective population size estimated from whole genome linkage disequilibrium

Hereditas (Beijing) ◽

10.3724/sp.j.1005.2012.00050 ◽

2012 ◽

Vol 34 (1) ◽

pp. 50-58 ◽

Cited By ~ 2

Author(s):

Gui-Yan NI ◽

Zhe ZHANG ◽

Li JIANG ◽

Pei-Pei MA ◽

Qin ZHANG ◽

...

Keyword(s):

Linkage Disequilibrium ◽

Population Size ◽

Effective Population Size ◽

Holstein Cattle ◽

Whole Genome ◽

Effective Population ◽

Chinese Holstein ◽

Chinese Holstein Cattle

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Estimates of linkage disequilibrium and the recombination parameter determined from segregating nucleotide sites in the alcohol dehydrogenase region of Drosophila pseudoobscura.

Genetics ◽

10.1093/genetics/135.2.541 ◽

1993 ◽

Vol 135 (2) ◽

pp. 541-552 ◽

Cited By ~ 5

Author(s):

S W Schaeffer ◽

E L Miller

Keyword(s):

Linkage Disequilibrium ◽

Alcohol Dehydrogenase ◽

Distance Effect ◽

Theoretical Distribution ◽

Drosophila Pseudoobscura ◽

Significant Linkage Disequilibrium ◽

Effective Population ◽

Nucleotide Distance ◽

Significant Linkage ◽

Recombination Parameter

Abstract The alcohol dehydrogenase (Adh) region of Drosophila pseudoobscura, which includes the two genes Adh and Adh-Dup, was used to examine the pattern and organization of linkage disequilibrium among pairs of segregating nucleotide sites. A collection of 99 strains from the geographic range of D. pseudoobscura were nucleotide-sequenced with polymerase chain reaction-mediated techniques. All pairs of the 359 polymorphic sites in the 3.5-kb Adh region were tested for significant linkage disequilibrium with Fisher's exact test. Of the 74,278 pairwise comparisons of segregating sites, 127 were in significant linkage disequilibrium at the 5% level. The distribution of five linkage disequilibrium estimators D(ij), D2, r(ij), r2 and D(ij) were compared to theoretical distributions. The observed distributions of D(ij), D2, r(ij) and r2 were consistent with the theoretical distribution given an infinite sites model. The observed distribution of D(ij) differed from the theoretical distribution because of an excess of values at -1 and 1. No spatial pattern was observed in the linkage disequilibrium pattern in the Adh region except for two clusters of sites nonrandomly associated in the adult intron and intron 2 of Adh. The magnitude of linkage disequilibrium decreases significantly as nucleotide distance increases, or a distance effect. Adh-Dup had a larger estimate of the recombination parameter, 4Nc, than Adh, where N is the effective population size and c is the recombination rate. A comparison of the mutation and recombination parameters shows that 7-17 recombination events occur for each mutation event. The heterogeneous estimates of the recombination parameter and the inverse relationship between linkage disequilibrium and nucleotide distance are no longer significant when the two clusters of Adh intron sites are excluded from analyses. The most likely explanation for the two clusters of linkage disequilibria is epistatic selection between sites in the cluster to maintain pre-mRNA secondary structure.

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How informative is Wright's estimator of the number of genes affecting a quantitative character?

Genetics ◽

10.1093/genetics/126.1.235 ◽

1990 ◽

Vol 126 (1) ◽

pp. 235-247 ◽

Cited By ~ 4

Author(s):

Z B Zeng ◽

D Houle ◽

C C Cockerham

Keyword(s):

Genetic Variance ◽

Estimation Procedure ◽

Expected Value ◽

Allele Frequencies ◽

Quantitative Character ◽

Base Population ◽

Single Population ◽

Number Of Genes ◽

Selection Limit ◽

The Difference

Abstract S. Wright suggested an estimator, m, of the number of loci, m, contributing to the difference in a quantitative character between two differentiated populations, which is calculated from the phenotypic means and variances in the two parental populations and their F1 and F2 hybrids. The same method can also be used to estimate m contributing to the genetic variance within a single population, by using divergent selection to create differentiated lines from the base population. In this paper we systematically examine the utility and problems of this technique under the influences of unequal allelic effects and initial allele frequencies, and linkage, which are known to lead m to underestimate m. In addition, we examine the effects of population size and selection intensity during the generations of selection. During selection, the estimator m rapidly approaches its expected value at the selection limit. With reasonable assumptions about unequal allelic effects and initial allele frequencies, the expected value of m without linkage is likely to be on the order of one-third of the number of genes. The estimates suffer most seriously from linkage. The practical maximum expectation of m is just about the number of chromosomes, considerably less than the "recombination index" which has been assumed to be the upper limit. The estimates are also associated with large sampling variances. An estimator of the variance of m derived by R. Lande substantially underestimates the actual variance. Modifications to the method can ameliorate some of the problems. These include using F3 or later generation variances or the genetic variance in the base population, and replicating the experiments and estimation procedure. However, even in the best of circumstances, information from m is very limited and can be misleading.

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