Dynamics of polygenic variability under stabilizing selection, recombination, and drift

SummaryWe study the transient dynamics of the genotypic variance of an additive trait under stabilizing selection, recombination and random drift. We show how interaction of these factors determines the form and the rates of change of different components of the genotypic variance. Let Vg be the genie variance of the trait and CL be the contribution of linkage disequilibrium to the genotypic variance. We demonstrate that the dynamics of the system on the plane (Vg, CL) are typically characterized by a quick approach to a straight line with slow evolution along this line afterwards. We show that the number of loci, n, and the population size, N, affect the expected dynamics of Vg mainly through the ratio N/n. We use our analytical and numerical results in interpreting the published results of artificial stabilizing selection experiments. The analysis suggests that it is drift and not selection that most likely led to the reduction of genetic variability in most of these experiments. Even very strong stabilizing selection only slowly removes polygenic variability from populations.

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Dynamics of genetic variability in two-locus models of stabilizing selection.

Genetics ◽

10.1093/genetics/138.2.519 ◽

1994 ◽

Vol 138 (2) ◽

pp. 519-532

Author(s):

S Gavrilets ◽

A Hastings

Keyword(s):

Linkage Disequilibrium ◽

Initial Conditions ◽

Fitness Function ◽

Stabilizing Selection ◽

Phenotypic Evolution ◽

Phenotypic Characteristics ◽

Locus Model ◽

Straight Line ◽

The Difference ◽

Slow Evolution

Abstract We study a two locus model, with additive contributions to the phenotype, to explore the dynamics of different phenotypic characteristics under stabilizing selection and recombination. We demonstrate that the interaction of selection and recombination results in constraints on the mode of phenotypic evolution. Let Vg be the genic variance of the trait and CL be the contribution of linkage disequilibrium to the genotypic variance. We demonstrate that, independent of the initial conditions, the dynamics of the system on the plane (Vg, CL) are typically characterized by a quick approach to a straight line with slow evolution along this line afterward. We analyze how the mode and the rate of phenotypic evolution depend on the strength of selection relative to recombination, on the form of fitness function, and the difference in allelic effect. We argue that if selection is not extremely weak relative to recombination, linkage disequilibrium generated by stabilizing selection influences the dynamics significantly. We demonstrate that under these conditions, which are plausible in nature and certainly the case in artificial stabilizing selection experiments, the model can have a polymorphic equilibrium with positive linkage disequilibrium that is stable simultaneously with monomorphic equilibria.

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Pleiotropy and multilocus polymorphisms.

Genetics ◽

10.1093/genetics/130.1.223 ◽

1992 ◽

Vol 130 (1) ◽

pp. 223-227

Author(s):

A Gimelfarb

Keyword(s):

Genetic Variation ◽

Linkage Disequilibrium ◽

Stabilizing Selection ◽

Additive Genetic Variation ◽

Very High

Abstract It is demonstrated that systems of two pleiotropically related characters controlled by additive diallelic loci can maintain under Gaussian stabilizing selection a stable polymorphism in more than two loci. It is also shown that such systems may have multiple stable polymorphic equilibria. Stabilizing selection generates negative linkage disequilibrium, as a result of which the equilibrium phenotypic variances are quite low, even though the level of allelic polymorphisms can be very high. Consequently, large amounts of additive genetic variation can be hidden in populations at equilibrium under stabilizing selection on pleiotropically related characters.

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The variance of linkage disequilibrium between three loci in a finite population

Canadian Journal of Genetics and Cytology ◽

10.1139/g83-026 ◽

1983 ◽

Vol 25 (2) ◽

pp. 139-145 ◽

Cited By ~ 3

Author(s):

C. Strobeck ◽

G. B. Golding

Keyword(s):

Linkage Disequilibrium ◽

Finite Population ◽

Intragenic Recombination ◽

Random Drift ◽

Third Order ◽

Linkage Disequilibria ◽

Order Of Magnitude ◽

Infinite Alleles Model

The variance of three-locus linkage disequilibria for an equilibrium infinite alleles model is solved numerically on a computer, using identity coefficients. It is shown that the variance of three-locus linkage disequilibrium created by random drift, although smaller than the variance of two-locus linkage disequilibrium, is of the same order of magnitude. Hence third-order disequilibria are not necessarily good indications of selection. The formula for the variance of linkage disequilibrium is given when there is no recombination between the genes. This model can also be interpreted as intragenic recombination between three sites within a gene.

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Linkage disequilibrium in experimental populations of Drosophila simulans: a test of the random drift hypothesis

Genetics Research ◽

10.1017/s0016672300023685 ◽

1987 ◽

Vol 50 (3) ◽

pp. 187-193

Author(s):

Catherine Montchamp-Moreau ◽

Mariano Katz

Keyword(s):

Linkage Disequilibrium ◽

Genetic Drift ◽

Natural Populations ◽

Aldehyde Oxidase ◽

Drosophila Simulans ◽

Random Drift ◽

Esterase 6 ◽

Experimental Populations ◽

Experimental Values ◽

Neutralist Hypothesis

SummaryLinkage disequilibrium between five polymorphic enzymic loci of the third chromosome (Esterase-6, Phosphoglucomutase, Esterase-C, Aldehyde Oxidase and Acid Phosphatase) was studied in experimental populations of Drosophila simulans. Gametic data were obtained by mating sampled males with homozygous females at the five loci. Four cage populations were initiated with flies caught from natural populations. Extensive linkage disequilibrium was detected after 25 or 34 generations. The effective size of these populations was estimated about 400. Monte-Carlo simulations were performed in order to determine whether the observed disequilibria could be due to genetic drift. The observed probability distribution of the experimental values of r (the gametic correlation coefficient) was consistent with the distribution expected under random genetic drift. Our results are thus in accordance with the neutralist hypothesis.

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Genetic, geographical and temporal variation of porcine reproductive and respiratory syndrome virus in Illinois

Microbiology ◽

10.1099/0022-1317-81-1-171 ◽

2000 ◽

Vol 81 (1) ◽

pp. 171-179 ◽

Cited By ~ 52

Author(s):

Tony L. Goldberg ◽

Edwin C. Hahn ◽

Ronald M. Weigel ◽

Gail Scherba

Keyword(s):

Genetic Variability ◽

Genetic Similarity ◽

Pseudorabies Virus ◽

Amino Acid Level ◽

Effective Vaccine ◽

Respiratory Syndrome Virus ◽

Stabilizing Selection ◽

Gene Sequences ◽

Long Distance ◽

Geographical Regions

Porcine reproductive and respiratory syndrome virus (PRRSV) ORF5 gene sequences were generated by RT–PCR from 55 field isolates collected in Illinois and eastern Iowa. Spatial and temporal patterns of genetic variation in the virus were examined on a local geographical scale in order to test the hypothesis that the genetic similarity of PRRSV isolates (measured as their percentage pairwise ORF5 nucleotide similarity) was positively correlated with their geographical proximity. Levels of genetic variability in the Illinois/eastern Iowa PRRSV sample were similar to levels of variability seen across broader geographical regions within North America. The genetic similarity of isolates did not correlate with their geographical distance. These results imply that the movement of PRRSV onto farms does not generally occur via distance-limited processes such as wind or wildlife vectors, but more typically occurs via the long-distance transport of animals or semen. Genetic distances between PRRSV isolates collected from the same farms at different times increased as the time separating the collection events increased. This result implies rapid movement of new genetic types of PRRSV into and out of farms. PRRSV ORF5 displayed a pattern of third-codon-position diversity bias that was not evident in a geographically comparable sample of pseudorabies virus (a swine alphaherpesvirus) gC gene sequences. This result provides evidence that PRRSV ORF5 is experiencing stabilizing selection against structural novelty. Despite high genetic variability at all geographical levels, PRRSV ORF5 nevertheless contained potentially antigenic regions that were invariant at the amino acid level. These regions should make effective vaccine targets if they prove to be immunogenic.

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The population genetics of haplo-diploids and X-linked genes

Genetics Research ◽

10.1017/s0016672300026550 ◽

1984 ◽

Vol 44 (3) ◽

pp. 321-341 ◽

Cited By ~ 48

Author(s):

P. J. Avery

Keyword(s):

Population Genetics ◽

Genetic Variability ◽

Population Size ◽

Effective Population Size ◽

Disease Genes ◽

Effective Population ◽

Random Drift ◽

Mutation Pressure ◽

Electrophoretic Data ◽

Fitness Parameters

SUMMARYFrom the available electrophoretic data, it is clear that haplodiploid insects have a much lower level of genetic variability than diploid insects, a difference that is only partially explained by the social structure of some haplodiploid species. The data comparing X-linked genes and autosomal genes in the same species is much more sparse and little can be inferred from it. This data is compared with theoretical analyses of X-linked genes and genes in haplodiploids. (The theoretical population genetics of X-linked genes and genes in haplodiploids are identical.) X-linked genes under directional selection will be lost or fixed more quickly than autosomal genes as selection acts more directly on X-linked genes and the effective population size is smaller. However, deleterious disease genes, maintained by mutation pressure, will give higher disease incidences at X-linked loci and hence rare mutants are easier to detect at X-linked loci. Considering the forces which can maintain balanced polymorphisms, there are much stronger restrictions on the fitness parameters at X-linked loci than at autosomal loci if genetic variability is to be maintained, and thus fewer polymorphic loci are to be expected on the X-chromosome and in haplodiploids. However, the mutation-random drift hypothesis also leads to the expectation of lower heterozygosity due to the decrease in effective population size. Thus the theoretical results fit in with the data but it is still subject to argument whether selection or mutation-random drift are maintaining most of the genetic variability at X-linked genes and genes in haplodiploids.

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Genetic Variability and Linkage Disequilibrium Within the DP Region in the CEPH Families

Human Immunology ◽

10.1016/s0198-8859(97)00208-5 ◽

1997 ◽

Vol 58 (2) ◽

pp. 112-121 ◽

Cited By ~ 11

Author(s):

P.V Moonsamy ◽

W Klitz ◽

M.G.J Tilanus ◽

A.B Begovich

Keyword(s):

Linkage Disequilibrium ◽

Genetic Variability

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Genetic variability in a genomic region with long-range linkage disequilibrium reveals traces of a bottleneck in the history of the European population

Human Genetics ◽

10.1007/s00439-005-0056-2 ◽

2005 ◽

Vol 118 (2) ◽

pp. 276-286 ◽

Cited By ~ 14

Author(s):

Claudia Schmegner ◽

Josef Hoegel ◽

Walther Vogel ◽

Günter Assum

Keyword(s):

Linkage Disequilibrium ◽

Genetic Variability ◽

Long Range ◽

European Population ◽

Genomic Region ◽

History Of

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Maintenance of genetic variability by mutation–selection balance: a child's guide through the jungle

Genome ◽

10.1139/g89-135 ◽

1989 ◽

Vol 31 (2) ◽

pp. 761-767 ◽

Cited By ~ 57

Author(s):

M. G. Bulmer

Keyword(s):

Genetic Variability ◽

Theoretical Work ◽

Complex Problem ◽

Recurrent Mutation ◽

Mutation Rates ◽

Stabilizing Selection ◽

House Of Cards ◽

Model Account ◽

Optimal Value ◽

Selection For

Metric characters closely connected with fitness have little additive genetic variability, presumably because it is quickly exhausted under continuous directional selection on fitness. Other metric characters have substantial additive genetic variability with a typical heritability of about 0.5. A popular model is that the second class of characters is subject to weak stabilizing selection for an optimal value, which depletes genetic variability, while recurrent mutation tends to restore it. Can this model account for the variability observed, given the evidence available about the strength of selection and mutation rates? Much theoretical work has been done on this complex problem. This work is reviewed, with the intention of simplifying it as much as possible.Key words: mutation–selection balance, genetic variability, continuum-of-alleles model, house-of-cards approximation.

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