Relationship between migration and DNA polymorphism in a local population.

Abstract Using the two subpopulation model, the expected numbers of segregating sites in a number of DNA sequences randomly sampled from a subdivided population were examined for several types of population subdivisions. It is shown that, in the case where the pattern of migration is symmetrical such as the finite island model, the expected number of segregating sites is independent of the migration rate when two or three DNA sequences are randomly sampled from the same subpopulation, but depends on the migration rate when more than three DNA sequences are sampled. It is also shown that the population subdivision can increase the amount of DNA polymorphism even in a subpopulation in some cases.

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Geographical variation in a quantitative character.

Genetics ◽

10.1093/genetics/136.1.361 ◽

1994 ◽

Vol 136 (1) ◽

pp. 361-381

Author(s):

T Nagylaki

Keyword(s):

Local Population ◽

Weighted Average ◽

Two Dimensions ◽

Quantitative Character ◽

Stabilizing Selection ◽

Convergence To Equilibrium ◽

Stepping Stone ◽

Evolutionary Forces ◽

Local Averages ◽

Stepping Stone Model

Abstract A model for the evolution of the local averages of a quantitative character under migration, selection, and random genetic drift in a subdivided population is formulated and investigated. Generations are discrete and nonoverlapping; the monoecious, diploid population mates at random in each deme. All three evolutionary forces are weak, but the migration pattern and the local population numbers are otherwise arbitrary. The character is determined by purely additive gene action and a stochastically independent environment; its distribution is Gaussian with a constant variance; and it is under Gaussian stabilizing selection with the same parameters in every deme. Linkage disequilibrium is neglected. Most of the results concern the covariances of the local averages. For a finite number of demes, explicit formulas are derived for (i) the asymptotic rate and pattern of convergence to equilibrium, (ii) the variance of a suitably weighted average of the local averages, and (iii) the equilibrium covariances when selection and random drift are much weaker than migration. Essentially complete analyses of equilibrium and convergence are presented for random outbreeding and site homing, the Levene and island models, the circular habitat and the unbounded linear stepping-stone model in the diffusion approximation, and the exact unbounded stepping-stone model in one and two dimensions.

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A cladistic measure of gene flow inferred from the phylogenies of alleles.

Genetics ◽

10.1093/genetics/123.3.603 ◽

1989 ◽

Vol 123 (3) ◽

pp. 603-613 ◽

Cited By ~ 26

Author(s):

M Slatkin ◽

W P Maddison

Keyword(s):

Mitochondrial Dna ◽

Gene Flow ◽

Migration Rate ◽

Local Population ◽

Geographic Location ◽

Island Model ◽

Simple Function ◽

Average Level ◽

Minimum Number ◽

Parsimony Criterion

Abstract A method for estimating the average level of gene flow among populations is introduced. The method provides an estimate of Nm, where N is the size of each local population in an island model and m is the migration rate. This method depends on knowing the phylogeny of the nonrecombining segments of DNA that are sampled. Given the phylogeny, the geographic location from which each sample is drawn is treated as multistate character with one state for each geographic location. A parsimony criterion applied to the evolution of this character on the phylogeny provides the minimum number of migration events consistent with the phylogeny. Extensive simulations show that the distribution of this minimum number is a simple function of Nm. Assuming the phylogeny is accurately estimated, this method provides an estimate of Nm that is as nearly as accurate as estimates obtained using FST and other statistics when Nm is moderate. Two examples of the use of this method with mitochondrial DNA data are presented.

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GENE FLOW AND GENETIC DIFFERENTIATION

Genetics ◽

10.1093/genetics/78.3.961 ◽

1974 ◽

Vol 78 (3) ◽

pp. 961-965

Author(s):

P T Spieth

Keyword(s):

Gene Flow ◽

Genetic Differentiation ◽

Population Size ◽

Local Population ◽

Biological Significance ◽

Island Model ◽

Genetic Identity ◽

Biological Interpretation ◽

Different Populations ◽

Stepping Stone Model

ABSTRACT A brief analysis is presented for the effects of gene flow upon genetic differentiation within and between populations generated by mutation and drift. Previous results obtained with the "island" model are developed into a form that lends itself to biological interpretation. Attention is focused upon the effective local population size and the ratio of the genetic identity of two genes in different populations to that of two genes in the same population. The biological significance of this ratio, which is independent of population size, is discussed. Similarities between the results of this model and those of the "stepping-stone" model are noted.

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Genetic correlation in the stepping stone model with non-symmetrical migration rates

Journal of Applied Probability ◽

10.2307/3212095 ◽

1969 ◽

Vol 6 (3) ◽

pp. 463-477 ◽

Cited By ~ 15

Author(s):

Takeo Maruyama

Keyword(s):

Genetic Correlation ◽

Migration Rate ◽

Short Range ◽

Present Report ◽

Stepping Stone ◽

Migration Rates ◽

Random Samples ◽

Range Migration ◽

Grid Points ◽

Stepping Stone Model

Kimura (1953) proposed a “stepping stone” model for the study of the genetic structure of a subdivided population. In this model, it was assumed that a population consists of infinitely many colonies located at grid points of an n-dimensional lattice and that each colony exchanges individuals with neighboring colonies in each generation, and also receives immigrants as random samples from the whole population. The former type of migration has been called “short range migration” and the latter type “long range migration”. Later, Kimura and Weiss (1964), and Weiss and Kimura (1965) have obtained formulas for the genetic correlation and variance between colonies for general cases of the model, assuming that the short range migration is symmetrical in each fixed direction. The purpose of the present report is to extend the results of Kimura and Weiss to cover situations where the restriction of symmetry of short range migration is removed, so that migration rates in opposite directions need not be equal. I believe that in nature there are cases which require the model presented in this report. For example, consider a plant population distributed along a river, or on a plain where the wind at the time when the seeds are scattered is stronger in one direction than in others. For animals and plants it is often true that the centre of habitat is more densely populated than the marginal regions where the environment is less suitable for the species. In such a case the migration rate toward the outside from the centre is larger than that in the opposite direction. As in other theories of population genetics, we will assume that the size of each colony is determined by the carrying capacity of the environment and is not affected by the migration rate. Thus we assume that in each generation each colony produces many more gametes than those which contribute to the next generation, and, among those many gametes, a certain number, say 2N, are chosen from various colonies to form the individuals of a particular colony.

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Genetic correlation in the stepping stone model with non-symmetrical migration rates

Journal of Applied Probability ◽

10.1017/s0021900200026541 ◽

1969 ◽

Vol 6 (03) ◽

pp. 463-477 ◽

Cited By ~ 6

Author(s):

Takeo Maruyama

Keyword(s):

Genetic Correlation ◽

Migration Rate ◽

Short Range ◽

Present Report ◽

Stepping Stone ◽

Migration Rates ◽

Random Samples ◽

Range Migration ◽

Grid Points ◽

Stepping Stone Model

Kimura (1953) proposed a “stepping stone” model for the study of the genetic structure of a subdivided population. In this model, it was assumed that a population consists of infinitely many colonies located at grid points of an n-dimensional lattice and that each colony exchanges individuals with neighboring colonies in each generation, and also receives immigrants as random samples from the whole population. The former type of migration has been called “short range migration” and the latter type “long range migration”. Later, Kimura and Weiss (1964), and Weiss and Kimura (1965) have obtained formulas for the genetic correlation and variance between colonies for general cases of the model, assuming that the short range migration is symmetrical in each fixed direction. The purpose of the present report is to extend the results of Kimura and Weiss to cover situations where the restriction of symmetry of short range migration is removed, so that migration rates in opposite directions need not be equal. I believe that in nature there are cases which require the model presented in this report. For example, consider a plant population distributed along a river, or on a plain where the wind at the time when the seeds are scattered is stronger in one direction than in others. For animals and plants it is often true that the centre of habitat is more densely populated than the marginal regions where the environment is less suitable for the species. In such a case the migration rate toward the outside from the centre is larger than that in the opposite direction. As in other theories of population genetics, we will assume that the size of each colony is determined by the carrying capacity of the environment and is not affected by the migration rate. Thus we assume that in each generation each colony produces many more gametes than those which contribute to the next generation, and, among those many gametes, a certain number, say 2N, are chosen from various colonies to form the individuals of a particular colony.

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The effect of change in population size on DNA polymorphism.

Genetics ◽

10.1093/genetics/123.3.597 ◽

1989 ◽

Vol 123 (3) ◽

pp. 597-601 ◽

Cited By ~ 61

Author(s):

F Tajima

Keyword(s):

Population Size ◽

Dna Sequences ◽

Dna Polymorphism ◽

Population Bottleneck ◽

Expected Number ◽

Original Population ◽

Current Population ◽

Segregating Sites

Abstract The expected number of segregating sites and the expectation of the average number of nucleotide differences among DNA sequences randomly sampled from a population, which is not in equilibrium, have been developed. The results obtained indicate that, in the case where the population size has changed drastically, the number of segregating sites is influenced by the size of the current population more strongly than is the average number of nucleotide differences, while the average number of nucleotide differences is affected by the size of the original population more severely than is the number of segregating sites. The results also indicate that the average number of nucleotide differences is affected by a population bottleneck more strongly than is the number of segregating sites.

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A New Statistic for Detecting Genetic Differentiation

Genetics ◽

10.1093/genetics/155.4.2011 ◽

2000 ◽

Vol 155 (4) ◽

pp. 2011-2014 ◽

Cited By ~ 10

Author(s):

Richard R Hudson

Keyword(s):

Genetic Differentiation ◽

Dna Sequences ◽

Genetic Data ◽

Island Model ◽

Wide Range ◽

Infinite Sites Model ◽

Parameter Values

Abstract A new statistic for detecting genetic differentiation of subpopulations is described. The statistic can be calculated when genetic data are collected on individuals sampled from two or more localities. It is assumed that haplotypic data are obtained, either in the form of DNA sequences or data on many tightly linked markers. Using a symmetric island model, and assuming an infinite-sites model of mutation, it is found that the new statistic is as powerful or more powerful than previously proposed statistics for a wide range of parameter values.

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