The many-demes limit for selection and drift in a subdivided population.

A diffusion approximation is obtained for the frequency of a selected allele in a population comprised of many subpopulations or demes. The form of the diffusion is equivalent to that for an unstructured population, except that it occurs on a longer time scale when migration among demes is restricted. This many-demes diffusion limit relies on the collection of demes always being in statistical equilibrium with respect to migration and drift for a given allele frequency in the total population. Selection is assumed to be weak, in inverse proportion to the number of demes, and the results hold for any deme sizes and migration rates greater than zero. The distribution of allele frequencies among demes is also described.

[1]  A. W. F. Edwards,et al.  The statistical processes of evolutionary theory , 1963 .

[2]  S. Ethier,et al.  DIFFUSION APPROXIMATIONS OF MARKOV CHAINS , 1980 .

[3]  M. Kimura,et al.  The Stepping Stone Model of Population Structure and the Decrease of Genetic Correlation with Distance. , 1964, Genetics.

[4]  N. L. Johnson,et al.  Discrete Multivariate Distributions , 1998 .

[5]  H. Wilkinson-Herbots,et al.  Genealogy and subpopulation differentiation under various models of population structure , 1998 .

[6]  M. Notohara,et al.  The coalescent and the genealogical process in geographically structured population , 1990, Journal of mathematical biology.

[7]  A. Siegert.  On the Approach to Statistical Equilibrium , 1949 .

[8]  P. A. P. Moran,et al.  Random processes in genetics , 1958, Mathematical Proceedings of the Cambridge Philosophical Society.

[9]  W. Ewens.  Mathematical Population Genetics , 1980 .

[10]  J. L. Cherry.  Selection in a subdivided population with dominance or local frequency dependence. , 2003, Genetics.

[11]  F. Rousset,et al.  Selection and drift in subdivided populations: a straightforward method for deriving diffusion approximations and applications involving dominance, selfing and local extinctions. , 2003, Genetics.

[12]  C. J-F,et al.  THE COALESCENT , 1980 .

[13]  C. Cannings.  The latent roots of certain Markov chains arising in genetics: A new approach, II. Further haploid models , 1975, Advances in Applied Probability.

[14]  P. Moran,et al.  The statistical processes of evolutionary theory. , 1963 .

[15]  M. Slatkin.  FIXATION PROBABILITIES AND FIXATION TIMES IN A SUBDIVIDED POPULATION , 1981, Evolution; international journal of organic evolution.

[16]  John Wakeley,et al.  A diffusion approximation for selection and drift in a subdivided population. , 2003, Genetics.

[17]  M. Notohara,et al.  The strong-migration limit for the genealogical process in geographically structured populations , 1993 .

[18]  P. Moran,et al.  The Theory of Some Genetical Effects of Population Subdivision , 1959 .

[19]  J. Wakeley,et al.  Segregating sites in Wright's island model. , 1998, Theoretical population biology.

[20]  J. Wakeley.  Polymorphism and divergence for island-model species. , 2003, Genetics.

[21]  Chris Cannings,et al.  The latent roots of certain Markov chains arising in genetics: A new approach, II. Further haploid models , 1974, Advances in Applied Probability.

[22]  Rannala,et al.  The Sampling Theory of Neutral Alleles in an Island Population of Fluctuating Size , 1996, Theoretical population biology.

[23]  Montgomery Slatkin,et al.  Gene Flow in Natural Populations , 1985 .

[24]  S. Wright,et al.  Evolution in Mendelian Populations. , 1931, Genetics.

[25]  M. Feldman.  On the offspring number distribution in a genetic population , 1966, Journal of Applied Probability.

[26]  E. Pollak.  On random genetic drift in a subdivided population , 1968, Journal of Applied Probability.

[27]  J. L. Cherry.  Selection in a subdivided population with local extinction and recolonization. , 2003, Genetics.

[28]  P. A. P. Moran.  The effect of selection in a haploid genetic population , 1958 .

[29]  Hilde Maria Jozefa Dominiek Herbots,et al.  Stochastic Models in Population Genetics: Genealogy and Genetic Differentiation in Structured Populations. , 1994 .

[30]  P. Moran,et al.  The Genetic Effects of Family Structure in Natural Populations. , 1959 .

[31]  M. Whitlock.  Fixation probability and time in subdivided populations. , 2003, Genetics.

[32]  R. Punnett,et al.  The Genetical Theory of Natural Selection , 1930, Nature.

[33]  T. Nagylaki,et al.  The strong-migration limit in geographically structured populations , 1980, Journal of mathematical biology.

[34]  M. Notohara.  The structured coalescent process with weak migration , 2001, Journal of Applied Probability.

[35]  N. Takahata.  Genealogy of neutral genes and spreading of selected mutations in a geographically structured population. , 1991, Genetics.

[36]  S. Lessard,et al.  The two-locus ancestral graph in a subdivided population: convergence as the number of demes grows in the island model , 2004, Journal of mathematical biology.