Stochastic Spatial Processes pp 216-237
Neutral models of geographical variation
The amount and pattern of genetic variability in a geographically structured population under the joint action of migration, mutation, and random genetic drift is studied. The monoecious, diploid population is subdivided into panmictic colonies that exchange gametes. In each deme, the rate of self-fertilization is equal to the reciprocal of the number of individuals in that deme. Generations are discrete and nonoverlapping; the analysis is restricted to a single locus in the absence of selection; every allele mutates to new alleles at the same rate. It is shown that if the population is at equilibrium, the number of demes is finite, and migration does not alter the deme sizes, then population subdivision produces interdeme differentiation and the mean homozygosity and the effective number of alleles exceed their panmictic values. The equilibrium and transient states of the island, circular stepping-stone, and infinite linear stepping-stone models are investigated in detail.
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- Kimura, M., and Crow, J. F. 1964. The number of alleles that can be maintained in a finite population. Genetics 49, 725–738.Google Scholar
- Malécot, G. 1946. La consanguinité dans une population limitée. Comp. Rend. Acad. Sci. 222, 841–843.Google Scholar
- Nagylaki, T. 1978a. The geographical structure of populations. In Studies in Mathematics. Vol. 16: Studies in Mathematical Biology. Part II (S. A. Levin, ed.). Pp. 588–624. The Mathematical Association of America, Washington.Google Scholar
- Nagylaki, T. 1984. Some mathematical problems in population genetics. In Proc. Symp. Appl. Math. Vol. 30: Population Biology (S. A. Levin, ed.). Pp. 19–36. American Mathematical Society, Providence, R. I.Google Scholar
- Nei, M. 1975. Molecular Population Genetics and Evolution. North-Holland, Amsterdam.Google Scholar
- Wright, S. 1931. Evolution in Mendelian populations. Genetics 16, 97–159.Google Scholar