Abstract
An exact Markov chain model is formulated and computed for random mating in a haploid gamete pool. There are two versions of the gamete, and there is a finite number of diploid monoecious organisms. The founder population is given, and the subsequent generations allow a prescribed statistical distribution over different population sizes. The non-homogeneous Markov chain works on the haploid gamete level provided the probability of self-fertilization is 1/n, where n is the number of diploid individuals. Standard deviations of gamete frequencies and fixation probabilities are calculated. Effective population sizes for different population size distributions are estimated, including periodic bottlenecks.
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References
Cavalli-Sforza, L.L., Bodmer, W.F., 1971. The Genetics of Human Populations. Freeman, San Francisco.
Chia, A.B., 1968. Random mating in a population of cyclic size. J. Appl. Prob. 5, 21–30.
Ewens, W.J., 1989. The effective population sizes in the precence of catastrophes. In: Feldman, M.W. (Ed.), Mathematical Evolutionary Theory. Princeton University Press, Princeton, NJ.
Hedrick, P.W., 2000. Genetics of Populations, 2nd edition. Jones & Bartlett, Boston.
Kimura, M., 1964. Diffusion Models in Population Genetics. Methuen, London.
Li, W.-H., 1977. Stochastic Models in Population Genetics. Dowden, Hutchinson & Ross, Stroudsburg, Pa.
Tan, W.-Y., 2002. Stochastic Models with Applications to Genetics, Cancers, Aids and Other Biomedical Systems. World Scientific Publishing Co., Singapore.
Tyvand, P.A., 1993. An exact algebraic theory of genetic drift in finite diploid populations with random mating. J. Theor. Biol. 163, 315–331.
Wright, S., 1931. Evolution in Mendelian populations. Genetics 16, 97–159.
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Tyvand, P.A., Thorvaldsen, S. Markov Model of Haploid Random Mating with Given Distribution of Population Size. Bull. Math. Biol. 68, 807–819 (2006). https://doi.org/10.1007/s11538-005-9026-z
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DOI: https://doi.org/10.1007/s11538-005-9026-z