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Math Biosci. 2010 May;225(1):18-23. doi: 10.1016/j.mbs.2010.01.005. Epub 2010 Jan 25.

Exact Markov chains versus diffusion theory for haploid random mating.

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Department of Mathematical Sciences and Technology, Norwegian University of Life Sciences, P.O. Box 5003, 1432 As, Norway.


Exact discrete Markov chains are applied to the Wright-Fisher model and the Moran model of haploid random mating. Selection and mutations are neglected. At each discrete value of time t there is a given number n of diploid monoecious organisms. The evolution of the population distribution is given in diffusion variables, to compare the two models of random mating with their common diffusion limit. Only the Moran model converges uniformly to the diffusion limit near the boundary. The Wright-Fisher model allows the population size to change with the generations. Diffusion theory tends to under-predict the loss of genetic information when a population enters a bottleneck.

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