Summary
At first we introduce a simple stochastic difference equation, to simulate random sampling drift in population genetics, which is naturally obtained from a random collision model. Next, we introduce a random collision model to simulate overdominance model in population genetics. We assume in a time interval °t, a random collision of four particles, which represents overdominant selection, takes place at a certain probability, where a particle corresponds to a gene. We assume that mutation takes place by some rate and assume that every new mutation is different from extant alleles. We estimate mean heterozygosity by our simulation method and compare it with the result obtained by using a stochastic difference equation for overdominance model.
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Itoh, Y. Random collision model for random genetic drift and stochastic difference equation. Ann Inst Stat Math 36, 353–362 (1984). https://doi.org/10.1007/BF02481975
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DOI: https://doi.org/10.1007/BF02481975