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We present a series of elementary stochastic models arising from population genetics. Various mathematical aspects are investigated at the intuitive level. Special emphasis is put on the diffusion method. The focus is on the Wright–Fisher diffusion model and its variations, describing the forward evolution of one colony undergoing random sampling, possibly under the additional forces arising from mutation and selection with or without dominance. Some aspects of their dual coalescents obtained while running the diffusion process backward in time are also investigated.
Thierry Huillet (Fri,) studied this question.