On Wright–Fisher diffusion and its relatives

Abstract

We present a series of elementary stochastic models arising from population genetics.Various mathematical aspects are investigated at the intuitive level. Special emphasis is puton the diffusion method. The focus is on the Wright–Fisher diffusion model and itsvariations, describing the forward evolution of one colony undergoing random sampling,possibly under the additional forces arising from mutation and selection with or withoutdominance. Some aspects of their dual coalescents obtained while running the diffusionprocess backward in time are also investigated.