Stochastics Seminar

Speaker: Dr. Ming Liao

Title:  Population genetics and coalescent process, part 3

Abstract: In the previous discussion, we have mainly considered a haploid population.  Roughly speaking, an individual in a haploid population has only one copy of a gene, inherited from its single parent.  It is then relatively easy to trace the ancestors of a sample of genes taken at the present time, and it has been shown that, as the population size tends to infinity, the ancestral process converges in distribution to a continuous time Markov chain, called Kingman's coalescent process.  For a diploid population, each individual has two copies of a gene, one from each of its two parents, so the ancestral process of a gene sample has a quite complicated structure, but by a simple convergence result of Markov chains, it can be shown that the ancestral process still converges in distribution to Kingman's coalescent.