Mean and variance of absorption time in a population genetics model: Comparison between Markov chain and diffusion process methods.

Abstract: Finding the expected number of generations it takes before every individual in a population (of constant size) only has one type of gene at a particular locus of a chromosome, can be formulated as computing the mean absorption time in a Markov chain. However, the Markov chain approach is inappropriate when the population is large. This is commonly solved by approximating the Markov chain with a diffusion process, in which the mean absorption time is found by solving an ODE with boundary conditions. In this thesis, the formulas for the mean absorption time is derived in both cases. Using these formulas, the expected number of generations is computed numerically. The two different methods are compared, and we also discuss the genetic meaning of the results.