Population Genetics

Abstract

Questions:

• How does the distribution of alleles (genetic variants) change over time in a population when those alleles are randomly passed on to offspring?

This last chapter draws upon all the different methods discussed in the preceding, discrete structures, stochastics, analysis, and geometry. It introduces mathematical population genetics, the theory of the time course of the distribution of alleles in a population in the presence of mutation, selection, and recombination. The basic Wright-Fisher model is a discrete stochastic processes. In order to understand it better, it is advantageous to pass to its diffusion approximation which leads to a partial differential equation. For understanding this differential equation in turn a geometric approach is insightful.