Mathematical Models in Population Genetics

Abstract

Throughout the history of population genetics, mathematical models have played an important role in elucidating the effects of mutation and selection on the genetic diversity of organisms. Mathematical models provided the theoretical foundation of neo-Darwinism; sophisticated mathematical tools aided Kimura in establishing the neutral molecular theory. Mathematical models in population genetics today are crucial in the development of statistical tools for analyzing molecular data. This chapter emphasizes models for selection, but also includes the discussion of neutral models. After a brief history of the role of selection in evolution, basic mathematical models are introduced together with the diffusion approximation. A discussion of coalescent theory follows, with primary focus on selection. A short discussion on how to detect selection concludes the chapter. Keywords: selection; ancestral selection graph; coalescent; mathematical models in population genetics; Wright–Fisher model; diffusion approximation; statistical tests for selection