Moment expansion approach to the time dynamics of genetic evolution. Issue 3 (31st October 2019) - Rastegar‐Sedehi, Hamid‐Reza; Byrnes, Tim; Khordad, Reza
Abstract: We use moment expansion methods to analyze the time dynamics for genetic evolution under selection, mutation, and reproduction. We consider a N ‐allele diploid genotype reproducing randomly in a fitness landscape with either one or two maxima, and mutation is assumed to occur such that any allele can mutate into any other type. We find that the moment expansion works well, where a small number of moments can capture the general behavior toward equilibrium. Our methods allow a systematic way to capture the time dynamics of the evolutionary process efficiently using a small number of coupled equations. Abstract : Biological systems are typically highly nonequilibrium systems, which makes them very challenging to understand from a statistical mechanics perspective. In this article, the moment expansion method is used to analyze the time dynamics of genetic evolution under selection, mutation, and reproduction. It is found that the moment expansion works efficiently, where a small number of moments can capture the general behavior toward equilibrium.