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Moment expansion approach to the time dynamics of genetic evolution |
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| Authors: | Hamid-Reza Rastegar-Sedehi Tim Byrnes Reza Khordad |
| Affiliation: | 1. Department of Physics, Jahrom University, Jahrom, Iran;2. New York University Shanghai, Pudong, Shanghai, China State Key Laboratory of Precision Spectroscopy, School of Physical and Material Sciences, East China Normal University, Shanghai, China NYU-ECNU Institute of Physics at NYU Shanghai, Shanghai, China National Institute of Informatics, Chiyoda-ku, Tokyo, Japan Department of Physics, New York University, New York, New York, USA;3. Department of Physics, College of Sciences, Yasouj University, Yasouj, Iran |
| 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. |
| Keywords: | genetic evolution genotype time dynamics |