Fixation probabilities in evolutionary dynamics under weak selection
Abstract
In evolutionary dynamics, a key measure of a mutant trait's success is the probability that it takes over the population given some initial mutantappearance distribution. This "fixation probability" is difficult to compute in general, as it depends on the mutation's effect on the organism as well as the population's spatial structure, mating patterns, and other factors. In this study, we consider weak selection, which means that the mutation's effect on the organism is small. We obtain a weakselection perturbation expansion of a mutant's fixation probability, from an arbitrary initial configuration of mutant and resident types. Our results apply to a broad class of stochastic evolutionary models, in which the size and spatial structure are arbitrary (but fixed). The problem of whether selection favors a given trait is thereby reduced from exponential to polynomial complexity in the population size, when selection is weak. We conclude by applying these methods to obtain new results for evolutionary dynamics on graphs.
 Publication:

arXiv eprints
 Pub Date:
 August 2019
 arXiv:
 arXiv:1908.03827
 Bibcode:
 2019arXiv190803827M
 Keywords:

 Quantitative Biology  Populations and Evolution
 EPrint:
 42 pages