Evolutionary dynamics in fluctuating environment

Temporal environmental variations are ubiquitous in nature, yet most of the theoretical works in population genetics and evolution assume fixed environment. Here we analyze the effect of variations in selection sign, selection intensity, and population size on the fate of a mutant type. Using Kimura's diffusion approximation we present simple formulas for effective population size and effective selection, and use it to calculate the chance of ultimate fixation, the time to fixation, and the time to absorption (either fixation or loss). For simple models, in which the number of environmental states is relatively small, the effective parameters are obtained analytically. For more complicated models, where the monitoring of the weights of all microstates is complicated, we present a semianalytic solution whose parameters are obtained from short numerical experiments. Our analysis shows perfect agreement with numerical solutions for neutral, beneficial, and deleterious mutant, under periodic and stochastic environmental variations and different competition modes.