Evolutionary dynamics in populations with fluctuating size

TL;DR

This paper investigates how fluctuating environmental conditions, modeled as changes in population size, influence the evolutionary fate of mutants using a two-state Moran model and diffusion approximation, revealing that environmental variability affects fixation probabilities and times.

Contribution

It introduces a framework for analyzing the impact of environmental fluctuations on population genetics, deriving simple formulas for effective population size and selection, and demonstrating their applicability.

Findings

Effective population size and selection are derived for fluctuating environments.

Environmental variations influence fixation probabilities and times.

Periodic and stochastic fluctuations yield similar effects under weak selection.

Abstract

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 carrying capacity on the fate of a mutant type. We consider a two-state Moran model, where selection intensity at equilibrium may differ (in amplitude and in sign) from selection during periods of sharp growth and sharp decline. Using Kimura's diffusion approximation we present simple formulae 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). Our analysis shows perfect agreement with numerical solutions for neutral, beneficial and deleterious mutant. The contributions of different processes to the mean and the variance of abundance variations are additive and commutative. As a result, when selection intensity $s$ is weak such that ${\cal O}(s^2)$ terms are negligible, periodic or stochastic environmental variations yield identical results.