Environmental fitness heterogeneity in the Moran process

TL;DR

This paper investigates how environmental heterogeneity influences the Moran process, revealing that mutant heterogeneity suppresses fixation probability and can counteract selection, while resident heterogeneity has different effects depending on population size.

Contribution

It introduces a model of the Moran process with environmental heterogeneity and uncovers asymmetric effects of heterogeneity on mutant fixation probabilities.

Findings

Mutant heterogeneity suppresses fixation probability.

Strong mutant heterogeneity can offset selection effects.

Resident heterogeneity has minimal impact in large populations.

Abstract

Many mathematical models of evolution assume that all individuals experience the same environment. Here, we study the Moran process in heterogeneous environments. The population is of finite size with two competing types, which are exposed to a fixed number of environmental conditions. Reproductive rate is determined by both the type and the environment. We first calculate the condition for selection to favor the mutant relative to the resident wild type. In large populations, the mutant is favored if and only if the mutant's spatial average reproductive rate exceeds that of the resident. But environmental heterogeneity elucidates an interesting asymmetry between the mutant and the resident. Specifically, mutant heterogeneity suppresses its fixation probability; if this heterogeneity is strong enough, it can even completely offset the effects of selection (including in large populations). In contrast, resident heterogeneity has no effect on a mutant's fixation probability in large populations and can amplify it in small populations.