Evolutionary Dynamics in a Varying Environment: Continuous versus Discrete Noise

TL;DR

This paper investigates how different types of environmental noise, binary versus continuous, affect population dynamics and fixation probabilities in competing strains, revealing that continuous noise can significantly enhance fixation chances.

Contribution

It provides a systematic comparison of binary and continuous environmental fluctuations and their impact on population fixation, highlighting the importance of noise statistics.

Findings

Continuous environmental noise increases fixation probability more than binary noise.

Variance and mean of environmental fluctuations influence population size and fixation.

Continuous noise can enhance fixation even when moments match binary noise.

Abstract

Environmental variations can significantly influence how populations compete for resources, and hence shape their evolution. Here, we study population dynamics subject to a fluctuating environment modeled by a varying carrying capacity changing continuously in time according to either binary random switches, or by being driven by a noise of continuous range. We consider a prototypical example of two competing strains, one growing slightly slower than the other, and consider also the scenario where the slow strain is a public goods producer. By systematically comparing the effect of binary- versus continuously-varying environment, we study how different noise statistics (mean, variance) influence the population size and fixation properties. We show that the slow strain fixation probability can be greatly enhanced for a continuously-varying environment compared to binary switches, even when the first two moments of the carrying capacity coincide.