Neutral competition in a deterministically changing environment: revisiting continuum approaches

TL;DR

This paper extends a classical competitive Moran model to include periodic environmental fluctuations, revealing how fluctuation frequency influences fixation probabilities and times, with implications for understanding ecological competition.

Contribution

It introduces a method to analyze the effects of periodic environmental changes on competition dynamics, bridging deterministic and stochastic environmental models.

Findings

Low-frequency fluctuations mimic constant fitness differences.

High-frequency fluctuations lead to neutral competition behavior.

Intermediate frequencies produce complex, nontrivial dynamics.

Abstract

Environmental variation can play an important role in ecological competition by influencing the relative advantage between competing species. Here, we consider such effects by extending a classical, competitive Moran model to incorporate an environment that fluctuates periodically in time. We adapt methods from work on these classical models to investigate the effects of the magnitude and frequency of environmental fluctuations on two important population statistics: the probability of fixation and the mean time to fixation. In particular, we find that for small frequencies, the system behaves similar to a system with a constant fitness difference between the two species, and for large frequencies, the system behaves similar to a neutrally competitive model. Most interestingly, the system exhibits nontrivial behavior for intermediate frequencies. We conclude by showing that our results agree quite well with recent theoretical work on competitive models with a stochastically changing environment, and discuss how the methods we develop ease the mathematical analysis required to study such models.