Noise-induced stabilization and fixation in fluctuating environment

TL;DR

This paper investigates how environmental noise influences the fixation probability of mutants in two-species communities, revealing that global competition can significantly increase fixation chances through noise-induced stabilization.

Contribution

It introduces a model analyzing environmental fluctuations' impact on fixation probabilities, highlighting differences between local and global competition mechanisms.

Findings

Global competition enhances fixation probability via noise-induced stabilization.

Deleterious mutants have a constant fixation chance in global competition, independent of N.

Local competition causes fixation probability to decay as (ln N)^{-1} for deleterious mutants.

Abstract

The dynamics of a two-species community of $N$ competing individuals is considered, with an emphasis on the role of environmental variations that affect coherently the fitness of entire populations. The chance of fixation of a mutant population (and, in particular, of a single mutant) is calculated as a function of the mean relative fitness of the mutant, the amplitude of fitness variations and their typical duration. We emphasize the distinction between the case of local competition and the case of global competition; in the latter a noise-induced stabilization mechanism yields a higher chance of fixation for a single mutant. The distinction becomes dramatic in the weak selection phase, where the chance of fixation for a single deleterious mutant is an $N$-independent constant for global competition and decays like $(\ln N)^{-1}$ in the local competition case. The possibility of long-term persistence of ${\cal O} (N)$ suboptimal (and extinction-prone) populations is discussed, as well as its relevance to stochastic tunneling between fitness peaks.