Strong Noise Effects in one-dimensional Neutral Populations

TL;DR

This paper demonstrates that in one-dimensional neutral populations with negative frequency-dependent selection, strong internal noise can induce a phase transition between fixation and coexistence, challenging traditional weak-noise assumptions.

Contribution

It provides a counterexample showing that strong internal noise, amplified by spatial correlations, can lead to a phase transition in population dynamics.

Findings

Identification of a continuous phase transition in a one-dimensional neutral population

Demonstration that strong noise effects can dominate over weak-noise predictions

Evidence that spatial correlations amplify internal noise effects

Abstract

The dynamics of well-mixed biological populations is usually studied by mean-field methods and weak-noise expansions. Similar methods have been applied also in spatially extended problems, relying on the fact that these populations are organized in colonies with a large local density of individuals. We provide a counterexample discussing a one-dimensional neutral population with negative frequency-dependent selection. The system exhibits a continuous phase transition between genetic fixation and coexistence unexpected from weak-noise arguments. We show that the behavior is a non-perturbative effect of the internal noise that is amplified by presence of spatial correlations (strong-noise regime).