Velocity fluctuations of population fronts propagating into metastable states

TL;DR

This paper analyzes the fluctuations in the position of population fronts moving into metastable states, deriving the diffusion coefficient for typical fluctuations and the probability of rare large deviations, with implications for extinction risk.

Contribution

It introduces a Markov model for population front fluctuations into metastable states and calculates both typical and rare fluctuation behaviors in the weak noise limit.

Findings

Front motion is diffusive for small fluctuations.

The front diffusion coefficient is explicitly calculated.

The probability distribution of large fluctuations is determined.

Abstract

The position of propagating population fronts fluctuates because of the discreteness of the individuals and stochastic character of processes of birth, death and migration. Here we consider a Markov model of a population front propagating into a metastable state, and focus on the weak noise limit. For typical, small fluctuations the front motion is diffusive, and we calculate the front diffusion coefficient. We also determine the probability distribution of rare, large fluctuations of the front position and, for a given average front velocity, find the most likely population density profile of the front. Implications of the theory for population extinction risk are briefly considered.