Universal properties of population dynamics with fluctuating resources

TL;DR

This paper investigates how population extinction dynamics are affected by fluctuating environments modeled with relaxational dynamics, revealing new operators and potential shifts from continuous to first-order phase transitions.

Contribution

It introduces a field-theoretic framework coupling population dynamics with environmental fluctuations, identifying new operators and analyzing their impact on critical behavior.

Findings

Emergence of two new operators with upper critical dimension four.

Wilson-Fisher fixed point remains unaffected by environmental coupling.

Mismatch of time scales can lead to a first-order transition instead of a continuous one.

Abstract

Starting from the well-known field theory for directed percolation, we describe an evolving population, near extinction, in an environment with its own nontrivial spatio-temporal dynamics. Here, we consider the special case where the environment follows a simple relaxational (Model A) dynamics. Two new operators emerge, with upper critical dimension of four, which couple the two theories in a nontrivial way. While the Wilson-Fisher fixed point remains completely unaffected, a mismatch of time scales destabilizes the usual DP fixed point, suggesting a crossover to a first order transition from the active (surviving) to the inactive (extinct) state.