Intrinsic noise in systems with switching environments

TL;DR

This paper investigates the effects of intrinsic stochasticity in finite populations with randomly switching environments, extending existing models by deriving stationary distributions beyond the fast and slow switching regimes.

Contribution

It introduces a linear-noise approximation approach to explicitly include intrinsic stochastic effects in systems with switching environments, improving upon previous deterministic PDMP models.

Findings

Derived stationary distributions match simulations well.

Extended analysis beyond fast and slow switching regimes.

Enhanced understanding of stochastic effects in switching environments.

Abstract

We study individual-based dynamics in finite populations, subject to randomly switching environmental conditions. These are inspired by models in which genes transition between on and off states, regulating underlying protein dynamics. Similarly switches between environmental states are relevant in bacterial populations and in models of epidemic spread. Existing piecewise-deterministic Markov process (PDMP) approaches focus on the deterministic limit of the population dynamics while retaining the randomness of the switching. Here we go beyond this approximation and explicitly include effects of intrinsic stochasticity at the level of the linear-noise approximation. Specifically we derive the stationary distributions of a number of model systems, in good agreement with simulations. This improves existing approaches which are limited to the regimes of fast and slow switching.