Birth-death processes with quenched uncertainty and intrinsic noise

TL;DR

This paper introduces a novel effective jump process to model population dynamics with intrinsic noise and quenched uncertainty, avoiding repeated sampling of disorder, and applies it to evolutionary games with random payoffs.

Contribution

It formulates an ensemble-based jump process for populations with quenched uncertainty, providing a new simulation algorithm and diffusion approximations for weak noise.

Findings

Developed an algorithm for simulating the effective jump process.

Applied the method to evolutionary games with random payoff matrices.

Discussed diffusion limits in the weak noise regime.

Abstract

The dynamics of populations is frequently subject to intrinsic noise. At the same time unknown interaction networks or rate constants can present quenched uncertainty. Existing approaches often involve repeated sampling of the quenched disorder and then running the stochastic birth-death dynamics on these samples. In this paper we take a different view, and formulate an effective jump process, representative of the ensemble of quenched interactions as a whole. Using evolutionary games with random payoff matrices as an example, we develop an algorithm to simulate this process, and we discuss diffusion approximations in the limit of weak intrinsic noise.