The Stochastic Gause predator-prey model: noise-induced extinctions and invariance

TL;DR

This paper investigates how stochastic fluctuations influence predator-prey dynamics in a Gause model, revealing that noise can induce extinctions and alter stability even when deterministic models predict coexistence.

Contribution

It provides new conditions for solution boundedness, analyzes noise-induced extinctions, and studies stationary distributions in stochastic predator-prey models with sub-linear responses.

Findings

Noise can cause predator or prey extinction despite deterministic stability

Existence of stationary distributions under certain conditions

Stochastic effects significantly alter long-term ecological dynamics

Abstract

This paper explores a stochastic Gause predator-prey model with bounded or sub-linear functional response. The model, described by a system of stochastic differential equations, captures the influence of stochastic fluctuations on predator-prey dynamics, with particular focus on the stability, extinction, and persistence of populations. We provide sufficient conditions for the existence and boundedness of solutions, analyze noise-induced extinction events, and investigate the existence of unique stationary distributions for the case of Holing Type I functional response. Our analysis highlights the critical role of noise in determining long-term ecological outcomes, demonstrating that even in cases where deterministic models predict stable coexistence, stochastic noise can drive populations to extinction or alter the system's dynamics significantly.