No sensitivity to functional forms in the Rosenzweig-MacArthur model with strong environmental stochasticity

TL;DR

This paper demonstrates that strong environmental stochasticity reduces the sensitivity of predator-prey dynamics to the specific mathematical form of functional responses in the Rosenzweig-MacArthur model, contrasting with deterministic models.

Contribution

It shows that stochastic differential equations with strong noise exhibit similar community dynamics regardless of the functional response form, challenging previous notions of structural sensitivity.

Findings

Strong environmental noise leads to similar fluctuation patterns across different functional responses.

Eigenvalue magnitudes are insensitive to model structure, despite eigenvalue signs being sensitive.

Noise-driven oscillations occur over a broad range of parameters.

Abstract

The classic Rosenzweig-MacArthur predator-prey model has been shown to exhibit, like other coupled nonlinear ordinary differential equations (ODEs) from ecology, worrying sensitivity to model structure. This sensitivity manifests as markedly different community dynamics arising from saturating functional responses with nearly identical shapes but different mathematical expressions. Using a stochastic differential equation (SDE) version of the Rosenzweig-MacArthur model with the three functional responses considered by Fussman & Blasius (2005), I show that such sensitivity seems to be solely a property of ODEs or stochastic systems with weak noise. SDEs with strong environmental noise have by contrast very similar fluctuation patterns, irrespective of the mathematical formula used. Although eigenvalues of linearised predator-prey models have been used as an argument for structural sensitivity, they can also be an argument against structural sensitivity. While the sign of the eigenvalues' real part is sensitive to model structure, its magnitude and the presence of imaginary parts are not, which suggests noise-driven oscillations for a broad range of carrying capacities. I then discuss multiple ways to evaluate structural sensitivity in a stochastic setting, for predator-prey or other ecological systems.