Robust ecological pattern formation induced by demographic noise

TL;DR

This paper shows that demographic noise can cause persistent spatial patterns and oscillations in predator-prey models, expanding the conditions for pattern formation beyond traditional mean field predictions.

Contribution

It reveals that demographic noise significantly enlarges the parameter space for ecological pattern formation and introduces distinct spectral features, advancing understanding of stochastic effects in ecosystems.

Findings

Demographic noise induces persistent spatial patterns and oscillations.

Noise enlarges the parameter space for pattern formation.

Power spectrum analysis reveals fat tails unique to noise-driven patterns.

Abstract

We demonstrate that demographic noise can induce persistent spatial pattern formation and temporal oscillations in the Levin-Segel predator-prey model for plankton-herbivore population dynamics. Although the model exhibits a Turing instability in mean field theory, demographic noise greatly enlarges the region of parameter space where pattern formation occurs. To distinguish between patterns generated by fluctuations and those present at the mean field level in real ecosystems, we calculate the power spectrum in the noise-driven case and predict the presence of fat tails not present in the mean field case. These results may account for the prevalence of large-scale ecological patterns, beyond that expected from traditional non-stochastic approaches.