Oscillations and patterns in interacting populations of two species

TL;DR

This paper investigates how spatial patterns and oscillations emerge in two-species populations, using simulations of a host-parasitoid model, highlighting the role of noise and timescale separation in these dynamics.

Contribution

It introduces a new measure for spatial patterns and explains oscillations as resulting from timescale separation and noise, linking them through density-dependent spreading rates.

Findings

Spatial patterns lead to noise-sustained oscillations.

Oscillations are explained by timescale separation and noise effects.

The study links patterns and oscillations via density-dependent spreading rates.

Abstract

Interacting populations often create complicated spatiotemporal behavior, and understanding it is a basic problem in the dynamics of spatial systems. We study the two-species case by simulations of a host--parasitoid model. In the case of co-existence, there are spatial patterns leading to noise-sustained oscillations. We introduce a new measure for the patterns, and explain the oscillations as a consequence of a timescale separation and noise. They are linked together with the patterns by letting the spreading rates depend on instantaneous population densities. Applications are discussed.