Influence of local carrying capacity restrictions on stochastic predator-prey models

TL;DR

This study uses Monte Carlo simulations to explore how local carrying capacity restrictions affect stochastic predator-prey models, revealing differences in species coexistence and population dynamics across dimensions.

Contribution

It provides new insights into stochastic predator-prey systems without site restrictions, highlighting the impact of local capacity constraints on spatial structures and population oscillations.

Findings

Species coexistence in one dimension under no site restrictions

Finite systems exhibit transient population oscillations influenced by fluctuations

Suppression of oscillations at high reaction rates with local processes

Abstract

We study a stochastic lattice predator-prey system by means of Monte Carlo simulations that do not impose any restrictions on the number of particles per site, and discuss the similarities and differences of our results with those obtained for site-restricted model variants. In accord with the classic Lotka-Volterra mean-field description, both species always coexist in two dimensions. Yet competing activity fronts generate complex, correlated spatio-temporal structures. As a consequence, finite systems display transient erratic population oscillations with characteristic frequencies that are renormalized by fluctuations. For large reaction rates, when the processes are rendered more local, these oscillations are suppressed. In contrast with site-restricted predator-prey model, we observe species coexistence also in one dimension. In addition, we report results on the steady-state prey age distribution.