Stochastic spatial Lotka-Volterra predator-prey models

TL;DR

This paper explores stochastic spatial predator-prey models, revealing complex spatio-temporal structures, phase transitions, and ecological dynamics influenced by local interactions, resource variability, and evolutionary traits, with implications for disease spread and species competition.

Contribution

It introduces novel stochastic spatial models for predator-prey interactions, analyzing phase transitions, ecological stability, and evolutionary dynamics using field-theoretic and percolation methods.

Findings

Predator extinction threshold governed by directed percolation universality.

Seasonal resource variation stabilizes predator-prey dynamics.

Spatial heterogeneity influences species densities and extinction events.

Abstract

Stochastic, spatially extended models for predator-prey interaction display spatio-temporal structures that are not captured by the Lotka-Volterra mean-field rate equations. These spreading activity fronts reflect persistent correlations between predators and prey that can be analyzed through field-theoretic methods. Introducing local restrictions on the prey population induces a predator extinction threshold, with the critical dynamics at this continuous active-to-absorbing state transition governed by the scaling exponents of directed percolation. Novel features in biologically motivated model variants include the stabilizing effect of a periodically varying carrying capacity that describes seasonally oscillating resource availability; enhanced mean species densities and local fluctuations caused by spatially varying reaction rates; and intriguing evolutionary dynamics emerging when variable interaction rates are affixed to individuals combined with trait inheritance to their offspring. The basic susceptible-infected-susceptible and susceptible-infected-recovered models for infectious disease spreading near their epidemic thresholds are respectively captured by the directed and dynamic isotropic percolation universality classes. Systems with three cyclically competing species akin to spatial rock-paper-scissors games may display striking spiral patterns, yet conservation laws can prevent such noise-induced structure formation. In diffusively coupled inhomogeneous settings, one may observe the stabilization of vulnerable ecologies prone to finite-size extinction or fixation due to immigration waves emanating from the interfaces.