Spatial patterns and biodiversity in off-lattice simulations of a cyclic three-species Lotka-Volterra model

TL;DR

This paper explores off-lattice stochastic simulations of a three-species cyclic predator-prey model, revealing how spatial patterns, population density, and extinction probabilities influence biodiversity.

Contribution

It introduces off-lattice simulation methods for the Lotka-Volterra model and analyzes how total density affects pattern formation and biodiversity.

Findings

Spiral patterns emerge at high total densities.

Characteristic frequency and amplitude depend on total density.

Lower densities increase extinction risk.

Abstract

Stochastic simulations of cyclic three-species spatial predator-prey models are usually performed in square lattices with nearest neighbor interactions starting from random initial conditions. In this Letter we describe the results of off-lattice Lotka-Volterra stochastic simulations, showing that the emergence of spiral patterns does occur for sufficiently high values of the (conserved) total density of individuals. We also investigate the dynamics in our simulations, finding an empirical relation characterizing the dependence of the characteristic peak frequency and amplitude on the total density. Finally, we study the impact of the total density on the extinction probability, showing how a low population density may jeopardize biodiversity.