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

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.

5 pages, 7 figures; new version, with new title and figures

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• Perturbing cyclic predator-prey systems: how a six-species coarsening system with non-trivial in-domain dynamics responds to sudden changes
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• Invasion controlled pattern formation in a generalized multi-species predator-prey system
• Mobility-limiting antipredator response in the rock-paper-scissors model
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• Lotka-Volterra versus May-Leonard formulations of the spatial stochastic Rock-Paper-Scissors model: the missing link
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• When faster rotation is harmful: the competition of alliances with inner blocking mechanism
• Social dilemmas in off-lattice populations
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• Quantifying scale-free behaviors in Rock-Paper-Scissors Models as a function of Mobility