Lotka-Volterra versus May-Leonard formulations of the spatial stochastic Rock-Paper-Scissors model: the missing link

Abstract

The Rock-Paper-Scissors (RPS) model successfully reproduces some of the main features of simple cyclic predator-prey systems with interspecific competition observed in nature. Still, lattice-based simulations of the spatial stochastic RPS model are known to give rise to significantly different results, depending on whether the three state Lotka-Volterra or the four state May-Leonard formulation is employed. This is true independently of the values of the model parameters and of the use of either a von Neumann or a Moore neighborhood. With the objective of reducing the impact of the use of a discrete lattice, in this paper we introduce a simple modification to the standard spatial stochastic RPS model in which the range of the search of the nearest neighbor may be extended up to a maximum euclidean radius $R$. We show that, with this adjustment, the Lotka-Volterra and May-Leonard formulations can be designed to produce similar results, both in terms of dynamical properties and spatial features, by means of an appropriate parameter choice. In particular, we show that this modified spatial stochastic RPS model naturally leads to the emergence of spiral patterns in both its three and four state formulations.

6 pages, 4 figures

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Cited by in corpus (6)

• Adaptive movement strategy in rock-paper-scissors models
• How multiple weak species jeopardise biodiversity in spatial rock-paper-scissors models
• Chaotic behavior in Lotka-Volterra and May-Leonard models of biodiversity
• Spatial patterns and biodiversity in rock-paper-scissors models with regional unevenness
• Quantifying scale-free behaviors in Rock-Paper-Scissors Models as a function of Mobility
• Monitoring biodiversity on highly reactive rock-paper-scissors models