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

TL;DR

This paper introduces a modification to the spatial stochastic RPS model allowing extended neighbor search, which harmonizes the results of Lotka-Volterra and May-Leonard formulations, leading to similar dynamics and spiral pattern emergence.

Contribution

A simple modification enabling the Lotka-Volterra and May-Leonard models to produce comparable results and patterns in spatial stochastic RPS simulations.

Findings

Both formulations can produce similar dynamical behaviors.

Extended neighbor search range leads to spiral pattern formation.

The modification reduces discrepancies between the two models.

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.