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Predominance of the weakest species in Lotka-Volterra and May-Leonard formulations of the rock-paper-scissors model

P. P. Avelino, B. F. Oliveira, R. S. Trintin

Abstract
We revisit the problem of the predominance of the “weakest” species in the context of Lotka-Volterra and May-Leonard formulations of a spatial stochastic rock-paper-scissors model in which one of the species has its predation probability reduced by 0<Pw<1. We show that, despite the different population dynamics and spatial patterns, these two formulations lead to qualitatively similar results for the late time values of the relative abundances of the three species (as a function of Pw), as long as the simulation lattices are sufficiently large for coexistence to prevail—the “weakest” species generally having an advantage over the others (specially over its predator). However, for smaller simulation lattices, we find that the relatively large oscillations at the initial stages of simulations with random initial conditions may result in a significant dependence of the probability of species survival on the lattice size.

Keywords
Quantitative Biology - Populations and Evolution; Physics - Physics and Society

Physical Review E
Volume 100, Number 4
2019 October

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Instituto de Astrofísica e Ciências do Espaço Universidade do Porto Faculdade de Ciências da Universidade de Lisboa
Fundação para a Ciência e a Tecnologia COMPETE 2020 PORTUGAL 2020 União Europeia