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Expanding spatial domains and transient scaling regimes in populations with local cyclic competition

P. P. Avelino, J. Menezes, B. F. Oliveira, T. A. Pereira

Abstract
We investigate a six-species class of May-Leonard models leading to the formation of two types of competing spatial domains, each one inhabited by three species with their own internal cyclic rock-paper-scissors dynamics. We study the resulting population dynamics using stochastic numerical simulations in two-dimensional space. We find that as three-species domains shrink, there is an increasing probability of extinction of two of the species inhabiting the domain, with the consequent creation of one-species domains. We determine the critical initial radius beyond which these one-species spatial domains are expected to expand. We further show that a transient scaling regime, with a slower average growth rate of the characteristic length scale L of the spatial domains with time t, takes place before the transition to a standard L∝ t1/2 scaling law, resulting in an extended period of coexistence.

Keywords
Nonlinear Sciences - Adaptation and Self-Organizing Systems; Nonlinear Sciences - Pattern Formation and Solitons

Physical Review E
Volume 99, Number 5
2019 May

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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