Cyclical interactions with alliance-specific heterogeneous invasion rates

Details Cyclical interactions with alliance-specific heterogeneous invasion rates Cyclical interactions with alliance-specific heterogeneous invasion rates

2006-12-13

arxiv.org/abs/cond-mat/0612316v2

Physical Review E 75 (2007) 052102

Physics

Condensed Matter

Statistical Mechanics

4 pages, 4 figures

Scientific paper

10.1103/PhysRevE.75.052102

We study a six-species Lotka-Volterra type system on different two-dimensional lattices when each species has two superior and two inferior partners. The invasion rates from predator sites to a randomly chosen neighboring prey's site depend on the predator-prey pair, whereby cyclic symmetries within the two three-species defensive alliances are conserved. Monte Carlo simulations reveal an unexpected non-monotonous dependence of alliance survival on the difference of alliance-specific invasion rates. This behavior is qualitatively reproduced by a four-point mean-field approximation. The study addresses fundamental problems of stability for the competition of two defensive alliances and thus has important implications in natural and social sciences.

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