Cyclical interactions with alliance-specific heterogeneous invasion rates

2006/12/31 by Matjaz Perc, Matjaž Perc, Attila Szolnoki +2 · 129 citations
Agricultural and Biological Sciences · Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · Social Sciences · #Alliance #Biology #Competition (biology) #Computer science #Ecology #Econometrics #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #Geography #Homogeneous space #Mathematics #Monte Carlo method #Physics #Plant and animal studies #Predation #Predator #Stability (learning theory) #Statistical physics #Statistics #cond-mat.stat-mech #q-bio.PE

paper · pdf · doi:10.1103/physreve.75.052102

published in Physical Review E 75(5), 052102 (American Physical Society) · 4 pages, 4 figures

openalex publication_date 2007/05/30 · arxiv created 2007/06/02 · arxiv updated 2015/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

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 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 nonmonotonous 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.

Citations

• The Logic of Animal Conflict
• La intertextualidad como recurso poético
• Similarity-based cooperation and spatial segregation
• Theoretical analysis and simulations of the generalized Lotka-Volterra model
• Volunteering as Red Queen Mechanism for Cooperation in Public Goods Games
• Deterministic group selection model for the evolution of altruism

Cited by

• Perturbing cyclic predator-prey systems: How a six-species coarsening system with nontrivial in-domain dynamics responds to sudden changes
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• Survival behavior in the cyclic Lotka-Volterra model with a randomly switching reaction rate
• Self-organizing patterns maintained by competing associations in a six-species predator-prey model
• Stochastic population dynamics in spatially extended predator–prey systems
• The effect of habitats and fitness on species coexistence in systems with cyclic dominance