1981/01/01 by Tobias Reichenbach, Mauro Mobilia, Erwin Frey +1 · 9 citations
Arts and Humanities · Biochemistry, Genetics and Molecular Biology · Medicine · Physics and Astronomy · Social Sciences · #Comparative Literary Analysis and Criticism #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #Literacy and Educational Practices #Literary and Cultural Studies #Mathematical and Theoretical Epidemiology and Ecology Models #cond-mat.stat-mech #physics.bio-ph #q-bio.PE
paper · pdf · doi:10.1103/physreve.74.051907
published as Phys. Rev. E 74, 051907 (2006) · 12 pages, 9 figures, minor corrections
openalex publication_date 1981/01/01 · arxiv created 2006/10/05 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/04/28
Cyclic dominance of species has been identified as a potential mechanism to maintain biodiversity, see, e.g., B. Kerr, M. A. Riley, M. W. Feldman and B. J. M. Bohannan [Nature 418, 171 (2002)] and B. Kirkup and M. A. Riley [Nature 428, 412 (2004)]. Through analytical methods supported by numerical simulations, we address this issue by studying the properties of a paradigmatic non-spatial three-species stochastic system, namely, the "rock-paper-scissors" or cyclic Lotka-Volterra model. While the deterministic approach (rate equations) predicts the coexistence of the species resulting in regular (yet neutrally stable) oscillations of the population densities, we demonstrate that fluctuations arising in the system with a finite number of agents drastically alter this picture and are responsible for extinction: After long enough time, two of the three species die out. As main findings we provide analytic estimates and numerical computation of the extinction probability at a given time. We also discuss the implications of our results for a broad class of competing population systems.