Predator-Prey Cycles from Resonant Amplification of Demographic Stochasticity

2005/01/16 by Alan J. McKane, A. J. McKane, T. J. Newman · 5 citations
Biochemistry, Genetics and Molecular Biology · Environmental Science · Medicine · #Ecosystem dynamics and resilience #Evolution and Genetic Dynamics #Mathematical and Theoretical Epidemiology and Ecology Models #q-bio.PE

paper · pdf · doi:10.1103/physrevlett.94.218102

4 pages, 2 figures

arxiv created 2005/01/16 · openalex publication_date 2005/06/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We present the simplest individual level model of predator-prey dynamics and show, via direct calculation, that it exhibits cycling behavior. The deterministic analogue of our model, recovered when the number of individuals is infinitely large, is the Volterra system (with density-dependent prey reproduction) which is well known to fail to predict cycles. This difference in behavior can be traced to a resonant amplification of demographic fluctuations which disappears only when the number of individuals is strictly infinite. Our results indicate that additional biological mechanisms, such as predator satiation, may not be necessary to explain observed predator-prey cycles in real (finite) populations.

Citations

• A general method for numerically simulating the stochastic time evolution of coupled chemical reactions
• Stochastic models in population biology and their deterministic analogs
• The invasion, persistence and spread of infectious diseases within animal and plant communities
• Stochastic Processes in Physics and Chemistry

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