Predator-prey quasicycles from a path-integral formalism

2008/11/30 by Thomas Butler, David E. Reynolds, David Reynolds
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 #q-bio.QM

paper · pdf · doi:10.1103/physreve.79.032901

4 pages

arxiv created 2009/02/05 · openalex publication_date 2009/03/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The existence of beyond mean-field quasicycle oscillations in a simple spatial model of predator-prey interactions is derived from a path-integral formalism. The results agree substantially with those obtained from analysis of similar models using system size expansions of the master equation. In all of these analyses, the discrete nature of predator-prey populations and finite-size effects lead to persistent oscillations in time, but spatial patterns fail to form. The path-integral formalism goes beyond mean-field theory and provides a focus on individual realizations of the stochastic time evolution of population not captured in the standard master-equation approach.

Citations

• Influence of local carrying capacity restrictions on stochastic predator–prey models
• Stochastic models in population biology and their deterministic analogs
• Predator-Prey Cycles from Resonant Amplification of Demographic Stochasticity
• Phase Transitions and Spatio-Temporal Fluctuations in Stochastic Lattice Lotka–Volterra Models
• Stochastic Processes in Physics and Chemistry