We use spatial models of simple predator-prey interactions to predict that predator and prey numbers oscillate in time and space. These oscillations are not seen in the deterministic versions of the models, but are due to stochastic fluctuations about the time-independent solutions of the deterministic equations which are amplified due to the existence of a resonance. We calculate the power spectra of the fluctuations analytically and show that they agree well with results obtained from stochastic simulations. This work extends the analysis of these quasicycles from that previously developed for well-mixed systems to spatial systems, and shows that the ideas and methods used for nonspatial models naturally generalize to the spatial case.
Download full-text PDF |
Source |
|---|---|
| http://dx.doi.org/10.1103/PhysRevE.78.051911 | DOI Listing |
Publication Analysis
Top Keywords
Similar Publications
Rapidly forming, slowly evolving, spatial patterns from quasi-cycle Mexican Hat coupling.
Math Biosci Eng
July 2019
Department of Psychology and Brain Research Centre, 2136 West Mall, University of British Columbia, Vancouver, BC, V6T 1Z4 Canada.
Alattice-indexed familyof stochasticprocesses hasquasi-cycle oscillationsif itsotherwise-damped oscillations are sustained by noise. Such a family performs the reaction part of a discrete stochastic reaction-diffusion system when we insert a local Mexican Hat-type, difference of Gaussians, coupling on a one-dimensional and on a two-dimensional lattice. Quasi-cycles are a proposed mech-anism for the production of neural oscillations, and Mexican Hat coupling is ubiquitous in the brain.
View Article and Find Full Text PDFRole of noise in population dynamics cycles.
Phys Rev E Stat Nonlin Soft Matter Phys
June 2009
Instituto de Física, Universidade de São Paulo, Caixa Postal 66318, 05314-970 São Paulo, SP, Brazil.
Noise is an intrinsic feature of population dynamics and plays a crucial role in oscillations called phase-forgetting quasicycles by converting damped into sustained oscillations. This function of noise becomes evident when considering Langevin equations whose deterministic part yields only damped oscillations. We formulate here a consistent and systematic approach to population dynamics, leading to a Fokker-Planck equation and the associate Langevin equations in accordance with this conceptual framework, founded on stochastic lattice-gas models that describe spatially structured predator-prey systems.
View Article and Find Full Text PDFPredator-prey quasicycles from a path-integral formalism.
Phys Rev E Stat Nonlin Soft Matter Phys
March 2009
Department of Physics and Institute for Genomic Biology, University of Illinois at Urbana Champaign, 1110 West Green Street, Urbana, Illinois 61801, USA.
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.
View Article and Find Full Text PDFQuasicycles in a spatial predator-prey model.
Phys Rev E Stat Nonlin Soft Matter Phys
November 2008
Theoretical Physics Group, School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, United Kingdom.
We use spatial models of simple predator-prey interactions to predict that predator and prey numbers oscillate in time and space. These oscillations are not seen in the deterministic versions of the models, but are due to stochastic fluctuations about the time-independent solutions of the deterministic equations which are amplified due to the existence of a resonance. We calculate the power spectra of the fluctuations analytically and show that they agree well with results obtained from stochastic simulations.
View Article and Find Full Text PDFQuasicycles revisited: apparent sensitivity to initial conditions.
Theor Popul Biol
November 2003
Department of Ecology and Evolutionary Biology, University of Michigan, Ann Arbor, MI 48109-1048, USA.
Environmental noise is known to sustain cycles by perturbing a deterministic approach to equilibrium that is itself oscillatory. Quasicycles produced in this way display a regular period but varied amplitude. They were proposed by Nisbet and Gurney (Nature 263 (1976) 319) as one possible explanation for population fluctuations in nature.
View Article and Find Full Text PDFWant AI Summaries of new PubMed Abstracts delivered to your In-box?
Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!