Quasicycles in a spatial predator-prey model

Carlos A. Lugo; Alan J. McKane

doi:10.1103/PhysRevE.78.051911

Quasicycles in a spatial predator-prey model

Carlos A. Lugo, Alan J. McKane

Research output: Contribution to journal › Article › peer-review

Abstract

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. © 2008 The American Physical Society.

Original language	English
Article number	051911
Journal	Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume	78
Issue number	5
DOIs	https://doi.org/10.1103/PhysRevE.78.051911
Publication status	Published - 12 Nov 2008

Keywords

LOTKA-VOLTERRA MODELS
POPULATION-DYNAMICS
DIFFUSION
EQUATIONS
SYSTEM
FLUCTUATIONS
ECOLOGY

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

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10.1103/PhysRevE.78.051911

http://oai.aps.org/oai?verb=GetRecord&Identifier=oai:aps.org:PhysRevE.78.051911&metadataPrefix=oai_apsmeta_2

Cite this

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title = "Quasicycles in a spatial predator-prey model",

abstract = "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. {\textcopyright} 2008 The American Physical Society.",

keywords = "LOTKA-VOLTERRA MODELS, POPULATION-DYNAMICS, DIFFUSION, EQUATIONS, SYSTEM, FLUCTUATIONS, ECOLOGY",

author = "Lugo, \{Carlos A.\} and McKane, \{Alan J.\}",

note = "Lugo, Carlos A. McKane, Alan J. CONACYT (Mexico) ; EPSRC (UK) [GR/T11784/0] We thank Andrew Black and Tobias Galla for useful discussions. C. A. L. acknowledges the support from CONACYT (Mexico) and A.J.M. acknowledges Grant No. GR/T11784/0 from the EPSRC (UK). 36 AMER PHYSICAL SOC COLLEGE PK Part 1 376WL",

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doi = "10.1103/PhysRevE.78.051911",

language = "English",

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T1 - Quasicycles in a spatial predator-prey model

AU - Lugo, Carlos A.

AU - McKane, Alan J.

N1 - Lugo, Carlos A. McKane, Alan J. CONACYT (Mexico) ; EPSRC (UK) [GR/T11784/0] We thank Andrew Black and Tobias Galla for useful discussions. C. A. L. acknowledges the support from CONACYT (Mexico) and A.J.M. acknowledges Grant No. GR/T11784/0 from the EPSRC (UK). 36 AMER PHYSICAL SOC COLLEGE PK Part 1 376WL

PY - 2008/11/12

Y1 - 2008/11/12

N2 - 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. © 2008 The American Physical Society.

AB - 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. © 2008 The American Physical Society.

KW - LOTKA-VOLTERRA MODELS

KW - POPULATION-DYNAMICS

KW - DIFFUSION

KW - EQUATIONS

KW - SYSTEM

KW - FLUCTUATIONS

KW - ECOLOGY

UR - https://www.scopus.com/pages/publications/56749095462

U2 - 10.1103/PhysRevE.78.051911

DO - 10.1103/PhysRevE.78.051911

M3 - Article

SN - 1539-3755

VL - 78

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

IS - 5

M1 - 051911

ER -

Quasicycles in a spatial predator-prey model

Abstract

Keywords

UN SDGs

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