The Annals of Applied Probability

An explicitly spatial version of the Lotka-Volterra model with interspecific competition

Claudia Neuhauser and Stephen W. Pacala

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Abstract

We consider a spatial stochastic version of the classical Lotka-Volterra model with interspecific competition.

The classical model is described by a set of ordinary differential equations, one for each species. Mortality is density dependent, including both intraspecific and interspecific competition. Fecundity may depend on the type of species but is density independent. Depending on the relative strengths of interspecific and intraspecific competition and on the fecundities, the parameter space for the classical model is divided into regions where either coexistence, competitive exclusion or founder control occur.

The spatial version is a continuous time Markov process in which individuals are located on the d-dimensional integer lattice. Their dynamics are described by a set of local rules which have the same components as the classical model.

Our main results for the spatial stochastic version can be summarized as follows. Local competitive interactions between species result in (1) a reduction of the parameter region where coexistence occurs in the classical model, (2) a reduction of the parameter region where founder control occurs in the classical model, and (3) spatial segregation of the two species in parts of the parameter region where the classical model predicts coexistence.

Article information

Source
Ann. Appl. Probab., Volume 9, Number 4 (1999), 1226-1259.

Dates
First available in Project Euclid: 21 August 2002

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1029962871

Digital Object Identifier
doi:10.1214/aoap/1029962871

Mathematical Reviews number (MathSciNet)
MR1728561

Zentralblatt MATH identifier
0948.92022

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 92B05: General biology and biomathematics

Keywords
Competition contact process interacting particle system voter model

Citation

Neuhauser, Claudia; Pacala, Stephen W. An explicitly spatial version of the Lotka-Volterra model with interspecific competition. Ann. Appl. Probab. 9 (1999), no. 4, 1226--1259. doi:10.1214/aoap/1029962871. https://projecteuclid.org/euclid.aoap/1029962871


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