The Annals of Applied Probability

Coexistence results for some competition models

Rick Durrett and Claudia Neuhauser

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Barley yellow dwarf is a widespread disease that affects small grains and many grass species, as well as wheat, barley and oat. The disease is caused by an aphid transmitted virus. Rochow conducted a study near Ithaca, New York, which showed that a shift in the dominant strain occurred between 1957 and 1976. Motivated by this phenomenon, we develop a model for the competition between different strains of the barley yellow dwarf virus. Our main goal is to understand the phase diagram of the model, that is, to identify parameter values where one strain competitively excludes the other strain and where both strains coexist. Our analysis applies to a number of other systems as well, for example to a model of competition of water flea species studied by Hanski and Ranta and Bengtsson.

Article information

Ann. Appl. Probab., Volume 7, Number 1 (1997), 10-45.

First available in Project Euclid: 14 October 2002

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Interacting particle systems contact process successional model rescaling coexistence competitive exclusion barley yellow dwarf Daphnia


Durrett, Rick; Neuhauser, Claudia. Coexistence results for some competition models. Ann. Appl. Probab. 7 (1997), no. 1, 10--45. doi:10.1214/aoap/1034625251.

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