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June 2007 Stationary distributions of a model of sympatric speciation
Feng Yu
Ann. Appl. Probab. 17(3): 840-874 (June 2007). DOI: 10.1214/105051606000000916

Abstract

This paper deals with a model of sympatric speciation, that is, speciation in the absence of geographical separation, originally proposed by U. Dieckmann and M. Doebeli in 1999. We modify their original model to obtain a Fleming–Viot type model and study its stationary distribution. We show that speciation may occur, that is, the stationary distribution puts most of the mass on a configuration that does not concentrate on the phenotype with maximum carrying capacity, if competition between phenotypes is intense enough. Conversely, if competition between phenotypes is not intense, then speciation will not occur and most of the population will have the phenotype with the highest carrying capacity. The length of time it takes speciation to occur also has a delicate dependence on the mutation parameter, and the exact shape of the carrying capacity function and the competition kernel.

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Feng Yu. "Stationary distributions of a model of sympatric speciation." Ann. Appl. Probab. 17 (3) 840 - 874, June 2007. https://doi.org/10.1214/105051606000000916

Information

Published: June 2007
First available in Project Euclid: 22 May 2007

zbMATH: 1129.92053
MathSciNet: MR2326234
Digital Object Identifier: 10.1214/105051606000000916

Subjects:
Primary: 92D15
Secondary: 60J25, 60J27, 92D25

Rights: Copyright © 2007 Institute of Mathematical Statistics

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Vol.17 • No. 3 • June 2007
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