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Publication - Dr Feng Yu

    Stationary distributions of a model of sympatric speciation

    Citation

    Yu, F, 2007, ‘Stationary distributions of a model of sympatric speciation’. Annals of Applied Probability, vol 17 (3)., pp. 840 - 874

    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.

    Full details in the University publications repository