Stationary distributions of a model of sympatric speciation

TL;DR

This paper analyzes a modified model of sympatric speciation, demonstrating how competition intensity influences whether populations diverge into distinct phenotypes or remain concentrated, with results depending on mutation and ecological parameters.

Contribution

It introduces a Fleming--Viot type model for sympatric speciation and characterizes conditions under which speciation occurs or is inhibited.

Findings

Intense competition leads to population divergence into multiple phenotypes.

Weak competition results in populations concentrating on the phenotype with maximum carrying capacity.

Speciation timing depends on mutation rate and ecological function shapes.

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.