An analytically tractable model for competitive speciation

Several recent models have shown that frequency-dependent disruptive selection created by intraspecific competition can lead to the evolution of assortative mating and, thus, to competitive sympatric speciation. However, since most of these results rely on limited numerical analyses, their generality has been debated. Here, we consider one of the standard models (the so-called Roughgarden model) with a simplified genetics where the selected trait is determined by a single diallelic locus. This model is sufficiently complex to maintain key properties of the general multilocus case but simple enough to allow for comprehensive analytical treatment by means of invasion fitness arguments. Depending on (1) the strength and (2) the shape of stabilizing selection, (3) the strength and (4) the shape of pairwise competition, (5) the shape of the mating function, and (6) whether assortative mating leads to sexual selection, we find five different evolutionary regimes. In one of these regimes, complete reproductive isolation can evolve through arbitrarily small steps in the strength of assortative mating. Our approach provides a mechanistic understanding of several phenomena that have been found in previous models. The results demonstrate how even in a simple model, the evolutionary outcome depends in a complex way on ecological and genetic parameters.