A model of mating and population growth dependent on competition that suggests circumstances under which sympatric speciation might occur is described. The model is similar to one in a companion paper by Rosenzweig in that a heterozygote genotype, involving a new allele, is first selected by virtue of its ability to exploit a new niche and is then eliminated through competition. The superior competitor, which eliminates the heterozygote, is the homozygote for the new allele. For this process to occur the heterozygote must be sufficiently fit to exploit and invade a new niche, but not so fit that a classical polymorphism results from heterozygous advantage. This process of speciation is most likely to occur when there are vacant niches. When and where these might occur are discussed.