Competition between a newly formed polyploid and one of its diploid parental species has been modeled. Models were based on the Lotka-Volterra competition model, to which were added terms representing the positive frequency-dependent effect (minority disadvantage) as a result of lowered fertility caused by the receipt of inappropriate pollen from the other cytotype. A new polyploid may persist by replacing its diploid parent as a result of the combination of a very small diploid population, the existence of an unstable equilibrium between the two cytotypes, and chance events (probably the most common route); by coexisting with it as the result of niche separation; or by outcompeting and replacing it (probably very rare). However, the conditions for all of these possibilities are quite restrictive. The model and results are applicable in some degree to the establishment of other novel cytotypes, and also to pairs of species that compete for resources and also experience minority disadvantage (perhaps because of competition for pollinators) with respect to each other.