We develop a system of equations to analyse the existence of genetic polymorphisms under disruptive selection in heterogeneous environments. These equations have both a genetic and a population density regulation component. In the absence of the genetic component, the equations reduce to a discrete time description of competition between interacting clonal lines or species. We use these equations to demonstrate that different populations, competing along a resource spectrum, are able to dynamically coexist, as asymptotically periodic or chaotic solutions to our system of equations, despite the fact that a coexistence equilibrium - stable or unstable - does not exist. We then extend these results to environments in which several niches are explicitly defined. Our analysis of the ecological component of our model establishes that the answer to questions of coexistence among groups of individuals cannot rely on analyses of the existence of equilibria and their stability properties.
In the most general model presented here, we allow for an assortative mating structure that is induced by the spatial heterogeneity of the environment. The level of assortative mating is controlled by a parameter so that at one extreme mating is panmictic, while at the other extreme individuals mate within their natal niches before dispersing to oviposit in other niches. We refer to this spatial mating structure as heteropatry.