Ecological Character Displacement in Quantitative Genetic Models

We study, both analytically and numerically, models of ecological character displacement for two species that compete for the same set of food sources. These models include quantitative genetics and Lotka–Volterra type competition and are symmetric with respect to the two species. We allow for various shapes of the carrying capacity and the competition function, and we discuss under what general conditions large character displacement can occur. While some of these conditions, like genetic rigidity, or flat and truncated carrying capacity curves, were known before, we also find that slow dynamics of the genetic variance, steep slopes in the interaction function and carrying capacities that are not truncated can lead to large displacements. We interpret these conditions biologically and also give new insights into models which have been previously investigated.