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Evolution by Natural Selection is a process by which progeny inherit someproperties from their progenitors with small variation. These properties aresubject to Natural Selection and are called adaptive traits and carriers of thelatter are called phenotypes. The distribution of the density of phenotypes ina population is called Evolutionary Distributions (ED). We analyze mathematicalmodels of the dynamics of a system of ED. Such systems are anisotropic in thatdiffusion of phenotypes in each population (equation) remains positive in thedirections of their own adaptive space and vanishes in the directions of theother's adaptive space. We prove that solutions to such systems exist in asense weaker than the usual. We develop an algorithm for numerical solutions ofsuch systems. Finally, we conduct numerical experiments---with a model in whichpopulations compete---that allow us to observe salient attributes of a specificsystem of ED.

On a singular perturbation problem arising in the theory of Evolutionary Distributions