Evolutionary Behavior in a Two-Locus System

In this short note we study a dynamical system generated by two-parametric quadratic operator mapping 3-dimensional simplex to itself. This is an evolution of the frequencies gametes in two-locus system. We find set all (a continuum of) fixed points and show that each point nonhyperbolic. completely describe limit Namely, for any initial (taken from simplex) invariant containing unique operator, such trajectory converges point.