A Boundary Problem Arising in Population Genetics

Abstract

It is proved that for any genetic system having more than one stable equilibrium state, "between" these stable points must lie a boundary set of systems which move eventually to none of the stable equilibria. It is suggested that these boundary sets each contain a semi-stable equilibrium. Examples are given of this property, and the difficulty of determining the boundary sets even in fairly simple cases is discussed. A method of constructing such hypothetical systems mathematically is given.