Approaches to the Hardy-Weinberg manifold

Let fertilities and death rates be additive, let fertilities be positive, and let mating be random in the Nagylaki-Crow continuous model of selection at a multiallelic locus in a monoecious population. Then polymorphisms are in Hardy-Weinberg proportions. If some fertilities vanish, there is an example of a diallelic polymorphism that is not in Hardy-Weinberg proportions. If the fertilities are larger, in one sense or another, than the difference between any two death rates, then convergence to the Hardy-Weinberg manifold is shown. If, in addition, the Malthusian parameters are constant, and only a finite number of equilibria exist, then global convergence to equilibria is proved.