Nonmonotone invariant manifolds in the Nagylaki-Crow model

We use a change of dynamical variables to prove, subject to certain conditions on the parameters, that a nonmonotone invariant manifold exists and is the graph of a convex function for the planar Nagylaki-Crow fertility-mortality model from population genetics with n=2. Our results are obtained without the common assumption that fertilities or death rates are additive, and are not restricted to the case that the model is competitive in the new coordinates. We also provide numerical examples demonstrating that the manifold need not be the graph of a convex function, smooth, unique or globally attracting, and that the model exhibits a sequence of nonmonotone manifolds similar to those studied by Hirsch for competitive Kolmogorov systems (Hirsch 1988).