Two-Sex Population Dynamics in Space: Effects of Gestation Time on Persistence

Most single-species population models assume either that one sex dominates the growth dynamics (usually the female), or that the life cycles of the two sexes are identical; however, sexual differences in ontogenetic features can render this assumption invalid. Further, the interaction between sexes is necessarily nonlinear, and the dependence of dynamic behavior on sexual interactions can be complicated. Here we examine a two-sex population model, related to the well-known logistic model, with explicit sexual interactions. The model is bistable and, by the addition of diffusion, admits traveling wave solutions. Dominance of states via this spatial dynamic are examined. A simple condition for neutral dominance is obtained; sexual interactions inhibit the dominance of the nonzero population, making persistence more difficult.