Discrete-time population dynamics of spatially distributed semelparous two-sex populations

Spatially distributed populations with two sexes may face the problem that males and females concentrate in different parts of the habitat and mating and reproduction does not happen sufficiently often for the population to persist. For simplicity, to explore the impact of sex-dependent dispersal on population survival, we consider a discrete-time model for a semelparous population where individuals reproduce only once in their life-time, during a very short reproduction season. The dispersal of females and males is modeled by Feller kernels and themating by a homogeneous pair formation function. The spectral radius of a homogeneous operator is established as basic reproduction number of the population, R-0. If R-0 < 1, the extinction state is locally stable, and if R-0 > 1 the population shows various degrees of persistence that depend on the irreducibility properties of the dispersal kernels. Special cases exhibit how sex-biased dispersal affects the persistence of the population.