A delayed succession model with diffusion for the impact of diapause on population growth

Diapause, a period of arrested development driven by adverse environmental conditions, plays an important role in the establishment and invasion of insects and other invertebrate organisms in temperate and subtropical areas. In order to describe the spatial dynamics of diapausing species, we propose a novel model involving (a) seasonal succession to distinguish the normal growth period, diapause period, and postdiapause period; (b) a diffusion term to represent the random movement of species; and (c) a maturation delay term to describe the developmental duration of species. We first study the model in a bounded domain for the survival and establishment of a species. The extinction and persistence of the species can be predicted by the basic reproduction ratio \scrR ₀. Then we investigate the model in an unbounded domain for the spreading of the species. Our results show that the minimal wave speed for a periodic traveling wave is equal to the spreading speed. Numerical simulations are performed to validate theoretical results and in particular to compare the effects of two diapausing strategies: diapausing in the adult stage and in the immature stage.