A Stage-Structured Continuous-/Discrete-Time Population Model: Persistence and Spatial Spread

Population persistence and spatial propagation and their dependence on demography and dispersal are of great importance in spatial ecology. Many species with highly structured life cycles invade new habitats through the dispersal of organisms in their early life stages (e.g., seeds, larvae, etc.). We develop a stage-structured continuous/discrete-time hybrid model to describe the spatiotemporal dynamics of such species, in which a reaction-diffusion equation describes the random movement of dispersing individuals, while two difference equations describe the demography of sedentary individuals. We obtain a formula for the spreading speed of the population in terms of model parameters. We show that the spreading speed can be characterized as the slowest wave speed of a class of traveling wave solutions. We provide an explicit formula for the critical domain size that separates population persistence from extinction. By comparing our stage-structured model with a physically unstructured model, we find that the structured model reduces to the unstructured one in some special cases. Accordingly, the results about the spreading speed and the critical domain size for the unstructured model represent some special cases of those for the structured one. This highlights the significance of including stage structure in studying the spatial dynamics of species with complex life cycles.