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Starting from an age-structured diffusive population growth law for singlespecies in a discrete and periodic habitat, we formulate a stage structuredpopulation model with spatially periodic dispersal, mortality and recruitment.With a KPP type setting, after establishing the fundamental solution of adiscretized heat equation with spatially periodic dispersal, we apply somerecently developed dynamical system theories to obtain the existence of thespreading speed and its coincidence with the minimal speed of pulsating waves,as well as the variational characterization of the speed, by which we furtheranalyze how the habitat periodicity influences the speed. In particular, thereis a unique optimal dispersal strategy to maximize the speed.

On a population model in discrete periodic habitat. I. spreading speed and optimal dispersal strategy