A discrete-time model for population persistence in habitats with time-varying sizes.

In this paper, we use periodic and stochastic integrodifference models to study the persistence of a single-species population in a habitat with temporally varying sizes. We extend a persistence metric for integral operators on bounded domains to that of integral operators on unbounded domains. Using this metric in the periodic model, we present new perspectives of the critical habitat size problem in the case of dynamically changing habitat sizes. Specifically, we extend the concept of critical habitat size to that of lower minimal limit size in a period-2 scenario, and prove the existence of the lower minimal limit size. For the stochastic model, we point out the importance of considering multiple time scales in the temporal variability of the habitat size. The models are relevant to biological scenarios such as seasonal variability of wetland habitat sizes under precipitation variability.