Mean occupancy time: linking mechanistic movement models, population dynamics and landscape ecology to population persistence.

Reaction-diffusion models for the dynamics of a biological population in a fragmented landscape can incorporate detailed descriptions of movement and behavior, but are difficult to analyze and hard to parameterize. Patch models, on the other hand, are fairly easy to analyze and can be parameterized reasonably well, but miss many details of the movement process within and between patches. We develop a framework to scale up from a reaction-diffusion process to a patch model and, in particular, to determine movement rates between patches based on behavioral rules for individuals. Our approach is based on the mean occupancy time, the mean time that an individuals spends in a certain area of the landscape before it exits that area or dies. We illustrate our approach using several different landscape configurations. We demonstrate that the resulting patch model most closely captures persistence conditions and steady state densities as compared with the reaction-diffusion model.