A model for a spatially structured metapopulation accounting for within patch dynamics

• We develop a metapopulation model with spatial structure and within patch dynamics.
• For large populations, the process is approximated by a deterministic process.
• Conditions for extinction and persistence of the deterministic process are derived.
• Perturbation theory is used to discover an Allee effect for a two-patch model.

We develop a stochastic metapopulation model that accounts for spatial structure as well as within patch dynamics. Using a deterministic approximation derived from a functional law of large numbers, we develop conditions for extinction and persistence of the metapopulation in terms of the birth, death and migration parameters. Interestingly, we observe the Allee effect in a metapopulation comprising two patches of greatly different sizes, despite there being decreasing patch specific per-capita birth rates. We show that the Allee effect is due to the way the migration rates depend on the population density of the patches.