Metapopulation models
A metapopulation model represents a population distributed across distinct habitat patches connected by movement.
Patch states
If \(N_i(t)\) is the population in patch \(i\), a general model may be written
\[\frac{dN_i}{dt}=f_i(N_i)+\sum_{j\ne i}m_{ji}N_j-\sum_{j\ne i}m_{ij}N_i.\]The first term describes local dynamics and the remaining terms represent movement between patches.
Colonisation and extinction
Some metapopulation models track only whether each patch is occupied. Others track full population sizes or epidemic compartments within each patch.
Biological importance
Connectivity can rescue declining local populations, spread infection or invasive species, and strongly alter regional persistence.
Key idea. Metapopulation models represent discrete spatial structure by linking local biological systems through movement between patches.