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Metapopulation models are theoretical frameworks used in ecology to describe the dynamics of populations that are subdivided into smaller, discrete units, known as demes. These demes are connected by migration, allowing individuals to move between them. The metapopulation concept was first introduced by Levins (1969) and has since been widely applied to understand the persistence and extinction of species, as well as the spread of diseases and invasive species.

In a metapopulation, each deme can be in one of two states: occupied or unoccupied. Occupied demes contain individuals, while unoccupied demes are empty. The dynamics of a metapopulation are driven by two main processes: local extinction and colonization. Local extinction occurs when a deme becomes unoccupied due to stochastic events or environmental changes. Colonization happens when individuals from other demes migrate and establish a new population in an unoccupied deme.

The persistence of a metapopulation depends on the balance between colonization and extinction rates. If the colonization rate is higher than the extinction rate, the metapopulation is likely to persist. Conversely, if the extinction rate exceeds the colonization rate, the metapopulation may go extinct. This balance is influenced by factors such as habitat quality, dispersal ability, and environmental stochasticity.

Metapopulation models have been used to study various ecological phenomena, including the conservation of endangered species, the spread of invasive species, and the dynamics of disease outbreaks. By incorporating spatial structure and migration, these models provide a more realistic representation of population dynamics compared to traditional single-population models. However, they also require more complex data and assumptions, which can limit their applicability in some cases.