Stochastic versus Deterministic Models

Metapopulation dynamics are influenced by four kinds of stochasticity (Table 1): demographic and environmental stochasticity affecting separately each local population, and extinction-colonization and regional stochasticity affecting the entire metapopulation. Notice that the latter two forms of stochasticity are analogous to demographic and environmental stochasticity. Metapopulation dynamics are inherently stochastic, because population extinction and colonization are stochastic events, and real metapopu-lations are additionally affected by regional stochasticity. Nonetheless, stochasticity is often ignored and instead a deterministic model is constructed and analyzed. An important difference between stochastic and deterministic models is that the former predict a smaller or greater risk of metapopulation extinction, whereas the latter predict that for some parameter values the metapopulation has a positive equilibrium. However, for large metapopulations the stochastic model settles for a long time to what appears a stationary state, called a quasi-equilibrium. Thus for large metapopulations the essential behavior of the metapopulation is well captured by a deterministic model.

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