Two Population Models

The simplest metapopulation model extends models for single populations to two populations coupled by migration. For instance, local dynamics may be modeled with the familiar logistic model, and migration by assuming that a fraction m of individuals migrates to the other population. Migration may greatly influence the size of the metapopulation, depending on the form of population regulation, the difference in the carrying capacities in the two patches, and mortality during migration. If local dynamics are modeled with discrete-time models, which are inherently less stable than continuous-time models, more complex dynamics may emerge. Migration may now stabilize local populations that exhibit complex dynamics in the absence of migration, but migration may also amplify population fluctuations, all depending on the details of the model and the exact parameter values. Even limited amount of migration may bring population fluctuations into synchrony.

The two-population models may be extended to n populations, but typically at the cost of the analysis being restricted to simulations. n-population models have been used to study metapopulation viability for conservation. Such models are appealing to ecologists and conservationists because of their apparent realism, but because of the typically large number of untested structural model assumptions and unmeasured parameter values one cannot place much confidence on model predictions.

The two-population and n-population models have been used to study source-sink population dynamics. Some interesting results include the possibility of sink populations enhancing metapopulation stability when source populations exhibit large fluctuations leading to high risk of extinction. A metapopulation consisting of independent sink populations with temporal variation in growth rate may persist even if long-term growth rate is negative in each population in the absence of migration. Migration among such populations enhances metapopulation growth rate by spreading the risk of locally bad period among many independent populations.

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