A GENERAL-MODEL OF METAPOPULATION DYNAMICS

Metapopulation models describe the colonization and extinction of populations in a landscape of connected patches. Levins modeled the fraction of population sites occupied as a balance between the rate of successful immigration into empty sites and the rate of extinction in occupied sites. Several variants of Levins' model have been proposed that assume the probability of local colonization or extinction is either dependent or independent of regional occurrence. We show that the models of Levins, Hanski, and Gotelli are extreme cases of a single metapopulation model, which predicts the equilibrium fraction of sites occupied as a function of 4 parameters, 2 for colonization and 2 for extinction. We tested this model using single-species and multi-species data on patch occupancy. For the single-species test, we analyzed the distribution of fishes at 10 sites on the Cimarron River, Oklahoma, U.S.A. Significant metapopulation effects (correlations between the fraction of sites occupied and the probability of local colonization or extinction) were not detected in the distributions of carp, the Red River shiner, and the Arkansas River shiner. Instead, the best-fitting model was one of independent colonizations and extinctions among sites (island-mainland model). This model accurately predicted the fraction of sites occupied by carp and the Red River shiner. However, probabilities of colonization and extinction varied significantly among sites (carp, Red River shiner) and years (Arkansas River shiner). For the multi-species test, we used Simberloff's data on annual colonization of 9 mangrove islands by 254 insect species. These data revealed a significant metapopulation effect and were best fit by a linear extinction function and a quadratic colonization function. However, a Monte Carlo simulation using these functions failed to predict the observed species-occurrence distribution; there were too few insect species that occurred on no islands and too many species that occurred on most islands (bimodality). The explanation may be that species differed in their probabilities of colonization and extinction. Neither data set provided a fully satisfactory test of the metapopulation model. However, both analyses revealed the importance of spatial and temporal variation of colonization and extinction probabilities in a patchy landscape.