The metapopulation model presented in this paper was build in order to gain insight in the patch dynamics of species for which population density is high and migration is such a frequent event that it influences local population dynamics. We assumed that there are infinitely many patches and that dispersers are homogeneously distributed over space. In contrast to Gyllenberg and Hanski [4], who build a model on the same assumptions, we do not find dynamics which are directly comparable to the patch-occupancy model of Levins [8], i.e. empty patches are restarted by full ones. Hastings [6] build a model where migration does not influence the local dynamics. In that model rescue effects can not play a role and multiple steady states found here are not present.

On the level of patch occupancy our model is better described by that of Gotelli [3], than by that of Levins [8] or Hanski [7]. Though our model does not resemble Levins's [8] patch-occupancy, both models bear analogous requirements for the existence of a metapopulation.

Single population models build at the individual level and incorporating extra per capita losses due to migration and patch extinction serve as excellent predictors for the possible existence of a metapopulation. We favor single population models over the patch occupancy models while individual traits are experimentally more tractable on a shorter time scale than patch extinction. Of course patch extinction still is a major component in the predictions from the single species models. But even when the rate of patch extinction is unknown the information on the individual level can set parameter boundaries for patch extinction rates which still guarantee population persistence.

In general the local dynamics set total population dynamics, but density dependent disaster rates can make the appearant total population dynamics more complex than the underlying local growth dynamics. As a result we can add the following to the discussion on density dependence. The metapopulation concept can give rise to a mean population density following a sort of logistic growth (Eq. 33), while local growth can be exponential. For such dynamics it is required that disasters are influenced by local population size. This influence might result for example from aggression, from the success of the invasion of a lethal infectious disease, or switching of prey preference in multiple prey situations. This same mechanism allows for large (but rare) local outbrakes which can not be explained with a simple logistic growth model for the total population.

Conservation biology is concerned with endangered species and therefore with population dynamics at low population sizes. One question is how big a population must be in order to assure population survival (Minimal Viable Population)? For this question to be valid for our model, the combination of local dynamics and extinction must be such that it allows for a rescue effect. Examples include: demographic stochasticity ( ), a preference at low population density for organisms to migrate over participation in reproduction ( ), and partial disasters (b). It is very likely that at low densities demographic stochasticity always plays a role, but that its influence might be minor compared to a preference of migration over mating. The results so far indicate that partial disasters do not contribute much to a rescue effect.

In our model the metapopulation as a whole can go extinct only deterministically. The reason for this is the assumption that there are infinitely many patches. In a system with a finite number of patches the probability that the metapopulation as whole goes extinct is 1, even if our deterministic model guarantees a very safe situation. In future research we will address the question of how local dynamics influences the distribution of the time to extinction of a metapopulation in such system.

Wed Feb 26 07:30:07 EST 1997