RANDOM-WALKS IN A METAPOPULATION - HOW MUCH DENSITY-DEPENDENCE IS NECESSARY FOR LONG-TERM PERSISTENCE

1. We describe analytical and simulation models of metapopulations con sisting of local populations that obey a random walk between a reflect ing upper boundary (population 'ceiling') and an absorbing lower bound ary (local extinction). 2. We present analytical results for the expec ted time to local extinction, expected size of local populations, and incidence of density dependence. The latter is defined as the frequenc y of hitting the ceiling per generation per population. 3. With these models we examine the proposition that a metapopulation consisting of random walk local populations would persist without density dependence . 4. Long-term persistence of a metapopulation is not possible without local populations occasionally becoming large and hence being affecte d by density dependence. But it is possible to construct examples in w hich a metapopulation persists for a long time with a low incidence of density dependence, in which cases local populations typically have v ery short expected lifetimes. 5. We demonstrate that, paradoxically, a persisting metapopulation may consist of only 'sink' populations (neg ative average growth rate in the absence of migration). Contrary to so me previous suggestions, increasing migration rate generally increases density dependence in persisting metapopulations.