The effects of density-dependence and local dispersal in individual-based stochastic metapopulations

We describe simulation models for metapopulations of individual‐based random walk populations with local dispersal on a coupled map lattice. The models were used to assess the factors determining persistence time, in particular the incidence of density‐dependence required for long‐term persistence of a temporally and spatially stochastic metapopulation, the extent of persistence possible in the absence of density‐dependence, and the factors that affect this.
Metapopulation persistence depended on the overall rate of increase of the metapopulation mean. This was maximised by (in order of importance) high mean and variance in the local rate of increase, high dispersal rates (20% or more of individuals dispersing each generation), large lattice size, and large dispersal range (to at least 24 neighbouring subpopulations).
With density‐dependence, the emergent dynamics of the metapopulation mean following global perturbation (reduction in density) resembled those of the logistic growth model. However, the overall metapopulation rate of increase and equilibrium level bore no resemblance to those of the subpopulations: rate of increase was higher (negative mean local rates of increase may give positive overall growth), and equilibrium mean metapopulation density was well below the local carrying capacity. This highlights the need to sample populations at an appropriate scale when seeking to understand regulatory mechanisms.
Metapopulations with the strongest tendency to grow gave the highest equilibrium mean density, the highest incidence of density‐dependence, and the longest persistence time. However, long‐term persistence with low average density and very low incidence of density‐dependence was possible on a sufficiently large lattice. For example, with 40×40 subpopulations, mean metapopulation persistence time was around 10⁴ generations, with mean subpopulation size of 2% of the carrying capacity, and local density‐dependence acting just once every 2500 generations on average. Metapopulation processes may explain our inability to detect density‐dependence in many real populations, and may also play an important part in the persistence of rare species.