Intermediate landscape disturbance maximizes metapopulation density

Abstract

The viability of metapopulations in fragmented landscapes has become a central theme in conservation biology. Landscape fragmentation is increasingly recognized as a dynamical process: in many situations, the quality of local habitats must be expected to undergo continual changes. Here we assess the implications of such recurrent local disturbances for the equilibrium density of metapopulations. Using a spatially explicit lattice model in which the considered metapopulation as well as the underlying landscape pattern change dynamically, we show that equilibrium metapopulation density is maximized at intermediate frequencies of local landscape disturbance. On both sides around this maximum, the metapopulation may go extinct. We show how the position and shape of the intermediate viability maximum is responding to changes in the landscape’s overall habitat quality and the population’s propensity for local extinction. We interpret our findings in terms of a dual effect of intensified landscape disturbances, which on the one hand exterminate local populations and on the other hand enhance a metapopulation’s capacity for spreading between habitat clusters.

Appendix: Well-mixed metapopulations

When long-range dispersal is much more frequent than short-range dispersal, the metapopulation described by our model is well-mixed, so that all spatial correlations in the occupancy of sites are lost. This enables a simple analytical treatment, which we include here so as to demonstrate the crucial importance of spatial structure for our results.

Assuming a well-mixed metapopulation with a large number n of sites, the dynamics of the proportion of habitable occupied sites, N, is given by

$$\frac{dN}{dt} = N(p - N) - N\left(e + \frac{1}{2}f/p\right),$$

where time t is measured in units of n. This is a special case of the mean-field metapopulation dynamics studied by Keymer et al. 2000; in our model, the fraction p of habitable sites and the total number of sites remain constant).

The equilibrium metapopulation density $N^{\ast}=\max(0,\;p-e-\frac{1}{2}f/p)$ decreases as f increases. This shows that, as expected, mean-field models cannot capture the bridging effect of landscape disturbance and therefore only account for the local extinctions caused by such disturbance. Moreover, the effect of a small disturbance frequency f on $N^{\ast}$ is negligible for a well-mixed metapopulation, whereas it leads to marked changes in the equilibrium metapopulation densities of a spatially structured metapopulation (Fig. 5).