A dispersal-induced paradox: synchrony and stability in stochastic metapopulations
The effects of dispersal have important implications for the dynamics of populations that are separated in space. Dispersal can lead to spatial synchrony of patches of habitat containing subpopulations (causing population dynamics of nearby patches to vary similarly), or it can enhance their stability by allowing small subpopulations to be rescued from local extinction by immigrants from nearby patches. However, synchrony of patches can reduce the stabilizing effect of dispersal. The author, K. Abbott uses multiple models that incorporate environmental stochasticity to describe the synchrony/stability relationship. The results show that although in some contexts, factors such as dispersal can reduce stability by promoting synchrony, while in other contexts, these factors promote both at the same time. The first model was a first-order autoregressive model with subpopulations linked by global density independent dispersal, and a random variable representing environmental stochasticity, with a spatial correlation (representing the degree of spatial synchrony). Solving this model analytically, Abbott showed that synchrony and dispersal induced stability were positively related for all parameter values (except for two special cases of perfect synchrony and when population dynamics are entirely stochastic), and the strength of this relationship (i.e. the steepness of the slope) declines as the spatial correlation increased (i.e. as nearby populations became more synchronized).
Next, Abbott used two different non-linear (and more ecologically realistic) models to study the synchrony and dispersal induced stability (DIS) relationship. The first was the Ricker model for single species dynamics, that also incorporated environmental stochasticity and spatial correlation. The second was a negative binomial variant of the Nicholson–Bailey host–parasitoid metapopulation model. Spatial simulations using a 10 x 10 lattice of subpopulations were performed until the metapopulation went extinct or 500 time steps were reached. For both models, synchrony (of host populations) and DIS usually increased with dispersal. However, this was not always the case, and occasionally dispersal was destabilizing, no matter how synchronized subpopulations were. When stability was measured in terms of extinction (local and global) rather than host variance, then the relationship between synchrony and DIS became negative. Thus, this relationship appears to change for different definitions of stability, which likely also occurs for different causes. When Abbott tested the effect of environmental correlation on the synchrony-DIS relationships, the relationship was almost always negative, meaning that spatial correlations that promote synchrony weaken DIS.
Overall, this paper shows how the shape of the synchrony-DIS relationship can change depending on whether it is indirectly or directly assessed, and that factors such as dispersal that affect both processes can obscure the direct relationship. Therefore, thinking about how the effects of these factors on synchrony and stability interact will be important for applying these theoretical explorations to management of populations on fragmented landscapes.
Abbott, K. C. 2011. A dispersal-induced paradox: synchrony and stability in stochastic metapopulations. Ecology Letters 14, 1158–1169.