Demographic Stochasticity versus Spatial Variation in the Competition between Fast and Slow Dispersers

Dispersal is a key component of any metapopulation model and can influence competition between otherwise identical populations, however the role of dispersal is dependent on the environment, or quality, of patches. In general, spatial variability in patch quality favors slower dispersal rates, while temporal variables favors faster dispersal rates, at least in deterministic models. Introducing stochasticity to the system may influence the role dispersal plays on population dynamics, and therefore the selection on dispersal rates and coexistence outcomes. To explore this further, Waddell et al. (2010) develop a demographically stochastic model exploring the competitive outcome between slow and fast dispersing populations in a spatially variable multi-patch environment.

Specifically, the study addresses two questions: i) how does environmental variability influence the results of competition between fast and slow dispersers and ii) is there a “best” dispersal rate that reduces the implicit cost of dispersal and is capable of outcompeting dispersers with high or lower dispersal rates? This is approached using simulations and analytical moment-closure methods to solve for the eventual “winner” (there were no scenarios with co-existence) across a range of parameter space, to model phase boundaries between WORD by the slow and fast disperser. In order to solve the equations analytically, several important assumptions were made. Both forms of dispersal were considered at their limits, that is fast dispersers had the ability to sample every patch in the environment and slow dispersers did not disperse at all. This oversimplification may have resulted in the lack of coexistence outcomes, but allowed for an analytical solution to the equations. Additionally, they dropped, or closed, the third moment of the equations, which led to correct predictions when the third moment was small (in which case the slow population outcompetes the fast population), but led to impossible parameter space when the third moment was large. This obstacle was overcome by assuming that in these cases, when the ODEs demonstrate instability, the outcome was that the fast population outcompeted the slow population. Given that this was the value they were interested in measuring, this seems like a tenable assumption, especially since the simulations concur with the closed-moment model.

Both simulations and analytical solutions found that slow dispersers outcompeted fast dispersers when the carrying capacity of individual sites was high or environmental variation was low. This seems logical from a biological viewpoint, dispersal is advantageous when carrying capacity is low, as it allows individuals to avoid density dependence, and when there is large environmental variation, because an individual’s probability of moving to a higher quality patch is higher than with low variation. Deterministic models have found that environmental variation leads to lower dispersal rates (contrary to these results), most likely because the lack of demographic stochasticity reduces the benefit of dispersal, increasing its relative cost. Interestingly, the incorporation of spatial variation and demographic stochasticity into the model make it impossible to recover the deterministic result of slow dispersers outcompeting fast disperser. That is, for extremely large carrying capacities, there is always a level of environmental variation that can result in the fast disperser winning.