The emergence of the rescue effect from explicit within- and between-patch dynamics in a metapopulation

Eriksson A, Elías-Wolff F, Mehlig B, Manica A. 2014 The emergence of the rescue effect from explicit within- and between-patch dynamics in a metapopulation. Proc. R. Soc. B 281: 0133127. http://dx.doi.org/10.1098/rspb.2013.3127

Migration between patches can reduce the probability of local extinction, a phenomenon known as the “rescue effect.” The rescue effect can be particularly important when environmental variability increases local population fluctuations (and thus the likelihood of extinction independent of migration). Most studies of the rescue of effect of focused on one or a few local populations, so Eriksson et al. (2014) set out to ask how rescue effects can effect dynamics on the metapopulation level, especially given that local dynamics can differ between patches. Previous mechanistic metapopulation models have either assumed low migration rates, low patch occupancy, or both, which are often not realistic. In contrast, Eriksson et al. build a model that includes both within-patch stochasticity and between-patch migration at any level of occupancy or migration, and then use both simulations and numerical solutions to identify the cases in which stochasticity and the rescue effect have the largest effects on metapopulation dynamics.

Eriksson et al.’s model is a discrete-time model where non-overlapping generations first undergo within-patch dynamics (including both environmental and demographic stochasticity) and then migrate between patches at a constant rate. Using this framework, the authors found that local and global population dynamics occurred on separate time scales, where local populations changed quickly but global population sizes moved smoothly and predictably (and more slowly). In addition, contrary to what may be expected, average population sizes in the metapopulation were consistent across different dispersal probabilities and distances (unless both were very low, i.e. when probability of dispersal was below 0.01 and dispersers could only reach their nearest neighbor). Most importantly, both simulations and solutions showed that the rescue effect emerged naturally when the model included stochasticity in local dynamics; in other words, local dynamics had an effect on the overall metapopulation.

Using this model, the authors also examined the relative importance of different types of stochasticity (demographic, environmental influencing survival, and environmental influencing recruitment) on the probability of local extinction. Demographic recruitment stochasticity had the smallest effect and environmental recruitment stochasticity had the largest effect on probability of extinction, probably because demographic stochasticity effects only a portion of the population, whereas environmental stochasticity effects the entire local population at once. Overall, the Eriksson et al.’s results show that local stochasticity is important on the global scale under a variety of conditions. The authors further propose that their approach allows instantaneous assessment of the rescue effect (rather than having to collect long time series, as was previously suggested).