Relative size frequency of habitat fragments and long-distance dispersal critically influence long-term dynamics in a two-scale metapopulation model

Background/Question/Methods

Metapopulation models address species dynamics in fragmented habitats, depending on colonization and extinction events. Dispersal is a key process involved in the colonisation process. Although propagules are dispersed close to the source for most organisms, it has been shown that the rare long-distance dispersal events can strongly influence their spatial dynamics. In classical island metapopulation models, the colonization process is modelled by a single function representing the fluxes between islands, while panmixia is assumed within islands. However, this is not suitable to the cases where dispersal limitation entails a colonization-extinction dynamics of distinct populations within islands. We investigate here a new stochastic metapopulation model considering separated parameters for within-island colonization, cint, and between-island colonization, cext, both being mean-field processes. This model decomposes the process of dispersal into a local (short-distance), and a regional (long-distance) components. Furthermore, each island is composed of a limited number of sites defining the island size, n, and each population has a given extinction probability e. The two-scale metapopulation model acknowledges the effect of the relative frequency of island size in the stochastic process. We have simulated and analysed this process and the resulting occupancy patterns over time. 

Results/Conclusions

When cext is set to 0, the islands are isolated and their individual dynamics conformed to a finite-size stochastic Levins model. Depending on the distribution of island size, we find different distributions of extinction times and a slow decreases (metapopulation erosion) of the regional occupancy over time, so that no steady state is reached within ecological time. When cext is different from 0, external colonization could counterbalance metapopulation erosion and allow a long-term non-null steady state occupancy at regional scale. Long-distance dispersal thereby yields a rescue effect on metapopulation dynamics within islands. Long-term occupancy further depends on (i) a trade-off between local and global dispersal, (ii) a trade-off between local dispersal and population extinction rates, and (iii) the island size distribution. A key result is that long-term occupancy in large islands keep close to 1 – e/cint, consistent with a within island Levins's model, while smaller islands cannot include a viable metapopulation. These results highlight the importance of considering a hierarchical model of metapopulation dynamics acknowledging the relative impact of short- and long-distance colonization processes. They convey both theoretical and practical insights for understanding and managing metapopulations in fragmented habitats.