Connectivity and coherence thresholds in metapopulation networks

Background/Question/Methods

May’s seminal theoretical work in the 70’s guided a generation of ecologists in their attempts to understand the relationships between complexity, connectance and stability of large ecosystems. Interest in these issues has recently resurfaced especially in the study of marine ecosystems where connectivity and the role of dispersal in maintaining persistent metapopulations have become central themes. As yet, there is little understanding of how the architecture of marine networks control metapopulation persistence, and even fundamental concepts remain controversial. The metapopulation framework was also recently adopted in the EU Habitats Directive, the creation of an ecologically coherent Europe wide network of sites selected expressly to protect important habitats and species; coherency being defined "in terms of the capacity for individual protected areas to support each other.” Similar actions have been advocated for the development of Marine Protected Areas (MPA's). Given the practical significance of the metapopulation concept, several recent theoretical studies have attempted to characterize the key processes governing persistence in complex networks and thus yield tools for guidance. Hastings and Botsford concluded that multiple criteria are necessary to assess persistence which explains why they were unable to "obtain a single number [criterion] like the reproductive number for a single population."

Results/Conclusions

Here we develop persistence and coherency threshold criteria that are couched in terms of the metapopulation’s reproductive potential, network connectivity as well as the topology of cycles in the dispersal network. Unlike most modeling attempts to date which are unable to take into account the role of age structure, we are able to obtain explicit persistence conditions for age structured metapopulations. A formal theoretical analysis of this new model allows us to show rigorously which metapopulation architectures are preferable. This involves exploring random networks of arbitrary and heterogeneous degree distribution, including regular, Erdos-Renyi, scale-free and star-networks. We conclude that topologies with complex cyclical structures (in contrast to simple cycles) enhance the effect of larvae “returning home” thereby boosting persistence.  Moreover, we show how an understanding of network coherency and location of disconnected components make it possible to predict which local populations survive and which go extinct in a persisting metapopulation. Finally, we note that while May argued that increasing connectivity is necessarily a destabilizing feature of large complex equilibrium systems, here we show very generally that system connectivity enhances persistence for metapopulations close to extinction.