Understanding the long tail of patch extinction times in a classic metapopulation system

Background/Question/Methods: The spatial arrangement of habitat patches which constitute a metapopulation, and the dispersal connections between them, are related to the ability of the metapopulation to sustain species occupancy (``metapopulation persistence''). However, persistence is a dynamic phenomenon, while measures of persistence are typically based solely on structural properties of the spatial dispersal network. The extent to which the network topology informs network dynamics is unclear. Further, understanding the shape of the distribution of extinction times is a central goal in population ecology, and scaling to interconnected populations is a logical next step. Here, we examine the goodness of fit of the power law to the patch persistence time distribution using data on a foundational metapopulation system -- the Glanville fritillary butterfly in the Åland islands. Further, we address the relationship between structural (``model-based'') measures of metapopulation persistence (i.e., metapopulation capacity) and our temporal (``data-based'') distributional fits to patch persistence times based on a power law.

Results/Conclusions: Power law fits to the distribution of patch persistence times were favored for the majority of semi-independent networks. We find a positive relationship between structural (model-based) and temporal (data-based) measures of metapopulation persistence for a set of 88 semi-independent networks of dry meadow habitats. Further, several environmental variables and measures of network topology were correlated with both measures of metapopulation persistence, though correlations tended to be stronger for the structural (model-based) measure of metapopulation persistence (i.e., metapopulation capacity). Together, our findings suggest that persistence time distributions are useful dynamic properties of metapopulations, and provide evidence of a relationship between metapopulation structure and metapopulation dynamics.