Emergent encoding of dispersal network topologies in spatial metapopulation models

We address a generalization of the concept of metapopulation capacity for trees and networks acting as the template for ecological interactions. The original measure had been derived from an insightful phenomenological model and is based on the leading eigenvalue of a suitable landscape matrix. It yields a versatile predictor of metapopulation persistence through a threshold value of the eigenvalue determined by ecological features of the focal species. Here, we present an analytical solution to a fundamental microscopic model that incorporates key ingredients of metapopulation dynamics and explicitly distinguishes between individuals comprising the "settled population" and "explorers" seeking colonization. Our approach accounts for general network characteristics (in particular graph-driven directional dispersal which is known to significantly constrain many ecological estimates) and yields a generalized version of the original model, to which it reduces for particular cases. Through examples, including real landscapes used as the template, we compare the predictions from our approach with those of the standard model. Results suggest that in several cases of practical interest, differences are significant. We also examine, with both models, how changes in habitat fragmentation, including removal, addition, or alteration in size, affect metapopulation persistence. The current approach demonstrates a high level of flexibility, enabling the incorporation of diverse "microscopic" elements and their impact on the resulting biodiversity landscape pattern.