A Note on the Role of Seasonal Expansions and Contractions of the Flowing Fluvial Network on Metapopulation Persistence

Does a dynamic drainage density have a role on species persistence in the river basin? The general viability of a focus species under time-varying hydrologic connectivity and habitat quality is a topic gaining traction in view of recent advances in our understanding of flowing fluvial network dynamics and of ecological interactions occurring on directed trees. Here, we combine metapopulation dynamics and scaling theory to investigate how the structure of river networks and time-changing hydrological and geomorphological attributes control local metapopulation survival. This is done by introducing seasonal fluctuations of the drainage density subsuming overall time-changing connectivity and distributed changes in habitat quality of the fluvial domain. Suitable replicas of channel networks within an assigned domain are used to compute the statistics of evolving metapopulation capacities, properties of a landscape matrix measuring the viability of the focus species. To obtain consistent replicas of the substrate for ecological interactions, we employ constructs whose suitability for the task has long been established. We find that the river network structure blends the fluctuations into a nontrivial scaling of the metapopulation capacity with the sum of total active contributing sites at any point of the flowing network. The latter is proportional to the mean distance to the outlet of the flowing dendrite and to the tree diameter-a measure of the overall connectivity of the active stream links. Scaling emerges as a robust ensemble property that enables the linkage of ecological patterns across a river network to clearly identified hydrological and geomorphological factors.