UC Riverside

The branching structure of aquatic networks can have substantial ecological consequences. Recent advances have greatly improved our ability to analyze ecological data in the context of river networks, yet we still lack a well-integrated body of theory for predicting and explaining emerging patterns. One hindrance to achieving this goal is the absence of an appropriate framework for modeling ecological processes in aquatic networks. Previous attempts to model the effects of branching network structure on ecological dynamics have typically treated river networks as a set of interconnected patches, artificially discretizing an essentially continuous system. Recent reviews have highlighted the shortcomings of such an approach and called for alternative methods for modeling river habitat in a more natural way. Here, we introduce a framework for modeling branching river networks as continuous systems using dynamic, spatially-explicit models linked to metric graphs. Unlike traditional graphs, metric graphs encode a continuous branching system where edges represent actual domain rather than simple connections among discrete nodes. Graph edges are connected by junction conditions that represent branch confluences. Using the metric graph framework, we model the effects of movement, network geometry, and the distribution of habitat within the network on population persistence for three different types of hypothetical systems. Via numerical simulations, we found that movement rates, habitat length, and the distribution of habitable area all play large roles in determining persistence potential. In particular, movement behaviors and habitat distributions that reduce the encounter rate between individuals and lethal boundaries increase population persistence across all model types. We conclude by describing extensions and other potential applications of our framework, including suggested models for populations with in- and out-of-network movement modes and species interactions.