Modeling the effects of habitat distribution and movement behavior on population persistence in continuous-space aquatic networks using metric graphs

Background/Question/Methods

Many aquatic habitats, such as rivers, deltas, and estuaries, possess a continuous branching network structure. Recent advances have greatly improved our ability to analyze ecological data in the context of aquatic networks, yet we still lack a well-integrated body of theory for predicting and explaining emerging patterns. Here, we introduce a framework for modeling branching aquatic 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. The first represents a “river drift” model, where organisms show biased movement from upstream branches to a downstream outflow. The second is an “upstream crawling” model where the movement bias is reversed. Finally, the third is an “estuary drift” model where flow biases movement from a single upstream source to branching outflows to the ocean. Boundary conditions also vary among system types.

Results/Conclusions

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 habitat boundaries increase population persistence across all model types. The addition of habitat always increases population persistence, yet habitat that is distributed away from system outflows has a more beneficial effect. Additionally, movement biases that are towards system outflows or lethal habitat boundaries, as in the river and estuary drift models, decrease persistence because more individuals are being transported outside the system. In contrast, biased movement in the upstream crawling model moves individuals away from system outflows or lethal habitat boundaries, increasing persistence. 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.