Characterizing connectivity relationships in freshwaters using patch-based graphs

Spatial graphs in landscape ecology and conservation have emerged recently as a powerful methodology to model patterns in the topology and connectivity of habitat patches (structural connectivity) and the movement of genes, individuals or populations among these patches (potential functional connectivity). Most spatial graph's applications to date have been in the terrestrial realm, whereas the use of spatially explicit graph-based methods in the freshwater sciences has lagged far behind. Although at first patch-based spatial graphs were not considered suitable for representing the branching network of riverine landscapes, here we argue that the application of graphs can be a useful tool for quantifying habitat connectivity of freshwater ecosystems. In this review we provide an overview of the potential of patch-based spatial graphs in freshwater ecology and conservation, and present a conceptual framework for the topological analysis of stream networks (i.e., riverscape graphs) from a hierarchical patch-based context. By highlighting the potential application of graph theory in freshwater sciences we hope to illustrate the generality of spatial network analyses in landscape ecology and conservation.