Longitudinal connectivity loss in a riverine network: accounting for the likelihood of upstream and downstream movement across dams

Disruption of longitudinal connectivity is a major concern in most of the world's rivers. Approaches based on graph theory have proven to be a suitable tool for analysing functional connectivity. However, previous applications of graph-based connectivity methods to river systems have been oversimplified in that they have treated potential barriers as binary features and rivers as symmetric networks. We here apply a network analytical approach in which (a) upstream and downstream connectivity are considered so that fish passability values across dams are asymmetrical, and (b) it is possible to consider a continuous range of passability values for every dam. We build on previous and widely used connectivity metrics (Probability of Connectivity, PC), which here are generalised and adapted toward that end. We compare the results of our approach with those that would be obtained under the more simplified assumptions of symmetric movement and of barriers as binary features. We want to prove if there are substantial differences between considering or not the asymmetry in river networks. The application of symmetrical and asymmetrical PC highlights major differences between the upstream connectivity versus the downstream connectivity. We provide our methods in a free software package so that they can be used in any other application to riverscapes. We expect to provide a better graph-based approach for the prioritisation of the removal or permeabilization of artificial obstacles as well as for the preservation of target river segments for connectivity conservation and restoration.