River networks: An analysis of simulating algorithms and graph metrics used to quantify topology

River networks are frequently simulated for use in the development and testing of ecological theory. Currently, two main algorithms are used, stochastic branching networks (SBNs) and optimal channel networks (OCNs). The topology of these simulated networks and 'real' rivers is often quantified using graph theoretic metrics; however, to date, there has not been a comprehensive analysis of how these algorithms compare regarding graph theoretic metrics, or an analysis of metric redundancy and variability across dendritic ecological networks. We aim to provide guidance as to which algorithm and metrics should be used, and under what circumstances. We performed an extensive simulation study in which we (a) identified orthogonal sets of metrics that describe the topology of real and simulated river networks, (b) analysed the relationship between algorithm hyper-parameters and node topology metrics, (c) determined whether simulated and real rivers are indistinguishable in their graph metric scores and (d) examined how patterns of species abundances compare across the three network types. We identified two orthogonal sets of node metrics; those that describe centrality and those that describe neighbourhood characteristics. Both stochastic branching networks and optimal channel networks can reproduce network topology metric scores of real rivers, but this relationship is dependent on the algorithm hyper-parameters used. Finally, using a metapopulation model, we show that both SBNs and OCNs can reproduce ecological patterns of species abundances similar to those of real rivers. SBNs and OCNs can replicate the node topology of real rivers. The choice of which algorithm to use will depend on the research aims, SBNs are faster to generate and more tractable, whereas OCNs can reproduce a wider variety of the characteristics of real rivers, but are more time-consuming to generate. When quantifying node topology in river networks, we recommend the orthogonal node metrics eccentricity, when interested in network centrality, and mean neighbour degree, when interested in local node importance.

Automated summary

This study compares the performance of stochastic branching networks (SBNs) and optimal channel networks (OCNs) in topology metrics and provides guidance on using different algorithms and metrics. The results show that both algorithms can replicate the node topology of real rivers, and the choice of algorithm depends on research aims and time requirements.