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

Abstract

1. 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.2. 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.3. 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.4. 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.

Optimal Channel Networks accurately model ecologically-relevant geomorphological features of branching river networks

“…While we found that BBTs are highly inaccurate in reproducing ecological metrics of real river networks and should be therefore discarded altogether in future modelling applications, RBNs show a certain degree of similarity with OCNs and real river networks in this respect; moreover, RBNs (as is the case for any random tree 61 ) satisfy Horton's laws on bifurcation and length ratios. A relevant advantage of RBNs over OCNs is that their generation algorithm is at least one order of magnitude faster 49 . Therefore, we acknowledge that RBNs could be considered as a suitable surrogate for real river networks as null models in cases where a large number of network replicates is required.…”

“…While some studies acknowledged possible shortcomings of certain network approximations 25 , the effects of inadequate network analogues on the ecological dynamics analyzed have not been systematically addressed (but see ref. 49 ). Specifically, a first group of studies 25,33,34,36,37,43,45,50 modelled river networks as trees where all paths from the tree root to the source nodes (see Supplementary Note 1) have equal length; borrowing an analogy from computer science, these will hereafter be defined balanced binary trees (BBTs -Fig.…”

Network topology mediates freshwater fish metacommunity response to loss of connectivity

“…We constructed dendritic networks consisting of 50 patches using the optimal channel network (OCN) algorithm (Rinaldo et al, 2014). OCNs are oriented spanning trees (built on rectangular lattices) that reproduce some of the features characteristic of real river networks (Carraro & Altermatt, 2022; Lee et al, 2022; Rinaldo et al, 2014; Rodriguez‐Iturbe et al, 2009). The algorithm starts with a feasible network configuration imposed on a lattice landscape, and the OCNs are obtained by minimization of a function representing the total energy dissipated by water flowing through the network spanning the lattice.…”

Locality Analysis of Graph Reordering Algorithms

“…Analyzing Graph Structure. The study of different graph types and their structures has been performed in [29], [57], [58], [59], [12] that present different topological metrics and tools to analyze the differences between different graph types.…”