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Ecological networks: Pursuing the shortest path, however narrow and crooked

Abstract : Representing data as networks cuts across all sub-disciplines in ecology and evolutionary biology. Besides providing a compact representation of the interconnections between agents, network analysis allows the identification of especially important nodes, according to various metrics that often rely on the calculation of the shortest paths connecting any two nodes. While the interpretation of a shortest paths is straightforward in binary, unweighted networks, whenever weights are reported, the calculation could yield unexpected results. We analyzed 129 studies of ecological networks published in the last decade that use shortest paths, and discovered a methodological inaccuracy related to the edge weights used to calculate shortest paths (and related centrality measures), particularly in interaction networks. Specifically, 49% of the studies do not report sufficient information on the calculation to allow their replication, and 61% of the studies on weighted networks may contain errors in how shortest paths are calculated. Using toy models and empirical ecological data, we show how to transform the data prior to calculation and illustrate the pitfalls that need to be avoided. We conclude by proposing a five-point checklist to foster best-practices in the calculation and reporting of centrality measures in ecology and evolution studies. The last two decades have witnessed an exponential increase in the use of graph analysis in ecological and conservation studies (see refs. 1,2 for recent introductions to network theory in ecology and evolution). Networks (graphs) represent agents as nodes linked by edges representing pairwise relationships. For instance, a food web can be represented as a network of species (nodes) and their feeding relationships (edges) 3. Similarly, the spatial dynamics of a metapopulation can be analyzed by connecting the patches of suitable habitat (nodes) with edges measuring dispersal between patches 4. Data might either simply report the presence/absence of an edge (binary, unweighted networks), or provide a strength for each edge (weighted networks). In turn, these weights can represent a variety of ecologically-relevant quantities, depending on the system being described. For instance, edge weights can quantify interaction frequency (e.g., visitation networks 5), interaction strength (e.g., per-capita effect of one species on the growth rate of another 3), carbon-flow between trophic levels 6 , genetic similarity 7 , niche overlap (e.g., number of shared resources between two species 8), affinity 9 , dispersal probabilities (e.g., the rate at which individuals of a population move between patches 10), cost of dispersal between patches (e.g., resistance 11), etc. Despite such large variety of ecological network representations, a common task is the identification of nodes of high importance, such as keystone species in a food web, patches acting as stepping stones in a dispersal network , or genes with pleiotropic effects. The identification of important nodes is typically accomplished through centrality measures 5,12. Many centrality measures has been proposed, each probing complementary aspects of node-to-node relationships 13. For instance, Closeness centrality 14,15 highlights nodes that are "near" to all other
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Andrea Costa, Ana Martín González, Katell Guizien, Andrea Doglioli, José María Gómez, et al.. Ecological networks: Pursuing the shortest path, however narrow and crooked. Scientific Reports, Nature Publishing Group, 2019, 9 (1), ⟨10.1038/s41598-019-54206-x⟩. ⟨hal-02454786⟩

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