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

Abstract

21Representing data as networks cuts across all sub-disciplines in ecology and evolutionary biology. 22Besides providing a compact representation of the interconnections between agents, network analysis 23 allows the identification of especially important nodes, according to various metrics that often rely on 24 the calculation of the shortest paths connecting any two nodes. While the interpretation of a shortest 25 paths is straightforward in binary, unweighted networks, whenever weights are reported, the 26 calculation could yield unexpected results. We analyzed 129 studies of ecological networks published 27 in the last decade and making use of shortest paths, and discovered a methodological inaccuracy 28 related to the edge weights used to calculate shortest paths (and related centrality measures), 29 particularly in interaction networks. Specifically, 49% of the studies do not report sufficient information 30 on the calculation to allow their replication, and 61% of the studies on weighted networks may contain 31 errors in how shortest paths are calculated. Using toy models and empirical ecological data, we show 32 how to transform the data prior to calculation and illustrate the pitfalls that need to be avoided. We 33 conclude by proposing a five-point check-list to foster best-practices in the calculation and reporting of 34 centrality measures in ecology and evolution studies. 42Data might either simply report the presence/absence of an edge (binary, unweighted networks), or 43 provide a strength for each edge (weighted networks). In turn, these weights can represent a variety of 44 ecologically-relevant quantities, depending on the system being described. For instance, edge weights 45 can quantify interaction frequency (e.g., visitation networks 5 ), interaction strength (e.g., per-capita 46 effect of one species on the growth rate of another 3 ), carbon-flow between trophic levels 6 , genetic 47 similarity 7 , niche overlap (e.g., number of shared resources between two species 8 ), affinity 9 , dispersal 48 probabilities (e.g., the rate at which individuals of a population move between patches 10 ), cost of 49 dispersal between patches (e.g., resistance 11 ), etc. 51Despite such large variety of ecological network representations, a common task is the identification of 52 nodes of high importance, such as keystone species in a food web, patches acting as stepping stones 53 in a dispersal network, or genes with pleiotropic effects. The identification of important nodes is 54 typically accomplished through centrality measures 5,12 . A large number of centrality measures has 55 been proposed, each probing complementary aspects of node-to-node relationships 13 . For instance, 56Closeness centrality 14,15 highlights nodes that are "near" to all other nodes in the network in terms of 57 average distance (calculated as number of edges) from all other nodes. Whenever the effects of a 58 node on another weaken along the path 16 , then central nodes are those having the largest capacity to 59 influence the others...