Quantifying positional importance in food webs: A comparison of centrality indices

Conservation biology should focus more on the importance rather than the rarity of species, although the definition and quantification of importance are not easy. One approach involves measuring the positional importance (e.g. centrality) of species in ecological interaction networks to provide a basis for species ranking. However, there are many centrality indices, each reflecting a particular aspect of positional importance and therefore giving a rank order of species different from those provided by alternative formulations. Thus, there is a strong need for comparing the available indices and for examining their relative merits in network analysis. In this paper, we apply 13 centrality indices to the “species” (trophic components) of methodologically comparable trophic flow networks, in order to answer the following questions: (1) What is the disagreement between different indices regarding the rank of a given species in a given network? (2) How is this disagreement in performance influenced by the choice of the network? (3) What is the overall relationship among these indices and, in particular, which are the most similar to degree (the simplest index of all, being equal to the number of links pertaining to a given node)? We compare the 13 indices based on the data of nine networks using metric and rank statistics and multivariate analysis procedures. We conclude that (1) different centrality ranks differ in each network; (2) different webs can be characterized by different relationships between ranks but there is a robust pattern of relationships among the indices, some index pairs behaving very similarly in all networks; and (3) it is the index of closeness centrality which provides a rank most similar to that based on degree.