Characterization of topological keystone species: Local, global and “meso-scale” centralities in food webs

An important question in the network representation of ecological systems is to determine how direct and indirect interactions between species determine the positional importance of species in the ecosystem. Here we present a quantitative analysis of the similarities and differences of six different topological centrality measures as indicators of keystone species in 17 food webs. These indicators account for local, global and “meso-scale” – intermediate between local and global – topological information about species in the food webs. Using factor analysis we shown that most of these centrality indices share a great deal of topological information, which range from 75% to 96%. A generalized keystone indicator is then proposed by considering the factor loadings of the six-centrality measures, which contains most of the information encoded by these indices. However, the individual ordering of species according to these criteria display significant differences in most food webs. We simulate the effects of species extinction by removing species ranked according to a local and a “meso-scale” centrality indicator. The differences observed on three network characteristics – size, average distance and clustering coefficient of the largest component – after the removal of the most central nodes indicate that the consideration of these indices have different impacts for the ranking of species with conservational biology purposes. The “meso-scale” indicator appears to play an important role in determining the relative importance of species in epidemic spread and parasitism rates.