Succinctly assessing the topological importance of species in flower–pollinator networks

The topological importance of species within networks is an important way of bringing a species-level consideration to the study of whole ecological networks. There are many different indices of topological importance, including centrality indices, but it is likely that a small number are sufficient to explain variation in topological importance. We used 14 indices to describe topological importance of plants and pollinators in 12 quantitative mutualistic (plant–pollinator) networks. The 14 indices varied in their consideration of interaction strength (weighted versus unweighted indices) and indirect interactions (from the local measure of degree to meso-scale indices). We use principal components approximation to assess how well every combination of 1–14 indices approximated to the results of principal components analysis (PCA). We found that one or two indices were sufficient to explain up to 90% of the variation in topological importance in both plants and pollinators. The choice of index was crucial because there was considerable variation between the best and the worst approximating subsets of indices. The best single indices were unweighted degree and unweighted topological importance (Jordán's TI index) with two steps (a measurement of apparent competition). The best pairs of indices consisted of a measure of a TI index and one of closeness centrality (weighted or unweighted) or d′ (a standardised species-level measure of partner diversity). Although we have found indices that efficiently explain variation in topological importance, we recommend further research to discover the real-world relevance of different aspects of topological importance to species in ecological networks.