Combining centrality indices: Maximizing the predictability of keystone species in food webs

Network analysis offers a rich toolkit to study various graph models in biology. In ecology, centrality indices have been suggested to indicate keystone species in interaction networks and to quantify their importance in an ecosystem. There is a large number of centrality indices, however, and it is often unclear what is their precise biological meaning, how are they related to each other and which one is the “best” predicting the functioning of the modelled biological system. It is a major challenge to use simple structural indicators in order to predict the outcome of much more complicated dynamical simulations. The question is which one is the most preidictive one and what is the meaning of particular structural indices. Here we use machine learning techniques to combine k centrality indices out of n in such a way that the gained combined index (a “cocktail” of single indices) correlates better with simulated dynamics. In particular, we are interested in rank correlations between single-node and multi-node centrality and simulated node importance. We identify index families based on similarity. The best single-index correlations (weighted degree centrality) can predict simulated food web dynamics with an accuracy up to 70.06%. This accuracy can be raised reasonably, using the best cocktail, up to 78.42%. This is a combination of node degree (D) and 5-step-long weighted importance index (WI5). Since they have completely different properties (the former is local and binary, the latter is meso-scale and weighted), we can demonstrate that a good cocktail has to combine indices from different families in order to best improve predictions. If one needs to predict dynamics from structure, there is a way to use wise proxies of simple topological indices – instead of performing complicated simulations.