Googling Food Webs: Can an Eigenvector Measure Species' Importance for Coextinctions?

A major challenge in ecology is forecasting the effects of species' extinctions, a pressing problem given current human impacts on the planet. Consequences of species losses such as secondary extinctions are difficult to forecast because species are not isolated, but interact instead in a complex network of ecological relationships. Because of their mutual dependence, the loss of a single species can cascade in multiple coextinctions. Here we show that an algorithm adapted from the one Google uses to rank web-pages can order species according to their importance for coextinctions, providing the sequence of losses that results in the fastest collapse of the network. Moreover, we use the algorithm to bridge the gap between qualitative (who eats whom) and quantitative (at what rate) descriptions of food webs. We show that our simple algorithm finds the best possible solution for the problem of assigning importance from the perspective of secondary extinctions in all analyzed networks. Our approach relies on network structure, but applies regardless of the specific dynamical model of species' interactions, because it identifies the subset of coextinctions common to all possible models, those that will happen with certainty given the complete loss of prey of a given predator. Results show that previous measures of importance based on the concept of “hubs” or number of connections, as well as centrality measures, do not identify the most effective extinction sequence. The proposed algorithm provides a basis for further developments in the analysis of extinction risk in ecosystems.Author Summary: Predicting the consequences of species' extinction is a crucial problem in ecology. Species are not isolated, but connected to each others in tangled networks of relationships known as food webs. In this work we want to determine which species are critical as they support many other species. The fact that species are not independent, however, makes the problem difficult to solve. Moreover, the number of possible “importance'” rankings for species is too high to allow a solution by enumeration. Here we take a “reverse engineering” approach: we study how we can make biodiversity collapse in the most efficient way in order to investigate which species cause the most damage if removed. We show that adapting the algorithm Google uses for ranking web pages always solves this seemingly intractable problem, finding the most efficient route to collapse. The algorithm works in this sense better than all the others previously proposed and lays the foundation for a complete analysis of extinction risk in ecosystems.