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.