Secondary extinctions in food webs: a Bayesian network approach

1. Ecological communities are composed of populations connected in tangled networks of ecological interactions. Therefore, the extinction of a species can reverberate through the network and cause other (possibly distantly connected) species to go extinct as well. The study of these secondary extinctions is a fertile area of research in ecological network theory. 2. However, to facilitate practical applications, several improvements to the current analytical approaches are needed. In particular, we need to consider that (i) species have different a priori' probabilities of extinction, (ii) disturbances can simultaneously affect several species, and (iii) extinction risk of consumers likely grows with resource loss. All these points can be included in dynamical models, which are, however, difficult to parameterize. 3. Here we advance the study of secondary extinctions with Bayesian networks. We show how this approach can account for different extinction responses using binary - where each resource has the same importance - and quantitative data - where resources are weighted by their importance. We simulate ecological networks using a popular dynamical model (the Allometric Trophic Network model) and use it to test our method. 4. We find that the Bayesian network model captures the majority of the secondary extinctions produced by the dynamical model and that consumers' responses to species loss are best modelled using a nonlinear sigmoid function. We also show that an approach based exclusively on food web structure loses power when species at higher trophic levels are preferentially lost. Because the loss of apex predators is unfortunately widespread, the results highlight a serious limitation of studies on network robustness.