Can a complex ecosystem survive the loss of a large fraction of its species? A random matrix theory of secondary extinction

Recent estimates suggest that a quarter of species globally are under threat of extinction. Understanding what happens to ecological networks of interacting organisms when they lose a significant fraction of species is thus essential for assessing, and potentially mediating, the current biodiversity crisis. We introduce and explore a framework for studying the repercussions of mass extinctions in large model ecosystems. This random‐matrix approach reveals the statistical properties of the post‐extinction abundances to exhibit a simple structure, allowing us to determine analytically how susceptibility to secondary extinctions depends on the strength and nature of interspecies interaction. We find, for example, that mutualistic networks are particularly sensitive to species loss and that, for small primary extinctions, realistic food webs suffer fewer secondary extinctions than do random ones. Finally we show how the response to low‐level extinctions can be used to predict the effects of more severe events.