Identifying sensor species to predict critical transitions in complex ecosystems

Ecosystems provide key services needed for human well-being, such as purifying air and regulating our health, many of which are disrupted when these ecosystems undergo a critical transition to undesired states. Detecting early-warning signals of these critical transitions remains challenging for complex ecosystems with a large number of species. Here we built a mathematical formalism to identify minimal sets of \"sensor species\" from which we can determine the state of a whole ecosystem, allowing us to predict a critical transition in an ecosystem by monitoring a minimal subset of its species. We rigorously prove that minimal sets of sensor species can be generically identified knowing only the structure of the ecological network underlying the ecosystem, regardless of its population dynamics. We numerically validated our formalism to predict critical transitions in large complex ecosystems, and then we applied it to experimental data of a critical transition in a lake food-web. Our results contribute to better monitoring complex ecosystems, especially those with poorly known population dynamics such as host-associated microbial communities.