Elevated nonlinearity as indicator of transition to overexploitation in fish stocks

Ecosystems may experience abrupt changes such as species extinctions, reorganisations of trophic structure, or transitions from stable population dynamics to strongly irregular fluctuations. Although most of these changes have important ecological and at times economic implications, they remain notoriously difficult to detect in advance. Here, we use a Ricker-type model to simulate the transition of a hypothetical stable fisheries population either to irregular boom-bust dynamics or to overexploitation. Our aim is to infer the risk of extinction in these two scenarios by comparing changes in variance, autocorrelation, and nonlinearity between unexploited and exploited populations. We find that changes in these statistical metrics reflect the risk of extinction but depend on the type of dynamical transition. Variance and nonlinearity increase similarly in magnitude along both transitions. In contrast, autocorrelation depends strongly on the presence of underlying oscillating dynamics. We also compare our theoretical expectations to indicators measured in long-term datasets of fish stocks from the California Cooperative Oceanic Fisheries Investigation in the Eastern Pacific and from the Northeast Shelf in the Western Atlantic. Our results suggest that elevated variance and nonlinearity could be potentially used to rank exploited fish populations according to their risk of extinction.