Towards quantifying the mass extinction debt of the Anthropocene.

To make sense of our present biodiversity crises, the modern rate of species extinctions is commonly compared to a benchmark, or 'background,' rate derived from the fossil record. These estimates are critical for bounding the scale of modern diversity loss, but are yet to fully account for the fundamental structure of extinction rates through time. Namely, a substantial fraction of extinctions within the fossil record occurs within relatively short-lived extinction pulses, and not during intervals characterized by background rates of extinction. Accordingly, it is more appropriate to compare the modern event to these pulses than to the long-term average rate. Unfortunately, neither the duration of extinction pulses in the geological record nor the ultimate magnitude of the extinction pulse today is resolved, making assessments of their relative sizes difficult. In addition, the common metric used to compare current and past extinction rates does not correct for large differences in observation duration. Here, we propose a new predictive metric that may be used to ascertain the ultimate extent of the ongoing extinction threat, building on the observation that extinction magnitude in the marine fossil record is correlated to the magnitude of sedimentary turnover. Thus, we propose that the ultimate number of species destined for extinction today can be predicted by way of a quantitative appraisal of humanity's modification of ecosystems as recorded in sediments-that is, by comparing our future rock record with that of the past. The ubiquity of habitat disruption worldwide suggests that a profound mass extinction debt exists today, but one that might yet be averted by preserving and restoring ecosystems and their geological traces.

Resonant activation of population extinctions.

Understanding the mechanisms governing population extinctions is of key importance to many problems in ecology and evolution. Stochastic factors are known to play a central role in extinction, but the interactions between a population's demographic stochasticity and environmental noise remain poorly understood. Here we model environmental forcing as a stochastic fluctuation between two states, one with a higher death rate than the other. We find that, in general, there exists a rate of fluctuations that minimizes the mean time to extinction, a phenomenon previously dubbed "resonant activation." We develop a heuristic description of the phenomenon, together with a criterion for the existence of resonant activation. Specifically, the minimum extinction time arises as a result of the system approaching a scenario wherein the severity of rare events is balanced by the time interval between them. We discuss our findings within the context of more general forms of environmental noise and suggest potential applications to evolutionary models.