How predictable is extinction? Forecasting species survival at million-year timescales

A tenet of conservation palaeobiology is that knowledge of past extinction patterns can help us to better predict future extinctions. Although the future is unobservable, we can test the strength of this proposition by asking how well models conditioned on past observations would have predicted subsequent extinction events at different points in the geological past. To answer this question, we analyse the well-sampled fossil record of Cenozoic planktonic microfossil taxa (Foramanifera, Radiolaria, diatoms and calcareous nanoplankton). We examine how extinction probability varies over time as a function of species age, time of observation, current geographical range, change in geographical range, climate state and change in climate state. Our models have a 70-80% probability of correctly forecasting the rank order of extinction risk for a random out-of-sample species pair, implying that determinants of extinction risk have varied only modestly through time. We find that models which include either historical covariates or account for variation in covariate effects over time yield equivalent forecasts, but a model including both is overfit and yields biased forecasts. An important caveat is that human impacts may substantially disrupt range-risk dynamics so that the future will be less predictable than it has been in the past. This article is part of a discussion meeting issue 'The past is a foreign country: how much can the fossil record actually inform conservation?'