Mathematical Expression of a Global Environmental Catastrophe

Two hundred and fifty-two million years ago, life on Earth nearly vanished [1]. So many marine animal species disappeared—more than 90 percent—that the event, known as the end-Permian extinction, qualifies as the most severe mass extinction in the geologic record. Unlike the later demise of the dinosaurs, the end-Permian extinction is not linked to a meteor impact. Yet it is unquestionably associated with major environmental change, including a strong perturbation of Earth’s carbon cycle. Recently, an additional piece of the puzzle fell into place. Massive Siberian volcanism, long thought to coincide roughly with the extinction, is now known to have preceded it and continued beyond it [2]. A simple narrative emerges. Carbon dioxide degassed from millions of cubic kilometers of Siberian magma perturbed the carbon cycle, leading to an extreme form of our own contemporary concerns: global warming and ocean acidification. Life then nearly perished. It is an attractive story, but it fails. Geochemical studies reveal an influx of carbon dioxide that is much greater than Siberian volcanism would have provided on its own [3]. Something else must have happened. Mathematics now enters the picture. The same advances that allow us to identify the chronological order of magma in Siberia and fossils elsewhere also make possible mathematical analyses of the temporal evolution of geochemical signals. These analyses then aid the development and testing of hypotheses, which in turn help to identify underlying mechanisms. The best-understood geochemical signals are time series of the isotopic composition of carbon derived from