Periodicity of Extinctions in the Geologic Past: Deterministic Versus Stochastic Explanations

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Abstract
The temporal spacing and the magnitude of major extinctions over the past 250 and 570 million years, based on the use of different metrics of extinction probability, are analyzed by comparing deterministic and stochastic explanations. The best-fitting time series model is a stochastic autoregressive model that displays a pseudoperiodic behavior with a cycle length of 31 million years for the past 250 million years, regardless of the metric of extinction probability. The periodicity lengthens and weakens when the analysis is extended to the entire Phanerozoic. The history of the probability of extinction for the entire Phanerozoic, based on time series analysis, does not support the reported bipartite distribution of Van Valen. Rather, the probability of extinction has decreased uniformly over Phanerozoic time whereas the inertia or stability of the biotic system after the Late Permian crisis has increased.