Harmonic analysis of periodic extinctions

Abstract

Fourier analysis of percent extinction data for genera of fossil marine animals during the past 260 million years indicates the existence of a 26 m.y. extinction cycle. The first three harmonics, which account for 51.7 percent of the sum of squares, show the major extinction trends in the late Paleozoic, Mesozoic and Cenozoic. The first ten harmonics, which account for 89.5 percent of the sum of squares, are aligned with eight extinction peaks. The tenth harmonic, with a period of 26 million years, has an amplitude of 6.5 percent and accounts for 12.7 percent of the sum of squares.Several different methods are used to test the validity of the apparent 26 m.y. extinction cycle. Analysis of variance indicated that the 26 m.y. extinction cycle is statistically significant at the 95 percent level. When the 260 m.y. sample interval is divided into equal 130 m.y. segments, the phases and amplitudes for the 26 m.y. cycle were almost equal within the two independent segments. When the 260 m.y. interval is divided into 10 shorter time segments of different lengths, the 26 m.y. cycle is represented in each time segment.A series of experiments is run to test the influence of the Late Permian and Cretaceous peaks on the observed 26 m.y. cycle. When all peaks are smoothed out except for the two major peaks, a pseudo-cycle with a period of 26 m.y. is generated that accounts for 3.0 percent of the sum of squares. When the Permian and Cretaceous peaks are reduced to about half their observed height, the sum of squares accounted for by the 26 m.y. cycle is reduced from 12.7 to 11.0 percent. When the number of extinctions within each stage is used in the harmonic analysis in place of extinction percent, the 26 m.y. cycle accounts for 19.3 percent of the sum of squares.Therefore, the evidence from harmonic analysis of fossil marine animals points toward a distinct and persistent 26 m.y. cycle in mass extinctions in the late Paleozoic, Mesozoic and Cenozoic.