Periodicity in Extinction

Xu Cui

Whether periodicity exists in extinction process has long been debated since 1984 when Raup and Sepkoski first raised it. The debate has focused on the extinction database, the definition of mass extinction and the statistical methods. Much more data are needed before the debate is resolved. At the same time several extinction mechanisms, mostly extraterrestrial ones, had been put forward. But none seems to well explain the dynamics of extinction.

In the history of life a vast majority of species that have ever lived have been extinct^1,2, and the pattern and process of extinction is still in controversy³. One of the suggested patterns is that extinction happens periodically, first raised by Fisher and his student Arthur of Princeton University in 1977 in a virtually ignored paper⁴. They postulated a 32-million-year periodicity in extinction basing on data culled from the fossil record of the past 250 million years. However, their study was not supported by a rigorous  statistical analysis and the database itself was limited^2,4,5, leaving their postulation dubious. They also guessed that cycles of convection within the Earth, though still little understood, drove the extinction process⁴.

The suggestion was reexamined seven years later. In 1984 Raup and Sepkoski of University of Chicago advanced a hypothesis of a 26-million-year periodicity in extinction (published in PNAS²) which arrived in the heat of the debates on whether mass extinction was caused by extraterrestrial impacts triggered by Alvarez, et al ⁶ in 1980. The study of Raup and Sepkoski was based on a pioneering statistical analysis of the record of 3,500 families of marine animals (vertebrate, invertebrate, and protozoan) and thus arrested the attention of scientists, and triggered new research in broad fields, particularly in astronomy and astrophysics^7-12. More importantly, they also triggered a heated debate that does not end now: periodicity exists in extinction?

Periodic extinction?

First of all, why the Raup and Sepkoski 1984 paper² is so controversial? In the paper, Raup and Sepkoski investigated the temporal distribution of the 12 major extinctions, defined as the peaks (local maximum) in extinction intensity – time diagram, over the past 250 million years statistically using various forms of time series analysis: Fourier analysis, standard autocorrelation analysis and nonparametric testing. The database came from Sepkoski’s compilation of the temporal ranges of about 3,500 families of marine animals, mainly based on Harland time scales. The 12 events showed statistically significant periodicity and so they concluded, “It seems inescapable that the post-late Permian extinction record contains a 26-million-year periodicity, assuming that the Harland time scale is a reasonable approximation of reality.”²  The paper left 4 open questions: 1. What if the definition of  “major extinction” changes? 2. The statistic method is reliable? 3. The Harland time scale is reasonable? 4. The database is reliable? What if the database is expanded to continental organisms and longer geological time? These unsolved questions led to many objections to their periodicity conclusion.^13,14.

Just two months later Hallam¹³ gave some reasons why open-mindedness on the problem of periodic extinction was necessary. First he questioned that the accuracy of Harland time, and then he regarded only 5 of the 12 major extinctions defined by Raup and Sepkoski were unquestionable. The other 7 were either dubious themselves or minor extinctions. Thus he concluded that the evidence given by Raup and Sepkoski hardly seemed warrant the conclusion of periodicity¹³.

Then in November of the same year Kitchell and Pena questioned the periodicity using deterministic and stochastic methods¹⁴. They showed that in the past 250 million years extinction displayed a pseudoperiodic behavior with a cycle length of 31 million years. And more, the periodicity weakens when the analysis was extended to the entire Phanerozoic. They used a quite different analyzing method from Raup and Sepkoski’s and first extended the analysis beyond 250 million years and thus the paper attracted much interest from other scientists.

The database Raup and Sepkoski used was also challenged. Patterson and Smith^39,40, after checking the echinoderm and fish family extinctions which made up about 20% of the data, found that only 25% of their sample was signal and the 75% noise component included pseudoextinctions of non-monophyletic groups. Sepkoski ⁴¹admitted that data from echinoderm and fish failed to exhibit periodicity. But he argued the data were only 25% of the entire marine extinction data and he did not treat taxonomic families as real evolutionary entities in the analyses of extinction patterns. Thus the periodicity conclusion did not fail.

Raup and Sepkoski continued extending their analysis down to the more detailed taxonomic level of genera, analyzing 11,000 of them^17,18,19. As Sepkoski²⁰ said in 1990, the 26-million-year cycle, evident as peaks in the extinction rate, appeared even more strongly than it did in the original family data. What was remarkable was that almost at the same time, a new extinction peak, recognized in the same year in the Middle Jurassic Period, fell at a cycle time predicted by the periodicity hypothesis⁵.

However, when Benton considered both marine and continental organisms, support for periodicity of mass extinctions was not found⁴². But Benton did not use vigorous statistical methods and thus the question was still left open.

Hoffman of the University of Warsaw seriously disputed the data culling by Raup and Sepkoski, the definition of mass extinction, dating of extinction events and statistical methodology¹⁵. As Hoffman argued, because Raup and Sepkoski used “peaks” as the definition of mass extinctions, it was necessary that the number of families extinguished should be greater than in the preceding and succeeding stages. This effect was to exclude the possibility that consecutive stages could be associated with mass extinction, which was bound to prejudice the analysis towards a periodic interpretation. If the probabilities of extinction in successive stages were entirely independent, simply looking for peaks in the record of extinction implied a one-in-four chance that any stage would be recognized as a time of mass extinction and, given the exclusion of the possibility that consecutive stages may be thus described, the analysis was certain to yield the conclusion that, on the average, extinction peaks occur every four stages. This, said Hoffman, was the origin of Raup and Sepkoski’s periodicity^15,16.

At the same time Maddox ³³ suggested, “Defining a mass extinction is a more urgent need.” Hoffman argued that some objective criterion was needed and he would prefer a criterion based on the rate or probability of extinction per unit time (say a million years) rather than one based on counting the number of family extinctions in a stage, which he said was biased towards periodicity¹⁵. Again in October 1985 when replying Lewin’s criticisms, he said, “it (mass extinction defined by Raup and Sepkoski) accepts all peaks of extinction intensity, and not only truly major events as mass extinctions. Why should we wish to accept this particular-counterintuitive-definition rather than any other?” ³⁴

Raup and Sepkoski argued¹⁷ that most of the extinction events defined in the way they did² had long been recognized as times of high biological turnover and had been used since the mid-19^th century to define the major units of geologic time.

Stigler and Wagner³⁶ and Lutz ³⁵ questioned the statistical method used by Raup and Sepkoski. Stigler and Wagner³⁶ held that regardless of whether or not the data were periodic in origin (even regardless of the actual period if they were in fact periodic), the nonparametric test used by Raup and Sepkoski were substantially biased toward their periodicity conclusion. This was because the test was sensitive to measurement error due to the “Signor-Lipps effect”, early recording of extinctions due to missing fossil specimens. Also because of the unequal spacing in time, models used by Raup and Sepkoski might be expected to produce statistically significant but artifactual periods. (But according to Benton et al³⁷, the past 540 million years of the fossil record provided uniformly good documentation of the life of the past if scaled to the stratigraphic level of the stage and the taxonomic level of the family.) On the other hand, Lutz³⁵ argued that if episodic models were allowed as alternatives to the Poisson model, then no geologic time series were sufficiently regular over a long enough time interval to be convincingly periodic. At the same time he admitted that it was also not possible to positively exclude periodicity based on statistics alone.

Raup and Sepkoski ¹⁸ rebut that Stigler and Wagner ignored the geology of the situation and ignored their treatment. The qualitative model used by Stigler and Wagner was inappropriately applied over the entire time series and the parameter value was extreme and thus unreasonable. Stigler and Wagner’s response ³⁸ was that they remained convinced that their conclusion was correct and stated their evidence again.

The question of periodicity was placed in a new light in 1987 by Shaw³¹. In the pioneering paper, he used non-linear dynamics methods, which were different from conventional statistical analysis, to detect new symmetrical patterns and order in several earth processes. With respect to the periodicity debate, he thought it impossible to demonstrate valid periodicity patterns, because the data sets are too limited for both conventional and nonlinear analyses. Things would be better if more statisticians became versed in nonlinear-dynamics methods, but the “bridge between the two approaches to data analysis is just beginning to be built”⁵.

Debate still goes on. But it is obvious that in 1990s the debate cooled down. The papers involved in the debate from 1984 to 1989 are twice as those in the 10 years of 1990s, as shown by SCI. Further, a majority of the papers in 1990s did not take periodicity problem as their main subjects. This might due to the futility of debate if data is limited.

The mechanisms of periodic extinctions

Mechanisms of periodic extinctions were raised before the debate was settled down. It is interesting that even before the objection of periodic extinctions arose, several mechanisms of period extinctions had been put forward. This is partly because Raup and Sepkoski’s suggestion in their original paper². They suggested that the causes of periodicity might be related to extraterrestrial forces. Only two months later several scientists suggested possible causes^7-10. Alvarez and Muller indirectly supported the extraterrestrial causes¹¹. They subjected the records of large impact craters to time-series analysis and concluded that most occurred on a 28.4-million-year cycle. However, because only 13 craters met their rigorous criteria, their conclusion must be viewed with caution¹³. Jetsu et al ^43-45 also suspected the existence of periodicity in impact.

The causes suggested until now can be summarized as¹⁹:

(1) Orbital dynamics of an unobserved solar companion^9,10.

(2) Vertical oscillation of the solar system about the plane of the Galaxy^7,8.

(3) Transit of the solar system through the spiral arms of the Galaxy.

(4) Precession of an undetected tenth planet ²⁷.

(5) Biogeochemical cycles, climate and sea-level changes⁵.

(1) Davis et al.¹⁰ and Whitmire and Jackson⁹ independently put forward a model that postulated the existence of an unseen companion star to the Sun, occupying a highly eccentric orbit. Beginning with the assumption of an orbital periodicity of 26 to 28 million years, they calculated a major axis of about 3 light year for the companion’s orbit and a perihelion distance of 0.3-0.5 light year from the Sun. The estimated mass of the companion was 10^-3-10^-1 solar mass. When near the perihelion it is brought into the dense inner region of a comet cloud and by perturbing the cometary orbits initiates and intense comet shower, leading to a series of terrestrial impacts lasting up to a million years¹³.

This hypothesis was soon be seriously challenged by the stability analysis of the hypothesized companion.^23-26. The analysis indicated that the orbital periodicity should be somewhat irregular, varing over 10-20%, and that the expected half life for the orbital configuration should be on the order of 1000 million years. Thus the companion was unstable. However, Perlmutter et al ³⁰ argued that only the companion hypothesis was consistent with all the known data. Until 1990, they had rejected about 20% of the 2,691 stars in their list of candidates in the Northern Hemisphere and kept searching. However, because until now the companion has not been observed despite considerable searching by an automated telescope, the hypothesis probably failes¹.

(2) Schwartz and James⁸ and Rampino and Stothers⁷ proposed galactic models¹³. The former authors speculate that long-term changes in cosmic radiation flux, soft X-rays and hard UV radiation, due to the Sun’s oscillation about the galactic plane have provoked sufficient alterations of the biosphere (disturbing the ionization balance of the upper atmosphere) to cause mass extinctions. Rampino and Stothers’ reanalysis of Raup and Sepkoski’s data led them to suggest a extinction cyclicity of about 30 million years, which correlated strongly with a galactic cycle. They argued that tidal forces from intermediate-sized molecular clouds of 10³-10⁴ solar masses, concentrated near the galactic plane, might perturb the Oort Cloud and inner cometary reservoir as the solar system approached the plane. Such perturbations could produce comet showers of up to several million years duration, during which one large or several comets might impact the Earth⁷.

The problem with these hypotheses is the disparity between the 33-million-year half-period for solar oscillation and the 26-million-year period for extinction events¹⁹. Rampino and Stothers⁷ argued that the data of Raup and sepkoski² fitted a 30-million-year period and, molecular clouds were randomly distributed so there should be a fair amount of stochasticity in extinction events so that the extinction period estimated from a small number of events might not correspond precisely to the oscillatory half-period. However, as argued by Sepkoski and Raup¹⁹, analysis based on new data showed that a 30-million-year period was untenable as an estimate of the extinction periodicity, leaving the disparity unresolved²². Also, as stated by Bahcall, the apparent periodicity in the mass extinction and cratering records could not be caused by a population of objects that contributes a major fraction of the total mass density at the solar vicinity²⁹.

(3) As the solar system orbits the Milky Way Galaxy, it passes through spiral arms, or density waves, approximately every 50 million years¹⁹. Interstellar “planetismals” were captured by the sun during these transits and this capture could increase “asteroid” bombardment of the Earth during ensuing 20-30 million years intervals, as argued by Napier and Clube²¹. The major problem with this hypothesis, as argued by Sepkoski and Raup, was the periodicity in extinction it predicted of about twice the observed length, and thus it could be rejected as a plausible ultimate cause of periodic extinction¹⁹.

(4) An undetected tenth planet, often called “planet X”, was put forward to explain the periodicity of extinction in 1985 by Whitmire and Matese²⁷. They argued that such a planet might be able to produce periodic comet showers if its orbit were highly inclined and if the inner edge of the comet cloud extended as a thin disk almost to the orbit of Neptune. Under such conditions, the orbit of Planet X, would precess through the planetary plane. If the precession period were approximately 56 million years, the planet, with an estimated one to five Earth masses, would sweep comets out of the inner disk as it passed through the plane every half period. This hypothesis was largely ad hoc, said by Sepkoski and Raup¹⁹, since the precession period was determined entirely from periodicities in extinction and cratering that were being explained. Also, whether the planet would have sufficient mass to scatter a large number of comets was questioned by Kerr²⁸.

This hypothesis was further questioned by Collander-Brown and Williams⁴⁶. They found that the tenth planet had to be placed on an orbit at such a large heliocentric distance that no evidence for the existence, or non-existence, could be found.

(5) Hallam argued, in the same article as above¹³, that the most obvious relationship of mass extinctions was with sea-level changes, which had exhibited a cyclicity on more than one time scale throughout the Phanerozoic. Mass extinctions of marine groups took place as a result of the drastic reduction in area and quality of habitat when extensive epicontinental seas regressed because of a fall in the sea level. But it was noteworthy that the Cenomanian, Pliensbachian and Devonian events were not preceeded by significant falls in sea level, as Hallam said in the same article, so many problems and uncertainties remained.

Later the searching for mechanisms of extinction was turned to extinction itself.  Sneppen et al ³² and Sole et al³³ used the nonlinear methods to study the process evolution and extinction. Sneppen concluded that evolution was a self-organized critical phenomenon and thus large bursts of species and mass extinctions might be a simple consequence of ecosystems dynamics and required no external cause. Sole’s conclusion was that extinction process was self-similar fluctuation and a nonlinear response of the biosphere to perturbations provides the main mechanism for the distribution of extinction events. But as early as in 1990, Sepkoski disputed internal forces as the cause of extinction because “internal dynamics was not consistent with data”²⁰.

Until now none of the above mechanisms seems to well explain the periodicity of extinction. Indeed the existence of periodicity in extinction is still in debate. Further data collection and test methods are necessary to solve the debate.