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late Tom Schopf, told Sepkoski that he was up for tenure consideration that year. Such an announcement, like the discovery that one is to be hanged in a fortnight, "concentrates [the] mind wonderfully."3 In a "panic to publish quickly, the young professor decided that his best bet was to try to get out an article based on his compendium. Sepkoski worked frantically for months, only to have Schopf return to say that he had been mistaken—Sepkoski's tenure would be decided the following year. But by this time Sepkoski had gone too far to turn back.

Raup had the idea that instead of merely perusing the compendium (a task sufficiently boring as to cause even a quantitatively minded paleontologist to nod off) it might be examined with the aid of a computer to see whether any interesting patterns emerged. Raup and Sepkoski viewed an assortment of graphical computer plots, even standing across the room to see whether a pattern recognizable only as a "gestalt" would emerge. Sepkoski suggested that it might be interesting to compute how the rate of extinction had varied through time. A few days later, Raup brought the new plot, shown in Figure 25, into Sepkoski's office. "Do you see it?" he asked, "They're regularly spaced in time."4

Raup had culled Sepkoski's data in the following ways: He had examined only the most recent 250 million years, when geologic ages are more precisely known; he had removed families whose ranges or identity were poorly known; and, since we have no way of knowing how long they may live, he deleted families that have not yet become extinct. He divided the 250 million years up into the 39 stratigraphic stages that geologists have recognized (geologists divide time into eons, eras, and periods; rock units into systems, series, and stages—the

FIGURE 2 5 Raup and Sepkoski's 1984 plot of extinction periodicity.5 The best-fit cycle, at 26 million years, is shown by vertical lines.

Geologic time (106 yr)

FIGURE 2 5 Raup and Sepkoski's 1984 plot of extinction periodicity.5 The best-fit cycle, at 26 million years, is shown by vertical lines.

Geologic time (106 yr)

Maastrichtian, for example, is a stage in the Cretaceous system), and then plotted the percentage of extinction within each stage. Each data point came from calculating the number of families that became extinct within a stage as a percent of all the families that lived during that stage. (Removing the families that are still alive makes the denominator of this fraction smaller and the resulting fraction and peak larger. If half the families in a stage are still alive today, the denominator is half as large and the peak of percentage is twice as high as it would have been had they all been extinct. Although removing extant families affects the height of the peaks, it does not change their spacing.)

The chart clearly shows that extinction is not continuous (which geologists have known for a long time), and confirms the location of the three members of the Big Five that we know fall within the last 250 million years of earth history: the Permian-Triassic, the Triassic-Jurassic, and the K-T. Finding the three members of the Big Five exactly where they were expected to be told Raup and Sepkoski that nothing was seriously wrong with their methodology. The truly startling point, however, and the one that sent Raup rushing into Sepkoski's office, is that the peaks show up at regular intervals—every 26 million years. What could it mean?

Before answering that kind of question, when faced with such an unexpected and unprecedented pattern emerging from a complex set of data, a scientist has to make certain that the result is not merely an accident or an artifact of the way the chart was constructed. Raup spent the next several months testing these possibilities, trying to "kill the periodicity," as he put it. But no matter what he tried, the periodicity persisted, and at a confidence level of better than 99.5 percent.

Like many scientific suggestions, the idea of periodic extinction was not new. It had been proposed in 1977 by Alfred Fischer, then at Princeton, and his graduate student Michael Arthur.6 They assembled data from a variety of such geologic indicators as sealevel, temperature, number of species through time, and isotopic ratios. Their analysis revealed a cyclical pattern in species diversity with a period of 32 million years. Fischer and Arthur did not have enough data for rigorous statistical testing, and partly for that reason their suggestion was not followed up. Since no one knew why the earth should have behaved cyclically, the observation itself was discounted.

Raup and Sepkoski, having submitted their huge volume of data to careful statistical analysis and been unable to falsify their conclusion, were ready to go public. They did so with trepidation. Raup was a distinguished, if somewhat iconoclastic, paleontologist; Sepkoski's career was barely underway. Neither wanted to become a laughingstock, or perhaps worse, to be ignored. They stuck their toes in receptive water when Sepkoski presented their preliminary findings at a 1983 symposium in Flagstaff, Arizona, home of the Astrogeology Branch of the U.S. Geological Survey (founded by Shoemaker). This friendly audience, assembled to explore the implications of the Alvarez theory, was delighted, and Sepkoski was emboldened to suggest that the source of the periodicity might be extraterrestrial. As Raup tells it, this proposal arose merely because it is much easier to find cycles in the motions of the planets, stars, and galaxies, which wheel and circle each other periodically, than to find them in apparently random earthly processes. The astronomers and astrophysicists in attendance at the meeting, intrigued by the Raup and Sepkoski analysis, set to work with a vengeance to find the cause of the 26-million-year cycle.

With no reason to delay publishing, Raup and Sepkoski chose the Proceedings of the National Academy of Sciences (PNAS), the journal of that elite group of elected, eminent scientists, of which Luis Alvarez and Raup were members. The PNAS publishes only papers written by members, which it does not find necessary to subject to peer review. Their paper appeared in February 1984.7

The reaction came almost too quickly to be true. In the April 19, 1984, issue of Nature no fewer than five articles appeared based on the PNAS paper.8 Now, although Nature is one of the speedier journals to publish, the submission dates on the five papers showed that they were submitted even before the Raup and Sepkoski paper appeared] The explanation is that Raup and Sepkoski, like most scientists, sent preprints of their submitted paper to colleagues, giving them advance warning.

One of the five papers, by Michael Rampino and Richard Stothers, confirmed the periodicity of the fossil record. Using a different statistical technique, they reanalyzed the Raup-Sepkoski data set and came up with a period of 30 ± 1 million years, which they attributed to the passage of our solar system through the plane of the Galaxy. As everyone knows, our solar system is part of the Milky Way, a vast, rotating complex of stars shaped like a planar disk— broad and spiraling when viewed from "above" but flat when seen edge on. As the Galaxy rotates, the Sun and planets move slowly up and down across the plane of the disk, the round trip taking just over 60 million years. The solar system thus crosses the galactic plane twice in each such circuit—once every 30 million years or so, not too far off the period that Raup and Sepkoski, and Rampino and

Stothers, had found. Although no one knows exactly what effect the crossing of the galactic plane has, it could be that astronomical or climatic changes are somehow induced, which, in turn, drive the periodicity. However, the Sun is now close to the galactic plane, so that there should have been a recent mass extinction, yet the latest one that Raup and Sepkoski recognized occurred in the middle Miocene, about 10 million to 11 million years ago.

The second explanation, proposed in two of the papers in Nature, is that the Sun has a small companion star. Because most stars that we can observe are binary, the existence of a companion would not be a surprise. The Sun's fellow traveler might be on a highly eccentric orbit that takes it far out in space but periodically brings it back nearer the outer boundaries of the solar system, where lies the Oort cloud, a vast conglomeration of comets. Although no one has seen this cloud, there is good reason for believing that it exists and that it is the source of Halley's Comet and the other "long-period" comets that approach the Sun from all over the solar system. As the putative companion star passes near the Oort cloud, its gravity could pull comets out of their present orbits and launch a few on a collision course with Earth, where they would strike, producing craters and mass extinctions. The astronomers who wrote in Nature agreed that the companion star must be quite small and now be located about two light years from the Sun.

But why, since the buddy star would be closer to the earth by half than any other, have astronomers never seen it? It turns out that it could easily have been missed—only a small number of stars have ever been observed and catalogued—or it might have been mistaken for a brighter star much farther away. But would its orbit have remained stable over the 250 million years of geologic history that Raup and Sepkoski examined, or would it not have been degraded by the gravity of nearby stars? One calculation showed that it could have remained constant for as much as a billion years, more than enough time.

The authors of one of the papers suggested that the companion star be named Nemesis, after the Greek goddess who punished earthly beings for attempting to usurp the privileges of the Gods.9 In fact, they proposed other names, but the editors of Nature chose Nemesis and it stuck. (Muller and his co-authors noted that if the companion were never found, the paper claiming that it existed might turn out to be their nemesis.) Muller launched a program to search the heavens for Nemesis, using an automated telescope system that examines about 10 stars per night. So far, over 3,000 candidates have been studied, but none has yet turned out to have the characteristics of Nemesis, leaving Muller with an absence of evidence and a huge backlog of stars to go.

Stephen Jay Gould did not care for the name Nemesis and took Muller and his colleagues to task in an open letter in Natural History: "Nemesis is the personification of righteous anger. She attacks the vain or the powerful, and she works for definite cause. . . . She represents everything that our new view of mass extinction is struggling to replace—predictable, deterministic causes afflicting those who deserve it."10 He proposed the star be named Siva, after the Hindu god of destruction, who, "Unlike Nemesis, . . . does not attack specific targets for cause or for punishment. Instead, his placid face records the absolute tranquillity and serenity of a neutral process, directed toward no one."11 Siva's modus operandi comported better with the view that Gould, Raup, and others were developing in response to the Alvarez theory: Survival or extinction are essentially matters of chance, of bad luck rather than bad genes. A debate among serious scientists over which mythological name to give to a star that has never been seen and whose existence is barely even an educated guess, is one more curiosity stemming from the Alvarez theory. But perhaps it is salutary: Seldom before have paleontologists and astronomers had anything even to disagree about.

A third theory, proposed by Daniel Whitmire and Albert Jackson of the University of Southwest Louisiana, appeared soon after.12 They suggested that the periodicity could be due to an undiscovered tenth planet, Planet X, located beyond the orbit of Pluto. Regular changes in the orbit of Planet X, about every 28 million years, could have disturbed a cloud of comets beyond the orbit of Jupiter (not the Oort cloud, which is much further out). The idea that there might be a yet undetected planet was not completely ad hoc; it had come up before as a way to explain the tiny discrepancies that remain between the calculated and observed orbits of certain planets. On the other hand, calculations show that such a planet, unless it were well outside the plane of orbit of the others, would probably be bright enough to have been detected.

Astronomers may have taken the Raup-Sepkoski periodicity to heart, but others did not. Soon after their initial paper appeared, contrary views began to arrive. This was not surprising, for as scientists know better than most, if the only way to prove your point is by using statistics, you are in trouble—especially if you are not a statistician. To live by statistics is to run the risk of dying by statistics. As Disraeli said, "There are three kinds of lies: lies, damn lies, and statistics."

Antoni Hoffman, a paleontologist at Columbia University, wrote the contrary article13 that drew the most attention, even the blessing of John Maddox, the editor of Nature. Hoffman proffered three objections. First, he criticized Raup and Sepkoski for removing from their analysis species that were still living and those whose range is poorly known. This criticism is questionable, however, because although it is easy to imagine how the removal of some families could degrade an existing cyclic pattern, it is hard to see how the removal could create a strong periodicity where none existed. Surely it would merely produce more "noise." Second, Hoffman noted that because the periodicity is degraded, or disappears altogether, when a different time scale than the one used by Raup and Sepkoski is employed, their conclusion must be wrong. But this criticism is tantamount to claiming that, using an incorrect time scale, one can generate a false pattern that is periodic at a high confidence level, which seems contrary to logic. It is more likely that the degrading of the periodicity when a different scale is used means that (1) the fossil record is periodic, and (2) the time scale used by Raup and Sepkoski is closer to the true scale.

Hoffman's third argument was in a different class and purported to be the knockout punch to the proposal of periodic extinctions, and by extension, to the general notion of extraterrestrial impacts. Raup and Sepkoski had to distinguish mass extinction from the normal background extinction rate. They defined a mass extinction as having occurred whenever their data showed a rise in extinction rate from one geologic stage to the next, followed by a decline in rate in the third stage. Thus a mass extinction has occurred only when the rate of extinction is greater in a given geologic stage than in the stages above and below it. Hoffman pointed out that there is a 25 percent probability of this happening by chance. To understand his argument, label the three successive stages 1, 2, and 3. At random, stage 2 has a 50 percent probability of having a higher extinction rate than stage 1 and a 50 percent probability of having a lower rate. Stage 3 likewise has a 50 percent probability of having a higher rate than stage 2 and a 50 percent probability of having a lower one. Since probabilities multiply, 0.50 x 0.50 = 0.25 and the chance of stage 2 having a higher rate than either stages 1 or 3 is one in four, or 25 percent. Hoffman then went on to his clincher: 39 stages in 250 million years works out to an average stage length of 6.4 million years. But four times 6.4, rounded up a little, equals 26 million years—the periodicity found by Raup and Sepkoski! In other words, in a random set of extinction events, the 26-million-year frequency would show up 25 percent of the time, on the average.

This seemingly irresistible argument tempted John Maddox further out on a limb than journal editors ought to go. Not content to let the Hoffman paper speak for itself, he took the unusual step of writing an editorial comment: "The analysis is certain to yield the conclusion that, on the average, extinction peaks occur every four stages. . . . Hoffman has undermined the assumption on which all the excitement was based, the belief that there is a 26 million year periodicity to be explained." Maddox continued, "Human nature being what it is, it seems unlikely that the enthusiasts for catastro-phism will now abandon their quest."14

The trouble with Hoffman's third argument (and Maddox's endorsement) is that they miss the point, as Stephen Jay Gould has pointed out (and from whose article the rest of the discussion in this section is drawn15). Hoffman wrote: "There is 0.25 probability that any particular stage represents a peak of extinction. Peaks are, then, expected to occur approximately every fourth stage."16 Read that quotation carefully and think about what Raup and Sepkoski actually found. Hoffman is claiming that chance will produce peaks on the average every 26 million years, approximately every fourth stage. This is like saying that an honest coin, if tossed often enough, will produce heads on the average 50 percent of the time. But Raup and Sepkoski did not claim to have found a cycle with an average of 26 million years; they claimed to have found a peak every 26 million years, like a coin that, although it shows heads half the time, gives this precise sequence: HTHTHTHTHTHTHTHTHTHT. . . . Thus Hoffman's point is irrelevant to the arguments of Raup and Sepkoski, who in any case had thoroughly tested the possibility that their pattern was due to chance and rejected it at a very high confidence level. Hoffman also manipulated Sepkoski's family data using different time scales and extinction metrics, and came up with 20 different ways of gauging periodicity, on the basis of which he claimed to have falsified Raup and Sepkoski's theory. When Sepkoski subsequently combined all 20 of Hoffman's metrics, however, the 26-million-year periodicity reappeared, more robust than ever! Like the newspaper account of the death of a very-much-alive Mark Twain, the Hoffman-Maddox pronouncement of the demise of extinction periodicity was an exaggeration.

Is C RATERING P ERIODIC?

Though periodicity in the fossil record is still being criticized, Raup and Sepkoski have responded well to their critics, and as Sepkoski has added more data to his compendium, evidence for periodicity has grown stronger.1' At the very least we can say that extinction periodicity has not been falsified. We have also seen that in theory, impact could have caused all extinction. Both ideas are far from corroborated but at least deserve the status of working hypotheses. If both are correct, impact cratering ought also to be periodic, at least in part, and on the same time cycle as the mass extinctions. In the April 19, 1984, issue of Nature, Walter Alvarez and astronomer Richard Muller reported that they had found a periodicity of 28 million years for terrestrial craters,18 the same within its error as the 26-million-year cycle that Raup and Sepkoski had reported for mass extinctions. Alvarez and Muller used Grieve's 1982 compilation of terrestrial craters, selecting only those that are older than 5 million years and whose ages are known to better than ± 20 million years. Unfortunately, this tight filter produced only 13 imperfectly dated craters, too small a sample to allow their statistical conclusions to be convincing.

Reporting in the same issue of Nature, Rampino and Stothers applied a different statistical technique to Grieve's database and found a periodicity of 31 million years for impact craters.19 Stothers later culled, from Grieve's list, a set of seven Cenozoic craters with age errors of less than 1 million years.20 He compared each of the resulting ages with the ages of seven geologic stage boundaries. These data are plotted in Figure 26. (Stothers used the Manson, Iowa, crater

Age of geologic stage boundary

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