Sampling Effects

At the first Snowbird conference in 1981, paleontologists Phil Signor and Jere Lipps presented what has proven to be one of the most important papers in modern paleontology.11 Like some others that have had such a result, their paper was short and simple. The authors showed that sampling can have two separate but related effects on paleontological evidence, both of which make it harder to draw firm conclusions.

The first is illustrated by Figure 18, adapted from their paper, which shows how the diversity of ammonites, the beautifully coiled and chambered marine fossils that grace natural history museums, waxed and waned during the Mesozoic era, which includes the Tri-assic, Jurassic, and Cretaceous periods; and how the extent of sedimentary rocks deposited during the Mesozoic also varied (the Mesozoic lasted from 250 million to 65 million years ago). Though the match is not perfect, the chart shows that the more rock exposed, the more diverse the ammonites appear to be and the less rock exposed, the less diverse. For example, ammonite diversity appears to have declined from the middle to the end of the Cretaceous. But so does the amount of rock deposited. Thus the apparent decline in diversity can be explained entirely by the decreasing amount of rock available to be sampled. Ammonites might have been thriving when, by coincidence, the amount of rock being deposited and preserving

Diversity Sediment area

Diversity Sediment area

Triassic Jurassic Cretaceous

figure 18 The diversity of ammonite genera and the area of sedimentary rock across the Mesozoic era. Note that the two roughly correspond. [After Signor and Lipps. 2]

their remains was shrinking, causing us to conclude incorrectly that their true diversity had fallen. Of course, a direct link between the two might have existed: Whatever caused fewer deposits might also have caused ammonite diversity to decline, but that we cannot know. Signor and Lipps concluded that "diversity data cannot be taken at face value": The availability of rocks to be sampled can control the apparent abundance of fossils.13

This first effect has relevance to the diversity of dinosaurs. Several scientists have noted that there are fewer dinosaur species found in the last stage of the Cretaceous, called the Maastrichtian, than in the immediately older stage. (Each section of the geologic column is named either for a place where it was first recognized, or where it is thought to be particularly well exposed. In this case, the "type locality" is the Dutch town of Maastricht near the Belgian/German border.) This decline in species collected suggests that the dinosaurs were already on the wane by the middle and late Cretaceous, leaving nothing for meteorite impact but a possible coup de grace. But dinosaur specialist Dale Russell pointed out that since the Maastrichtian lasted for only about half as long as the Campanian, we would naturally expect it to produce only about half as many species.14 This conclusion has been disputed, but the ammonite and dinosaur examples remind us that apparent changes in diversity may simply be artifacts of differing sample sizes. To the extent they are, we underestimate the true range of species and conclude they went extinct before they actually did.

In order to understand the second of the two effects pointed out by Signor and Lipps, imagine that you have to approximate the Canada-United States boundary using one of two methods: (1) by locating the houses of the northernmost residing United States citizens, or (2) by locating the houses of the northernmost residing members of Congress.15 Obviously, using the abodes of citizens would give the more accurate result. Using the homes of the more rare congressional representatives would cause you to place the boundary further south than it really is. In the same way, the more rare a fossil species, the less likely we are to find its true geologic level of extinction. This gives rise to the "Signor-Lipps effect," a concept with which every paleontologist studying changes in diversity over time henceforth must wrestle.

Figure 19 represents a hypothetical cross section down through a formation that contains three fossil species, each marked by a different geometric symbol. The diagram assumes that each species became extinct at the same time, represented by the top of the draw-

figure i 9 The Signor-Lipps effect. [After Michael Williams."]

o • • * ♦ o ing. Suppose that we sample every portion of this imaginary section of rock, missing nothing. What do we conclude? That the rarest fossil, shown by the large white circles, went extinct first, below its actual extinction level as represented by the top of the drawing. Because this species is rare, our chances of finding it anywhere, much less at its true level of extinction, are small. The next rarest species, shown by the small filled circles, appears to have become extinct a little higher up. The most common, marked by the small diamonds, is found right up to the "true" extinction boundary. Thus the "diversity" of species in this formation over time—the number preserved at each level in the rock—appears to have steadily decreased upward toward the extinction boundary, where all three actually disappeared. We conclude that extinction was gradual—no sudden disappearances here—but we are dead wrong: All three species lived right up to the boundary.

Now, factor in our inability to ever collect more than a fraction of the fossils present in a rock formation, by imagining that our sampling catches '0 percent of each species present. Mentally strike out, at random, nine of ten of the symbols representing the three fossil types and see what conclusion you would draw. You would miss all specimens of the rarest species (fewer than nine are present to start with) and conclude that it had become extinct even before this geologic section formed. The apparent level of disappearance of the other two species would move down in the section, causing you to place each of their extinctions at a level even further below their actual occurrence.

Thus the rarer a species and the less perfect the sampling, the earlier and more gradual its extinction appears. We see, not reality, but the false, gradual extinction of the Signor-Lipps effect. If each of the three symbols stands for a dinosaur species and the time period represented is the late Cretaceous, we would conclude that dinosaur diversity gradually declined and therefore that they were already doomed—no meteorite impact is required. But we would be wrong, victims of the Signor-Lipps effect.

This has been a thought experiment. What about a real one? A clever geologist named Keith Meldahl went, not back in time, but to a modern tidal flat in Mexico, where the muds are full of shelled marine species." He imagined that an extinction suddenly occurred the day he visited the tidal flat, and that it was then preserved and sampled by some paleontologist far in the future. Meldahl drilled eight cores into the muds to a depth of about 70 cm and studied the extracted sediment centimeter by centimeter, making a careful record of each species and the highest point at which it was found. (Remember that all the species are alive today.) He located 45 different species in all; their positions in the cores are shown in Figure 20.

Even though this imaginary "extinction" was perfectly abrupt— far more so than any real extinction including that produced by impact—Meldahl actually observed the false, gradual pattern predicted by the Signor-Lipps effect. Of the 45 species that were present at the tidal flat, 35 appeared to go extinct below the surface, and this happened even though the cores were crammed full of "fossils-in-the-making," averaging almost 40 percent shell material by weight. In other words, the Signor-Lipps effect distorted the record even for relatively common species. Had the effect been forgotten with time, the paleontologist of the future, unaware, would naturally conclude that three out of four species had gone extinct gradually.

Sampling problems can never be entirely eliminated, but they lessen as more samples are collected, which is exactly what paleontologists have been doing since the Signor-Lipps effect was described. But no matter how exhaustive and exhausting the collecting, the inexorable mathematics of sampling means that some effect will always remain. "Gradual extinction patterns prior to a mass extinc-

Gradual Extinction
FIGURE 20 The Signor-Lipps effect in operation at a modern tidal flat. Depending on their rarity, species appear to become extinct at different depths in the core, equivalent to different times in the past. Yet each species is alive today. [After Meldahl.18]

tion do not necessarily eliminate catastrophic extinction hypotheses," Signor and Lipps concluded at Snowbird I. "The recorded ranges of fossils . . . may be inadequate to test either gradual or catastrophic hypotheses."

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