## The Frequency of Mass Extinctions

How often do mass extinctions take place? Perhaps the best way to address this question is to use the same methods that meteorologists and hydrologists use in assessing the risk from weather and floods. Many natural phenomena—such as floods, earthquakes, and droughts—are distributed through time in a similar way. Small events are common, large ones rare. The best way to see how frequent the really rare events are, is to assemble all the available data and arrange them by return time or waiting time. For instance, we might ask how often in a century, or in a thousand years, a flood of some given intensity occurs? We can then define "10-year" floods (events of such magnitude that we can expect one every 10 years on average) and compare them to much larger, 100-year events and the even more catastrophic 1000-year events. This does not mean that we cannot get two 100-year events in successive years, only that the probability of two such events taking place in successive years is vanishingly small. Hydrolo-gists use a technique called extreme-value statistics to extrapolate waiting times beyond the length of historical records. These estimates are, of course, imperfect. But they allow scientists to make estimates about, say, 1000-year events when only 100 years of historical records are available.

Paleontologist David Raup has adapted this same technique to investigating questions of mass extinction. Raup's questions are very similar to those posed by meteorologists interested in estimating how often giant floods may take place. Raup notes that we have a good record for the past 600 million years of Earth history, so we can define the 10-million-year and 30-million-year events with confidence. Using these statistics, Raup calculated what he called a kill curve.

The kill curve is a graph showing the expected waiting times for mass extinctions of varying magnitude. It depicts the average "species kill"—the percentage of all species on Earth at a given time suddenly going extinct as a result of some mass extinction event—for a series of waiting times. Raup's curve is not entirely theoretical; he derived it by first amassing the extinction records of more than 20,000 genera of organisms on the basis of their actual geological longevities. Raup used the Zoological Record, a compendium of the life now on Earth, found the first occurrence and last occurrence of all of these genera of organisms, and then tabulated the results in a colossal database. His data are thus derived from our best information about the actual geological ranges of the organisms he surveyed.

The kill curve gives us a sense of how many species go extinct over a given period of time. According to this curve, there is negligible extinction in the case of natural phenomena that occur about every 100,000 years. The million-year event is more consequential, with perhaps 5% to 10% of all species on Earth going extinct. That figure rises to 30% of all species at the 10-million-year event and to nearly 70% of all species at the 100-million-year event. These are frightening numbers. If nearly three-quarters of all species go extinct in a short-term planetary catastrophe of some sort every 100 million years, it suggests that we are living on quite an unsafe planet.

Raup discusses that last concern in the 1990 book Extinction: Bad Genes or Bad Luck. How often might we expect the event that kills off the entire biosphere of the planet—the complete sterilization of Earth of all its huge diversity of living things? "I once tried extreme-value statistics on extinction data to ask, 'How often should we expect extinction of all species on Earth?.' I don't have much confidence in the results, but they are at least comforting: Extinctions sufficient to exterminate all life should have an average spacing of well over 2 billion years."

Yet this should not be a comforting figure. Indeed, it goes to the heart of the Rare Earth Hypothesis. If we might expect a planetary catastrophe to exterminate all life on this planet every 2 billion years, and if life has already lasted 4 billion years, we are truly pressing our luck! And luck may be just what animals need to evolve for a long time when the grim reaper of planetary extermination is put off only through blind chance.