Paleobiology, 34(4), 2008, pp. 434–455 Adjusting global extinction rates to account for taxonomic susceptibility Steve C. Wang and Andrew M. Bush Abstract.—Studies of extinction in the fossil record commonly involve comparisons of taxonomic extinction rates, often expressed as the percentage of taxa (e.g., families or genera) going extinct in a time interval. Such extinction rates may be influenced by factors that do not reflect the intrinsic severity of an extinction trigger. Two identical triggering events (e.g., bolide impacts, sea level changes, volcanic eruptions) could lead to different taxonomic extinction rates depending on fac- tors specific to the time interval in which they occur, such as the susceptibility of the fauna or flora to extinction, the stability of food webs, the positions of the continents, and so on. Thus, it is pos- sible for an extinction event with a higher taxonomic extinction rate to be caused by an intrinsically less severe trigger, compared to an event with a lower taxonomic extinction rate. Here, we isolate the effects of taxonomic susceptibility on extinction rates. Specifically, we quan- tify the extent to which the taxonomic extinction rate in a substage is elevated or depressed by the vulnerability to extinction of classes extant in that substage. Using a logistic regression model, we estimate that the taxonomic susceptibility of marine fauna to extinction has generally declined through the Phanerozoic, and we adjust the observed extinction rate in each substage to estimate the intrinsic extinction severity more accurately. We find that mass extinctions do not generally occur during intervals of unusually high susceptibility, although susceptibility sometimes increas- es in post-extinction recovery intervals. Furthermore, the susceptibility of specific animal classes to extinction is generally similar in times of background and mass extinction, providing no evi- dence for differing regimes of extinction selectivity. Finally, we find an inverse correlation between extinction rate within substages and the evenness of diversity of major taxonomic groups, but fur- ther analyses indicate that low evenness itself does not cause high rates of extinction. Steve C. Wang. Department of Mathematics and Statistics, Swarthmore College, Swarthmore, Pennsylvania 19081. E-mail: [email protected] Andrew M. Bush. Department of Ecology and Evolutionary Biology and Center for Integrative Geosciences, University of Connecticut, 75 North Eagleville Rd, Unit 3043, Storrs, Connecticut 06269. E-mail: [email protected] Accepted: 2 June 2008 Introduction identity of taxa going extinct in a geologic time interval determine the consequences of Measuring extinction intensity by the per- an extinction event for the history of life, but centage of taxa that go extinct is like measur- these rates are a measure of the intensity of ing the strength of an earthquake by the effect, which may not directly reflect the in- amount of damage inflicted, either in lives lost tensity of cause. Given the same environmen- or property destroyed. In actuality, the dam- tal conditions or extinction trigger, two faunas age caused by an earthquake reflects two fac- may have different extinction rates, just as two tors: the strength of the earthquake itself and locations may suffer different amounts of the susceptibility of the local population and death and damage from an earthquake of the infrastructure. The former (intensity of cause) same intensity. Here, we attempt to infer the can be measured on the familiar Richter scale, intensity of cause of extinctions in the marine but the latter (intensity of effect) is affected by fossil record, at least in a partial fashion. Spe- factors like population density and the resis- cifically, we focus on the potential of faunas of tance of buildings to damage. From the stand- different taxonomic composition to suffer dif- point of an earthquake’s effects on society, the ferent extinction rates given causal triggers of amount of damage is the more important var- similar physical intensity. Our goal is to an- iable, but for understanding the causes of an swer the following questions: (1) Does the re- earthquake, its physical intensity must be lationship between the intensity of cause and known as well. Likewise, the proportion and effect change in important ways through the ᭧ 2008 The Paleontological Society. All rights reserved. 0094-8373/08/3404-0002/$1.00 TAXONOMIC SUSCEPTIBILITY AND EXTINCTION 435 Phanerozoic, or among mass extinctions, re- jects, including gender bias in graduate ad- coveries, and background intervals? (2) Are missions (Bickel et al. 1975), airline on-time there other ways, at a very broad scale, in rates (Barnett 1994), and racial bias in capital which the changing taxonomic composition of punishment (Gross and Mauro 1984). A clas- the marine fauna affected extinction rates? sic example of Simpson’s paradox occurred in Other paleontologists have also examined a study on heart disease and a follow-up the relationship between extinction rates and study conducted 20 years later (Appleton et al. the changing composition of the marine biota, 1996). The authors found, surprisingly, that ascribing the Phanerozoic decline in extinc- women who smoked had a lower death rate af- tion rates to a shift in dominance from taxa ter 20 years than women who had never with high rates to those with low rates (Stan- smoked (24% mortality rate versus 31%, re- ley 1979, 2007; Sepkoski 1984, 1991; Van Valen spectively). Because this finding contradicted 1985, 1987; Gilinsky 1994). Our goal is not to a priori medical knowledge, the authors in- replicate these efforts, but rather to analyti- vestigated further, dividing the women into cally remove the effects of changing taxonom- subgroups according to age. A different pic- ic composition on observed extinction rates, ture then emerged: the smokers’ death rate allowing us to see how changes in composi- equaled or exceeded the non-smokers’ death tion might bias our views of the intrinsic in- rate in every age subgroup, as would be ex- tensity of extinction triggers. For example, pected. Why, then, when the subgroups were were the effects of some mass extinctions mit- aggregated, did smoking appear to increase igated by a particularly extinction-resistant longevity? fauna? Were the effects of other mass extinc- This apparent paradox occurred because tions especially severe because they affected the smokers’ age distribution differed from extinction-prone taxa? We also introduce a that of the non-smokers. The non-smokers in- method for analytically estimating how much cluded a higher percentage of older women of the decline in extinction rates resulted from (who grew up when smoking among women the changing taxonomic composition of the was less common), and older women have in- marine biosphere. herently higher death rates regardless of whether or not they smoke. The smokers, on Simpson’s Paradox: Do Smokers the other hand, disproportionately included Live Longer? younger women. Once age differences in the Comparisons of taxonomic extinction rates two groups were taken into account, it became (whether using percentage extinction or an- clear that smoking did indeed increase mor- other metric) are the basis of many quantita- tality. tive studies of mass extinction events (e.g., This kind of pattern defines Simpson’s par- Raup and Sepkoski 1982, 1984; Benton 1995; adox: trends in aggregated percentages dis- Wang 2003; Bambach et al. 2004; MacLeod appear or even reverse themselves when one 2004; Rohde and Muller 2005; Bambach 2006). partitions the data into subgroups, such as age However, such comparisons of aggregate ex- groups. In this example, discovering Simp- tinction rates can be misleading. It is possible son’s paradox was not difficult: the aggregat- for one event to have a higher extinction rate ed data were clearly misleading, because we for each of several subgroups within the data knew a priori that smoking is detrimental to set, yet for another event to have a higher ex- one’s health. We also knew that age is related tinction rate for the data set as a whole. This to mortality rate, so it was natural to separate apparent contradiction can appear when sub- the data into subgroups by age. groups with different extinction rates change In other cases, however, Simpson’s paradox in relative abundance through time—a statis- can be more insidious. We may have no a tical artifact known as Simpson’s paradox priori belief that an aggregated data set is (Simpson 1951). yielding a misleading conclusion, so we may Examples of Simpson’s paradox appear in not suspect a need to partition the data into the statistical literature on a variety of sub- subgroups. Even if we have reason to subdi- 436 STEVE C. WANG AND ANDREW M. BUSH TABLE 1. Diversity of major molluscan classes in the Ordovician (Ashgillian) and end-Permian (Djhulfian) mass extinctions. Columns give the number of genera going extinct in the interval (Extinct), total diversity in the interval (Diversity), and extinction rate (Percent) for each extinction event. These data demonstrate Simpson’s paradox: the Permian has a higher intrinsic severity, because the extinction rate for each class is higher in the Permian than in the Ordovician. However, when the classes are combined, the overall molluscan extinction rate is higher in the Ordovician. This misleading effect occurs because the Ordovician fauna has a large number of extinction-suscep- tible cephalopods, whereas the Permian fauna has a large number of extinction-resistant gastropods. Data are from Sepkoski’s genus compendium (2002), as compiled by Bambach (1999) and Bambach et al. (2004); non-integer counts are due to fractional allocation of poorly-resolved genera. Ordovician Permian Extinct Diversity Percent Extinct Diversity Percent Cephalopoda 77.9 103.9 75 37.3 48.3 77 Bivalvia 48.1 80.1 60.0 48.3 80.3 60.1 Gastropoda 31.6 73.6 43 52.2 101.2 52 Mollusca 157.6 257.6 61 137.8 229.8 60 vide the data, there may no natural criterion Considering all three classes combined, by which to do so.