OUP CORRECTED PROOF – FINAL, 18/10/2010, SPi CHAPTER 19 Estimating extinction with the fossil record Peter J. Wagner and S. Kathleen Lyons 19.1 Introduction are essentially identical to those for estimating extinction, save that they are done ‘in reverse’. Many ecological and palaeontological studies focus Thus, discussions of how one estimates extinction on extinction. The fossil record is particularly rates using fossil data can almost double for dis- important for studying long-term patterns in cussion of how one estimates origination from fossil extinction: although analyses of extant phyloge- data. nies can estimate extinction rates (e.g. Alfaro et al. The other parameter that will be important 2009) and even suggest mass extinctions (e.g. Crisp throughout this review is preservation (i.e. sam- & Cook 2009), they cannot imply trilobites ever pling) rate. Just as ecologists know that incom- existed or that sphenodonts (now represented only plete sampling affects sampled richness (e.g. Hurl- by the tuatara) were once as diverse as lepi- bert 1971) and implied extinction (e.g. Solow dosaurs (lizards and snakes). However, workers 1993a), palaeontologists know that incomplete sam- also use the fossil record to test ideas about the pling affects the first and last appearances of fos- pace of major extinction events that use meth- sils, both in local sedimentary sections (Signor & ods similar to those that conservation biology Lipps 1982) and globally (Sepkoski 1975). Work- might use. Here we will review current palaeobi- ers have expressed concern that major extinctions ological methods for inferring extinction patterns, are exaggerated by or possibly even illusions of spanning ‘traditional’ methods using stratigraphic intervals of poor preservation (Raup 1979; Smith ranges to methods using more exact information et al. 2001; Peters & Foote 2002). Because sam- about distributions of finds within stratigraphic pling intensity is of interest to both fields, we shall ranges. also discuss how palaeontological studies address Palaeontological studies of diversity patterns also sampling when estimating diversity and diversity focus extensively on standing richness and origi- dynamics. nation rates. We do not focus on either of these parameters for their own sake. However, stand- ing richness (usually referred to simply as ‘diver- 19.2 State of the field sity’ in palaeontological studies) is an important 19.2.1 Basic metrics parameter when discussing extinction as extinc- tion metrics necessarily rely on changes in stand- Palaeontological studies of richness and diversity ing richness. Origination rates also can be an dynamics (i.e. extinction and origination) date back important parameter as the distribution of origi- to the 19th century (Phillips 1860). Traditional nations within time spans (i.e. evenly throughout palaeontological studies use synoptic databases (e.g. the interval vs concentrated in the beginning) have Sepkoski 1982, 2002), which catalogue the first small but important effects on the predictions of and last appearances of taxa. These almost always extinction rate hypotheses. Moreover, palaeonto- are binned into chronostratigraphic units: typically logical techniques for estimating origination rates stages and substages, but sometimes as fine as 265 OUP CORRECTED PROOF – FINAL, 18/10/2010, SPi 266 BIOLOGICAL DIVERSITY I II V Per-capita extinction rate measures the survivor- ship of taxa present at the outset of an interval. t 3 This is: raphy III IV tig ra t2 St Sa Ïpc =ln (19.2) me/ i Saz T t1 where Sa is the number of taxa crossing the bound- ary from the prior interval and S is the number Figure 19.1 Chronostratigraphic ranges of five hypothetical taxa. Each az t gives a separate chronostratigraphic unit, with t1 the oldest. Dashed of the taxa also crossing through both the base vertical line for V indicates that taxon V is not actually found in unit t2. and the top (i.e. the range-through taxa). Note that Modified from Foote (2000), Fig. 1. ‘per capita’ here refers not to individuals within a species, but to taxa as operational units. For t2 in Fig. 19.1, S is 3 (taxa I, III, and V) and S is 2 faunal zones. (We use ‘intervals’ to refer chronos- a az (taxa I and V), giving Ï =0.41. The most likely tratigraphic units because of the correspondence pc probability of a taxon becoming extinct in an inter- between units of time and strata; see Grad- Ï val is now 1 − e pc . However, this is identical to stein et al. (2005)). For numerous reasons, synop- μ if we restrict per-taxon rates to only boundary tic studies typically use supraspecific taxa, with pc crossers. genera being the most common taxon since the Chronostratigraphic intervals vary considerably mid 1980s. in temporal length (Gradstein et al. 2005). Accord- Fig. 19.1 presents a simple example. We use ingly, workers often divide rates by interval length last appearances in each unit t to infer rates of to get rates per million years instead of rates per extinction. Two types of metrics commonly are interval. This is appropriate if extinction is dis- used: per taxon (pt) and per capita (pc; see Foote tributed throughout an interval. One expectation (2000)). Per-taxon metrics measure the propor- of continuous turnover rates is that longer inter- tion of standing richness, S, that have their last vals should have higher extinction rates. However, appearance in an interval. Per-taxon extinction Foote (1994) showed that ‘raw’ extinction metrics thus is: are random with respect to the length of chronos- S tratigraphic units, whereas per million year rates Ï = L (19.1) pt S show a negative correlation. We will return to this issue below when we summarize tests of pulsed vs where SL is the number of taxa last appearing in an continuous rates. interval. In Fig. 19.1, taxa III and IV last appear in The distribution of extinctions and originations t2,soSL =2. S is not the sum of taxa sampled in plays a role in whether we should prefer per-taxon an interval, but the sum of taxa with chronostrati- or per-capita extinction rates. If extinction and orig- graphic ranges spanning the interval. Taxon V in ination happen throughout an interval, then per- t2 illustrates the difference: because it first appears taxon rates overestimate immediate extinction risk before t2 and last appears after t2, we assume that as well as exaggerating S from any one slice of it existed in t2 even though V is not sampled in time. ‘Singletons,’ that is those taxa known from t2. This assumption is unsound only if taxon V is only one interval, such as taxon IV in Fig. 19.1, polyphyletic. As the synoptic data for taxa I and V exacerbate this problem. Singletons often reflect are identical, we need a more detailed database to differences in research effort and/or available fos- recognize cases like taxon V. Thus, St2 = 5 regardless sils (Raup & Boyajian 1988) and excluding single- of how many ‘range-through’ taxa (e.g. I and V) tons greatly reduces the volatility of per-taxon rates . actually are sampled in t2,andÏpt =040. (Per-taxon (Alroy 1996). Although per-capita rates are excel- origination, Îpt, simply replaces SL with SF, the taxa lent for describing continuous rates, they still can first appearing in t2). accurately reflected pulsed extinction. OUP CORRECTED PROOF – FINAL, 18/10/2010, SPi ESTIMATING EXTINCTION WITH THE FOSSIL RECORD 267 19.2.2 Survivorship curves constant over time and among taxa. First, if we measure stratigraphic ranges in discrete bins (as is Per-capita rates lead conceptually to survivorship −Ï almost always done), then f (N =1)=e pc only if curves. The per-capita rate for any one interval all taxa originate at the very base of intervals. If reflects the proportion of taxa expected to survive origination is continuous throughout intervals, then the entire interval into the next interval. Survivor- we expect (for example) half of the taxa lasting one ship curves reflect the proportion of taxa that sur- half an interval to span from tx to tx+1. Thus, only vive multiple successive intervals. Some survivor- the slope from taxa with ranges of 2+ intervals will ship analyses contrast rates among higher taxa in reflect Ïpc under continuous diversification. Second, order to assess whether extinction rates in some extinction rates do not make predictions about the groups differ markedly from those in other groups ages of extant taxa: instead, the age distribution of (e.g. Simpson 1944, 1953) or whether there are com- contemporaneous taxa (i.e. a ‘backwards survivor- mon patterns among higher taxa (Van Valen 1973, ship’ curve sensu Pease (1988) or a ‘prenascence’ 1979; Raup 1991). Alternatively, cohort analyses curve sensu Foote (2001b)) reflects origination rates contrast sets of taxa that originate in the same inter- (Foote 2001b). val (i.e. Raup 1978; Foote 1988) to examine whether The third reason is the most critical: extinc- extinction rates change markedly over time. Given tion rates make predictions about temporal dura- a per-taxon extinction rate, we expect the pro- tions, but we can observe only stratigraphic ranges. portion of taxa that survive N intervals, f (N), As preservation rates strongly affect stratigraphic to be: ranges, ‘survivorship’ curves using fossil ranges − Ï N pc actually reflect both preservation and extinction f (N)=Ïpc = e (19.3) (Sepkoski 1975; Pease 1988; Foote & Raup 1996). Ï − 3 Given pc = ln( 2 ) from our example above, we Consider a simple example of two clades where expect 66.7% of the taxa to survive 1+ intervals, origination and extinction occur at the beginning . 44.4% to survive 2+ intervals, etc., and thus 33.3% and end of each interval, and for whichÏ ¯ pc =069 of the taxa to have durations of 1 interval, 22.2% (Fig.