the red queen revisited: reevaluating the age selectivity...

� 2008 The Paleontological Society. All rights reserved. 0094-8373/08/3403-0002/$1.00

Paleobiology, 34(3), 2008, pp. 318–341

The Red Queen revisited: reevaluating the age selectivity ofPhanerozoic marine genus extinctions

Seth Finnegan, Jonathan L. Payne, and Steve C. Wang

Abstract.—Extinction risk is inversely related to genus age (time since first appearance) in mostintervals of the Phanerozoic marine fossil record, in apparent contradiction to the macroevolu-tionary Red Queen’s Hypothesis, which posits that extinction risk is independent of taxon age. Age-dependent increases in the mean species richness and geographic range of genera have been in-voked to reconcile this genus-level observation with the presumed prevalence of Red Queen dy-namics at the species level. Here we test these explanations with data from the Paleobiology Da-tabase. Multiple logistic regression demonstrates that the association of extinction risk with genusage is not adequately explained by species richness or geographic range: there is a residual asso-ciation between age and extinction risk even when range and richness effects are accounted for.Throughout most of the Phanerozoic the age selectivity gradient is highest among the youngestage cohorts, whereas there is no association between age and extinction risk among older age co-horts. Some of the apparent age selectivity of extinction in the global fauna is attributable to dif-ferences in extinction rate among taxonomic groups, but extinction risk declines with genus ageeven within most taxonomic orders. Notable exceptions to this pattern include the Cambrian–Ordovician, latest Permian, Triassic, and Paleocene intervals. The association of age with extinctionrisk could reflect sampling heterogeneity or taxonomic practice more than biological reality, but atpresent it is difficult to evaluate or correct for such biases. Alternatively, the pattern may reflectconsistent extinction selectivity on some as-yet unidentified covariate of genus age. Although thislatter explanation is not compatible with a Red Queen model if most genus extinctions have re-sulted from biological interactions, it may be applicable if most genus extinctions have instead beencaused by recurrent physical disturbances that repeatedly impose similar selective pressures.

Seth Finnegan and Jonathan L. Payne. Department of Geological and Environmental Sciences, StanfordUniversity, 450 Serra Mall, Building 320, Stanford, California 94305. E-mail: [email protected]

Steve C. Wang. Department of Mathematics and Statistics, Swarthmore College, 500 College Ave, Swarth-more, Pennsylvania 19081.

Accepted: 19 April 2008

Introduction

Many factors have been suggested or shownto be associated with extinction risk in the fos-sil record (Raup 1992; McKinney 1997). Ofthese, perhaps the most controversial andleast understood is taxon age. FollowingSimpson’s (1944) observation that the meanage of living bivalve genera is greater than themean duration of extinct bivalve genera, nu-merous workers have evaluated the relation-ship between taxon age and extinction risk inmany groups and across widely varying timescales. In the most widely cited of these stud-ies, Van Valen examined the age distributionsof both living and extinct members of approx-imately 50 major clades, concluding that innearly all cases extinction risk was indepen-dent of taxon age (Van Valen 1973). To explainthis finding he proposed the Red Queen’s Hy-pothesis: ‘‘the effective environment of any

homogenous group of organisms deterioratesat a stochastically constant rate’’ and hence fit-ness at any given time—as measured by ex-tinction risk—is independent of prior evolu-tionary success (Van Valen 1973).

Although the Red Queen’s Hypothesis hasbeen extremely influential, Van Valen’s empir-ical determination that extinction risk is in-dependent of taxon age has been challengedon methodological grounds (Foin et al. 1975;Raup 1975; Salthe 1975; Sepkoski 1975; Hal-lam 1976). Van Valen has responded to thesecriticisms (Van Valen 1976a, 1979), but subse-quent analyses using different data sets andmethodologies have usually found some as-sociation between taxon age (typically of fam-ilies or genera, as in most of Van Valen’s anal-yses) and extinction risk. This association ismost commonly inverse—extinction risk de-clines as taxa age (Anstey 1978; Raup 1975,1978a; Boyajian 1986, 1991; Jones and Nicol

319AGE SELECTIVITY OF GENUS EXTINCTIONS

1986; Foote 1988, 2001a; Gilinsky 1988; Boya-jian and Lutz 1992; Baumiller 1993) but sometaxa, particularly planktonic groups, show anincrease in extinction risk with taxon age(Hoffman and Kitchell 1984; Pearson 1992,1995; Arnold et al. 1995; Doran et al. 2004,2006). A minority of groups show no associ-ation between extinction risk and taxon age,most notably the Cenozoic mammals of NorthAmerica (Foote and Miller 2007).

Taken at face value, these studies appear tocontradict Van Valen’s conclusion: extinctionrisk does tend to vary systematically with tax-on age in most families and genera. However,the prevalence of age-dependent extinctiondynamics among higher taxa does not neces-sarily imply that the same is true at the specieslevel. Several factors have been suggested toreconcile these observations with the pre-sumption of Red Queen (i.e., age-indepen-dent) extinction dynamics at the species level.

One such factor is geographic range. Generatend to expand their geographic rangesthrough time (Willis 1922; Miller 1997), andwidely distributed taxa are buffered againstextinction (Jablonski 1986; Payne and Finne-gan 2007; Wagner et al. 2007). Wide geograph-ic range can be viewed as both a cause and aconsequence of long duration: under a passivediffusion model of range expansion, generathat escape extinction will tend to widen theirdistribution through time, and this passive ex-pansion will tend to reduce their risk of ex-tinction in the future.

Species richness is, similarly, expected to bepositively associated with genus age. All gen-era begin as single species and must maintainor increase species richness to avoid extinc-tion. Hence, under a time-homogenousbranching model of evolution, older generawill on average contain more species thanyounger genera (Raup et al. 1973), and willconsequently be less susceptible to stochasticextinction even if extinction risk is indepen-dent of age at the species level (Raup 1978b;Flessa and Jablonski 1985; Boyajian 1991;Foote 2001a).

Finally, dynamic survivorship analysesbased on the distributions of taxon durationssuffer from a variety of statistical artifacts re-lated to variation in extinction rates across

time and among taxonomic groups (Van Valen1973, 1976a,b, 1979; Raup and Sepkoski 1982;Van Valen and Boyajian 1987; Pearson 1992;Foote 2001a) (see Appendix for further dis-cussion), and are further complicated by lackof knowledge regarding the ultimate dura-tions of extant taxa (Van Valen 1979; Gilinsky1988; Foote 2001a; Doran et al. 2004, 2006).

Various combinations of the above effectshave been invoked to reconcile the age-depen-dent family and genus extinction patternscommonly observed in the fossil record withthe age-independent species extinction regimeposited by the Red Queen model, but therehave been only limited efforts to evaluate theirexplanatory power. Consequently, more thanthree decades after the Red Queen’s Hypoth-esis was initially proposed, it remains unclearwhether Phanerozoic extinction patterns sup-port an age-independent extinction model atthe species level. There has been no attempt toexplicitly examine the explanatory power ofspecies richness and geographic range effectsin accounting for the observed age selectivityof family and genus extinctions, largely owingto the absence of suitable data: studies sub-sequent to Van Valen’s initial (1973) analysishave been based largely on Sepkoski’s com-pendia (Sepkoski 1993, 2002) of biostrati-graphic ranges for marine animal families andgenera, which do not contain information oneither geographic range or species richness.

The development of the geographically ex-plicit, occurrence-based Paleobiology Data-base (PaleoDB) (Alroy et al. 2001) now permitsdirect evaluation of the influence of range andrichness on genus extinction risk. Using datafrom the PaleoDB, we apply maximum-like-lihood model selection to a series of nested lo-gistic regression models to determine whetherage-dependent increases in geographic rangeand species richness adequately account forthe observed association between genus ageand extinction risk, both in composite taxo-nomic samples and within individual orders.Our approach to the age selectivity questionis different from that taken by precedingworkers, in that the fundamental unit of ouranalysis is the extinction versus survival ofgenera across stratigraphic boundaries, ratherthan their ultimate durations. By evaluating

320 SETH FINNEGAN ET AL.

extinction risk at each of 47 boundaries ratherthan drawing inferences from the cumulativedistribution of genus durations, our analysissidesteps many of the issues that have com-plicated previous survivorship analyses, par-ticularly the confounding of age and time ef-fects and censorship of the future durations ofextant genera. In our analyses we address thefollowing principal questions:

1. Does the inverse association between genusage and extinction risk simply reflect thepositive associations between genus ageand species richness and geographic range,or does it require additional explanation?

2. Is the association between genus age andextinction risk a simple monotonic func-tion, or is the relationship more complex?Does it vary through time?

3. Is the association between genus age andextinction risk expressed within individualtaxonomic orders as well as in the globalcomposite fauna?

Data

Genera Included. We evaluated the age de-pendence of genus extinction throughout thePhanerozoic by using the 280,048 occurrencesof marine animal genera that were resolvedwithin the 49 �11-Myr bins in the PaleoDB asof 16 August 2006. Although they are of some-what coarser resolution than stratigraphicstages, the PaleoDB time bins have the advan-tage that they are of approximately equal du-ration and thus reduce the potentially seriouseffects of uneven interval duration on survi-vorship analyses (Sepkoski 1975). We exclud-ed genera that could not be assigned to a tax-onomic order (often because they representmisspellings of valid genera), leaving 261,616occurrences of 14,911 genera. Because we eval-uated survivorship separately at each binboundary, genera that occur in more than onebin are included in multiple analyses: in totalthere are 39,397 actual or potential boundary-crossing events (hereafter referred to as ex-tinction/survival events) in the full data set,and the median number of genera evaluated ateach bin boundary is 753.

Genus Age. Following Foote (2001a), wemeasured genus age as the number of �11-

Myr bins from the first appearance of a genus(scored as 1) to the bin in which extinction se-lectivity is evaluated. Thus, for a given timebin Bt, the genera that first appear in that binwere assigned an age of 1, those that first ap-peared in the previous bin, Bt�1, and rangeinto Bt were assigned age of 2, those that firstappear in Bt�2 and range into Bt were assignedan age of 3, etc.

Genera extant within a given time bin werescored as survivors if the genus was sampledin a subsequent time bin; otherwise they werescored as extinctions. The age-dependence ofgenus extinctions in the PaleoDB can be illus-trated by compiling all extinction/survivalevents and comparing their relative propor-tions as a function of genus age (Fig. 1). Pro-portional extinction is highest among generathat first appear in a given interval and be-comes successively lower for genera with lon-ger prior stratigraphic ranges, showing littlevariation among genera older than ten timebins. Only 4% of all genera ever exceed thisage, and many of these may be effectively‘‘immortal’’ (Foote 2001b), representing eithergenuine lineages that are exceptionally extinc-tion-resistant or the repeated convergent evo-lution of ecologically advantageous morpho-types (Plotnick and Wagner 2006; Wagner andErwin 2006). Regardless of the reason for theirpersistence, these genera may exaggerate theapparent age selectivity of extinction by en-suring that extinction rates are always verylow over a very large portion of the upper endof the potential age range. To reduce the influ-ence of this long tail of old and highly extinc-tion-resistant genera, we excluded all generaolder than ten time bins when analyzing se-lectivity within each interval. Note that this isnot equivalent to eliminating all genera withan ultimate duration greater than ten time bins:these genera were included in analyses for thefirst ten time bins of their range but were ex-cluded from analyses in all subsequent inter-vals within their range. In addition, generawith a total duration of more than 25 binswere entirely removed from the data set, asmany of these represent polyphyletic formgenera (e.g., Spirorbis, Lingula). These cullsleave 14,834 genera and 35,330 extinction/sur-vival events.


FIGURE 1. Selectivity of extinction with respect to genus age for all genera in the PaleoDB. Bars are scaled to therelative proportions of extinctions (white) versus survivals (black) for all extinction/survival events involving gen-era of the appropriate age. Because of the short duration of most genera, the relatively young age bins contain thegreat majority of extinction/survival events.

Species Richness and Geographic Range. Wetabulated species richness as the total numberof named species recorded for each genus ineach time bin; genera that had no species-levelidentifications within a given bin (i.e., generain which species occurrences were only re-corded as ‘‘sp.,’’ ‘‘aff.,’’ or ‘‘cf.’’) were assigneda minimal richness of one. Species reported asdistinct but left in open nomenclature (e.g.,Zygospira sp. A, Zygospira sp. B) were countedas separate species.

As a measure of geographic range, wecounted the number of cells in a 10� by 10� pa-leolatitudinal-paleolongitudinal grid in whicheach genus occurs for each time bin. Althoughthe precision of latitudinal and especially lon-gitudinal paleocoordinates deteriorates with

age, this measure of geographic range isstrongly correlated with an alternative mea-sure of geographic range that is independentof paleocoordinates, the number of tectonicplates occupied by each genus in each time bin(R � 0.90, p � .001).

Clearly, the absolute values of geographicrange and species richness in any compilationof fossil occurrences will be highly sensitive tointerval-to-interval variation in data coverage,with genera from well-sampled intervalstending to exhibit larger sampled geographicranges and greater species richness than gen-era in poorly sampled intervals. However, it isimportant to emphasize the distinction be-tween analyzing geographic range or speciesrichness as absolute quantities and analyzing


the strength of association between these vari-ables and extinction risk. The goal of thisstudy is not to estimate absolute changes inrange or richness through time but, rather, todetermine whether differences in these factorsamong genera within a given time interval ade-quately account for the association betweenextinction risk and genus age in that interval.Although it may be argued that sampling ofrichness and range degrade as a function oftime before present, this bias, or any othertime-dependent sampling bias, would affectthe sampled range and richness of each genussimilarly within any given time interval. Toassess the relationship between range and/orrichness and survivorship, it is only necessaryto assume that differences in observed geo-graphic range or species richness among gen-era within each time bin are proportional tothe true differences in range and richness (seeAppendix for additional discussion of the re-liability of the data). Both species richness andgeographic range were log transformed for alllogistic regression analyses to reduce the in-fluence of outliers, but using the untrans-formed linear variables has little effect on ourresults. For the sake of clarity, range and rich-ness are presented as untransformed variablesin the figures.

Range-Through Genera. Genera that couldbe inferred via interpolation to have been ex-tant in the time bin analyzed, but which werenot sampled in that bin (‘‘range-through’’genera) were assigned species richness andgeographic range values drawn as paired val-ues from the richness and range distributionsof genera of the same age that belong to thesame taxonomic order and, like the range-through genera, survive into the next time bin.This is conservative because it assumes thatrange-through genera, which by definition donot go extinct at the end of the interval, havethe same geographic range and species rich-ness distributions as the surviving genera thatare actually sampled in a given time bin. Infact range-through genera are likely to haveon average fewer species and more limitedgeographic distributions than sampled sur-viving genera; hence this assumption proba-bly inflates the richness and range distribu-tions of surviving genera and biases against

finding any residual association between ageand extinction risk (see Appendix for addi-tional discussion of range-through genera).

Methods

We used binomial logistic regression (Hos-mer and Lemeshow 2000) to evaluate multiplemodels of extinction selectivity across each of47 boundaries in the time series of �11-Myrbins (the first Cambrian time bin was excludedbecause of its very small sample size and themost recent time bin was excluded because itis impossible to evaluate extinction at the endof the time series). Most previous analyses ofage selectivity have been based on the inter-pretation of survivorship curves for cohortswith a common time of origination (Raup1978b; Jones and Nicol 1986; Foote 1988) or cu-mulative distributions of taxon durations (VanValen 1973; Raup 1975). In addition to thewell-known statistical artifacts associatedwith this approach (see Appendix for addi-tional discussion), its major limitation is thatit provides no statistical framework for ex-amining the effects of confounding variablessuch as species richness or geographic range.Boyajian (1986, 1991) took an approach morecomparable to ours in contrasting the age dis-tributions of extinct and surviving families atseveral stage boundaries, but although he sug-gested that the age selectivity of family ex-tinctions was attributable to species richnessand geographic range effects, he did not testthis hypothesis.

By evaluating extinction risk as a function ofgenus age separately at each bin boundaryrather than inferring it from the distributionof ultimate genus durations, our approachavoids many of the pitfalls involved in inter-preting cumulative survivorship curves. Forexample, it is not necessary to apply a correc-tion factor to adjust for temporal variation inextinction rate (Holman 1983; Pearson 1992,1995) if extinction patterns are consideredseparately for each time bin. Our approach isalso unaffected by censoring of the future du-rations of living taxa (Gilinsky 1988; Foote2001a) because it considers the age of a genusat the time of analysis, rather than its ultimateduration. Moreover, using the PaleoDB is ad-vantageous because it reduces ‘‘The Pull of the


Recent’’ (Raup 1972): the PaleoDB contains re-cords of fossil occurrences only, and hence itdoes not extend the biostratigraphic ranges ofextant genera beyond their last fossil occur-rences to the present day. Consequently, thereis no systematic increase in the number of gen-era with interpolated biostratigraphic rangesas the Recent is approached.

Logistic regression is functionally analo-gous to ordinary linear regression, but it is de-signed for data in which the outcome is binaryrather than continuous (Hosmer and Leme-show 2000), such as extinction versus survivalof a genus through a given interval. Logisticregression is used to model the probability, p,that a given observation will exhibit one out-come versus the other for a given value of theexplanatory variable(s). The model assumes amonotonic relationship between p and the ex-planatory variable(s); more specifically, thelogit ln[p/(1 � p)] and the explanatory vari-able(s) are assumed to have a linear relation-ship (Hosmer and Lemeshow 2000). Unlike or-dinary linear regression, however, logistic re-gression does not assume homoscedasticity,nor does it assume normality of the residuals.

In logistic regression, the estimated associ-ation between a explanatory variable and theoutcome is expressed in the form of an oddsratio. The odds ratio expresses the effect of anincrease of one unit in the explanatory vari-able (in this case genus age, log2 geographicrange, or log2 species richness) on the odds [p/(1 � p)] of a successful outcome in the re-sponse variable, which is here measured assurvival versus extinction of genera at eachbin boundary. Odds ratios are analogous toslope coefficients in linear regression, andthey can be expressed in comparable units byconverting to a natural logarithm (log-odds),so that a value of zero indicates no associationbetween the explanatory and response vari-ables, whereas values above and below zeroindicate positive and inverse associations, re-spectively.

As an example, consider two time bins, Aand B, each of which has genera of two ages,1 and 2. In time bin A the extinction rate is30% for genera with an age of 1 and 20% forgenera with an age of 2, whereas in time binB the extinction rate is 30% for genera with an

age of 1 and 40% for genera with an age of 2.In the first case the odds of survival for generawith an age of 1 are 0.70/0.30 � 2.33 and theodds of survival for genera with an age of 2are 0.80/0.20 � 4.00, and therefore the oddsratio is 4.00/2.33 � 1.72 and the log-odds isln(1.72) � 0.54. This positive log-odds valueindicates that taxon age is positively associ-ated with the probability of survival. In thesecond case the odds of survival for generawith an age of 2 are 0.60/0.40 � 1.50, givingan odds ratio of 1.50/2.33 � 0.64 and a log-odds of ln(0.64) � �0.44. Here the negativelog-odds value indicates that taxon age is in-versely associated with the probability of sur-vival. Thus, in all of our figures and tables log-odds greater than zero indicate dispropor-tionate survival of older genera and extinctionof younger genera and log-odds less than zeroindicate disproportionate survival of youngergenera and extinction of older genera.

Figure 2 illustrates the odds ratios and theirrelationship to survivorship patterns for threetime bins, Devonian 3 (Eifelian–Givetian),Cretaceous 7 (Campanian), and Permian 4(Wuchiapingian–Changhsingian). Note thatthe odds ratio is a measure of extinction selec-tivity, not overall extinction intensity. Al-though the overall extinction rate in Creta-ceous 7 is less than half that of Devonian 3,Cretaceous 7 exhibits stronger selectivity inthat a greater proportion of all extinctions oc-cur among very young genera. Comparedwith both Devonian 3 and Cretaceous 7, Perm-ian 4 exhibits only a very weak relationshipbetween genus age and extinction risk.

In contrast to the least-squares approachused in ordinary linear regression, the logisticregression model is fit by using a maximum-likelihood estimation approach in which an it-erative algorithm seeks to maximize the like-lihood function (L). We used Akaike’s modi-fied information criterion (AICc) to evaluateand compare goodness-of-fit for each of eightregression models accounting for all sevenpossible combinations of the three explanato-ry variables plus the possibility that there is nosignificant selectivity associated with any ofthe explanatory variables.

AICc values express goodness-of-fit whilepenalizing the addition of new parameters,


←

FIGURE 2. Selectivity of extinction with respect to ge-nus age for three time bins: Devonian 3 (A), Cretaceous7 (B), and Permian 4 (C). As in Figure 1, bars are scaledto the relative proportions of extinctions (white) versussurvivals (black) for all extinction/survival events in-volving genera of the appropriate age. Gray lines showthe odds ratio estimate (solid line) and the upper andlower 95% confidence interval (dotted lines). Permian 4exhibits the highest extinction intensity and the least se-lectivity with respect to genus age. Devonian 3 and Cre-taceous 7 both exhibit relatively strong selectivity de-spite large differences in extinction intensity.

which will always improve the fit of a multi-ple-regression model. Thus, the ‘‘best’’ modelis the one that explains the most variation inthe response variable with the fewest explan-atory variables. AICc values were convertedinto Akaike weights (Burnham and Anderson2002), which provide a proportional measureof the support for each model relative to all ofthe models considered—an Akaike weight of0.75 indicates 75% confidence that a givenmodel is the ‘‘best’’ model among all of themodels considered. Akaike weights can becompared to determine the ratio of support(the evidence ratio) for one model or group ofmodels versus another model or group ofmodels. Akaike weights were summed for thefour models that are consistent with an age-independent extinction regime (range, rich-ness, range � richness, no selectivity) and forthe four models that include an age term (age,age � richness, age � range, age � richness �range), and the cumulative weights were com-pared to measure the relative support for age-inclusive versus age-free models of extinctionselectivity. Akaike weights were also used toproduce a weighted average for the associa-tion between age and extinction risk from allfour age-inclusive models.

Results

Association of Genus Age and Extinction Risk.Extinction rates are significantly higheramong young genera than among older gen-era extant in the same time bin for most Phan-erozoic intervals. This age selectivity is ex-pressed in Figure 3 as log-odds from a singlelogistic regression of extinction risk on genusage for each interval. Genus age is inverselyassociated with extinction risk (i.e., the log-


FIGURE 3. Age selectivity of extinction throughout thePhanerozoic. Log-odds estimates for the association be-tween extinction risk and genus age (black dots) and95% confidence intervals (gray lines) from logistic re-gression analyses of each �11-Myr time bin in the Phan-erozoic. Positive log-odds indicate that survival is high-est among older genera, negative log-odds indicate sur-vival is highest among younger genera, and log-oddsnear zero indicate no association between age and sur-vival. Log-odds are significantly greater than zero in 41out of 47 time bins, indicating that older genera are atlower risk of extinction. Cm � Cambrian, O � Ordovi-cian, S � Silurian, D � Devonian, C � Carboniferous, P� Permian, T � Triassic, J � Jurassic, K � Cretaceous,Pg � Paleogene, N � Neogene.

odds is significantly above zero) in 87% oftime bins, including every post-Ordoviciantime bin except for the terminal Permian (Ta-ble 1). The nonselective extinction model is re-jected by an evidence ratio of at least 99:1 inall post-Ordovician time bins except for theterminal Permian, the terminal Triassic, andthe Paleocene. The median log-odds for the as-sociation of genus age and extinction risk inall Phanerozoic time bins is 0.33 (odds ratio �1.40), meaning that the odds of survival [p/(1� p)] increase by 40% for each �11 Myr of ge-nus age. Note again that this does not implythat the probability of survival increases by40%; rather, the ratio of surviving to extinctgenera increases by 40% for each additional�11 Myr of genus age.

Effects of Species Richness and GeographicRange on Age selectivity Estimates. When allPhanerozoic genera are considered as a single

sample, there is a tendency for mean speciesrichness and mean geographic range to in-crease with genus age (Fig. 4A,B), as demon-strated in prior studies (Miller 1997). The as-sociation of genus age with species richness issimilar to that of genus age with geographicrange, reflecting the expected collinearity ofgeographic range and species richness underan allopatric speciation model (Mayr 1942).

Does the inverse association between genusage and extinction risk simply reflect the col-linearity of age with geographic range andspecies richness? If so, after controlling forthese variables there should be no residual as-sociation between age and extinction risk.However, this is not the case: extinction risk ishighest for genera that are both young andnarrowly distributed or species-poor, butthere is a strong relationship between extinc-tion risk and genus age across the entire spec-trum of geographic range and species richnessvalues (Fig. 5A,B). Extinction risk is also as-sociated with geographic range and speciesrichness among genera of all ages (Fig. 5A,B),as would be expected under most extinctionmodels. Thus, at least in the composite sampleof all extinction/survival events in the entirePhanerozoic, the association between extinc-tion risk and genus age is not fully explainedby geographic range or species richness. Incontrast, the association of extinction risk withspecies richness does appear to reflect pri-marily the collinearity of richness and geo-graphic range. There is relatively little resid-ual association between species richness andextinction risk after controlling for geographicrange (Fig. 5C), suggesting that species rich-ness is the least significant of the three ex-planatory variables considered here.

That range and richness are insufficient toaccount for the association between age andextinction risk is illustrated by the multiple lo-gistic regression models for each time bin:age-selectivity estimates when these variablesare included (Fig. 6) are generally very similarto those given by the single-regression modelbased only on age (Fig. 3). When all possiblecombinations of range, richness, and age areconsidered, age-based models are still pre-ferred by an evidence ratio greater than 99:1in all post-Ordovician time bins except for the


TA

BL

E1.

Ak

aike

wei

ghts

oflo

gis

tic

reg

ress

ion

mod

els

for

each

tim

ein

terv

al.T

he

wei

ght

ofth

eb

est

mod

elis

inb

old

text

.

Inte

rval

No.

ofg

ener

a

Ak

aike

wei

ght

Ag

eA

ge

�ra

ng

eA

ge

�ri

chn

ess

Ag

e�

ran

ge

�ri

chn

ess

Non

eR

ang

eR

ich

-n

ess

Ran

ge

�ri

chn

ess

Cu

mu

lati

ve

All

age

mod

els

All

age-

free

mod

els

Nat

ura

llo

gar

ith

mof

evid

ence

rati

o

Cen

ozoi

c5

1264

0.00

0.00

0.00

1.00

0.00

0.00

0.00

0.00

1.00

E�

001.

55E

�18

41.0

1C

enoz

oic

410

160.

000.

040.

010.

950.

000.

000.

000.

001.

00E

�00

2.42

E�

0919

.84

Cen

ozoi

c3

1172

0.00

0.73

0.00

0.27

0.00

0.00

0.00

0.00

1.00

E�

006.

22E

�15

32.7

1C

enoz

oic

210

390.

000.

700.

000.

300.

000.

000.

000.

001.

00E

�00

3.72

E�

0817

.11

Cen

ozoi

c1

952

0.00

0.35

0.00

0.29

0.00

0.20

0.00

0.16

6.42

E�

013.

58E

�01

0.58

Cre

tace

ous

891

00.

090.

030.

140.

740.

000.

000.

000.

001.

00E

�00

9.23

E�

1941

.53

Cre

tace

ous

774

60.

000.

730.

000.

270.

000.

000.

000.

001.

00E

�00

3.43

E�

1021

.79

Cre

tace

ous

670

70.

250.

430.

170.

150.

000.

000.

000.

001.

00E

�00

2.57

E�

1533

.59

Cre

tace

ous

565

60.

390.

150.

320.

140.

000.

000.

000.

001.

00E

�00

3.08

E�

1533

.41

Cre

tace

ous

469

90.

010.

470.

200.

320.

000.

000.

000.

001.

00E

�00

4.68

E�

1123

.79

Cre

tace

ous

361

00.

220.

160.

460.

170.

000.

000.

000.

001.

00E

�00

3.39

E�

2147

.13

Cre

tace

ous

260

20.

190.

490.

090.

230.

000.

000.

000.

001.

00E

�00

4.49

E�

3272

.18

Cre

tace

ous

159

60.

440.

260.

200.

100.

000.

000.

000.

001.

00E

�00

1.39

E�

2045

.72

Jura

ssic

667

00.

010.

710.

020.

260.

000.

000.

000.

001.

00E

�00

1.22

E�

1943

.55

Jura

ssic

510

240.

000.

050.

000.

950.

000.

000.

000.

001.

00E

�00

5.64

E�

2351

.23

Jura

ssic

468

10.

000.

390.

000.

610.

000.

000.

000.

001.

00E

�00

9.81

E�

1736

.86

Jura

ssic

347

00.

420.

150.

270.

150.

000.

000.

000.

001.

00E

�00

4.10

E�

2351

.55

Jura

ssic

244

70.

440.

260.

200.

090.

000.

000.

000.

001.

00E

�00

3.81

E�

1533

.20

Jura

ssic

141

20.

400.

220.

160.

220.

000.

000.

000.

001.

00E

�00

2.19

E�

0817

.64

Tri

assi

c4

595

0.02

0.07

0.60

0.22

0.00

0.01

0.06

0.02

9.08

E�

019.

16E

�02

2.29

Tri

assi

c3

578

0.00

0.05

0.51

0.44

0.00

0.00

0.00

0.00

1.00

E�

003.

47E

�15

33.2

9T

rias

sic

249

10.

400.

270.

140.

190.

000.

000.

000.

001.

00E

�00

6.95

E�

1021

.09

Tri

assi

c1

314

0.28

0.32

0.28

0.12

0.00

0.00

0.00

0.00

1.00

E�

001.

48E

�10

22.6

3P

erm

ian

440

80.

070.

190.

030.

190.

050.

230.

020.

234.

77E

�01

5.23

E�

01�

0.09

Per

mia

n3

662

0.00

0.73

0.00

0.27

0.00

0.00

0.00

0.00

1.00

E�

001.

35E

�08

18.1

2P

erm

ian

257

00.

000.

110.

000.

880.

000.

000.

000.

001.

00E

�00

5.28

E�

0816

.76

Per

mia

n1

440

0.00

0.13

0.22

0.65

0.00

0.00

0.00

0.00

1.00

E�

003.

31E

�06

12.6

2C

arb

on.5

440

0.00

0.34

0.00

0.66

0.00

0.00

0.00

0.00

1.00

E�

002.

44E

�14

31.3

4C

arb

on.4

458

0.00

0.29

0.14

0.56

0.00

0.00

0.00

0.00

1.00

E�

002.

08E

�19

43.0

2C

arb

on.3

486

0.00

0.29

0.14

0.57

0.00

0.00

0.00

0.00

1.00

E�

005.

09E

�14

30.6

1C

arb

on.2

546

0.00

0.73

0.00

0.27

0.00

0.00

0.00

0.00

1.00

E�

001.

23E

�13

29.7

3C

arb

on.1

626

0.00

0.48

0.00

0.52

0.00

0.00

0.00

0.00

1.00

E�

001.

05E

�09

20.6

7D

evon

ian

557

80.

070.

620.

070.

240.

000.

000.

000.

001.

00E

�00

7.62

E�

1941

.72

Dev

onia

n4

628

0.03

0.06

0.64

0.27

0.00

0.00

0.00

0.00

1.00

E�

002.

92E

�26

58.8

0D

evon

ian

311

350.

000.

030.

000.

970.

000.

000.

000.

001.

00E

�00

1.30

E�

1431

.97

Dev

onia

n2

1063

0.00

0.65

0.00

0.35

0.00

0.00

0.00

0.00

1.00

E�

006.

43E

�13

28.0

7D

evon

ian

111

370.

000.

500.

000.

500.

000.

000.

000.

001.

00E

�00

1.08

E�

0920

.65


TA

BL

E1.

Con

tin

ued

.

Inte

rval

No.

ofg

ener

a

Ak

aike

wei

ght

Ag

eA

ge

�ra

ng

eA

ge

�ri

chn

ess

Ag

e�

ran

ge

�ri

chn

ess

Non

eR

ang

eR

ich

-n

ess

Ran

ge

�ri

chn

ess

Cu

mu

lati

ve

All

age

mod

els

All

age-

free

mod

els

Nat

ura

llo

gar

ith

mof

evid

ence

rati

o

Silu

rian

215

000.

000.

730.

000.

270.

000.

000.

000.

001.

00E

�00

1.32

E�

0818

.14

Silu

rian

110

210.

000.

140.

000.

860.

000.

000.

000.

001.

00E

�00

8.93

E�

0611

.63

Ord

ovic

ian

510

190.

000.

250.

000.

100.

000.

460.

000.

193.

52E

�01

6.48

E�

01�

0.61

Ord

ovic

ian

413

160.

000.

000.

000.

280.

000.

000.

000.

722.

82E

�01

7.18

E�

01�

0.93

Ord

ovic

ian

380

30.

000.

020.

000.

250.

000.

060.

000.

682.

67E

�01

7.33

E�

01�

1.01

Ord

ovic

ian

270

40.

000.

210.

000.

080.

000.

500.

000.

202.

90E

�01

7.10

E�

01�

0.90

Ord

ovic

ian

145

10.

000.

070.

000.

190.

000.

200.

000.

532.

68E

�01

7.32

E�

01�

1.00

Cam

bria

n4

438

0.23

0.08

0.13

0.07

0.24

0.09

0.12

0.05

5.14

E�

014.

86E

�01

0.06

Cam

bria

n3

324

0.00

0.24

0.00

0.09

0.00

0.49

0.00

0.18

3.33

E�

016.

67E

�01

�0.

69C

ambr

ian

245

10.

000.

000.

000.

550.

000.

000.

000.

445.

55E

�01

4.45

E�

010.

22

FIGURE 4. Dependence of species richness (A) and geo-graphic range (B) on genus age, showing that generatend to increase their richness and geographic rangeover time. The richness and range of each genus in eachtime bin was divided by the average richness and rangefor all genera in the time bin, to obtain measures of rich-ness and range normalized to sampling intensity.Changes in range and richness throughout each genus’sduration were quantified by dividing its normalizedrange and richness in each bin in which it occurs by itsnormalized range and richness in the bin in which it firstappeared. A genus’s geographic range and richness at agiven age is thus expressed in multiples of its initialrange and richness; this ratio is presented as a naturallog to preserve the proportionality of positive and neg-ative changes. Black dots are means with 95% confi-dence bars and dotted lines are 1 standard deviation oneither side of the mean. Genus age is measured as num-ber of �11 Myr bins.

terminal Permian, the terminal Triassic, andthe Paleocene (Table 1). Of the intervals inwhich an age-based model is not preferred,one of the models incorporating richness,


←

FIGURE 5. Extinction risk as a function of age versusgeographic range (A), age versus species richness (B),and geographic range versus species richness (C). Ge-nus age is inversely associated with extinction risk, evenafter controlling for geographic range and species rich-ness. All extinction/survival events were placed in bi-variate bins (for example, all extinction/survival eventsinvolving genera with an age of 3 and a range of 4) andextinction risk was calculated as the proportion of ex-tinctions among all extinction/survival events. Only bi-variate bins that contained at least ten events were plot-ted. Darker shading signifies higher proportional sur-vival, and lighter shading signifies higher proportionalextinction (see key at top of figure).

range, or both is preferred over the nonselec-tive (null) model by an evidence ratio �99:1 inmost cases—the hypothesis of nonselectiveextinction can be rejected for all intervals ex-cept for the terminal Cambrian and the ter-minal Permian. In neither of these cases isthere strong support for the nonselectivemodel, which receives an Akaike weight of0.24 for the terminal Cambrian and 0.05 forthe terminal Permian.

The relative importance of each explanatoryvariable in controlling extinction risk can beevaluated for each time bin by comparing theAkaike weight of the complete model, includ-ing all explanatory variables, with the weightof a model lacking the variable of interest. Forexample, in Cenozoic 3 (Bartonian–Priaboni-an), the Akaike weight of the full model, age� range � richness, is 0.27, the weight of theage � range model is 0.73, the weight of theage � richness model is 4.3 10�8, and theweight of the range � richness model is 1.8 10�15. Hence the evidence ratio associated withadding age to the range � richness model is0.27/1.8 10�15 � 1.5 1014, with addingrange to the age � richness model is 0.27/4.3 10�8 � 6.3 106, and with adding richnessto the age � range model is 0.27/0.73 � 0.37.In this case both range and age improve themodel fit substantially, but species richnessdoes not. Comparing such evidence ratioswithin all time bins gives an estimate of theoverall explanatory power of each variableover the entire time series. By this criterion,species richness is the least important deter-minant of extinction risk: the evidence ratioassociated with adding species richness ex-


FIGURE 6. Age selectivity of extinction throughout thePhanerozoic after accounting for the effects of speciesrichness and geographic range. Log-odds estimates forthe association between extinction risk and genus age(black dots) and 95% confidence intervals (gray lines)from logistic regression analyses of each �11-Myr timebin in the Phanerozoic. Log-odds and confidence inter-vals were averaged across all age-inclusive models ac-cording to their relative Akaike weights. Period abbre-viations as in Figure 3. Note the similarity of this figureto Figure 1, indicating that little of the association be-tween genus age and extinction risk is explained by geo-graphic range or species richness.

FIGURE 7. Decline in extinction risk as a function of ge-nus age: the logit [ln(p/(1 � p))] of proportional extinc-tion is plotted against genus age for each time bin in theCambro-Ordovician (A), the post-Ordovician Paleozoic(B), the Mesozoic (C), and the Cenozoic (D). Dotted linerepresents 50% extinction. Initial indicate the strati-graphic boundaries presented by selected lines: P-T �Permian–Triassic, T-J � Triassic–Jurassic, K-Pg � Cre-taceous–Paleogene, Pal.-E � Paleocene–Eocene. Eachline connects logit(extinction) for each genus age cohortwithin a time interval. Logit(extinction) drops initiallyfor younger genus age cohorts and then tends to leveloff as genus age increases.

ceeds 99:1 in only three time bins (6%), where-as comparable improvements in model fit areobtained by adding geographic range in 24time bins (51%) and by adding genus age in36 time bins (77%).

Consistency of Selectivity across Age Cohorts.Logistic regression assumes that there is a lin-ear relationship between the explanatory var-iables and the logit of the response variable,and hence attempts to describe the change inextinction risk with a single log-linear func-tion. However, the association between genusage and extinction risk is not perfectly log-lin-ear—rather, from the Silurian onward, extinc-tion risk usually declines rapidly among thethree youngest age cohorts and then levels off(Fig. 7). Hence, log-odds based on the simul-taneous analysis of genera in all age cohortsare likely to imply a higher degree of selectiv-ity among relatively old cohorts than is actu-ally observed, especially given that regression

slopes are weighted by the number of obser-vations, most of which are in the youngest agecohorts.

To evaluate the consistency of selectivityacross all age cohorts, we ran a series of mul-tiple logistic regressions using the full model(age � richness � range) in which only adja-cent age cohorts were compared (i.e., age 1versus age 2, age 2 versus age 3, etc.) for allpost-Ordovician time bins: if extinction riskchanged as a linear function of genus age, wewould expect the median log-odds to be com-


FIGURE 8. Selectivity of extinction between adjacentage cohorts. Log-odds are plotted for the association be-tween age and extinction risk in comparisons of adja-cent age cohorts (i.e., genera aged 2 versus genera aged3) in each post-Ordovician time bin. The x-axis indicateswhich cohorts are included in each analysis, and blackdots represent log-odds for the association of age andextinction risk between those cohorts, after accountingfor range and richness effects, in each 11-Myr bin (forexample, the difference in proportional extinction be-tween genera with an age of 2 and genera with an ageof 3 within the Devonian 3 time bin). Horizontal bars aremedians, boxes enclose 25th and 75th percentiles, andwhiskers are 5th and 95th percentiles. The median(black line) and 25th and 75th percentiles of the log-odds distribution (gray boxes) are also depicted asslopes across the top. The increasing variance of log-odds for older cohort comparisons reflects increasinguncertainty as sample sizes decrease. As suggested byFigure 7, age selectivity is greatest among in youngerage cohorts and declines in older age cohorts.

parable for all such comparisons. Log-oddsare generally high when age 1 and age 2 co-horts are compared (Fig. 8). Log-odds arelower but remain mostly positive when age 2and age 3 cohorts are compared, and are lowerstill but dominantly positive for the age 3 toage 4 cohort comparison. Thereafter, however,there is no consistently identifiable associationbetween age and extinction risk—the medianlog-odds is near zero for both the age 4 to age5 and age 5 to age 6 comparison (relatively fewtime bins have sufficient numbers of oldergenera to make robust comparisons with gen-era aged 7 and older). Thus, the associationbetween age and extinction risk is primarilylimited to the youngest age cohorts, and is not

consistently observed among genera with pri-or durations exceeding a few tens of millionsof years.

This pattern is consistent with many dy-namic survivorship analyses: taxa with rela-tively short durations are often overrepresent-ed, but the frequency distributions of mediumto long-ranging taxa are usually approximate-ly log-linear (e.g., Anstey 1978; Baumiller1993). We emphasize that these short-rangingtaxa represent the majority of taxa at any giv-en time—in the PaleoDB, only 20% of generasurvive longer than three time bins. Hence, itmay make sense to view the age-indepen-dence of extinction among older cohorts as theexception to the rule of age-selective extinc-tion, rather than vice versa.

Selectivity among Taxonomic Orders. Analy-ses of age selectivity and survivorship haveoften considered all marine invertebrates as asingle composite sample, as we have thus far(Raup 1975, 1978b; Boyajian 1986, 1991), butVan Valen originally proposed that the RedQueen’s Hypothesis applies only within eco-logically homogeneous groups occupying thesame adaptive zone (Van Valen 1973). In ad-dition, it is possible to generate the appear-ance of age selectivity by mixing taxonomicgroups with differing—but internally age-independent—extinction rates (see Appendixfor additional discussion). Therefore, an anal-ysis of the global fauna is not an adequate testof the Red Queen model.

Most of Van Valen’s original examples ofage-independent extinction rates concernedthe age distributions of genera and familieswithin classes and orders, which he consid-ered to occupy similar adaptive zones in mostcases. Hence, we analyzed the age selectivityof genus extinctions separately for each orderwithin each time bin. We restricted the anal-ysis to orders containing at least 30 genera forany given bin so that the ratio of observationsto explanatory variables was at least 10:1, ashas been recommended for logistic regressionanalyses (Peduzzi et al. 1996). This cull alsoreduces the influence of the imprecise selectiv-ity estimates associated with very small sam-ple sizes. Additional culling was necessary be-cause in some cases all genera in the samplehad identical values for one or more of the ex-


FIGURE 9. Age selectivity of extinction among taxo-nomic orders. Log-odds for the association between ge-nus age and extinction risk are plotted for all ordershaving at least 30 genera and sufficient variation in age,range, and richness in each time bin. Log-odds deter-mined by model averaging, as in Figure 5. Smoothingline is a loess regression (sampling proportion � 0.20).Period abbreviations as in Figure 3. Log-odds values aresignificantly greater than zero for most orders, suggest-ing that age selectivity is found even among genera in-habiting the same adaptive zone.

planatory variables or the response variable(e.g., all genera go extinct or all survive), mak-ing a maximum-likelihood estimate impossi-ble (Albert and Anderson 1984). Of 1557 or-der–time bin combinations, 261 contained 30or more genera and had sufficient variation inthe explanatory variables to yield reliable like-lihood estimates (see Supplementary Table 1online at http://dx.doi.org/10.1666/07008.s1).

Most orders exhibit positive log-odds (i.e.,an inverse association between genus age andextinction risk) even after accounting for theeffects of range and richness (Fig. 9). The me-dian weighted log-odds for the association be-tween genus age and extinction risk among allorders and across all time bins is 0.21, some-what lower than the median log-odds for com-posite samples. Although it is difficult to com-pare these numbers directly because of themuch greater variation among orders, the pre-dominance of positive log-odds at the ordinallevel confirms that the age selectivity of ex-

tinction in the global composite fauna cannotbe attributed primarily or simply to the effectsof combining groups with different extinctionrates (Appendix).

There are some important differences be-tween the composite and the ordinal-leveltrends that are probably attributable to taxo-nomic mixing effects. In particular, whereasthe Triassic, Jurassic, and Lower Cretaceousare characterized by relatively strong selectiv-ity in the composite curve, the median age-selectivity log-odds of Jurassic and LowerCretaceous orders are comparable to mostother post-Ordovician intervals, and the log-odds associated with Triassic orders are no-tably low. The greater log-odds in the com-posite curve are likely related to the high di-versity of cephalopods in the Mesozoic. Am-monoids in particular are characterized byvery rapid evolutionary rates (Berg 1983), andhence when mixed with genera from slower-evolving groups will inflate the composite ex-tinction rates of young age cohorts.

Because individual orders contain far fewergenera than the global composite sample,there is much greater uncertainty at this leveland it is rarely possible to choose a singlemodel or group of models with 99% confi-dence (Supplementary Table 1). We thereforerelaxed the evidence ratio cutoff to 3:1, corre-sponding to a confidence level of 75% (i.e.,there is a 75% or greater chance that the set ofmodels including age predict extinction riskbetter than the set of models that exclude age).Nevertheless, it is difficult to select a model setin most cases: neither model set is preferredby an evidence ratio �3:1 in 186 out of 262 cas-es (71%). Among the order–time bin combi-nations for which one model set is preferredover the other by an evidence ratio of at least3:1, the age-inclusive model set is preferred infive times as many cases (63) as the age-in-dependent model (12). Moreover, this ratio in-creases sharply at higher evidence ratio cut-offs: if an evidence ratio cutoff of 4:1 is usedthe age-inclusive model set is preferred in 54cases and the age-independent model set isnever preferred. Thus, although the evidenceis equivocal for many orders, when there isunequivocal evidence it nearly always favorsmodels that include an age term.


Discussion

Suitability of Genera as Units of Analysis. Al-though the Red Queen’s hypothesis has pri-marily been applied to explain evolutionarypatterns at the species level and below, onlyfour of the compilations of taxon durationsconsidered by Van Valen (1973) in formulatingthe law of constant extinctions were at the spe-cies level; the rest were at the genus and familylevels. Genera are thus an appropriate unit ofanalysis for reconsidering this law. Raup(1975, 1978b) also considered genus-level sur-vivorship data, and first pointed out the in-verse relationship between lineage age andsurvivorship expected under a homogenousbranching model of evolution and a stochasticextinction regime. Since Raup’s work, this hasbeen the prevailing explanation for the con-cavity of many survivorship curves. What hasnot been available up to this point are the spe-cies richness and geographic range data nec-essary to test the sufficiency of this model formultiple clades and time periods. Clearly, itwould be in some ways preferable to examinethe age selectivity of extinction in species di-rectly, rather than the indirect approach takenhere of examining genus extinction patternsand controlling for species richness and geo-graphic range. However, there are major prac-tical impediments to such analysis. Most spe-cies are short-ranging, so that even with fairlyfine scale stratigraphic subdivisions the pro-portion of species that range through multiplestratigraphic intervals is usually quite small.Finer-scale subdivision can be achieved local-ly, but at this scale it is not always possible todifferentiate between local extirpation andglobal extinction. New optimization-basedbiostratigraphic methods (Sadler 2004) holdgreat promise for ameliorating this limitation,but at present species-level survivorship anal-yses would be difficult and likely ambiguousfor most invertebrate groups.

The most obvious exceptions to this limita-tion are planktonic microfossils, which areboth widely distributed and represented byan exceptionally complete record. These pro-vided the species-level data sets considered byVan Valen, and have subsequently been stud-ied by several workers (Hoffman and Kitchell

1984; Pearson 1992, 1995; Arnold et al. 1995;Doran et al. 2004, 2006). Interestingly, severalof these groups, most notably the Foraminif-era, show a positive relationship between ex-tinction risk and species age: extinction risk islowest among the youngest species, especially(or only) following major extinction events(Pearson 1992, 1995; Doran et al. 2004, 2006).This is the opposite of the pattern commonlyobserved for invertebrate genera in this andother studies. Whether the difference is attrib-utable to taxonomic level of analysis, to dif-ferences in taxonomic practice, or to ecologicaldifferences between planktonic microfaunaand benthic macrofauna is an interesting areafor further work.

Reliability of the Data. Geographic rangeand species-richness data in the PaleoDB arecoarsely resolved and incompletely sampled.Additionally, the stratigraphic ranges of gen-era in the PaleoDB often underrepresent theirknown ranges in the fossil record, and eventheir genuine first and last appearances in thefossil record may not represent true times oforigination and extinction (Foote 2001b).These sampling biases can exert a strong effecton diversity analyses, and the ways in whichthey may also affect apparent selectivity pat-terns should be carefully considered.

There are significant uncertainties associ-ated with all of the variables, but sampling ofrange and richness may be particularly prob-lematic. It is possible, for example, that the un-certainty in range and richness estimates isgreater than that in age estimates. In this case,the association of age with extinction riskcould be spurious: age may appear to have aneffect simply because the greater noise inrange and richness degrades the correlationbetween these variables and extinction risk,leaving significant residual variation to be ex-plained by age because it is independentlycorrelated with these explanatory variables.We cannot rule this out, but we find it to be anunlikely explanation for the pattern. In simu-lations of this scenario (available upon re-quest), the log-odds for the association be-tween extinction risk and genus age are al-ways substantially lower in the multiple-regression model than in the age-only model,and the confidence intervals wider. That is, al-


though the noise in range and richness resultsin some of the true association between ex-tinction risk and range/richness being spuri-ously partitioned onto age in the single-re-gression model, the strength of this associa-tion is always reduced when range and rich-ness are also accounted for. However,accounting for range and richness actually hasvery little effect on age-selectivity log-oddsestimates and their confidence intervals inmost time bins (compare Figs. 3 and 6). Onlyin the Cambro-Ordovician are age-selectivityestimates substantially lower in the multiple-regression model than in the single-regressionmodel. It thus seems improbable that the cor-relation between age and extinction risk is aspurious artifact of noise in range and rich-ness.

In fact, the extinction selectivity associatedwith taxonomic age appears to be largely in-dependent of the selectivity associated withrange or richness (Fig. 5A,B). Extinction risk issignificantly associated with both geographicrange and species richness in most time binswhen these variables are considered separately(Supplementary Fig. 1A,B, http://dx.doi.org/10.1666/07008.s2), and both remain significantpredictors of extinction risk in many intervalseven in the multiple-regression model includinggenus age (Supplementary Fig. 2A,B, http://dx.doi.org/10.1666/07008.s3), indicating thatthey are associated with extinction risk be-yond their correlation with genus age.

It is also notable that the trend in age-selec-tivity log-odds is quite different from eitherrange or richness selectivity trends (compareSupplementary Fig. 1A,B with Fig. 3). If genusage simply supplies a more precise estimate ofrange and/or richness, we should expecttrends in age selectivity to parallel trends inrange and richness selectivity, but this is notthe case: the trend in extinction selectivitywith respect to genus age is distinct from theselectivity trends associated with geographicrange or species richness. Although range andrichness selectivity trends are strongly corre-lated with one another (R � 0.82, p � 0.001),the age selectivity trend is not correlated witheither range (R � �0.02, p � 0.87) or richness(R � 0.06, p � 0.71). Consequently, we suggestthat observed extinction selectivity with re-

spect to genus age in multiple-regressionanalyses is unlikely to reflect poor sampling ofgeographic range or species richness.

Other potential complications stem fromuncertainty in the measurement of genus ageand the timing of apparent versus actual ex-tinctions. Some of the genera that first appearin any given time bin actually originated inprior bins, and some of the genera that last ap-pear in that bin in fact persisted into subse-quent time bins (Foote 2000). One way of eval-uating our confidence that the first and lastappearances of a genus in the PaleoDB reflectits actual origination and extinction is by mea-suring the completeness of its record withinits known stratigraphic range (Foote 1997,2001b; Foote and Raup 1996). Genera with alow probability of being sampled within theirknown stratigraphic range are also likely tohave stratigraphic ranges substantially short-er than their true duration. If uncertaintyabout genus age and/or timing of extinctioninfluences the association of genus age and ex-tinction risk, then we expect there to be an as-sociation between the average sampling prob-ability of genera within an order and the ap-parent age selectivity of extinction within thatorder.

To evaluate preservation probability, we cal-culated the proportion of all time bins withineach genus’s stratigraphic range for which thegenus has at least one recorded occurrence inthe PaleoDB. Because only internal occurrenc-es can be meaningfully evaluated (FAD andLAD bins must be excluded) this limits theanalysis to genera with durations of at leastthree bins. Each genus thus is scored from 1to 0, with 1 signifying total completeness and0 signifying total incompleteness. We aver-aged these scores for all genera in each orderto produce an estimate of preservation prob-ability at the ordinal level. We compared theseestimates with the median log-odds for the as-sociation between genus age and extinctionrisk (controlling for range and richness) for allorders having at least 30 genera in at least onetime bin (Supplementary Fig. 3; http://dx.doi.org/10.1666/07008.s4); there is no obvi-ous correlation. As an additional test, we splitgenera in each time bin into two groups: thosebelonging to orders with above-average pres-


ervation probabilities and those belonging toorders with below-average preservation prob-abilities. There is no consistent difference inthe log-odds for the association of genus ageand extinction risk for these two groups (Sup-plementary Fig. 4; http://dx.doi.org/10.1666/07008.s5) again suggesting that apparent ageselectivity is not strongly influenced by vari-ation in the reliability of age estimates or bythe backsmearing of last appearances.

Potential Effects of Taxonomic Artifacts. Ge-nus diversity data reflect a combination of bi-ological, stratigraphic, and taxonomic signals,and hence taxonomic practice can potentiallyhave a strong influence on survivorship. Thereare two primary type of taxonomic artifact tobe concerned about.

It is likely that within any time slice, oldergenera contain a higher proportion of poly-phyletic ‘‘form’’ genera, because the strati-graphic ranges of these genera may far exceedthose of their constituent lineages. Such formgenera are not necessarily biologically mean-ingless—in many cases they represent the it-erative evolution of ecologically successfulmorphotypes (Plotnick and Wagner 2006;Wagner and Erwin 2006; Wagner et al. 2007)—but including them in survivorship analysescould create a spurious negative associationbetween genus age and extinction risk. Wag-ner et al. (2007) determined that taxonomicstandardization tended to increase extinctionand origination rate estimates for Paleozoicgastropods (but affected only origination rateestimates for Jurassic bivalves and had littleeffect on origination or extinction rate esti-mates for Jurassic or Cenozoic bivalves). Al-though Wagner et al. did not examine strati-graphic ranges explicitly, the elevation of ex-tinction and origination rates in the standard-ized Paleozoic gastropod data set implies ashortening of mean stratigraphic duration,likely due in part to the splitting of long-rang-ing polyphyletic genera. Their taxonomicstandardizations also reduced the richnessesof the most speciose genera, many of whichhave quite long stratigraphic ranges. This im-plies that long-ranging polyphyletic generaalso tend to be relatively speciose at any giventime, and hence polyphyly alone may not ac-count for the tendency of extinction risk to de-

cline with age even among species-poor gen-era (Fig. 5B). Nevertheless, polyphyly cannotbe ruled out as an explanation for the ob-served pattern without detailed taxonomic re-vision far beyond the scope of this study.

Although polyphyly is likely to extendstratigraphic ranges artificially, the durationsof some lineages are prematurely truncated byparaphyly—the genus ceases to occur inyounger strata not because of lineage extinc-tion but rather because after some point intime the species in the lineage are sufficientlymorphologically distinct from their ancestorsthat they are removed from it and assigned toa new genus ( Simpson 1944; Van Valen 1973;Boucot 1978; Stanley 1979). It has been sug-gested that pseudo-extinction of paraphyletictaxa artificially inflates turnover rates (Smithand Patterson 1988; Forey 2004), but Uhen(1996) studied both simulations and empiricaldata on mammal families and found that par-aphyletic taxa are actually often more extinc-tion resistant than monophyletic taxa; othersimulation (Robeck et al. 2000; Sepkoski andKendrick 1993) and empirical studies (Wagner1995) have found that paraphyletic taxa gen-erally do not increase overall extinction prob-abilities.

The effect of pseudo-extinction on the as-sociation between taxonomic age and extinc-tion risk depends not on its overall prevalencebut on its frequency distribution with respectto age. Pseudo-extinction is often assumed tobe more common in older genera, an assump-tion that would tend to create a positive as-sociation between age and extinction risk. Al-though this has been observed in some groups(Pearson 1992, 1995; Doran et al. 2004, 2006),it is the opposite of the pattern we observe formost groups in most time intervals. Pseu-doextinction could only contribute to a nega-tive association between extinction risk andgenus age if it occurred more frequently in re-cently originated genera. Such an associationcould exist, if there is sufficient variation inrates of morphological evolution such that,within each cohort of originating genera,some subset of genera is likely to experiencepseudoextinction before the other genera in itscohort. Under this scenario the proportion ofeach cohort composed of rapidly evolving lin-


eages would decline as the cohort ages, andhence extinction risk would again appear todecrease with genus age at any given time.

A third possible source of bias is erroneoustaxonomy. Smith and Jeffery (1998) found thattaxonomic standardization of a database ofCretaceous–Paleogene echinoid occurrencesresulted in a marked decrease in the apparentselectivity of extinction with respect to geo-graphic range. They attributed this to a taxo-nomic misidentification bias that occurs whenspecies that should properly be assigned to ex-isting genera are instead assigned to newlyerected genera. The resulting junior synonymis usually recognized only in a limited area,and will also be very likely to go ‘‘extinct’’ inthe following time bin because surviving spe-cies will instead be properly assigned to thesenior synonym.

Although Smith and Jeffery considered onlygeographic range selectivity, it is clear thatsuch a bias would have a similar effect on spe-cies richness and genus age selectivity pat-terns. There is again no way to address thisproblem directly at the scale of this study.However, this bias would result primarily inan inflation of the proportion of singleton gen-era, and hence should have little effect on ex-tinction rates in older age cohorts. The factthat extinction is age selective even when theyoungest age cohort is excluded (Fig. 8) sug-gests that erroneous taxonomy is not a domi-nant component of the association betweenage and extinction risk.

Possible Evolutionary Explanations. If thepattern does reflect, at least in part, a genuinepositive association between genus age andaverage evolutionary fitness, there are twomodes by which this could occur. There couldin theory be a tendency for the average fitnessof species themselves to increase throughouttheir duration, so that the relative fitness of thegenus as a whole increases with time. Alter-natively, and in our opinion more plausibly,the inverse association of extinction risk andgenus age could reflect the accumulation ofgenera with extinction-resistant traits in olderage cohorts, even if there is no tendency forthe fitness of species within those genera to in-crease through time. This pattern would be ex-pected if extinction were acting selectively on

some as-yet-undetermined trait—such as en-vironmental range or dietary flexibility—suchthat species with unfavorable trait states wereculled by extinction early in the history of agiven age cohort. This would be expressedmost strongly at the genus level if the trait inquestion is highly conservative, so that speciesin the genus tend to give rise to new specieswith similar traits.

In both cases the mean fitness of the globalfauna would tend to increase through time.Without detailed species-level phylogeneticinformation it is not possible to distinguishbetween the microevolutionary mode of fit-ness increase within species and the macro-evolutionary mode of species (or genus) selec-tion (sensu Stanley 1979). However, neithermode is consistent with the Red Queen’s Hy-pothesis, because in both cases prior durationis an important determinant of extinction riskat any given time.

What then does the age selectivity of genusextinctions imply about extinction dynamicsand the veracity of the Red Queen’s Hypoth-esis? Despite its macroevolutionary origins,the Red Queen’s hypothesis has had its great-est impact on microevolutionary and ecologi-cal theory (Dawkins and Krebs 1979; Stensethand Maynard-Smith 1984; Dieckmann et al.1995; Clay and Kover 1996; Marrow et al. 1996;Warwick and Clarke 1996), and it is thereforehelpful to consider it as two related but dis-tinct hypotheses (Lively 1996): a ‘‘microevo-lutionary Red Queen’’ concerned with the ef-fect of biological competition on the produc-tion and maintenance of genetic variation(Lively 1996) and on community structure(Marrow et al. 1996), and a ‘‘macroevolution-ary Red Queen’’ concerned with its effect onextinction risk.

Each hypothesis involves some metric of rel-ative fitness, but measured in quite differentways. In the former case, fitness is measureddirectly as short-term reproductive success,whereas in the latter case fitness is inferredfrom taxonomic survivorship on geologicaltime scales. Although taxonomic survivorshipis contingent on reproductive success, it is dif-ficult to scale short-term reproductive successto geological time scales because rare eventshave a disproportionate influence on geologi-


cal and macroevolutionary processes (Grete-ner 1967; Raup 1991). Thus, even though thereis abundant evidence that microevolutionaryRed Queen dynamics are a pervasive featureof coevolutionary systems in nature (see ref-erences above, as well as numerous others) itis by no means clear that similar dynamicsshould be observed at the macroevolutionaryscale.

To explain the disparity between microevo-lutionary process and macroevolutionary pat-tern, it may be helpful to consider the expect-ed differences between biologically drivenand physically driven extinctions. In theirsynthesis of the Red Queen’s Hypothesis withisland biogeographic theory (MacArthur andWilson 1967) and species packing and limit-ing similarity theory (MacArthur and Levins1964), Stenseth and Maynard Smith (1984)concluded that two end-member states aremost likely to characterize the evolution ofmultispecies systems on geological timescales: a ‘‘Red Queen’’ state, dominated by bi-ological interactions and exhibiting fairly con-stant rates of origination and extinction, or aso-called ‘‘stationary’’ state dominated byphysical perturbations and exhibiting pulsedextinction and origination.

Organism-organism and organism-envi-ronment interactions differ critically in thatonly the former are symmetrical and escala-tory. Red Queen dynamics are predicted toarise in biological systems because all com-ponents of the system are involved in a zero-sum competition for energy: a new adaptationthat allows one species to increase its share ofavailable energy decreases the amount of en-ergy available to competitor species, whichadapt in response. In such a system it is dif-ficult for one species to maintain a consistentfitness advantage over evolutionary timescales. Hence, if biological interactions domi-nate long-term ecological dynamics and ex-tinction ultimately results from failure to com-pete successfully (the Red Queen state), priorevolutionary success does not predict presentextinction risk.

There is no comparable adaptive symmetryin the interactions between a species and itsphysical environment: the species evolves toadapt to its environment, but, with a few im-

portant exceptions, the environment itselfdoes not change meaningfully in response.Thus, organism-environment interactions donot have the escalatory quality of organism–organism interactions. Whereas the adaptivesymmetry of biological interactions meansthat ability to outrun a predator at presentdoes not guarantee the ability to escape pred-ators in the future, the traits that allow a spe-cies to survive a given physical perturbationonce (for example, ability to survive low-oxygen conditions) will also help it to survivecomparable perturbations in the future. Al-though the magnitude of such perturbations isof course highly variable, their magnitudedoes not escalate in response to the ability ofspecies to survive them. Moreover, in contrastto the essentially infinite and ever-changingvariety of potential biological threats, the po-tential physical threats faced by species (fluc-tuations in temperature, salinity, ocean pH,oxygen availability, habitat availability, nutri-ent availability) are comparatively limited.Over geological time scales, species are likelyto face many of the same physical threats overand over again (Hallam and Wignall 1997;Stanley 1990).

Thus, if a large proportion of extinctions aredue to geologically frequent physical pertur-bations that repeatedly impose similar envi-ronmental stresses (the stationary state), somedegree of age selectivity is expected. Prior du-ration should be negatively associated withextinction risk because long-ranging speciesare more likely to have previously faced—andsurvived—a given disturbance, and are there-fore more likely to posses whichever physio-logical or ecological traits enhance the likeli-hood of survival when a similar perturbationrecurs. Van Valen in fact noted this in his dis-cussion of perturbations: ‘‘It is the organismsin the adaptive zone that can link the pertur-bations across time in that the effects of oneperturbation may depend on the effects ofthose before it. Species easily removed by onekind of perturbation are not there if it comesagain soon, and may accumulate if it does notcome for a long time’’ (Van Valen 1973, p. 18).To this we add only that a single perturbationwill rarely remove all of the species that are ill-suited to the conditions that it imposes; rather,


each time the perturbation recurs it will re-move some fraction of the most susceptiblespecies and some smaller fraction of the lesssusceptible species. Under this model, somedegree of age selectivity seems unavoidable,as the composition of the biota at any time willalways have been shaped by previous pertur-bations.

The effect of an iterative culling mechanismwould be greatly enhanced if the trait(s) inquestion were conserved at the genus level, asis commonly the case for many physiologicaland ecological and possibly even some ma-croecological traits (Jablonski 1987). Progres-sive culling might also explain the lack of aconsistent relationship between extinctionrisk and genus age when the youngest age co-horts are excluded. Once a given cohort haspassed through the selective filter multipletimes, most of the genera that lack whichevertraits promote survival will have been elimi-nated and extinction risk among the remain-ing genera will no longer show a strong as-sociation with age. Exceptionally rare events(for example, large bolide impacts or severeocean acidification) would be expected to ex-hibit much less age selectivity because veryfew genera will have previously encounteredthe conditions that these events impose. Ageselectivity is in fact very low for some, thoughnot all, of the major mass extinctions (the mostnotable exception being the terminal Creta-ceous).

Recent analyses of marine extinction andorigination patterns and their relationships tochanges in sea level also suggest a primarilyphysical mechanism for most extinctions. Theclose correlation between metrics of sea leveland continental flooding and extinction rate,and similarities in the age distributions of sed-imentary basins and marine genera suggest aprimary role for relative sea level in control-ling global extinction rates at many times (Pe-ters and Foote 2002; Peters 2005, 2006). Fur-ther, correcting for variations in sampling in-tensity indicates that Phanerozoic extinctions(and originations) have been even morepulsed and episodic in time than suggested bythe raw data (Foote 2005, 2007). All of theseobservations are more easily reconciled with aprimarily physically driven extinction model

than with the biologically driven extinctionregime posited by the Red Queen model.

Some paleoecological evidence also sug-gests a dominant role for physical factors indriving most extinctions. The basic ecologicalstructure of marine communities has often re-mained markedly stable for long intervals,suggesting that the ecological environmentexperienced by species does not necessarilydeteriorate steadily through time (Morris et al.1995; Bambach 2002; Bambach et al. 2002;Bush and Bambach 2004a,b; Wagner et al.2006), contrary to the Red Queen’s Hypothe-sis. Furthermore, only events as severe as theera-bounding mass extinctions may be suffi-cient to disrupt the large-scale ecologicalstructure of communities (Bambach et al.2002; McGhee et al. 2004).

Aside from the terminal Permian and ter-minal Triassic, age selectivity is notably lowduring the Cambro-Ordovician, the Triassic(though this is manifest only within orders),and the Paleocene. This is somewhat surpris-ing—given that these intervals have excep-tionally high origination rates and that younggenera usually exhibit the highest extinctionrates, we would expect them to exhibit strongselectivity. We have no favored interpretationof this pattern, but it is notable and perhapsworthy of further attention that the advantag-es of incumbency appear to be reduced or ab-sent during these intervals of elevated origi-nation.

As initially pointed out by Boyajian (1986),the age selectivity of extinction, whatever itsfundamental causes, is an important compo-nent of the Phanerozoic decline in extinctionrates of marine genera (Raup and Sepkoski1982). Because our analysis suggests that thisselectivity is not explained by species richnessor geographic range effects, it supports thehypothesis that the decline in extinction ratesreflects, at least in part, an increase in meanfitness (where fitness is defined simply as ex-tinction resistance at the species level). Here itis important, once again, to distinguish be-tween fitness with respect to biological com-petition and fitness with respect to physicalperturbations. Although biological competi-tion has likely driven an increase in absolute fit-ness, such that the average Cambrian species


would be ill equipped to compete with the av-erage Neogene species (Vermeij 2004), the rel-ative competitive fitness distribution has likelyremained static, constrained by microevolu-tionary Red Queen dynamics. Rather, meanfitness may have increased because repeatedphysical perturbations have culled the taxathat are least equipped to survive the condi-tions they impose, leading to a progressive ac-cumulation of extinction-resistant taxa and aconsequent decline in extinction rates throughthe Phanerozoic.

Summary

Within nearly all Phanerozoic time inter-vals, there is a significant inverse associationbetween genus age and extinction risk, in con-tradiction to a Red Queen macroevolutionarymodel. Surprisingly, very little of this age se-lectivity is accounted for by the fact that oldergenera tend to be more species rich and widerranging within any given interval. Extinctionrisk does not decline as a simple function ofgenus age but rather drops off rapidly amongthe youngest age cohorts and thereafter showslittle relationship to age. Some of the age se-lectivity in the global fauna can be explainedby combining higher taxa with differing in-trinsic extinction rates in a single analysis, buta statistically significant age-selective signalremains even within many taxonomic orders.This pattern may be influenced by taxonomicartifacts, but this possibility is difficult to eval-uate. Alternatively, we suggest that the asso-ciation reflects selective extinction acting onsome other, as-yet unidentified covariate(s) ofgenus age, resulting in the progressive accu-mulation of extinction-resistant species andgenera. Such a pattern is difficult to reconcilewith a Red Queen model in which most ex-tinctions result from escalatory biologicalcompetition, but it is consistent with geolog-ical evidence for recurrent physical perturba-tions, rather than biological interactions, asthe major drivers of extinction through thePhanerozoic. Red Queen dynamics may dom-inate much of evolutionary time, but large, in-frequent disturbances of the physical environ-ment appear to play a disproportionate role inmacroevolutionary dynamics.

Acknowledgments

We would like to thank C. Simpson for veryhelpful discussions; A. Bush, S. Peters, and P.Wagner for comments on the manuscript; M.Foote and N. Doran for extremely thoroughand thoughtful reviews; and the members ofthe Paleobiology Database for providing thedata. This is Paleobiology Database publica-tion number 76.

Appendix

Analytical Artifacts Related to Mixing of Taxa andTime Intervals

A potentially important statistical artifact arises when generafrom many higher taxonomic groups are combined in a singlestatistical sample, which we will hereafter refer to as a compos-ite sample (Van Valen 1973, 1976a,b, 1979; Raup and Sepkoski1982; Van Valen and Boyajian 1987; Foote 2001a). Taxa withcharacteristically high extinction rates contain proportionatelymore young genera than taxa with lower extinction rates, justas the mean age of individuals is lower in countries with highmortality rates than it is in countries with low mortality. Con-sequently, the younger genera in a composite sample are drawndisproportionately from taxa with high extinction rates, andwill therefore be at greater risk of extinction than older generaeven if extinction is entirely independent of age within highertaxa. On a standard semilogarithmic survivorship plot of genusage versus time this is expressed as concavity in the survivor-ship curve, resulting from the averaging of multiple taxon-specificsurvivorship curves, each of which is log-linear but which arecharacterized by differing exponential decay rates (Van Valen1979; Holman 1983; Foote 2001a). The distinction between ap-parent age selectivity in the composite sample and genuine ageselectivity within higher taxa is an important one, because un-der the Red Queen model extinction is predicted to be indepen-dent of age only within ecologically homogenous groups—forpractical purposes usually considered to be orders or classes(Van Valen 1973).

Cumulative (or dynamic) survivorship analyses, which com-bine genera from many different time intervals in a single sta-tistical sample, can suffer from a similar analytical artifact, at-tributable in this case to variation in extinction rates throughtime rather than among higher taxa. Because overall extinctionrates have fallen through the Phanerozoic, Paleozoic genera aregenerally shorter lived than Meso-Cenozoic genera. Hence, inthe Phanerozoic cumulative sample young genera will appearto be at greater risk of extinction than old genera because youngage classes contain disproportionate numbers of genera thatoriginated in the Paleozoic, when genera of all ages appear tohave experienced higher extinction risk than in the Meso-Ce-nozoic. Cumulative survivorship analyses thus confound the ef-fects of age and time (Holman 1983; Pearson 1992, 1995; Doranet al. 2004, 2006) in the same way that composite samples con-found the effects of age and phylogeny. Cumulative survivor-ship analyses are also complicated by temporal variation in theduration of sampling bins (Sepkoski 1975) and by ‘‘censoring’’of the future durations of extant genera: because we have noknowledge of how long extant genera will ultimately persist,the durations of these genera cannot be directly compared withthose of extinct genera (Van Valen 1979; Gilinsky 1988; Foote2001a; Doran et al. 2004, 2006). Our approach, which considersindividual extinction/survival events rather than ultimate du-rations, does not suffer from these complications.


Accounting for Range-Through Genera

When comparing the relative effects of genus age, geographicrange, and species richness, genera that are unsampled in oneor more time bin between their first and last appearances (here-after referred to as ‘‘range-through’’ genera) pose a potentialproblem. Although their existence can be inferred by range in-terpolation, it is impossible to evaluate the species richness orgeographic range of a genus for an interval in which it is un-sampled. Range-through genera are a combination of generathat, though documented in the literature, have not yet been en-tered into the PaleoDB and ‘‘Lazarus’’ genera (Flessa and Ja-blonski 1983) that are actually missing from the fossil record.As such, their distribution is strongly affected by sampling. Theproportion of range-through occurrences would be expected toincrease toward the present in the PaleoDB if, like the Sepkoskidatabase, it incorporated intensive sampling of the living fauna.Instead, the proportion of range-through occurrences peaks inthe late Paleozoic and Mesozoic and declines in the Cenozoic,reflecting both variation in sampling intensity and the edge ef-fects associated with truncation of the time series late in the Ce-nozoic.

It is not reasonable to exclude range-through genera, giventhat they account for as much as 42% of extant genera in sometime intervals (the maximum proportion of range-through gen-era in any interval rises to 46% if genera older than ten time binsare included, because these genera are much less likely thanyounger genera to have been sampled in the prior interval). Fur-thermore, many range-through occurrences are likely attribut-able to low richness and/or narrow geographic range; ignoringthem would bias the sample by preferentially excluding narrow-ly distributed and/or species-poor genera that nonetheless es-cape extinction, inflating apparent extinction rates in low rich-ness and narrow range classes and thereby artificially exagger-ating the influence of range and richness on extinction risk. Inaddition, because range-through genera have necessarilypassed through at least one bin boundary prior to the bin inwhich they go unsampled, their average age is greater than thatof other genera in the same bin, and hence ignoring them biasesthe age distribution of the sample.

To address this issue we generated two alternative sets of sim-ulated geographic range and species-richness values for range-through occurrences, designed to represent end-members in thespectrum of reasonable values. In the first case, all range-through genera in all time bins were assigned minimal richnessand range values of 1, under the assumption that they were dis-proportionately dominated by species-poor and narrowly dis-tributed genera. In the second case, range-through genera ineach time bin were assigned richness and range values drawnrandomly (as paired values, so that the association betweenrichness and range is preserved) from the richness and rangedistributions of genera that are sampled in that time bin, belongto the same order as the range-though genus (or class, if therewere no genera of equivalent age in the order), are of the sameage and, like the range-through genus, survive into the next bin.

The latter case is an unrealistically conservative model, be-cause it assumes that there is no difference in species richnessor geographic range between the genera that are actually sam-pled and those that are not. This is almost certainly not true.Although it is impossible to evaluate directly the species rich-ness and geographic range of genera in the intervals from whichthey are missing, it is interesting to note that low species rich-ness and geographic range in one interval appear to be impor-tant predictors of the likelihood that a given genus will not besampled in the subsequent interval: in 37 out of 47 time bins thatdirectly precede bins with range-through genera (the two mostrecent time bins are excluded because of edge effects), meanrichness and range are higher for genera that are sampled in the

subsequent time bin than for genera that range through the sub-sequent bin but are unsampled within it. The impact of range-through occurrences on observed age-selectivity trends turnsout to be quite minor (median log-odds � 0.29 using minimumrange and richness values, 0.26 using maximum range and rich-ness values). Because these results differ only slightly, we usemaximum values in all analyses.

Literature CitedAlbert, A., and J. A. Anderson. 1984. On the existence of max-

imum likelihood estimates in logistic regression models.Biometrika 71:1–10.

Alroy, J., C. R. Marshall, R. K. Bambach, K. Bezusko, M. Foote,F. T. Fursich, T. A. Hansen, S. M. Holland, L. C. Ivany, D. Ja-blonski, D. K. Jacobs, D. C. Jones, M. A. Kosnik, S. Lidgard, S.Low, A. I. Miller, P. M. Novack-Gottshall, T. D. Olszewski, M.E. Patzkowsky, D. M. Raup, K. Roy, J. J. Sepkoski Jr., M. G.Sommers, P. J. Wagner, and A. Webber. 2001. Effects of sam-pling standardization on estimates of Phanerozoic marine di-versification. Proceedings of the National Academy of Scienc-es USA 98:6261–6266.

Anstey, R. L. 1978. Taxonomic survivorship and morphologiccomplexity in Paleozoic bryozoan genera. Paleobiology 4:407–418.

Arnold, A. J., D. C. Kelly, and W. C. Parker. 1995. Causality andCope’s rule: evidence from the planktonic foraminifera. Jour-nal of Paleontology 69:203–210.

Bambach, R. K. 2002. Supporting predators: changes in the glob-al ecosystem inferred from changes in predator diversity. Pp.319–352 in M. Kowalewski and P. H. Kelley, eds. The fossil re-cord of predation. The Paleontological Society, New Haven.

Bambach, R. K., A. H. Knoll, and J. J. Sepkoski Jr. 2002. Anatom-ical and ecological constraints on Phanerozoic animal diver-sity in the marine realm. Proceedings of the National Acad-emy of Sciences USA 99:6854–6859.

Baumiller, T. K. 1993. Survivorship analysis of Paleozoic Cri-noidea: effect of filter morphology on evolutionary rates. Pa-leobiology 19:304–321.

Berg, H. C. 1983. Random walks in biology. Princeton Univer-sity Press, Princeton, N.J.

Boucot, A. J. 1978. Community evolution and rates of cladogen-esis. Evolutionary Biology 11:545–655.

Boyajian, G. E. 1986. Phanerozoic trends in background extinc-tion; consequences of an aging fauna. Geology 14:955–958.

———. 1991. Taxon age and selectivity of extinction. Paleobiol-ogy 17:49–57.

Boyajian, G. E., and T. Lutz. 1992. Evolution of biological com-plexity and its relation to taxonomic longevity in the Am-monoidea. Geology 20:983–986.

Burnham, K. P., and D. R. Anderson. 2002. Model selection andmultimodel inference: a practical information-theoretic ap-proach. Springer, New York.

Bush, A. M., and R. K. Bambach. 2004a. Are secular changes intiering, motility, and predation real? Quantifying and testingchanges in ecospace use between the Paleozoic and Cenozoic.Geological Society of America Annual Meeting Abstractswith Program 36:457.

———. 2004b. Phanerozoic increases in alpha diversity andevenness: linked consequences of increased ecospace use.Geological Society of America Meeting Abstracts with Pro-grams 36:457.

Clay, K. K., and P. P. X. Kover. 1996. The Red Queen hypothesisand plant/pathogen interactions. Annual Review of Phyto-pathology 34:29–50.

Dawkins, R., and J. R. Krebs. 1979. Arms races between andwithin species. Proceedings of the Royal Society of London B205:489–511.


Dieckmann, U., P. Marrow, and R. Law. 1995. Evolutionary cy-cling in predator-prey interactions: population dynamics andthe Red Queen Journal of Theoretical Biology 176:91–102.

Doran, N. A., A. J. Arnold, W. C. Parker, and F. W. Huffer. 2004.Deviation from Red Queen behaviour at stratigraphic bound-aries: evidence for directional recovery. Geological Societyspecial publication 230:35–46.

———. 2006. Is extinction age-dependent? Palaios 21:571–579.Flessa, K. W., and D. Jablonski. 1983. Extinction is here to stay.

Paleobiology 9:315.———. 1985. Declining Phanerozoic background extinction

rates: effect of taxonomic structure. Nature 313:216–218.Foin, T. C., J. W. Valentine, and F. J. Ayala. 1975. Extinction of

taxa and Van Valen’s law. Nature 257:514–515.Foote, M. 1988. Survivorship analysis of Cambrian and Ordo-

vician trilobites. Paleobiology 14:258–271.———. 1997. Estimating taxonomic durations and preservation

probability. Paleobiology 23:278–300.———. 2000. Origination and extinction components of taxo-

nomic diversity: general problems. Paleobiology 26:74–102.———. 2001a. Evolutionary rates and the age distributions of

living and extinct taxa. Pp. 245–294 in J. B. C. Jackson, S. Lid-gard, and F. K. McKinney, eds. Evolutionary patterns: growthform and tempo in the fossil record. University of ChicagoPress, Chicago.

———. 2001b. Inferring temporal patterns of preservation, orig-ination, and extinction from taxonomic survivorship analysis.Paleobiology 27:602–630.

———. 2005. Pulsed origination and extinction in the marinerealm. Paleobiology 31:6–20.

———. 2007. Extinction and quiescence in marine animal gen-era. Paleobiology 33:261–272.

Foote, M., and A. I. Miller. 2007. Principles of paleontology, 3ded. W. H. Freeman, New York.

Foote, M., and D. M. Raup. 1996. Fossil preservation and thestratigraphic ranges of taxa. Paleobiology 22:121–140.

Forey, P. L. 2004. Taxonomy and fossils: a critical appraisal. Phil-osophical transactions of the Royal Society of London B 359:639–653.

Gilinsky, N. L. 1988. Survivorship in the Bivalvia: comparingliving and extinct genera and families. Paleobiology 14:370–386.

Gretener, P. E. 1967. Significance of the rare event in geology.AAPG Bulletin 51:2197–2206.

Hallam, A. 1976. Red Queen dethroned. Nature 259:12–13.Hallam, A., and P. B. Wignall. 1997. Mass extinctions and their

aftermaths. Oxford University Press, New York.Hoffman, A., and J. A. Kitchell. 1984. Evolution in a pelagic

planktic system: a paleobiologic test of models of multispe-cies evolution. Paleobiology 10:9–33.

Holman, E. W. 1983. Time scales and taxonomic survivorship.Paleobiology 9:20–25.

Hosmer, D. W., and S. Lemeshow. 2000. Applied logistic regres-sion. Wiley, New York.

Jablonski, D. 1986. Background and mass extinctions: the alter-nation of macroevolutionary regimes. Science 231:129–133.

———. Heritability at the species level: analysis of geographicranges of cretaceous mollusks. Science 238:360–363.

Jones, D. S., and D. Nicol. 1986. Origination, survivorship, andextinction of rudist taxa. Journal of Paleontology 60:107–115.

Lively, C. M. 1990. Red Queen hypothesis supported by para-sitism in sexual and clonal fish. Nature 344:864.

Lively, C. M. 1996. Host-Parasite Coevolution and Sex. Bio-Science 46:107.

MacArthur, R. H., and R. Levins. 1964. Competition, habitat se-lection, and character displacement in a patchy environment.Proceedings of the National Academy of Sciences USA 51:1207–1210.

MacArthur, R. H., and E. O. Wilson. 1967. The Theory of IslandBiogeography. Princeton University Press, Princeton, N.J.

Marrow, P., U. Dieckmann, and R. Law. 1996. Evolutionary dy-namics of predator-prey systems: an ecological perspective.Journal of Mathematical Biology 34:556–578.

Mayr, E. 1942. Systematics and the Origin of Species From theViewpoint of a Zoologist. Columbia University Press, NewYork.

McGhee, G. R., P. M. Sheehan, D. J. Bottjer, and M. L. Droser.2004. Ecological ranking of Phanerozoic biodiversity crises:ecological and taxonomic severities are decoupled. Palaeo-geography, Palaeoclimatology, Palaeoecology 211:289–297.

McKinney, M. L. 1997. Extinction vulnerability and selectivity:combining ecological and paleontological views. Annual Re-view of Ecology and Systematics 28:495–516.

Miller, A. I. 1997. A new look at age and area: the geographicand environmental expansion of genera during the Ordovi-cian Radiation. Paleobiology 23:410–419.

Morris, P. J., L. C. Ivany, K. M. Schopf, and C. E. Brett. 1995. Thechallenge of paleoecological stasis: reassessing sources ofevolutionary stability. Proceedings of the National Academyof Sciences USA 92:11269–11273.

Payne, J. L., and S. Finnegan. 2007. The effect of geographicrange on extinction risk during background and mass extinc-tion. Proceedings of the National Academy of Sciences USA104:10506–10511.

Pearson, P. N. 1992. Survivorship analysis of fossil taxa whenreal-time extinction rates vary: the Paleogene planktonic fo-raminifera. Paleobiology 18:115–131.

———. 1995. Investigating age-dependency of species extinctionrates using dynamic survivorship analysis. Historical Biology10:119–136.

Peduzzi, P., J. Concato, E. Kemper, T. R. Holford, and A. R. Fein-stein. 1996. A simulation study of the number of events pervariable in logistic regression analysis. Journal of Clinical Ep-idemiology 49:1373–1379.

Peters, S. E. 2005. Geologic constraints on the macroevolution-ary history of marine animals. Proceedings of the NationalAcademy of Sciences USA 102:12326–12331.

———. 2006. Genus richness in Cambrian-Ordovician benthicmarine communities in North America. Palaios 21:580–587.

Peters, S. E., and M. Foote. 2002. Determinants of extinction inthe fossil record. Nature 416:420–424.

Plotnick, R. E., and P. J. Wagner. 2006. Round up the usual sus-pects: common genera in the fossil record and the nature ofwastebasket taxa. Paleobiology 32:126–146.

Raup, D. M. 1972. Taxonomic diversity during the Phanerozoic.Science 177:1065–1071.

———. 1975. Taxonomic survivorship curves and Van Valen’sLaw. Paleobiology 1:82–96.

———. 1978a. Approaches to the extinction problem. Journal ofPaleontology 52:517–523.

———. 1978b. Cohort analysis of generic survivorship. Paleo-biology 4:1–15.

———. 1991. A kill curve for Phanerozoic marine species. Pa-leobiology 17:37–48.

———. 1992. Extinction: bad genes or bad luck? Norton, NewYork.

Raup, D. M., S. J. Gould, T. J. M. Schopf, and D. S. Simberloff.1973. Stochastic-models of phylogeny and evolution of diver-sity. Journal of Geology 81:525–542.

Raup, D. M., and J. J. Sepkoski Jr. 1982. Mass extinctions in themarine fossil record. Science 215:1501–1503.

Robeck, H. E., C. C. Maley, and M. J. Donoghue. 2000. Taxonomyand temporal diversity patterns. Paleobiology 26:171–187.

Sadler, P. M. 2004. Quantitative biostratigraphy—achieving fin-er resolution in global correlation. Annual Review of Earthand Planetary Sciences 32:187–213.


Salthe, S. N. 1975. Some comments on Van Valen’s law of ex-tinction. Paleobiology 1:356–358.

Sepkoski, J. J., Jr. 1975. Stratigraphic biases in the analysis of tax-onomic survivorship. Paleobiology 1:343–355.

———. 1993. Ten years in the library; new data confirm pale-ontological patterns. Paleobiology 19:43–51.

———. 2002. A compendium of fossil marine animal genera.Bulletins of American Paleontology 363:560.

Sepkoski, J. J., Jr., and D. C. Kendrick. 1993. Numerical experi-ments with model monophyletic and paraphyletic taxa. Pa-leobiology 19:168–184.

Simpson, G. G. 1944. Tempo and mode in evolution. ColumbiaUniversity Press, New York.

Smith, A. B., and C. H. Jeffery. 1998. Selectivity of extinctionamong sea urchins at the end of the Cretaceous period. Nature392:69–71.

Smith, A. B., and C. Patterson. 1988. The influence of taxonomicmethod on the perception of patterns of evolution. Evolution-ary Biology 23:127–216.

Stanley, S. M. 1979. Macroevolution: pattern and process. W. H.Freeman, San Francisco.

———. 1990. Delayed recovery and the spacing of major extinc-tions. Paleobiology 16:401–414.

Stenseth, N. C., and J. Maynard-Smith. 1984. Coevolution in eco-systems: Red Queen evolution or stasis? Evolution 38:870–880.

Uhen, M. D. 1996. An evaluation of clade-shape statistics usingsimulations and extinct families of mammals. Paleobiology22:8–22.

Van Valen, L. 1973. A new evolutionary law. Evolutionary The-ory 1:1–30.

———. 1976a. Energy and evolution. Evolutionary Theory 1:179–229.

———. 1976b. The red queen lives. Nature 260:575.———. 1979. Taxonomic survivorship curves. Evolutionary The-

ory 4:129–142.Van Valen, L. M., and G. E. Boyajian. 1987. Phanerozoic trends

in background extinction: consequence of an aging fauna—Comment and reply. Geology 15:875–876.

Vermeij, G. J. 2004. Nature: an economic history. Princeton Uni-versity Press, Princeton, N.J.

Wagner, P. J. 1995. Diversification among early Paleozoic gas-tropods: contrasting taxonomic and phylogenetic descrip-tions. Paleobiology 21:410–439.

Wagner, P. J., and D. H. Erwin. 2006. Patterns of convergence ingeneral shell form among Paleozoic gastropods. Paleobiology32:316–337.

Wagner, P. J., M. A. Kosnik, and S. Lidgard. 2006. Abundancedistributions imply elevated complexity of post-Paleozoicmarine ecosystems. Science 314:1289–1292.

Wagner, P. J., M. Aberhan, A. Hendy, and W. Kiessling. 2007. Theeffects of taxonomic standardization on sampling-standard-ized estimates of historical diversity. Proceedings of the Roy-al Society B 274:439–444.

Warwick, R. M., and K. R. Clarke. 1996. Relationships betweenbody-size, species abundance and diversity in marine benthicassemblages: facts or artefacts? Journal of Experimental Ma-rine Biology and Ecology 202:63–71.

Willis, J. C. 1922. Age and area. Cambridge University Press,Cambridge.

the red queen revisited: reevaluating the age selectivity...

Documents