Local and global abundance associated with extinction risk ... · mates from the Paleobiology Database. Close similarity in the overall diversity histories of the Sepkoski database

Local and global abundance associated with extinction risk in latePaleozoic and early Mesozoic gastropods

Jonathan L. Payne, Sarah Truebe, Alexander Nutzel, and Ellen T. Chang

Abstract.—Ecological theory predicts an inverse association between population size and extinctionrisk, but most previous paleontological studies have failed to confirm this relationship. The reasonsfor this discrepancy between theory and observation remain poorly understood. In this study, wecompiled a global database of gastropod occurrences and collection-level abundances spanning theEarly Permian through Early Jurassic (Pliensbachian). Globally, the database contains 5469occurrences of 496 genera and 2156 species from 839 localities. Within the database, 30 collectionsdistributed across seven stages contain at least 75 specimens and ten genera—our minimum criteriafor within-collection analysis of extinction selectivity. We use logistic regression analysis, based onglobal and local measures of population size and stage-level extinction patterns in Early Permianthrough Early Jurassic marine gastropods, to assess the relationship between abundance andextinction risk. We find that global genus occurrence frequency is inversely associated with extinctionrisk (i.e., positively associated with survival) in 15 of 16 stages examined, statistically significantly soin five stages. Although correlation between geographic range and occurrence frequency may accountfor some of this association, results from multivariable regression analysis suggest that the associationbetween occurrence frequency and extinction risk is largely independent of geographic range. Withinlocal assemblages, abundance (number of individuals) is also inversely associated with extinction risk.The strength of association is consistent across time and modes of fossil preservation. Effect strength ispoorly constrained, particularly in analyses of local collections. In addition to limited power dueto small sample size, this poor constraint may result from confounding by ecological variablesnot controlled for in the analyses, by taphonomic or collection biases, or from non-monotonicrelationships between abundance and extinction risk. Two factors are likely to account for thedifference between our results and those of most previous studies. First, many previous studiesfocused on the end-Cretaceous mass extinction event; the extent to which these results can begeneralized to other intervals remains unclear. Second, previous findings of nonselective extinctioncould result from insufficient statistical power rather than the absence of an underlying effect, becausenonselective extinction is generally used as the null hypothesis for statistical convenience.Survivorship patterns in late Paleozoic and early Mesozoic gastropods suggest that abundance hasbeen a more important influence on extinction risk through the Phanerozoic than previouslyappreciated.

Jonathan L. Payne and Sarah Truebe.* Department of Geological and Environmental Sciences, StanfordUniversity, Stanford, California 94305. E-mail: [email protected]. *Present address: Department ofGeosciences, University of Arizona, 1040 East Fourth Street, Tucson, Arizona 85721

Alexander Nutzel. Bayerische Staatssammlung fur Palaontologie und Geologie, Ludwig-Maximilians-University Munich, Department fur Geo- und Umweltwissenschaften, Sektion fur Palaontologie,Geobiocenter LMU, Richard Wagner Strasse 10, Munich 80333, Germany

Ellen T. Chang. Division of Epidemiology, Department of Health Research and Policy, Stanford UniversitySchool of Medicine, Stanford, California 94305 and Cancer Prevention Institute of California, 2201 WalnutAvenue, Suite 300, Fremont, California 94538

Accepted: 4 March 2011Supplemental materials deposited at Dryad: doi: 10.5061/dryad.8330

Introduction

Population size is predicted to scale inverse-ly with extinction risk under a wide variety ofextinction scenarios (Pimm et al. 1988; Lande1993; Hubbell 2001). However, the fossil recordprovides at best mixed support for thisprediction. Four paleontological studies usedspecimen counts to test explicitly for anassociation between population size and ex-tinction risk for identified extinction events and

none found a significant association (McClureand Bohonak 1995; Hotton 2002; Lockwood2003; Leighton and Schneider 2008). Simpsonand Harnik (2009) assessed the relationshipbetween longevity and average abundance inmarine bivalves, finding a significant butnonlinear relationship between abundanceand longevity: longevity increased with abun-dance among the very rare to common taxa,but then decreased again among the propor-tionally most abundant taxa. Several other

Paleobiology, 37(4), 2011, pp. 616–632

’ 2011 The Paleontological Society. All rights reserved. 0094-8373/11/3704–0006/$1.00

studies used occurrence frequency (i.e., thenumber of distinct localities from which ataxon has been reported) as a proxy forabundance, with mixed results. Kiessling andBaron-Szabo (2004) found no association be-tween occurrence frequency and survivorshipfor Maastrichtian coral genera, and Powell(2008) found no association for Late Mississip-pian brachiopod genera. In contrast, Kiesslingand Aberhan (2007) found a significant inverseassociation between occurrence frequency andgenus extinction risk during most stages of theLate Triassic and Early Jurassic in a combinedanalysis of marine genera from several inver-tebrate phyla. Wilf and Johnson (2004) reportedthe preferential survival of rare plant speciesacross the Cretaceous/Paleogene boundary,although they did not present an explicitstatistical test of this association. Stanley(1986), on the other hand, argued that popula-tion size was the key determinant of species-level extinction in Pacific Neogene bivalves,using a variety of qualitative proxies forabundance. Overall, the small number ofprevious studies, differences among them interms of temporal and taxonomic coverage andstatistical methodology, and disproportionatefocus on episodes of mass extinction limit anyattempt at generalization.

Clarifying the relationship between popula-tion size and extinction risk is essential forassessing the extent to which simple ecologicalmodels can be scaled to geological time scales,over which rare events associated with rapidenvironmental change appear to be the primarycauses of extinction (Raup 1991b; Foote 2005,2007). Moreover, extinction selectivity may varydepending upon the nature or scale of thecausal process (Jablonski 1986, 2005; Payne andFinnegan 2007), highlighting the need fordata from multiple time intervals to assessthe persistence of selectivity patterns throughgeological time. Rare events could select uponcharacteristics unrelated to success duringquiescent times, leaving traits such as abun-dance poor predictors of extinction risk onmacroevolutionary time scales or during epi-sodes of rapid environmental change—Raup’s(1991a) ‘‘Wanton Destruction’’ extinction mode.

In this study, we assess the associationbetween abundance and extinction risk for

Early Permian through Early Jurassic marinegastropods, using both global occurrencefrequency and local population density asmeasures of population size. This intervalspans three major extinction events (MiddlePermian, end-Permian, end-Triassic) and theirrespective recoveries as well as the interveningstages. It thus provides the opportunity toassess the degree of similarity in extinctionselectivity across a range of macroevolutionaryconditions. Gastropods are especially suitablefor such an analysis because they representone of the most diverse and abundant clades ofmarine animals during this interval. Theywere not marginalized by any of the extinctionevents, so a within-group analysis of extinctionpatterns is especially promising.

Data and Methods

In this study, we use both local and globaldata to assess the relationship between abun-dance and extinction risk in genera. We com-piled gastropod occurrences from the publishedtaxonomic literature, including collection-levelspecimen counts wherever possible. Below wedescribe the database size and structure, ourtreatment of the data fields, and our statisticalapproach to the analysis of extinction selectivity.

Databases

Global Database.—We compiled occurrenceand abundance data from published mono-graphs of gastropod assemblages of EarlyPermian through Early Jurassic (Pliensbach-ian) age (299-183 Ma). The resultant databaseincludes taxonomic assignments and specimencounts as well as summary information re-garding the locality, preservation, collectionmode, and depositional environment. Thestandardized global data set includes 5469occurrences of 496 genera and 2156 speciesfrom 839 localities spanning 19 geologicalstages. We merged the Asselian with theSakmarian, the Wordian with the Capitanian,and the Induan with the Olenekian forpurposes of analysis, yielding 16 discrete timeintervals that we refer to below as stages forsimplicity. The mean stage length is 7.25 Myrand the stages range in duration from 2.6 Myr(Roadian) to 14.6 Myr (Asselian–Sakmarian).The data set analyzed in this study is archived

ABUNDANCE AND EXTINCTION RISK 617

at Dryad (http://dx.doi.org/10.5061/dryad.8330).

Local Collections.—Analyses of individualcollections were restricted to those containing75 or more specimens representing ten or moregenera, of which at least four were extinctionvictims and at least four survived to thefollowing stage. We required a minimumnumber of victims and survivors becauseregression analysis requires variation in boththe predictor and outcome variables andpower is limited by the number of observa-tions with the less common outcome; theperformance of logistic regression can becomeunreliable when the number of instances of theless common outcome per variable is extreme-ly small (Peduzzi et al. 1996). In total, 30collections distributed among seven stagesmet our sample-size criteria. Thirteen of thecollections examined were from bulk rockmaterial, six were from hand-picked surfacecollections, and 11 were mixed or unknown.The bulk-rock collections were preservedprimarily via silicification, whereas the hand-picked and mixed collections were preservedprimarily as original shells or via calcitereplacement (Table 1).

Data Fields

Taxonomy.—Taxonomic assignments werestandardized on the basis of recent taxonomicliterature and Alexander Nutzel’s unpub-lished taxonomic database. Subgenera wereelevated to genus rank. Only specimensclassified to species level in the primaryliterature were included in the analysis be-cause taxonomic standardization is oftenimpossible for specimens assigned only at thegenus level (see Wagner et al. 2007). Mostspecimens assigned to extant genera wereremoved from the data set because these fossilgenera frequently are polyphyletic form gen-era (i.e., ‘‘garbage bin’’ genera), often reflectingbasic shell shapes, rather than monophyletic(or even paraphyletic) groups (Nutzel 2005;Plotnick and Wagner 2006). For example,Turritella has been used simply to refer tohigh-spired shells and Patella to many limpets.Specimens assigned to Emarginula were in-cluded in the analysis because we consider thisgenus to be a phylogenetically meaningful

entity in Permian–Triassic samples, even if it isnot the same clade represented by morpho-logically similar living species. Monophyly ofgenera cannot be ascertained with certainty forthe late Paleozoic and early Mesozoic. How-ever, comparisons of molecular and morpho-logical phylogenies show that morphologicallybased genera can serve as good proxies forclosely related molluscan species (Jablonskiand Finarelli 2009).

Survivorship.—From our database we deter-mined minimum stage-level stratigraphicranges of genera and subgenera. If youngerlast occurrences were reported in Sepkoski’s(2002) compendium of the stratigraphic rangesof marine animal genera, then the times ofextinction were adjusted accordingly. Only 22genera (4.4%) were affected by this adjustmentin time of extinction. We used Sepkoski’scompendium because it provides stable esti-mates of global origination and extinctiontime, in contrast to potentially variable esti-mates from the Paleobiology Database. Closesimilarity in the overall diversity histories ofthe Sepkoski database and the PaleobiologyDatabase (Alroy et al. 2008) and the smallnumber of genera affected by adjustments intime of extinction suggest that the choice ofcompendium is unlikely to substantially influ-ence the results.

Geographic Range.—We determined geo-graphic range for each genus in each stage,and thus treated it as a dynamic variable ratherthan a taxon trait. This approach avoidscomplications introduced by the bidirectionalrelationship between taxon longevity andmaximum geographic range (Foote et al.2008). Geographic range was quantified as themaximum great circle distance between anytwo occurrences of a genus within a givenstage. To calculate the paleolatitude and paleo-longitude of each locality, we used paleograph-ic reconstructions embedded in Chris Scotese’sPoint Tracker software (Scotese 2007).

Global Occurrence Frequency.—Occurrencefrequency has been shown to correlate withpopulation density for a wide range of extantand fossil taxa (Buzas et al. 1982; Brown 1984).In this study we use global occurrence fre-quency as a proxy for global population size.We calculate occurrence frequency as the

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number of localities at which a given genus hasbeen reported. Each locality is counted as oneoccurrence regardless of the number of indi-viduals or species within the genus reportedfrom that locality.

Local Specimen Counts.—In our analyses oflocal collections, we used the number ofreported specimens as a proxy for localpopulation size. Live-dead comparisons sug-gest that dead shell abundance is correlatedwith the size of the living population forbenthic mollusks (Kidwell 2001, 2002). Spec-imen counts were log10-transformed prior toanalysis.

Statistical Analysis

Analytical Method.—We used logistic re-gression to measure the association betweenpredictor variables and extinction risk. Logis-tic regression is a special case of a generalizedlinear model in which the link function is thelogit: ln(p/[12p]). In other words, the modelassumes

p= 1{pð Þ~1= 1zexp b0zb1xð Þ½ � ð1Þor

ln p= 1{pð Þ½ �~b0zb1x ð2Þand can be generalized to include multiplepredictor variables

ln p= 1{pð Þ½ �~b0zb1x1zb2x2z . . . zbnxn ð3Þwhere p is the probability of the outcome ofinterest, xi is a predictor variable, b0 is aconstant, and bi (where i . 0) is a coefficientof association. Relative risk estimated fromlogistic regression is conventionally expressedas an odds ratio, exp(bi), which describes thechange in the odds (p/[12p]) as a function ofchange of one unit the predictor variable.Thus, an odds ratio of 0.5 indicates a halvingof extinction risk per unit change in thepredictor, whereas an odds ratio of 2 indicatesa doubling. An odds ratio of 1 indicates noassociation. To preserve symmetry, we simplyreport the bi values below and refer to these aslog-odds to simplify terminology, followingprevious paleobiological studies (Payne andFinnegan 2007; Finnegan et al. 2008). In con-trast to these previous studies, we present thenatural logarithm of the odds ratio rather thanthe common logarithm (base 10) because it is

the most natural expression of bi values andthe default output of nearly all statisticalpackages.

Logistic regression is applied in cases wherethe response variable is binary (dichotomous)rather than continuous, such as extinctionversus survival. The model is used to estimatethe probability that a given observation willexhibit one outcome versus the other at a givenvalue of the explanatory variable(s). The logitfunction is widely used because of its favorablemathematical properties and easily interpretedresults. The approach assumes a monotonicrelationship between p and the explanatoryvariable(s) and a linear relationship betweenthe logit and the explanatory variable(s).Estimation of model parameters does notfollow the least-squares approach used instandard linear regression because variancedoes not remain constant for all levels of theexplanatory variable(s). Instead, a maximumlikelihood approach is used. Figure 1 illus-trates two examples from this study: Figure 1Aillustrates the relationship between abundanceand extinction risk for a Norian collection fromAustria and Figure 1B illustrates the relation-ship between global occurrence frequency andextinction risk for the Kungurian stage (EarlyPermian). We refer readers to Hosmer andLemeshow (2000) for a more detailed descrip-tion of logistic regression and its applications.

Logistic regression offers several advantagesrelative to simple parametric or nonparametriccomparisons of means or distributions be-tween victims and survivors. First, it allowsfor estimation of effect strength separatelyfrom statistical significance. This separationdiffers from comparisons of mean values ordistributions (e.g., t-test, Mann-Whitney,Kolmogorov-Smirnov), which can be usedonly to assess statistical significance. The coef-ficient of association (analogous to slope inlinear regression) is a measure of effect strength.The confidence bounds on the coefficient (aswell as the associated p-value) can be used toassess statistical significance. Second, like anyregression analysis, the effects of other corre-lates of extinction risk can be controlled for, anddifferent models compared. Third, modelweights derived from Akaike’s InformationCriterion corrected for small sample size (AICc)


can be used to evaluate relative support forextinction selectivity models without privileg-ing any particular model as the null hypothesis(Johnson and Omland 2004). Such modelweights sum to one and indicate the propor-tional distribution of support among the modelsconsidered (Johnson and Omland 2004). In thisanalysis, we interpret statistical significancewith type I error set at the conventional valueof 0.05 (i.e., p # 0.05 is considered as statisticallysignificant). All analyses were run using SASversion 9.2.

Results

We explored the relationship betweenpopulation size and extinction risk, usingboth global and local metrics of abundance.

We also explored the extent to which anyobserved association can be explained by theinfluence of geographic range on extinctionrisk and the correlation between abundanceand geographic range. Extinction victims tendto be less common than surviving genera bothin terms of global occurrence frequency andin terms of specimen abundance in localcollections. This tendency remains even afteraccounting for the association between geo-graphic range and extinction risk.

Global Occurrence Frequency

Single Regression Globally.—Occurrence fre-quency is inversely associated with genusextinction risk in 15 out of 16 stages, signifi-cantly so in five stages (Fig. 2). The coefficientsof association for the intervals with statisticallysignificant associations are not systematicallygreater than those for the intervals with non-significant associations. Rather, the intervalswith non-significant results differ from thosewith significant results by having feweroccurrences and genera and more poorlyconstrained coefficients (Table 2). Intervalswith significant associations contain on aver-age nearly three times as many occurrences(means: 610 versus 220; Mann-Whitney p 5

0.08) and more than twice as many genera(means: 108 versus 51; Mann-Whitney p 5

0.008) as those without. These differences insample size suggest that many instances ofapparently nonselective extinction may resultfrom type II error. The only interval to exhibit apositive association between occurrence fre-quency and extinction risk is the Scythian(Early Triassic), and this effect is not statisti-cally significant.

Controlling for Geographic Range.—Occur-rence frequency tends to correlate with geo-graphic range (Brown 1984) as well as totalpopulation size (Buzas et al. 1982; Brown 1984).Geographic range and occurrence frequencyare correlated in our data set as well (Table 3).Because geographic range is associated withextinction risk (Jablonski 1986; Brown 1995;McKinney 1997; Payne and Finnegan 2007), theassociation between occurrence frequency andextinction risk could result from an indepen-dent correlation between occurrence frequencyand geographic range rather than from a direct

FIGURE 1. Examples of logistic regression. Circles repre-sent individual observations of extinction (0) or survival(1), with diameters scaled to the number of observationswith the same value along the ordinate. Gray horizontallines represent aggregate probabilities of genus survivalfor observations within a given range along the ordinate.For local abundance, aggregate probabilities are calculat-ed binning all observations between integer values. Forglobal occurrence frequency, aggregate probabilities arecalculated for each value of occurrence frequency. Blackcurves represent best-fit logistic curves to the raw data. A,Graph of probability of survival versus log-transformedabundance for collection 638 (see Table 1 for additionalinformation). B, Graph of probability of genus survivalversus occurrence frequency for the Kungurian stage (seeTable 2 for additional information).


causal link between occurrence frequency andextinction risk.

To estimate the associations of occurrencefrequency and geographic range with extinc-tion risk independently of one another, weconducted a multivariable logistic regressionanalysis modeling extinction as a functionof both geographic range and occurrencefrequency. Geographic range was measured

as the maximum great circle distance betweenoccurrences of a given genus in a given stage.Other measures of geographic range, such asthe number of tectonic plates occupied, pro-vide qualitatively similar results. In the mul-tivariable logistic regression analysis, occur-rence frequency is inversely associated withextinction risk in 13 of 16 stages, and signifi-cantly so in one (Table 2).

FIGURE 2. Association between genus occurrence frequency and survival into the subsequent stage. The association isexpressed as the common logarithm (i.e., base 10) of the odds ratio. Positive values indicate preferential survival ofabundant genera; negative values indicate preferential survival of rare genera. A, Log-odds of survival and 95%confidence intervals presented by geological stage, showing positive associations in 15 of 16 stages. B, Frequencydistribution of log-odds from Figure 2A.

TABLE 2. Summary information and logistic regression results for the analysis of extinction selectivity by stage.

Stage Occurrences Genera Victims

Abundancelog-odds (b1)with 95% C.I.(univariate)

Abundancelog-odds

(b1) 6 95%confidence interval

(multivariate)

Range log-odds(b1) 6 95%confidence

interval(univariate)

Range log-odds(b1) 6 95%confidence

interval(multivariate)

Assel.–Sak. 265 42 1 0.35 6 1.29 0.37 6 1.36 0.09 6 1.77 20.02 6 1.13Artinskian 156 47 9 0.28 6 0.41 0.16 6 0.44 1.47 6 8.31 0.53 6 2.53Kungurian 645 104 25 0.48 6 0.37 20.02 6 0.44 15.38 6 13.38 15.84 6 20.93Roadian 170 53 13 1.34 6 1.17 0.97 6 1.34 34.31 6 47.04 5.94 6 33.62Word.–Cap. 203 48 22 0.28 6 0.32 0.16 6 0.37 1.36 6 1.43 0.99 6 1.54Wuchiap. 126 49 15 0.12 6 0.44 20.37 6 0.81 1.06 6 2.53 2.30 6 3.96Changhs. 131 64 52 0.55 6 0.53 0.21 6 0.74 0.37 6 0.3 0.30 6 0.37Scythian 38 19 5 20.35 6 0.55 0.00 6 1.13 20.64 6 1.93 20.62 6 2.28Anisian 695 103 16 0.21 6 0.28 0.00 6 0.21 0.74 6 1.08 0.76 6 1.24Ladinian 132 45 5 7.94 6 74.58 7.51 6 89.5 28.78 6 115.13 0.53 6 102.47Carnian 1781 210 115 0.16 6 0.07 0.12 6 0.07 0.60 6 0.35 0.41 6 0.3Norian 323 109 64 0.28 6 0.25 20.12 6 0.25 0.46 6 0.35 0.60 6 0.53Rhaetian 262 66 33 0.21 6 0.28 0.21 6 0.3 0.07 6 0.21 0.00 6 0.23Hettangian 103 30 4 1.06 6 1.8 0.53 6 3.36 4.10 6 7.67 1.96 6 13.1Sinemur. 90 41 6 0.32 6 0.83 0.00 6 0.92 7.14 6 77.99 14.67 6 207.69Pliensb. 349 67 21 0.23 6 0.28 0.14 6 0.32 0.60 6 0.71 0.44 6 0.78


We compared weights for models of nonse-lective extinction, selectivity based upon rangeonly, selectivity based upon occurrence fre-quency only, and selectivity based upon bothrange and occurrence frequency using weightscalculated from Akaike’s Information Criteri-on corrected for small sample size (AICc)(Johnson and Omland 2004; Hunt 2006). Thereis comparatively little support for nonselectiveextinction; support is relatively evenly dividedamong the full model and models includingeither range or occurrence frequency (Table 4).The full model is the best-supported modelin many of the best-sampled intervals—over-

whelmingly so in the best-represented stage(Carnian). Total support for the two modelsincluding abundance as a predictor of extinc-tion risk ranges from 0.28 (Anisian) to 0.99(Carnian), with a mean among stages of 0.47.The absence of convincing support for a singlemodel in many intervals likely reflects insuf-ficient statistical power due to the size of thedata set.

Local Abundance

Single Regression by Collection.—To assessthe relationship between population size andextinction risk further, we used 30 largecollections representing seven stages in aggre-gate. More than 90% of these collections (27 of30) exhibit an inverse association between localabundance and the probability of genus ex-tinction into the next geological stage (Table 1,Fig. 3). Although no collection exhibits astatistically significant association, the over-whelming tendency toward positive log-oddscannot be explained by chance alone. In thecase of no underlying association, half of thelog-odds should fall above zero and half below.The probability of obtaining 27 or morepositive log-odds in 30 collections by chancealone (in the absence of any underlying asso-ciation) is less than 0.0001.

Temporal Patterns.—The strength of associ-ation between abundance and extinction risk

TABLE 4. Model support calculated from Akaike’s Information Criterion weighted for small sample size (AICc) formodels of genus survival.

Stage Nonselective Full model Range onlyOccurrence

frequency onlyTotal support for models

including frequency

Asselian–Sakmarian 0.48 0.09 0.18 0.25 0.34

Artinskian 0.22 0.16 0.33 0.29 0.45Kungurian 0.00 0.27 0.73 0.01 0.27Roadian 0.00 0.30 0.31 0.38 0.68Wordian–

Capitanian 0.10 0.24 0.41 0.25 0.49Wuchiapingian 0.31 0.19 0.36 0.13 0.33Changhsingian 0.05 0.23 0.55 0.17 0.41Scythian 0.25 0.13 0.35 0.26 0.39Anisian 0.01 0.26 0.71 0.02 0.28Ladinian 0.04 0.19 0.25 0.52 0.71Carnian 0.00 0.98 0.01 0.00 0.99Norian 0.00 0.33 0.67 0.00 0.33Rhaetian 0.31 0.15 0.15 0.39 0.54Hettangian 0.22 0.13 0.33 0.32 0.45Sinemurian 0.30 0.15 0.39 0.17 0.32Pliensbachian 0.16 0.20 0.37 0.27 0.47

TABLE 3. Correlation coefficients (Pearson’s r) betweenoccurrence frequency and geographic range by stage andassociated p-values.

Stage r p

Asselian–Sakmarian 0.08 0.60Artinskian 0.57 ,0.0001Kungurian 0.56 ,0.0001Roadian 0.65 ,0.0001Wordian–Capitanian 0.55 ,0.0001Wuchiapingian 0.61 ,0.0001Changhsingian 0.67 ,0.0001Scythian 0.90 ,0.0001Anisian 0.59 ,0.0001Ladinian 0.47 0.001Carnian 0.44 ,0.0001Norian 0.52 ,0.0001Rhaetian 0.44 0.0002Hettangian 0.33 0.07Sinemurian 0.75 ,0.0001Pliensbachian 0.62 ,0.0001


is generally consistent among geologicalstages. Figure 4 illustrates the log-odds ofextinction for individual collections by stage,demonstrating a consistent tendency towardpositive log-odds of similar magnitude. Thereis no evidence of a secular trend in extinctionselectivity or of substantial variation in

extinction selectivity among stages. There isno strong relationship between stage durationand extinction selectivity, although the short-est stages may have been somewhat moreselective than average (Roadian, Changhsin-gian, Hettangian) (Fig. 5). Thus, the associa-tion between local abundance and globalextinction pattern appears pervasive withinthe study interval and does not simply reflectanalysis of collections from a particular stageor region with unusual biological or tapho-nomic properties.

FIGURE 3. Association between collection-level abundance and survival into the subsequent stage in marine gastropodgenera. The association is expressed as the common logarithm (i.e., base 10) of the odds ratio. Positive values indicatepreferential survival of abundant genera; negative values indicate preferential survival of rare genera. A, Log-odds ofsurvival and 95% confidence intervals presented by geological stage, showing positive associations in 27 of 30 stages.Collections are ordered by the width of the 95% confidence interval on the log-odds. B, Frequency distribution of log-odds from Figure 3A.

FIGURE 4. Log-odds for individual collections plottedagainst geological age, illustrating consistency of associ-ation between abundance and extinction risk throughgeological time and across modes of preservation.Confidence bounds have been omitted for clarity.

FIGURE 5. Cross-plot of extinction selectivity versus stageduration, illustrating consistency of selectivity as afunction of stage duration.


Preservation Type.—The apparent relation-ship between abundance and extinction riskmay differ depending upon preservationtype, as different modes of preservation maypresent different taphonomic filters alteringboth abundance distributions and the appar-ent presence or absence of species in differentways. The collections studied here are dom-inated by three different modes of preserva-tion: original shell material (largely from theSt. Cassian Formation of Italy), calcite re-placement, and silicification (largely from thePermian of West Texas, but also from severalother localities and ages) (Table 1). Thedistributions of log-odds are similar amongpreservation modes, although silicified as-semblages exhibit slightly more positive log-odds on average (Fig. 4). Thus, although these

different modes of preservation undoubtedlyresult in altered abundance distributionsrelative to living populations, and likely doso in different ways, the tendency for abun-dance to be associated with extinction risk isnot confined to a single preservation mode.

Effect of Sample Size.—Associations betweenabundance and survivorship are stronglyinclined toward positive log-odds, but notsignificantly so within individual collections.This pattern appears to reflect limited statis-tical power rather than the absence of anunderlying association. As expected whensample size is the primary influence, collec-tions containing fewer genera exhibit morevariable and more poorly constrained log-odds (Fig. 6A). The 21 most diverse collec-tions all exhibit positive log-odds (Fig. 6B).

Multivariable Regression.—To control forglobal geographic range, which is significantlycorrelated with local abundance in somecollections (Table 5), we conducted a multi-variable regression analysis of extinction as afunction of both local abundance and global

FIGURE 6. Relationship between collection size andmeasures of selectivity. A, Log-odds versus number ofgenera in collection, illustrating greater variability incollections containing fewer genera but no simple trendin log-odds with respect to collection size. B, Width of the95% confidence interval versus the number of genera inthe collection, illustrating greater uncertainty in estimatedlog-odds in smaller collections.

TABLE 5. Correlation between log-transformed localabundance and global geographic range, by collection.

Collection No. of genera r p

73 14 20.05 0.87278 25 0.38 0.06500 19 20.002 0.99518 18 20.07 0.79523 22 0.003 0.99525 20 20.19 0.42570 74 0.01 0.92571 23 0.3 0.17593 16 20.1 0.72619 19 20.15 0.54638 16 0.2 0.46642 18 0.24 0.34718 29 20.001 0.99875 27 0.06 0.76

1014 14 0.75 0.0021356 32 0.32 0.071380 26 0.45 0.021489 50 0.12 0.391493 47 0.37 0.011497 74 20.02 0.841498 24 0.73 0.00011499 41 0.31 0.051500 73 0.02 0.871676 27 0.21 0.281677 29 20.07 0.721678 32 20.17 0.351679 29 0.1 0.621719 42 20.01 0.941722 40 0.49 0.001


geographic range. In the multivariable regres-sion, local abundance is associated withextinction risk in 25 out of the 30 collections(Table 1). The weighted mean log-odds ofassociation between local abundance andextinction risk are similar in the univariableand multivariable regression models (0.25 6

0.38 versus 0.19 6 0.41, respectively, for eachlog10-unit increase in local abundance), sug-gesting that geographic range does not accountfor most of the observed association betweenlocal abundance and global extinction risk.AICc weights are roughly equal among mod-els with nonselective extinction, selection onlocal abundance, selection on global geograph-ic range, and selection on both local abundanceand geographic range (Table 6). Proportionalsupport for models including local abundanceas a predictor of extinction ranges from 0.28 togreater than 0.92 using AICc weights. Supportfor models including some form of selectivityon local abundance, geographic range, or both,ranges from 0.54 to greater than 0.99, with a

mean value of 0.86. Thus, genus extinction isinversely associated with local abundance, butthe data are insufficient to determine with highconfidence whether this reflects an effect ofpopulation size itself or correlation of localabundance with global geographic range and/or other variables causally associated withextinction risk.

Assessment of Statistical Power

The consistent association between abun-dance and extinction risk in our regressionanalysis suggests an underlying association,even if we are not able to identify thisassociation with 95% confidence in manycases. Because knowledge of the type II errorrate (i.e., the probability of failing to reject thenull hypothesis when it is false) is critical tointerpreting our data, we used a simulationapproach to investigate the power of logisticregression for data sets similar to ours. Power,or the probability of correctly rejecting thenull hypothesis when it is false (i.e., the

TABLE 6. Model support calculated from Akaike’s Information Criterion weighted for small sample size (AICc) forregression models of extinction risk within local collections.

Collection Nonselective Full model Abundance only Range onlySupport for abundance

alone or full model

73 0.00 0.59 0.00 0.41 0.59278 0.15 0.22 0.13 0.50 0.35500 0.33 0.16 0.18 0.33 0.34518 0.38 0.13 0.35 0.14 0.48523 0.04 0.54 0.35 0.07 0.89525 0.11 0.54 0.16 0.20 0.69570 0.01 0.32 0.01 0.67 0.32571 0.03 0.27 0.01 0.69 0.28593 0.06 0.26 0.66 0.02 0.92619 0.38 0.13 0.15 0.34 0.28638 0.10 0.35 0.12 0.43 0.47642 0.06 0.27 0.02 0.65 0.29718 0.39 0.15 0.21 0.25 0.36875 0.03 0.66 0.18 0.13 0.84

1014 0.52 0.08 0.21 0.19 0.291356 0.07 0.26 0.06 0.61 0.321380 0.35 0.13 0.18 0.34 0.311489 0.01 0.35 0.01 0.62 0.361493 0.28 0.17 0.17 0.38 0.341497 0.01 0.30 0.00 0.68 0.311498 0.03 0.25 0.04 0.67 0.291499 0.14 0.21 0.08 0.56 0.291500 0.00 0.27 0.00 0.73 0.271676 0.26 0.20 0.19 0.36 0.381677 0.08 0.57 0.17 0.18 0.731678 0.22 0.27 0.12 0.39 0.391679 0.11 0.37 0.38 0.14 0.751719 0.00 0.38 0.00 0.62 0.381722 0.04 0.25 0.04 0.66 0.29


complement of the probability of type IIerror), is a function of effect strength andsample size. Using the distribution of occur-rence frequency from the Carnian and of localabundance from collection 1356, we created500 simulated data sets each for samplescontaining 10, 20, 30, 50, 75, 100, 150, and 200taxa by bootstrap sampling. We assumed thatthe extinction risk versus abundance wasdescribed by a logistic function and assignedsurvival status for each genus probabilistical-ly. Then, using logistic regression, we testedfor an association between abundance andextinction risk. We varied b0 values with b1

values to preserve a constant expected rate ofextinction across values of b1. (Assuming aconstant value for b0 would cause the totalextinction rate in the simulated collection tovary as a function of selectivity.) Figure 7illustrates statistical power as a function ofsample size and effect strength for these twoscenarios. In general, power is extremelylimited in data sets smaller than 50 taxa andfor effects magnitudes smaller than 0.2. Halfof the studied stages and 87% (26/30) ofcollections contain fewer than 50 genera. Formost intervals and collections, we lack the

power to consistently detect effects of themagnitude that are likely to exist in the dataeven when the data match the model perfect-ly. Our power may be further limited by otherfactors, such as mismatch between our statis-tical model and the true structure of therelationship between abundance and extinc-tion risk.

Discussion

The preferential extinction of less frequent-ly occurring genera globally and less abun-dant genera within local collections suggestsan inverse association between populationsize and extinction risk, even if the associationis complex. This interpretation is furthersupported by the fact that the association isobserved across a broad span of geologicaltime and modes of fossil preservation. Someof the observed association between abun-dance and extinction risk can be explained bythe association between abundance and geo-graphic range, which is a strong predictor ofextinction risk in the fossil record (Jablonski2005; Kiessling and Aberhan 2007; Payne andFinnegan 2007), and therefore need not reflecta direct causal link between abundance and

FIGURE 7. Statistical power of logistic regression for data sets similar to those analyzed in this study, illustrating thelimited power associated with intervals and collections containing fewer than 50 genera. A, Power calculated using theoccurrence structure of the Carnian global data and assuming that extinction risk is described by the logistic functionthat best fits our data. B, Power calculated using the abundance structure of collection number 1356 and assuming thatextinction risk is described by the logistic function that best fits our data.


extinction risk. However, we find evidence ofan association between abundance and ex-tinction risk even in multivariable regressionanalyses that control for the effects of geo-graphic range. Occurrence frequency andgeographic range are both significantly asso-ciated with extinction risk in the best-sampledstages, with log-odds similar to those formore poorly sampled stages. Therefore, thefact that the association with abundance is notstatistically significant in most time intervalsor collections likely reflects insufficient statis-tical power given the moderate magnitudeof the effect rather than the absence of anassociation. Our results are thus consistentwith the predicted relationship betweenpopulation size and extinction risk (Pimmet al. 1988; Lande 1993; Hubbell 2001).

The estimated association between abun-dance and survivorship may be confoundedby a variety of biogeographic, ecological, orphysiological factors. Variability in extinctionrisk among geographic regions (e.g., Claphamet al. 2009) could obscure the relationshipbetween occurrence frequency and survivor-ship. The abundance-survivorship relation-ship could also be confounded by ecologicalor physiological differences among taxa thatwere not controlled for in the analysis. Theautecology of late Paleozoic and early Meso-zoic gastropods is largely unknown. Howev-er, abundant taxa likely were more basal inthe food chain, on average, than rarer taxa,owing to fundamental constraints from tro-phic energy transfer and the fact that preda-tors are generally larger than their prey(Cohen et al. 2003). Ecologically and physio-logically selective extinction patterns areknown from both background and massextinction events (Jablonski and Raup 1995;Knoll et al. 1996; McKinney 1997; Smith andJeffery 1998; Jablonski 2005; Knoll et al. 2007;Payne and Finnegan 2007; Friedman 2009).The substantial ecological diversity of marinegastropods suggests that they would beparticularly susceptible to confounding fromselectivity on traits such as trophic mode orenvironmental distribution.

Several taphonomic and sampling factorscould also confound the relationship betweenabundance and survivorship as observed in

the fossil record. At the global scale, unevengeographic distribution of sampling mayresult in disproportionately high occurrencefrequencies for genera inhabiting well-sampledregions and disproportionately low occurrencefrequencies for those inhabiting poorly sam-pled regions. In some intervals, many occur-rences derive from a few relatively smallregions such as the Early and Middle Permianof West Texas (Yochelson 1956, 1960; Batten1958, 1989; Erwin 1988a,b,c, 1989), the Carnianof northern Italy (Leonardi and Fiscon 1959;Zardini 1978), and the Norian and Rhaetian ofPeru (Haas 1953). At local and global scales,taphonomic factors may also play an importantrole in confounding the abundance-survivor-ship association. In particular, species withsmaller and thinner shells may be preferential-ly lost from dead shell accumulations relativeto living communities because they are moresusceptible to chemical and mechanical de-struction (Flessa and Brown 1983; Kosnik et al.2009). Smaller shells also tend to be moredifficult to recover and identify even whenthey are not destroyed (Cooper et al. 2006;Hendy 2009; Sessa et al. 2009). On the otherhand, silicification may favor the preservationof smaller individuals (Daley and Boyd 1996;Pan and Erwin 2002). The similarities amonglog-odds and among the widths of their 95%confidence intervals across modes of collectionand preservation (Table 1, Fig. 4) suggest thateither taphonomic noise is introduced prior toburial or the amount of taphonomic noise doesnot differ substantially between preservationmodes.

At present, it is not possible to determinehow much of the noise in our data sets mayreflect biological versus taphonomic processes.However, recent taphonomic studies suggestthat the taphonomic contribution of simpleshell destruction may not be as large as oncefeared. Rank-order abundance patterns inliving molluscan communities appear to bewell preserved in associated dead shell assem-blages (Kidwell 2001). On the other hand, thepreferential undersampling of smaller speciesis increasingly well documented (Cooper et al.2006; Hendy 2009; Sessa et al. 2009) anddifficult to control for at the global scale,especially when analyzing older data sets for


which explicit sampling protocols cannot bedetermined.

The discordance between our results andthose of many previous studies likely reflectstwo factors, one inherent in the choice ofstatistical methods and the other involvingselection bias in the choice of study intervals.We discuss each of these factors below.

Nonselective extinction is commonly used asthe null hypothesis because it is the scenariomost easily tested with simple parametric ornonparametric approaches. Although nonse-lective extinction is a statistically convenientnull hypothesis, it does not reflect expectationsfrom simple demographic models. Lande(1993) showed that mean time to extinctionscales exponentially with population size (i.e.,carrying capacity) when governed by demo-graphic stochasticity alone and as a powerfunction of population size when stochasticvariation in environmental quality and suddencatastrophes are also considered. Thus, whennonselective extinction is used as the nullhypothesis, a finding of nonselective extinctionmay reflect type II error due to insufficientstatistical power to detect a true selective effect,rather than a clear demonstration that popula-tion size was decoupled from extinction risk.The likelihood of type II error is higher fornonparametric tests, which have been usedin nearly all previous studies (McClure andBohonak 1995; Lockwood 2003; Kiessling andBaron-Szabo 2004; Kiessling and Aberhan2007). Nearly all individual collections in ourstudy exhibit no statistically significant associ-ation between abundance and extinction risk.However, rare genera are more likely to goextinct in nearly all of these collections and thebest-sampled stages are the ones that tend toexhibit statistically significant extinction selec-tivity. An assessment of statistical power bynumerical simulation shows that we have verylimited power to reject the null hypothesisgiven our sample sizes and apparent effectmagnitudes.

Most previous studies have focused on massextinction events, including all previous studiesusing specimen counts (McClure and Bohonak1995; Hotton 2002; Lockwood 2003; Leightonand Schneider 2008), whereas our study andmost others that have reported an inverse

association between abundance and extinctionrisk (Stanley 1986; Kiessling and Aberhan 2007)primarily address background intervals. Thus,the contrasting results could reflect genuinedifferences in extinction mode between back-ground intervals and (at least some) massextinctions. On the other hand, several lines ofevidence suggest that even mass extinctionevents have been selective to some extent.Kiessling and Aberhan (2007) found that theend-Triassic event was not selective when allmarine invertebrate genera were assessedsimultaneously, but that it was selective whenbivalve occurrence frequencies were analyzedalone. In light of the result for bivalves, thenonselective extinction pattern for invertebratesas a whole could be interpreted to reflectconfounding from ecological or physiologicaldifferences among phyla and classes (see Wangand Bush 2008). Our results for gastropods areconsistent with Kiessling and Aberhan’s (2007)results for bivalves; moreover, they indicatethat extinction selectivity with respect to abun-dance was not markedly different during theRhaetian than during Permian and Triassicbackground stages. Although Lockwood (2003)did not find a significant association betweenabundance and extinction risk for westernAtlantic bivalves during the end-Cretaceousmass extinction, she did observe an approxi-mately twofold difference in mean abundanceand proportional abundance between victimsand survivors. Our data provide little constrainton the relationship between abundance andextinction risk during the end-Permian massextinction. No Changhsingian collections metour minimum criteria for sample size. Globaloccurrence frequency is associated with genusextinction risk, but this finding could beaccounted for by correlation between occur-rence frequency and geographic range. Leightonand Schneider (2008) found no significantassociation between abundance and extinctionrisk, but interpretation of their results is compli-cated by the long time gap between the age ofthe samples (Late Pennsylvanian and EarlyPermian) and the timing of the extinction event(end-Permian).

If the association between abundance andextinction risk does not simply reflect correla-tion between abundance and geographic range,


what other factors might explain this observa-tion? Association between population size andextinction risk is predicted if environmentaldisturbances cause extinction through effectson population growth rate or population size(Lande 1993). Under this model, differences ininitial population size (i.e., carrying capacity)are implicitly determined by ecological orphysiological factors, as suggested by Brown(1984). However, under Lande’s (1993) model,these ecological differences determine extinc-tion risk only indirectly through their influenceon carrying capacity. Alternatively, extinctioncould be ecologically selective and the associ-ation between abundance and extinction riskcould thus be an indirect reflection of thetendency for more abundant taxa to havebroader ecological and physiological tolerancesor to have particular ecological traits that conferextinction resistance (e.g., abundance tends tocorrelate with trophic level). In other words, theobserved association of population size withextinction risk may be due to a true differencein likelihood of extinction between larger andsmall populations, or it may be that abundanceis an indicator of other, direct determinants ofextinction. Although we cannot rule out theformer scenario, the latter is consistent withgeological observations that many extinctionevents were likely caused by specific environ-mental stresses (Hallam and Wignall 1997;Bambach 2006; Finnegan et al. 2008) that wouldtend to drive the most susceptible taxa toextinction regardless of initial population size.

Conclusions

Our local and global analyses indicate thatpopulation size was inversely associated withgenus extinction risk in marine gastropodsduring the late Paleozoic and early Mesozoic.Although some of the association betweenabundance and survival can be accounted forby the correlation between abundance andgeographic range, analysis of well-sampledintervals suggests abundance is independent-ly associated with extinction risk. We inter-pret the uncertainty in the log-odds ofextinction to result from small sample sizeas well as ecological and physiological corre-lates of extinction risk not assessed in thisstudy and taphonomic and sampling factors

that alter abundances in paleontological as-semblages relative to living communities. Theprevalence of the association between abun-dance and extinction risk through geologicaltime may be underestimated for methodolog-ical reasons: nonselective extinction is astatistically convenient null hypothesis, leav-ing underpowered studies susceptible to typeII error, and disproportionate attention hasfocused on mass extinction events.

Acknowledgments

We thank S. Finnegan and P. Harnik fordiscussion and comments and M. Kosnik andP. Novack-Gottshall for constructive reviews.Data from the Sepkoski Database were ac-cessed by using S. Peters’s searchable, web-based interface. This research was supportedby funds from Stanford University.

Literature Cited

Alroy, J., M. Aberhan, D. J. Bottjer, M. Foote, F. T. Fursich, P. J.

Harries, A. J. W. Hendy, S. M. Holland, L. C. Ivany, W.

Kiessling, M. A. Kosnik, C. R. Marshall, A. J. McGowan, A. I.

Miller, T. D. Olszewski, M. E. Patzkowsky, S. E. Peters, L.

Villier, P. J. Wagner, N. Bonuso, P. S. Borkow, B. Brenneis, M. E.

Clapham, L. M. Fall, C. A. Ferguson, V. L. Hanson, A. Z. Krug,

K. M. Layou, E. H. Leckey, S. Nurnberg, C. M. Powers, J. A.

Sessa, C. Simpson, A. Tomasovych, and C. C. Visaggi. 2008.

Phanerozoic trends in the global diversity of marine inverte-

brates. Science 321:97–100.

Bambach, R. K. 2006. Phanerozoic biodiversity mass extinctions.

Annual Review of Earth and Planetary Sciences 34:127–155.

Bandel, K. 1994. Triassic Euthyneura (Gastropoda) from the St.

Cassian Formation (Italian Alps) with a discussion on the

evolution of the Heterostropha. Freiberger Forschungshefte C

452:79–100.

Batten, R. L. 1958. Permian Gastropoda of the southwestern

United States, Part 2. Pleurotomariacea, Portlockiellidae,

Phymatopleuridae, and Eotomariidae. American Museum of

Natural History Bulletin 114:153–246.

———. 1972. Permian gastropods and chitons from Perak,

Malaysia. American Museum of Natural History Bulletin

147:1–44.

———. 1979. Gastropods from Perak, Malaysia, Part 2. The

trochids, patellids, and neritids. American Museum Novitates

2685:1–26.

———. 1985. Permian gastropods from Perak, Malaysia, Part 3.

The murchisoniids, cerithids, loxonematids, and subulitids.

American Museum Novitates 2829:1–40.

———. 1989. Permian Gastropoda of the southwestern United

States. 7. Pleurotomariacea: Eotomariidae, Lophostiridae, Gos-

seletinidae. American Museum Novitates 2829:1–40.

Blaschke, F. 1905. Die Gastropodenfauna der Pachycardientuffe

der Seiseralpe in Sudtirol nebst einem Nachtrag zur Gastro-

podenfauna der roten Raibler Schichten vom Schlernplateau.

Beitrage zur Palaontologie und Geologie Osterreich-Ungarns

und des Orients 17.

Brown, J. H. 1984. On the relationship between abundance and

distribution of species. American Naturalist 124:255.

———. 1995. Macroecology. University of Chicago Press, Chicago.


Buzas, M. A., C. F. Koch, S. J. Culver, and N. F. Sohl. 1982. On the

distribution of species occurrence. Paleobiology 8:143–150.

Clapham, M. E., S. Shen, and D. J. Bottjer. 2009. The double mass

extinction revisited: reassessing the severity, selectivity, and

causes of the end-Guadalupian biotic crisis (Late Permian).

Paleobiology 35:32–50.

Cohen, J. E., T. Jonsson, and S. R. Carpenter. 2003. Ecological

community description using the food web, species abundance,

and body size. Proceedings of the National Academy of

Sciences USA 100:1781.

Cooper, R. A., P. A. Maxwell, J. S. Crampton, A. G. Beu, C. M.

Jones, and B. A. Marshall. 2006. Completeness of the fossil

record: estimating losses due to small body size. Geology

34:241–244.

Daley, R. L., and D. W. Boyd. 1996. The role of skeletal

microstructure during selective silicification of brachiopods.

Journal of Sedimentary Research 66:155–162.

Dubar, G. 1948. Faune domerienne du Jebel Bou-Dahar, pres de

Beni-Tajite. Etudes paleontologiques sur le Lias du Maroc.

Notes et Memoires du Service Geologique du Maroc 68:1–247.

Erwin, D. H. 1988a. Permian Gastropoda of the southwestern

United States: Subulitacea. Journal of Paleontology 62:56–69.

———. 1988b. Permian Gastropoda of the southwestern United

States: Cerithiacea, Acteonacea, and Pyramidellacea. Journal of

Paleontology 62:566–575.

———. 1988c. The Genus Glyptospira (Gastropoda, Trochacea)

from the Permian of the southwestern United States. Journal of

Paleontology 62:868–879.

——— . 1989. Regional paleoecology of Permian gastropod

genera, southwestern United States and the end-Permian mass

extinction. Palaios 4:424–438.

Finnegan, S., J. L. Payne, and S. C. Wang. 2008. The Red Queen

revisited: reevaluating the age selectivity of Phanerozoic

marine genus extinctions. Paleobiology 34:318–341.

Flessa, K. W., and T. J. Brown. 1983. Selective solution of

macroinvertebrate calcareous hard parts: a laboratory study.

Lethaia 16:193–205.

Foote, M. 2005. Pulsed origination and extinction in the marine

realm. Paleobiology 31:6–20.

———. 2007. Extinction and quiescence in marine animal genera.


Foote, M., J. S. Crampton, A. G. Beu, and R. A. Cooper. 2008. On

the bidirectional relationship between geographic range and

taxonomic duration. Paleobiology 34:421–433.

Friedman, M. 2009. Ecomorphological selectivity among marine

teleost fishes during the end-Cretaceous extinction. Proceed-

ings of the National Academy of Sciences USA 106:5218–5223.

Haas, O. 1953. Mesozoic invertebrate faunas of Peru. Part 1,

General introduction; Part 2, Late Triassic gastropods from

central Peru. American Museum of Natural History Bulletin

101:1–328.

Hallam, A., and P. B. Wignall. 1997. Mass extinctions and their

aftermaths. Oxford University Press, New York.

Hendy, A. J. W. 2009. The influence of lithification on Cenozoic

marine biodiversity trends. Paleobiology 35:51–62.

Hosmer, D. W., and S. Lemeshow. 2000. Applied logistic

regression. Wiley, New York.

Hotton, C. L. 2002. Palynology of the Cretaceous-Tertiary

boundary in central Montana: evidence for extraterrestrial

impact as a cause of the terminal Cretaceous extinctions. In J. H.

Hartman, K. R. Johnson, and D. J. Nichols, eds. The Hell Creek

Formation and the Cretaceous-Tertiary boundary in the

northern Great Plains: an integrated continental record of the

end of the Cretaceous. Geological Society of America Special

Paper 361:473–502.

Hubbell, S. P. 2001. The unified neutral theory of biodiversity and

biogeography. Princeton University Press, Princeton, N.J.

Hunt, G. 2006. Fitting and comparing models of phyletic

evolution: random walks and beyond. Paleobiology 32:578–601.

Jablonski, D. 1986. Background and mass extinctions—the

alternation of macroevolutionary regimes. Science 231:

129–133.

———. 2005. Mass extinctions and macroevolution. In E. S. Vrba

and N. Eldredge, eds. Macroevolution: diversity, disparity,

contingency. Paleobiology 31(Suppl. to No. 3):192–210.

Jablonski, D., and J. A. Finarelli. 2009. Congruence of morpho-

logically defined genera within molecular phylogenies. Pro-

ceedings of the National Academy of Sciences USA 106:8262–

8266.

Jablonski, D., and D. M. Raup. 1995. Selectivity of end-Cretaceous

marine bivalve extinctions. Science 268:389–391.

Johnson, J. B., and K. S. Omland. 2004. Model selection in ecology

and evolution. Trends in Ecology and Evolution 19:101–108.

Kidwell, S. M. 2001. Preservation of species abundance in marine

death assemblages. Science 294:1091–1094.

——— . 2002. Time-averaged molluscan death assemblages:

palimpsests of richness, snapshots of abundance. Geology

30:803–806.

Kiessling, W., and M. Aberhan. 2007. Geographic distribution and

extinction risk: lessons from Triassic-Jurassic marine benthic

organisms. Journal of Biogeography 34:1473–1489.

Kiessling, W., and R. Baron-Szabo. 2004. Extinction and recovery

patterns of scleractinian corals at the Cretaceous-Tertiary

boundary. Palaeogeography, Palaeoclimatology, Palaeoecology

214:195–223.

Kittl, E. 1891. Die Gastropoden der Schichten von St. Cassian der

sudalpinen Trias. I. Theil. Annalen des Kaiserlich-Koniglichen

Naturhistorischen Hofmuseums 6:166–262.

———. 1912. Trias-Gastropoden des Bakonyer Waldes. Resultate

der wissenschaftlichen Erforschung des Balatonsees, Vol 2,

section 5, pp. 1–58.

Knoll, A. H., R. K. Bambach, D. E. Canfield, and J. P. Grotzinger.

1996. Comparative earth history and Late Permian mass

extinction. Science 273:452–457.

Knoll, A. H., R. K. Bambach, J. L. Payne, S. Pruss, and W. W.

Fischer. 2007. Paleophysiology and end-Permian mass extinc-

tion. Earth and Planetary Science Letters 256:295–313.

Koken, E. 1897. Gastropoden der Trias um Hallstadt. Abhandlun-

gen der Kaiserlich Koniglichen Geologischen Reichsanstalt

17:1–111.

Kosnik, M. A., Q. Hua, D. S. Kaufman, and R. A. Wust. 2009.

Taphonomic bias and time-averaging in tropical molluscan

death assemblages: differential shell half-lives in Great Barrier

Reef sediment. Paleobiology 35:565–586.

Kutassy, A. 1927. Beitrage zur Stratigraphie und Palaontologie

der alpinen Triasschichten in der Umgebung von Budapest.

Magyar kir. Foldtani Intezet Evkonyve 27:105–177.

Lande, R. 1993. Risks of population extinction from demographic

and environmental stochasticity and random catastrophes. The

American Naturalist 142:911–927.

Leighton, L. R., and C. L. Schneider. 2008. Taxon characteristics

that promote survivorship through the Permian-Triassic inter-

val: transition from the Paleozoic to the Mesozoic brachiopod

fauna. Paleobiology 34:65–79.

Leonardi, P., and F. Fiscon. 1959. La fauna Cassiana di Cortina

d’Ampezzo. 3. Gasteropodi. Memorie degli Insituti de Geologia

e Mineralogia dell’Universita di Padova 21:1–103.

Lockwood, R. 2003. Abundance not linked to survival across the

end-cretaceous mass extinction: Patterns in North American

bivalves. Proceedings of the National Academy of Sciences

USA 100:2478–2482.

McClure, M., and A. J. Bohonak. 1995. Non-selectivity in

extinction of bivalves in the Late Cretaceous of the Atlantic

and Gulf Coastal Plain of North America. Journal of Evolu-

tionary Biology 8:779–794.


McKinney, M. L. 1997. Extinction vulnerability and selectivity:

combining ecological and paleontological views. Annual

Review of Ecology and Systematics 28:495–516.

Nutzel, A. 2005. A new Early Triassic gastropod genus and the

recovery of gastropods from the Permian/Triassic extinction.

Acta Palaeontologica Polonica 50:19–24.

Nutzel, A., and D. H. Erwin. 2004. Late Triassic (Late Norian)

gastropods from the Wallowa Terrane (Idaho, USA). Palaonto-

logische Zeitschrift 78:361–416.

Pan, H.-Z., and D. H. Erwin. 2002. Gastropods from the Permian

of Guangxi and Yunnan provinces, south China. Journal of

Paleontology Memoir 56:1–49.

Payne, J. L., and S. Finnegan. 2007. The effect of geographic range on

extinction risk during background and mass extinction. Proceed-

ings of the National Academy of Sciences USA 104:10506–10511.

Peduzzi, P., J. Concato, E. Kemper, T. R. Holford, and A. R.

Feinstein. 1996. A simulation study of the number of events per

variable in logistic regression analysis. Journal of Clinical

Epidemiology 49:1373–1379.

Pimm, S. L., H. L. Jones, and J. Diamond. 1988. On the risk of

extinction. American Naturalist 132:757.

Plotnick, R. E., and P. J. Wagner. 2006. Round up the usual

suspects: common genera in the fossil record and the nature of

wastebasket taxa. Paleobiology 32:126–146.

Powell, M. G. 2008. Timing and selectivity of the Late Mississip-

pian mass extinction of brachiopod genera from the Central

Appalachian Basin. Palaios 23:525–534.

Raup, D. M. 1991a. Extinction: bad genes or bad luck? W.W.

Norton, New York.

———. 1991b. A kill curve for Phanerozoic marine species.


Sachariewa-Kowatschewa, K. 1961. Die Trias von Kotel (Ost-

Balkan). II. Teil. Scaphopoden und Gastropoden. Annuaire de

l’Universite de Sofia, Faculte de Biologie, Geologie et Geogra-

phie, Livre 2, Geologie 55:91–140.

Scotese, C. R. 2007. Point Tracker, Version 2.0d. Department of

Geology, University of Texas, Austin.

Sepkoski, J. J. 2002. A compendium of fossil marine animal

genera. Bulletins of American Paleontology 363:1–560.

Sessa, J. A., M. E. Patzkowsky, and T. J. Bralower. 2009. The

impact of lithification on the diversity, size distribution, and

recovery dynamics of marine invertebrate assemblages. Geol-

ogy 37:115–118.

Simpson, C., and P. G. Harnik. 2009. Assessing the role of

abundance in marine bivalve extinction over the post-Paleozoic.


Smith, A. B., and C. H. Jeffery. 1998. Selectivity of extinction

among sea urchins at the end of the Cretaceous period. Nature

392:69–71.

Stanley, S. M. 1986. Population size, extinction, and speciation:

the fission effect in Neogene Bivalvia. Paleobiology 12:89–110.

Wagner, P. J., M. Aberhan, A. Hendy, and W. Kiessling. 2007. The

effects of taxonomic standardization on sampling-standardized

estimates of historical diversity. Proceedings of the Royal

Society of London B 274:439–444.

Wang, S. C., and A. M. Bush. 2008. Adjusting global extinction

rates to account for taxonomic susceptibility. Paleobiology

34:434–455.

Wilf, P., and K. R. Johnson. 2004. Land plant extinction at the end

of the Cretaceous: a quantitative analysis of the North Dakota

megafloral record. Paleobiology 30:347–368.

Yochelson, E. L. 1956. Permian Gastropoda of the southwestern

United States. 1. Euomphalacea, Trochonematacea, Pseudo-

phoracea, Anomphalacea, Craspedostomatacea, and Platycer-

atacea. American Museum of Natural History Bulletin 110:

173–276.

———. 1960. Permian Gastropoda of the southwestern United

States, Part 3. Bellerophontacea and Patellacea. American

Museum of Natural History Bulletin 119:205–294.

Zardini, R. 1978. Fossili Cassiani (Trias medio-superiore) Atlante

dei Gasteropodi della Formazione di S. Cassiano Raccolti nella

Regione Dolomitica Attorno a Cortina d’Ampezzo. Ed Ghe-

dina, Cortina d’Ampezzo.


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Local and global abundance associated with extinction risk ... · mates from the Paleobiology Database. Close similarity in the overall diversity histories of the Sepkoski database