global climate change and north american mammalian evolutionpkoch/pdfs/koch papers/2000... · the...

q 2000 The Paleontological Society. All rights reserved. 0094-8373/00/2604-0011/$1.00

Copyright ( 2000, The Paleontological Society

Global climate change and North American mammalianevolution

John Alroy, Paul L. Koch, and James C. Zachos

Abstract.—We compare refined data sets for Atlantic benthic foraminiferal oxygen isotope ratiosand for North American mammalian diversity, faunal turnover, and body mass distributions. Eachdata set spans the late Paleocene through Pleistocene and has temporal resolution of 1.0 m.y.; themammal data are restricted to western North America. We use the isotope data to compute fiveseparate time series: oxygen isotope ratios at the midpoint of each 1.0-m.y. bin; changes in theseratios across bins; absolute values of these changes (5 isotopic volatility); standard deviations ofmultiple isotope measurements within each bin; and standard deviations that have been detrendedand corrected for serial correlation. For the mammals, we compute 12 different variables: standingdiversity at the start of each bin; per-lineage origination and extinction rates; total turnover; netdiversification; the absolute value of net diversification (5 diversification volatility); change in pro-portional representation of major orders, as measured by a simple index and by a G-statistic; andthe mean, standard deviation, skewness, and kurtosis of body mass. Simple and liberal statisticalanalyses fail to show any consistent relationship between any two isotope and mammalian timeseries, other than some unavoidable correlations between a few untransformed, highly autocor-related time series like the raw isotope and mean body mass curves. Standard methods of detrend-ing and differencing remove these correlations. Some of the major climate shifts indicated by ox-ygen isotope records do correspond to major ecological and evolutionary transitions in the mam-malian biota, but the nature of these correspondences is unpredictable, and several other such tran-sitions occur at times of relatively little global climate change. We conclude that given currentlyavailable climate records, we cannot show that the impact of climate change on the broad patternsof mammalian evolution involves linear forcings; instead, we see only the relatively unpredictableeffects of a few major events. Over the scale of the whole Cenozoic, intrinsic, biotic factors likelogistic diversity dynamics and within-lineage evolutionary trends seem to be far more important.

John Alroy. National Center for Ecological Analysis and Synthesis, University of California, 735 StateStreet, Santa Barbara, California 93101. E-mail: [email protected]

Paul L. Koch and James C. Zachos. Department of Earth Sciences, University of California, 1156 High Street,Santa Cruz, California 95064. E-mail: [email protected], [email protected]

Accepted: 22 June 2000

Introduction

Paleontologists since Cuvier and Lyell havesought to explain both sudden extinctionevents and long-term evolutionary trends bypointing to changes in global climate (Rud-wick 1972). Two of the most obvious possibleexamples are the global extinction of dino-saurs and other vertebrates at the Cretaceous/Tertiary (K/T) boundary, and the extinction ofmost large mammals in the Americas at theend of the Pleistocene. Both of these events cannow be attributed to catastrophic perturba-tions that are unrelated, or only weakly relat-ed, to global climate change: the K/T mass ex-tinction was probably due to the impact of alarge bolide in the Yucatan peninsula (Alva-rez et al. 1980; Hildebrand et al. 1991), and aconsensus is forming that the end-Pleistocene

extinctions were caused largely, or possiblysolely, by human impacts (MacPhee 1999).

Despite these developments, much of the lit-erature going back to Matthew (1915) contin-ues to argue for climate change as a majordriver of North American mammalian evolu-tion in the Tertiary. This literature is motivat-ed by clearly climate-related geographical dif-ferences among Recent mammalian faunas.Very strong tropical-to-temperate zone gradi-ents in species richness (Simpson 1964; Kauf-man 1995) and differences in body mass dis-tributions between wet and dry habitats (Le-gendre 1989) have to have evolved somehow,so it stands to reason that progressive climatechange would cause these biotic variables torespond in a highly predictable way.

Many recent studies have worked withinthe climate/evolution paradigm. Rose (1981)

260 JOHN ALROY ET AL.

quantified changes in alpha diversity throughthe Paleocene and early Eocene and attributedthem directly to climate change. Webb (1977,1984) and Barnosky (1989) attributed NorthAmerican mammalian extinctions throughoutthe late Cenozoic to climate change. In aground-breaking analysis, Stucky (1990) sug-gested that although continental diversity waslargely static throughout the Cenozoic, cli-mate change progressively decreased alphadiversity and increased beta diversity. VanValkenburgh and Janis (1993) presented quan-titative data that showed a clear decrease, notincrease, in beta diversity—but still sought toexplain both this pattern and the overall di-versity trajectory in terms of climate changeand orogeny. Janis (1993, 1997) and Janis andWilhelm (1993) explicitly tied extinction rates,continental diversity levels, and changes introphic structure and ecomorphology to glob-al climate trends. Gunnell et al. (1995) empha-sized climate as a driver of body mass evolu-tion in Cenozoic mammals, and joined manyother authors in arguing that mammalianbody mass distributions are robust indicatorsof habitat and climate.

Because traditional timescales for the Ce-nozoic terrestrial fossil record have had poor(;3-m.y.) resolution, many other authors haveattacked the climate/evolution problem by fo-cusing on critical intervals of known climatechange, and by working with highly resolvedfaunal data for localized stratigraphic sec-tions. For example, Clyde and Gingerich(1998) were able to cite considerable evidencefor abrupt climate change at the Paleocene/Eocene boundary both at the global scale (Za-chos et al. 1993; papers in Aubry et al. 1998)and at regional scales (Koch et al. 1995; Winget al. 1995; Fricke et al. 1998). Following Gin-gerich (1989), they showed that major faunalturnover events and ecological shifts in Wyo-ming were stratigraphically coincident withthe boundary climate event. Thus, they wereable to make a persuasive, albeit circumstan-tial, case for a causal connection between cli-mate change and an important immigrationpulse.

Meng and McKenna (1998) developed asimilar argument for mammalian evolutionacross the Paleocene/Eocene and Eocene/Ol-

igocene boundaries in Asia, although evi-dence for regional climate change in Asia ateither of these boundaries is currently lacking.In contrast, Alroy (1996, 1998d) and Prothero(Prothero and Heaton 1996; Prothero 1999) de-bated whether there was any substantial turn-over among North American mammals at theEocene/Oligocene boundary, but agreed thatclimate in general plays a minor role in pacingevolutionary change. Cerling et al. (1998) at-tributed late Miocene mammalian faunalturnover around the world to floral changesdriven by a drop in CO2 levels. Behrensmeyeret al. (1997) tested and rejected the hypothesisof Vrba (1985, 1992, 1995) that climate drove amajor pulse of turnover in the Pliocene of Af-rica. Vrba (1992) tried to extend her theory toaccount for faunal turnover during the GreatAmerican Interchange, although these faunalchanges seem already to be explained by di-rect effects of this large-scale migration be-tween North and South America (Marshall etal. 1982).

Many other, similar studies could be cited.We are not opposed to the ‘‘critical interval’’strategy that this literature employs, and infact we employ it ourselves in part of our dis-cussion. However, we will begin our analysisby trying to take a broader view. Our maingoal will be to compare climate and fossil datawith equal temporal resolution for a large partof the Cenozoic. Thanks to improvements inquantitative biochronological methods, wecan now resolve the North American mam-malian fossil record down to uniformlyspaced, 1.0-m.y.-long intervals (Alroy 1992,1994, 1996, 1998d, 2000). Likewise, greatly in-creased sampling of long deep-sea cores andimprovements in correlation now make it pos-sible to examine small-scale changes in cli-mate, sometimes even at Milankovitch time-scales, throughout much of the Cenozoic (e.g.,Zachos et al. 1996, 1997). Earlier studies wereonly able to point to general, long-term trendsand a small number of obvious, large-scaleisotope value transitions (e.g., Miller et al.1987), but the new isotope data even allow usto quantify the range of variation in climatewithin individual 1.0-m.y. bins.

Instead of looking for broad-brush, quali-tative correspondences between our isotope

261CLIMATE CHANGE AND MAMMALIAN EVOLUTION

and mammal data sets, we will begin by tak-ing a rigidly quantitative approach based onbasic time series analysis. Our strategy will beto look for any possible causal relationship be-tween the data sets. Therefore, each and everymammalian time series will be cross-correlat-ed with each and every isotope time series. Be-cause of the large number of comparisons, weexpect some correlations to be suggestivelyhigh just at random. Therefore, we will set ahigh bar in testing for statistical significance.We also will avoid overinterpreting cases inwhich two autocorrelated time series show astrong cross-correlation, because such corre-lations are expected of random walks regard-less of whether there is any common causalfactor (McKinney 1990).

Although this point about time series auto-correlation is widely understood in the statis-tical literature, we feel that it needs to be em-phasized. There is a strong temptation to (say)look at a decreasing climate curve and an in-creasing diversity curve, note that each onehas a strong trend, and then infer that deteri-orating climate has spurred diversification.But any two curves with strong trends willshow such apparent correlations. For example,the episodically increasing Cenozoic marineoxygen isotope curve would correlate strong-ly with data showing the longitude of NorthAmerica during the same period of time, ifonly because the steady westward march ofthe continent happened to have occurred justwhile climate happened to be changing moreor less unidirectionally. In general, then, thequestion isn’t whether pairs of curves showtrends that go in the same direction or oppo-site direction. Instead, we want to knowwhether the blow-by-blow, interval-by-inter-val variation in these curves is correlated. Inother words, after taking the long-term trendsand autocorrelation into account, are fine-scale correlations still visible (McKinney1990)?

Our time series analysis should identify lin-ear forcings of major aspects of mammalianevolution by climate, should they operate onthe timescale of one or two m.y. or less. Forexample, noting the current latitudinal gra-dient in mammalian species richness (Simp-son 1964; Kaufman 1995), and the fact that lat-

itude is correlated with mean annual temper-ature, we might posit that time intervals withrapidly rising temperatures should be associ-ated with increased speciation or decreasedextinction rates. Yet climate may influencemammalian evolution in ways that are notstrongly linear. Rather, the response to a cli-mate change of a particular magnitude mightdepend on the recurrence time of such events,or even on whether it is the first such event inthe Cenozoic. If mammal faunas respond toclimate in ways that are strongly contingenton past major events, or if they respond onlyafter extreme lags such as 5, 10, or 20 m.y., ourtime series approach may not capture the re-sponse.

To search for climatic forcing of this sort, wewill conduct a second set of analyses some-what analogous to the ‘‘critical interval’’ ap-proach. We will identify all the time intervalswhere one or more of the mammalian datasets present clear outliers, and then test to seeif any of the climatic parameters are also sig-nificantly outside the normal range of varia-tion at the same time. If the majority of themammalian ‘‘events’’ occurred at times whensome aspect of climate is unusual, we wouldbe able to conclude that climate exerts a non-linear influence on mammalian evolution,with effects not being visible until somethreshold of disturbance is crossed.

After running through all possible compar-isons of the mammalian faunal data and iso-topic data, we will conclude that not only arealmost all of them insignificant, but the fewsignificant linear correlations cannot be dis-tinguished from statistical artifacts. We thenwill argue that the mammalian biota wentthrough only a handful of major reorganiza-tions during this interval, and although somekind of environmental change is thought tohave occurred at some of these times, the bi-otic responses and types of environmentalchange vary in each case. Furthermore, reduc-tionistic concerns about the relevance of con-tinental data are misplaced because the mam-malian data pertain only to a narrow, and cli-matically relatively uniform, region of thecontinent. Therefore, we will argue that nocase can be made at this time for invokinglong-term global climate change as a major


and consistent driver of mammalian evolu-tion.

Our analysis is unlikely to be the final wordon this topic. As we discuss below, tempera-ture estimates based on marine isotope datamay have systematic errors and are not nec-essarily good estimates of climate in continen-tal interiors even when they are accurate. Fur-thermore, temperature per se may not be asimportant to mammals as, say, precipitation.Nonetheless, we will suggest that the resultsare not due to lack of power and are likely tobe replicated by future studies using thesetypes of data. In making this argument, wewill side with a relatively small number of au-thors who believe that most major patterns inmammalian evolution result from biotic fac-tors like competition (Van Valen 1973; Alroy1996, 1998d, 2000) and key innovation (VanValen 1971; Hunter and Jernvall 1995; Jernvallet al. 1996), with the underlying biotic dynam-ics being reset periodically by major environ-mental perturbations.

Isotopes and Climate

Our climate proxy will be a compositecurve of oxygen isotope values for benthic fo-raminifera from the Atlantic Ocean. This ben-thic oxygen isotope (d18O) curve has beenviewed as a proxy for ‘‘global climate’’ instudies of biotic response (e.g., Vrba 1995;Prothero 1999). It is worth briefly consideringthe controls on this record to evaluate theplausibility of this assumption.

The d18O of an organism is a function ofgrowth temperature, as well as the d18O of thewater from which it precipitates calcite (Ep-stein et al. 1951). The d18O of the world’soceans is relatively constant spatially, withsubtle variations in the surface ocean inducedby evaporation and freshwater runoff (Zachoset al. 1994). Yet the world’s oceans experiencefairly large temporal shifts in d18O owing tothe preferential sequestration of 16O-enrichedwater in glacial ice. Consequently, shifts in thed18O of benthic foraminifera at least partiallyrecord changes in the global volume of conti-nental ice (Shackleton and Opdyke 1973). Forexample, in the Pleistocene it is estimated thattwo-thirds of the shift in benthic foraminiferald18O values between glacial and interglacial

times results from ice volume changes (Schraget al. 1996). For the mid-Miocene this propor-tion may be as high as five-sixths, and the Eo-cene/Oligocene shift may have resulted large-ly (50–100%) from the growth of Antarctic icesheets (Zachos et al. 1993; Lear et al. 2000).However, in the warm Paleocene and early-to-middle Eocene the extent of continental gla-ciation was low (Zachos et al. 1994; Lear et al.2000), so the impact of this parameter onshort-term changes in benthic foraminiferald18O values should be minimal. Shifts in d18Ovalues in this time interval should correspondprincipally to changes in bottom-water tem-perature.

The temperature of ocean bottom water isdetermined at the sites of deep water forma-tion, not at sites of sedimentary deposition.Today, deep water forms at high latitudes inthe North Atlantic and off Antarctica, wheretemperatures are low and salinity increasesseasonally as sea ice forms. This situation hasexisted since the late Miocene (Wright et al.1992). Prior to the late Miocene, all evidencesuggests that Antarctica had been the domi-nant source of global deep waters (Zachos etal. 1994). There has been speculation thatdeep-water formation may have taken place atlow latitudes in some time periods: the mech-anism would be the sinking of dense, warmbrines generated in equatorial regions underextremely warm climates (e.g., during the LateCretaceous or at the Eocene thermal maxima[Brass et al. 1982; Kennett and Stott 1991]). Atpresent, however, there is little support forthis view from either geochemistry or simu-lations of ocean circulation (Sloan et al. 1995).We suspect that deep-water formation has re-mained focused at polar regions for most, ifnot all, of the Cenozoic. Temperature varia-tions in subpolar regions, and by extensionthe poles, not the Tropics or midlatitudes, arebeing recorded in the d18O of benthic forami-nifera.

Thus, isotopic records from benthic organ-isms reflect a complex mixture of changes inboth high-latitude temperature and ice vol-ume, and are not recording ‘‘global’’ climatein any simple sense. Nonetheless, we believethere are several good reasons to compare ourmammalian data sets with this record. Some


reasons involve expediency, but the othershave a more general rationale. The foremostpractical issue is that only the benthic d18O re-cord is both dense and complete enough to al-low the types of tests presented here. Mg/Cadata may be a more direct proxy for oceantemperatures, but existing data sets are ex-tremely sparse (Lear et al. 2000), and the ro-bustness of this proxy remains to be fully test-ed. Records of climate on land for NorthAmerica are incomplete. Isotopic records fromsurface-dwelling marine organisms in themiddle latitudes of the Atlantic and Pacific aremore complete, but still too patchy for our cur-rent purposes. Also, metabolic isotope effectsassociated with the presence of endosymbi-onts in the tissues of some planktonic fora-minifera make it difficult to compare recordsamong different taxa without careful, species-by-species analyses of paleoecology (Speroand Lea 1993; Norris 1996). More importantly,where comparisons between benthic d18O re-cords and high-resolution records of continen-tal North American climate are available, theydo reveal synchronous trends—at least in thePaleogene (an issue we will return to in theDiscussion). Finally, a number of authors whohave linked climate change to mammalianevolution have used the marine record of cli-mate change as their primary reference point.

Scale of Analysis

One might ask why we have restricted ouranalyses to a single, fairly large geographic re-gion (western North America), and a singletemporal scale of resolution (1.0 m.y.). Thereare three major reasons.

Implausibility of Opposed Local Effects. Acurrent trend in the literature is to claim thatdifferent geographic regions show fundamen-tally different macroevolutionary patterns(Miller 1998). However, splitting our mam-malian data geographically would matteronly if different subregions within westernNorth America experienced not just differenttrends, but opposed ones. Only reversed cli-mate gradients could cancel out biotic re-sponses if the response functions are mono-tonic—otherwise, at least some part of ourdata set would still pick up the biotic re-sponse. That would occur, for example, if it

mattered to mammals that during the mid-and late Tertiary the Great Plains grew colder,drier, and more seasonal but the West Coastchanged much less. Canceling out, as opposedto slight masking, only would be appreciableif (say) West Coast climate actually becamewarmer, wetter, and more equable during thisperiod. Given that no major latitudinal chang-es and no joining or splitting of continents oc-curred near our study region during ourstudy interval, mechanisms for generatingthese kinds of reversed intracontinental cli-mate trends would have to be complex.

Lack of Finer-Scale Data. Using substantial-ly finer temporal bins is impossible becausethe temporal resolution of the mammaliandata is just slightly less than 1.0 m.y. (Alroy1996, 1998d, 2000), even though the methodused to generate the time series is some threetimes more precise than conventional, subjec-tive approaches (Alroy 1998c). Greater im-provements in the mammalian timescale arehighly unlikely given that the resolution ofour ordination-based timescale is regulated bythe underlying rate of faunal turnover, andthat some 91% of all fossil mammal collectionscannot be associated with independent geo-chronological age estimates (Alroy 1996,1998d, 2000). Likewise, studying smaller geo-graphic regions would create unavoidablylengthy temporal gaps. Even a study restrict-ed merely to the Great Plains and RockyMountains would suffer from a major gap inthe Uintan and Duchesnean (late Eocene),which can be filled only with data from South-ern California (Alroy 1998d). Furthermore,even the two most fossiliferous states in theUnited States present highly episodic records:Nebraska has no substantial faunas older thanabout 38 Ma, and Wyoming yields an order ofmagnitude more data from the Paleocene andEocene than from younger epochs.

Low Power of Coarser Analyses. Expandingthe geographic scale of coverage would addvery little data, and therefore would provide alargely redundant data set. The already ex-treme geographic concentration of data ishighlighted by the fact that 4787 (96%) of thelists fall in the western half of North America.Furthermore, 2966 (60%) can be placed in amuch smaller rectangle centered within the


TABLE 1. Benthic foraminiferan d18O data for 1.0-m.y.-long Cenozoic sampling bins. n 5 number of samplesfalling in each bin; Midpoint 5 estimated d18O value atmidpoint of each bin, based on linear regression of d18Oon time for all values falling within the bin; Change 5difference between current d18O midpoint value andpreceding one; SD 5 standard deviation of all residualsaround the regression line, i.e., a measure of variabilityindependent of gradual secular trends within bins; De-trended SD 5 generalized difference of standard devi-ation (see text); N/A 5 not applicable because data arelacking. Volatility (absolute value of change) is omittedbecause these values differ from the changes only bytheir sign.

Bin (Ma) n Midpoint Change SD Detrended SD

59.558.557.556.5

8191413

0.6170.4140.2700.113

N/A20.20320.14420.157

0.1120.2090.1880.144

20.0470.0640.005

20.03255.554.553.552.5

953412

7

20.04720.20320.22820.578

20.16020.15620.02520.350

0.4670.1970.1260.172

0.30720.09020.057

0.01651.550.549.548.5

4036

20.584N/A

20.60020.492

20.006N/AN/A0.108

0.146N/A

0.2260.165

20.129N/A0.098

20.03447.546.545.544.5

1413

610

20.2020.0750.1970.384

0.2900.2770.1220.187

0.0810.1630.1640.049

20.0950.019

20.01320.129

43.542.541.540.5

31131417

0.2230.4080.2680.584

20.1610.185

20.1400.316

0.2190.3030.3430.123

0.0850.1010.107

20.12939.538.537.536.5

14151527

0.7190.8501.0061.112

0.1350.1310.1560.106

0.1000.0910.1300.227

20.06720.06820.027

0.05435.534.533.532.5

3893

12799

1.1791.1321.8161.968

0.06720.047

0.6840.152

0.1660.1610.2590.215

20.04620.028

0.07120.012

31.530.529.528.5

114673148

1.8501.9692.1152.038

20.1180.1190.146

20.077

0.1810.2130.2140.387

20.0300.0140.0020.173

27.526.525.524.5

3141

139210

2.1512.0371.1980.966

0.11320.11420.83920.232

0.2980.3850.2900.260

0.0160.1370.0070.013

23.522.521.520.5

19999

914

1.3551.1171.4081.573

0.38920.238

0.2910.165

0.2950.2300.1920.176

0.05920.02120.03520.037

19.518.517.516.5

17192326

1.4141.2981.3431.151

20.15920.116

0.04520.192

0.1470.1730.1630.163

20.06020.02420.04520.042

15.514.513.512.5

147

84160

1.2131.2091.6211.802

0.06220.004

0.4120.181

0.1020.1560.1920.232

20.10420.02720.013

0.01111.510.5

15663

1.8811.982

0.0790.101

0.2120.165

20.02520.065

9.5 38 2.144 0.087 0.129 20.090

TABLE 1. Continued.

Bin (Ma) n Midpoint Change SD Detrended SD

8.5 186 2.057 0.075 0.179 20.0347.56.55.54.5

60267328316

2.0702.2062.2662.334

20.0740.1360.0600.068

0.1990.2420.3300.232

20.0020.0130.083

20.0503.52.51.50.5

304493513528

2.4572.8983.1213.433

0.1230.4410.2230.312

0.2520.3270.3610.492

0.0070.0730.0770.194

Western Interior that spans less than 6% of thecontinental area. Meanwhile, analyzing thetime series data with larger temporal bins(say, 2.0 m.y.) would reduce the number ofdata points so much that finding any robustcross-correlations between mammalian andisotopic data sets would be rendered almostimpossible.

Data

Isotopic Data. Isotopic data for benthic fo-raminifera were compiled from 17 DSDPcores in the Atlantic basin (Table 1, Fig. 1). Agemodels for each core were based on a combi-nation of magnetostratigraphy and biostratig-raphy, using dates for chron and biozoneboundaries from Berggren et al. (1995). Wherepossible, correlations among cores at the 104

timescale were determined by matching cyclicpatterns in carbon isotope values or sedimentproperties. Details of the construction and pa-leoclimatic implications of the benthic curvewill be discussed in a future paper. The den-sity of data generally decreases with increas-ing age (Fig. 2). This problem is so severe forthe early Paleocene that we have had to re-strict our analysis of isotopic data to the pe-riod from 60 Ma to the Recent.

Once placed in age models, d18O data fromall cores were combined to produce a com-posite curve. The curve was divided into 1.0-m.y. bins to facilitate comparison with thesimilarly parsed mammal record. Four basicmetrics were determined from these binneddata (Table 1, Fig. 1A–D): midpoint d18O value,rate of change, volatility, and variability. Todetermine the midpoint d18O value of each bin,we regressed d18O on age for values falling ineach bin, then calculated the d18O value for the


FIGURE 1. Cenozoic oxygen isotope records for Atlantic benthic foraminifera. Gap in each line at 50.5 Ma reflectsmissing data for that interval. Vertical gray lines show international epoch boundaries; epochs are listed at bottom.Abbreviations: Pal. 5 Paleocene; Olig. 5 Oligocene; P P 5 Pliocene and Pleistocene. A, Midpoint d18O value: esti-mated value at the midpoint of each bin based on a regression of d18O values against time within each bin. Thesedata show a strong trend and strong autocorrelation. The y-axis is reversed because positive values are correlatedwith low temperatures. B, Change in value: difference between consecutive bins in midpoint d18O value. These dataare first differences and show no trend and no autocorrelation. The y-axis is reversed as in the preceding panel;negative changes indicate warming/ice sheet melting and positive changes cooling/ice sheet growth. C, Isotopicvolatility: absolute values of first differences. D, Standard deviation: variability of the residuals produced by re-gressing d18O values against time. These data show a weak trend and weak autocorrelation. E, Detrended standarddeviation: generalized differences of the standard deviation data. These data show no trend and no autocorrelation.


FIGURE 2. Number of oxygen isotope ratio determina-tions per 1.0-m.y.-long sampling bin.

bin’s temporal midpoint from the regressionequation (Fig. 1A). This method should pro-vide a more robust measure of the averaged18O of a time interval than simple averaging,especially in cases where data show direction-al, within-bin d18O shifts and the sampling isuneven through time. We measured the rate ofchange in d18O as the difference in midpointd18O value between sequential bins (youngerbin 2 older bin: Fig. 1B). We then took the ab-solute values of the changes in order to esti-mate isotopic volatility—that is, the magni-tude of changes regardless of their direction(Fig. 1C). Finally, to estimate variability wedetermined the standard deviation of the re-gression residuals for each bin (Fig. 1D).

Both the midpoint and standard deviationtime series show secular trends and autocor-relation. The midpoint data (Fig. 1A) are verystrongly correlated with time (r 5 20.866; p ,0.001), and even after removing this trendthey still have a high serial correlation (i.e., thecorrelation between the variable and its ownvalues lagged backwards by one bin: r 510.887; p , 0.001). Cross-correlating a timeseries like this one with other autocorrelatedvariables would be meaningless, so detrend-ing and differencing is necessary. The gener-alized differencing method discussed by Mc-Kinney (1990) would be appropriate, but ow-ing to the strong serial correlation it turns outthat the first differences we already have ob-tained (i.e., rate of change: Fig. 1B) and gen-eralized differences (not shown) are almost

identical for this variable. Therefore, we treatthe differenced midpoint d18O value data set(Fig. 1B) as our main standard for evaluatingthe Cenozoic trend in average d18O values.This data set exhibits neither a significant cor-relation with time (r 5 10.227; n.s.) nor a sig-nificant serial correlation (r 5 10.141; n.s.).The volatility data set (Fig. 1C) is just a simpletransform of the unproblematic differenceddata, so it was not subjected to further manip-ulations.

By contrast, the standard deviation data(Fig. 1D) present more typical features of timeseries: a weak but significant correlation withtime (r 5 20.300; p , 0.05), and a similarlyweak and significant serial correlation (r 510.391; p , 0.01). A correction is needed, buttaking first differences would remove toomuch of the signal in this data set. Therefore,here we did apply the much less draconiangeneralized differencing method (McKinney1990): the data were regressed against time,residuals were taken, the correlation of the re-siduals with themselves at a lag of one timeinterval was computed, each of the lagged val-ues was multiplied by this correlation, and fi-nally the lagged values were subtracted fromthe data. The resulting, corrected curve (Fig.1E) resembles the raw data fairly closely be-cause of the weak correlations, but differs inlacking a visible secular trend (correlationagainst time: r 5 20.033; n.s.) and having lessdramatic medium-duration swings (serial cor-relation: r 5 0.000; n.s.).

While we are confident that the values formidpoint d18O and rate of change are ade-quately captured for all bins with more than10 or 15 values, we are less sanguine about ourestimator of variability. We explored the sen-sitivity of our estimator to the dramatic tem-poral variation in sample size (Fig. 2) by an-alyzing data from the 0.5-Ma bin. This bin notonly had the most data but also showed thehighest variability, no doubt in response toPleistocene glacial cycles. We randomly sam-pled the regression residuals from this binand generated new sequences of residualswith samples sizes of 500, 300, 150, 75, 50, 25,10, and 5. We generated 20 randomized se-quences for sample sizes from 500 to 25, and40 sequences for sample sizes of 10 and 5. We


recalculated standard deviations for each ran-domly generated sequence of residuals, thendetermined the mean and standard deviationof these 20 or 40 sequences at each sample size.For bins with sample sizes great than 50, onestandard deviation for the randomized repli-cates was less than 0.05‰. For samples sizesof 25, one standard deviation rose to 0.07‰,and for sample sizes of 10 or less, the deviationwas 0.1‰. Thus, our interpretations of the re-lationship between variability and mammali-an evolution must be tempered by the fact thatour confidence in the variability values is lowfor many bins. Fortunately, the density of d18Osamples is high around many (but not all) ofthe key intervals of mammalian evolution dis-cussed below.

Mammalian Faunal and Body Mass Data. Theprimary data used here to document NorthAmerican mammalian evolution are 4978 listsof species occurring in faunal samples and23,125 measurements of individual first lowermolar teeth (Alroy 2000). The lists form thebasis of our diversity curves and turnover rateestimates, and the tooth measurements areused as proxies for body mass. The data havefigured in a series of earlier publications (Al-roy 1992, 1996, 1998a,b,c,d, 1999a,b; Wing etal. 1995). Both data sets are restricted to ter-restrial, nonflying mammals; are derived froma set of 2828 publications; and are taxonomi-cally standardized using the companion data-base of synonymies and genus-species combi-nations included in the North American fossilmammal systematics database (NAFMSD:http://www.nceas .ucsb.edu/;alroy/nafmsd.html).

The set of faunal lists includes 30,951 taxo-nomic occurrences and now extends back tothe Early Cretaceous, documenting age rangesfor 1241 genera and 3243 species. The lists canbe viewed on the World Wide Web at the NorthAmerican mammalian paleofaunal database(http://www.nceas.ucsb.edu/;alroy/nampfd.html). All of the Cretaceous and Ce-nozoic lists were used in a maximum likeli-hood appearance event ordination analysis(Alroy 2000), which establishes age ranges forgenera and species. For reasons outlined byAlroy (1996, 1998d), 191 Cenozoic localitiesfrom outside of the west (i.e., Mexico, south-

western Canada, and the western UnitedStates) were excluded from the diversity anal-yses.

The expanded body mass data set now in-cludes 3398 population samples of 1969 dif-ferent species. A current version is available atthe NAFMSD. Although body mass estimatesare available for only 61% of the species, thesespecies tend to be common and long-ranging.The estimates were derived from the lowerfirst molar measurements using standard al-lometric equations that are cited and dis-cussed elsewhere (Alroy 1998b, 1999a,b). Mostof these equations depend on the logarithm ofthe length-times-width of the first lower mo-lar, but following Damuth (1990) the log oflength is used for ungulates, and second lowermolar measurements were used for probosci-deans. The regression-based estimates mayhave substantial errors, and indeed some fam-ilies and genera may exhibit systematic de-partures from the relationship seen for theirrespective orders. However, occasional esti-mates that are off by a factor of two, three, oreven ten are unlikely to have much of an effecton distributions spanning nearly seven ordersof magnitude.

Biotic Time Series Statistics

Methods used to transform the faunal listsinto age ranges and diversity curves are de-scribed elsewhere (Alroy 1996, 1998d, 2000).In particular, Alroy 2000 serves as a compan-ion to this paper. It details some of the newmethods used to prepare the data, which ex-pand and refine earlier techniques. There havebeen improvements in the multivariate ordi-nation method used to establish the mam-malian age-range data; the interpolationmethod used to calibrate these age ranges tonumerical time; and the random subsamplingmethods used to standardize the resulting di-versity and turnover-rate data. Furthermore,we use the new, much more methodologicallysound equations of Foote (1999) to translateraw age-range data into proper turnover rates.In total we consider five turnover metrics inaddition to the standardized diversity curve:instantaneous origination and extinctionrates; net diversification (the difference oforigination and extinction); diversification


FIGURE 3. Sampling-standardized diversity curve forNorth American Cenozoic mammals. Curve is based onsubsampling lists that total occurrences-squared quotasshown in Alroy (2000: Fig. 4). The method allows forgradual changes through time in alpha diversity.

volatility (the absolute value of net diversifi-cation); and total turnover (the sum of origi-nation and extinction).

Additionally, we computed two statistics in-tended to measure the rate of change of pro-portional species richness of major orders. Inother words, these ‘‘proportional volatility’’statistics measure the rate with which ordersreplace each other. The first statistic, a simpleindex, is correlated with turnover rates. Thesecond, a G-statistic (i.e., likelihood ratio),measures how much the dominance of differ-ent orders changes in excess of what onewould expect at random given the observedoverall origination and extinction rates in eachbin, plus the average turnover rates throughthe whole time series for each order. Full equa-tions and time series data are given by Alroy(2000).

For the body mass data, we relied upon fourstandard univariate statistics (the mean, stan-dard deviation, skewness, and kurtosis) com-puted across all of the species that rangedanywhere into each 1.0-m.y. bin. Alroy (2000)discusses our reasons for believing that theseslightly time- and space-averaged data are bi-ologically meaningful, and for rejecting themuch more common use of ‘‘cenogram’’ sta-tistics (Legendre 1989).

Time Series Analyses

Diversity and Turnover. While the diversitycurve (Fig. 3) reflects patterns seen in earlieranalyses (Alroy 1996, 1998d, 1999a), severalfeatures are subtly different. In this studythere is less of a consistent difference betweenearly Eocene and mid-to-late Eocene diversity,resulting in a more unpredictable overall Eo-cene trend. Likewise, the recovery from thelatest Miocene extinction is sharper, puttinglate Pleistocene levels close the Miocene av-erage.

Also of interest is overall variation withinthe turnover rate curves (Fig. 4A–E; see alsoAlroy 2000: Table 4). There is a general declinein turnover rates, especially after the Paleo-cene; spikes in origination are higher thanspikes in extinction, especially during the Pa-leocene; and very few discrete pulses of turn-over are visible in any of the curves. Nonethe-less, in a later section we discuss how some of

the outlying points in these curves may relateto episodes of global climatic change.

Standard deviations within our 60-m.y.-long study interval are comparable for origi-nation (0.100), extinction (0.110), and net di-versification (0.124). Because of mathematicalconstraints, values are lower for diversifica-tion volatility (0.077) and higher for total turn-over (0.169). These sampling-standardizeddata do exhibit comparable variability fororigination and extinction, but fully 36% of thevariation in the origination rates could be re-moved by correlating this variable against logstanding diversity for the relatively monoto-nous 60-m.y. interval (r 5 20.602, t 5 5.737, p, 0.001). In other words, more than a third ofthe variance can be explained by diversity-de-pendent models that are based on entirely in-trinsic, biological interactions like competition(Alroy 1998d).

Meanwhile, regressing extinction ratesagainst log diversity (r 5 20.224; t 5 1.749; p, 0.10) would reduce the variance by a mere5%. Although unimpressive, this relationshipalso could be attributed to intrinsic factors.The weak correlation is due to the fact that ex-tinction rates fall off during the Cenozoic asdiversity rises. Thus, it may be a side effect ofthe Paleocene/Eocene replacement of volatile,archaic groups such as multituberculates withless volatile ‘‘modern’’ groups such as rodents(Alroy 2000: Fig. 7). A decrease in average ex-


FIGURE 4. Cenozoic trends in turnover rates and the proportional volatility of ordinal diversity. The statistics arediscussed by Alroy (2000). A, Origination. B, Extinction. C, Net diversification. D, Diversification volatility. E, Totalturnover. F, Proportional volatility G-statistic.

tinction rates that results from the loss of vol-atile taxonomic groups is well known forPhanerozoic marine invertebrates, and it hasbeen held up as a clear demonstration that ma-jor features of biodiversity dynamics can begoverned by intrinsic, biological factors (Gil-insky 1994).

In light of the fact that so much of the turn-over pattern can be explained by intrinsic dy-namics, it comes as no great surprise thatcross-correlations of the five taxonomic-turn-over time series against the isotope data fail torecover compelling evidence for a causal in-terrelationship (Table 2). Before discussing


FIGURE 5. Cenozoic trends in body mass distributions. Each point describes the distribution of body mass estimatesforall species ranging into that 1.0-m.y.-long sampling bin. A, Mean. B, Standard deviation. C, Skewness. D, Kur-tosis.

these results in detail, we need to set someground rules for evaluating nominally ‘‘sig-nificant’’ results:

1. Many of the variables are more-or-lessnormal but do include notable outliers (whichwe will discuss in detail in our evaluation of‘‘critical intervals’’). Because of this, we will becareful to make sure that a correlation holdsup even after removing one or two outlyingdata points.

2. Because of the presence of outliers andslight skewness in many variables, we will ex-plore both Pearson’s parametric and Spear-man’s nonparametric correlation techniques.These results typically will agree, but whenthey do not we will take this as evidence thatthe correlations are not very robust.

3. We will be careful not to overinterpretcorrelations with low significance values, be-cause our reporting of a large number of cor-

relations makes it relatively likely that a few‘‘significant’’ values will crop up at random.

The results are completely unambiguous.Several weak correlations involving the mid-point d18O data crop up, but these consistentlyreflect coincidental trends in each time seriesand are not replicated by the correlations forchange in midpoint d18O. Meanwhile, just onecorrelation is significant for any comparisonbetween d18O data and the remaining fourmeasures of mammalian turnover. This in-volves a weak correlation between detrendedd18O SD and origination. However, the rela-tionship is seen only when using Pearson’sproduct-moment coefficient (rP); it disappearsonce we switch to the nonparametric Spear-man’s rank-order correlation coefficient (rS).

Despite the lack of even a close call here, thequestion still arises whether some real corre-lations might be masked by errors in the data


TABLE 2. Time series analyses contrasting benthic foraminiferal oxygen isotope data with mammalian biotic data.Pearson’s product-moment correlation coefficients are reported above; Spearman’s rank-order correlations are re-ported below. The latter are favored because they lessen potential problems with outliers and non-normal distri-butions of variables. ‘‘Volatility’’ is just the absolute value of the change in d18O values. Sample size is 60 data pointsfor serial correlation and correlation against time; 59 for correlations with midpoint and standard deviation isotopedata, which omit the 50.5-Ma bin because of lack of data; and 57 for correlations with changes in d18O and volatility,which additionally omit the 59.5-bin (because of differencing) and 49.5-Ma bin (because of lack of data). * 5 p ,0.05; ** 5 p , 0.01; *** 5 , 0.001.

Variable Time Serial Midpoint Change Volatility SD Detrended SD

Pearson’s product-moment correlations

Log richnessOriginationExtinction

20.433**0.317*0.359**

0.792***0.1410.247

0.294*20.275*20.360**

20.0320.0630.122

0.1650.012

20.003

0.1490.109

20.136

20.0020.275*

20.021Net diversificationDiversification volatilityTotal turnoverProportional volatility (index)

20.0610.0150.420***0.477***

0.0400.0190.282*0.244

0.09720.05120.397***20.444***

20.05920.023

0.1660.145

0.01220.103

0.0050.191

0.2080.122

20.0240.083

0.2390.1380.1490.208

Proportional volatility (G)Mass (mean)Mass (standard deviation)Mass (skewness)Mass (kurtosis)

0.05120.712***20.865***

0.430***0.686***

0.0860.762***0.939***0.702***0.812***

20.0450.611***0.724***

20.311*20.639***

0.03020.11020.284*

0.0900.169

0.17020.04120.050

0.03520.165

0.341**0.0240.1110.129

20.237

0.379**20.14320.081

0.22420.021

Spearman’s rank-order correlations

Log richnessOriginationExtinctionNet diversification

20.370**0.319*0.284*

20.011

0.780***0.0970.1360.065

0.22020.263*20.272*

0.056

20.1120.0530.120

20.051

0.1880.1200.0050.030

0.21120.07520.248

0.191

0.1350.039

20.1540.156

Diversification volatilityTotal turnoverProportional volatility (index)Proportional volatility (G)

20.0430.371**0.467***0.098

20.0190.1490.1900.127

20.00920.354**20.416***20.150

0.0470.1450.054

20.151

0.0060.0520.1840.199

0.11120.22520.115

0.155

0.14120.11220.121

0.147Mass (mean)Mass (standard deviation)Mass (skewness)Mass (kurtosis)

20.745***20.865***

0.393***0.708***

0.722***0.904***0.690***0.829***

0.655***0.673***

20.278*20.535***

20.14120.273*

0.0360.110

20.05420.158

0.04320.100

0.1240.1050.119

20.230

20.07020.080

0.272*20.038

or other factors. Perhaps these difficultiesmake immediate causal relationships betweenclimate and evolution hard to see in side-by-side comparisons of values. Three such factorsmight be important: (1) miscalibration of onetime series or another may mean that we arecomparing bins of nominally identical, but ac-tually different, ages; (2) backwards-smearingof extinction events and forwards-smearing oforigination events may mean (for example)that climate events in a bin 1.0 m.y. after anapparent series of extinctions may actuallyhave caused those extinctions; and (3) causalinteractions may be mediated by intermediatefactors like evolutionary changes in vegetationthat may delay responses on the million-yeartimescale. For all of these reasons, it is of in-terest to examine correlations where we lagthe isotope data by one sampling bin either

backward or forward relative to the faunalturnover data.

The lagged correlations show no greater bi-ological significance (Table 3). At first glance,it seems as if there is a series of weak but per-haps important correlations involving changein d18O. Most of these involve extinction or to-tal turnover. However, these correlations arehighly suspect for two reasons: (1) none of thecorrelations are also seen in the unlaggeddata, and (2) the extinction correlation is seeneither with backwards or forwards lagging,which makes no sense in causal terms—howcould an isotopic shift 1 m.y. in the future bejust as important as one 1 m.y. in the past? In-stead, the pattern of correlations suggests apersistent problem with artifactual cross-cor-relations between time series that have tem-poral trends: all four of the biotic variables


TABLE 3. Lagged cross-correlations among key time series. Lags are of 1.0 m.y. (i.e., one sampling bin) in eitherdirection. Abbreviations as in Table 6. Forward lags are considered more meaningful because if climate changedrives turnover, then climate change in the past that is lagged forward one interval may be relevant to the currentinterval. In contrast, climate change in the future that is lagged backward cannot be.

Variable Backward changeBackwardvolatility

Backwarddetrended SD Forward change

Forwardvolatility

Forwarddetrended SD

Pearson’s product-moment correlations

Log richnessOriginationExtinctionNet diversificationDiversification volatilityTotal turnover

20.0560.2460.1880.038

20.1890.268*

0.19320.05720.00520.04220.02120.037

20.0900.051

20.0980.127

20.17820.031

20.03220.046

0.262*20.279*

0.0400.139

0.14320.06020.083

0.0250.035

20.087

0.08520.10620.07220.022

0.07720.109

Proportional volatility (index)Proportional volatility (G)Mass (mean)Mass (standard deviation)Mass (skewness)Mass (kurtosis)

0.308*0.110

20.05620.288*20.045

0.157

20.11820.09020.070

0.0400.146

20.080

20.10720.06820.07320.046

0.14320.031

0.18620.10920.15520.272*

0.0820.137

20.10420.00320.01920.003

0.11520.139

0.0720.115

20.19020.135

0.14320.145

Spearman’s rank-order correlations

Log richnessOriginationExtinctionNet diversification

20.0800.2480.283*

20.014

0.1780.0310.0040.063

0.0470.020

20.1110.101

20.1170.0050.373**

20.232

0.19820.08120.08820.049

0.19720.15920.133

0.006Diversification volatilityTotal turnoverProportional volatility (index)Proportional volatility (G)

20.2080.340**0.315*0.093

20.0280.0120.0180.073

20.19420.07120.09020.012

0.0160.2410.250*

20.132

0.12220.16320.065

0.163

0.04220.156

0.1230.204

Mass (mean)Mass (standard deviation)Mass (skewness)Mass (kurtosis)

20.07420.270*20.062

0.096

20.10820.081

0.17520.039

20.01720.080

0.1670.005

20.17520.248

0.0150.077

20.05120.157

0.03720.092

20.09620.099

0.17120.081

show moderately to very strong trends (Table2), and even though the 10.227 correlation ofthe change in d18O values with time was insig-nificant at the p , 0.05 level, it was barely so.Indeed, after detrending the isotopic variableevery single one of the suggestive cross-cor-relations drops far below the level of signifi-cance.

Even if one wanted to interpret the few con-sistent correlations, it would be unwise be-cause we have subjected the data to a largenumber of analyses without correcting formultiple comparisons. Just at random, weshould expect several comparisons to be sig-nificant at the p , 0.05, and possibly even p ,0.01, level.

For example, a standard Bonferroni correc-tion for these multiple comparisons wouldwork as follows: we have performed back-ward, forward, and non-lagged cross-corre-lations for three key isotope variables matchedwith five distinct turnover rate metrics, so ifwe want to examine all of our tests one by one

then we really should multiply our alpha lev-els by 3 3 3 3 5 5 45. Therefore, an apparentp , 0.001 result actually is equivalent to p ,0.045, and an apparent p , 0.05 or even p ,0.01 outcome is simply not significant. As ithappens, none of the Pearson’s correlations inTable 3 are ‘‘significant’’ at p , 0.01.

The lack of any strong results here arguesagainst the ‘‘turnover pulse’’ scenario outlinedby Vrba (1985, 1992, 1995), which has beencriticized for other reasons in previous studies(Alroy 1996, 1998d; Behrensemeyer et al.1997). This theory specifically predicts thatboth origination and extinction rates shouldrise at the same time as, or no later than 1.0m.y. after, any major positive excursion in iso-tope values. That is, global cooling/ice vol-ume buildup should strongly encourage bothspeciation and extinction. No such pattern isseen in our data.

In summary, we find no evidence for linearabiotic forcings of turnover rates throughoutthe Cenozoic. Quite to the contrary, this and


earlier studies (Stucky 1990; Alroy 1996,1998d) have shown that a strong linear bioticforcing accounts for a substantial amount ofthe variation in origination rates. Thus, thedata clearly would have been capable of pro-viding support for a strong causal mechanismif one had existed.

Relative Diversity of Major Orders. We ex-amined two measures of the rate of change inspecies richness within mammalian orders:the proportional volatility index and G-statis-tic (Alroy 2000: Fig. 7). Both show insignifi-cant autocorrelation but only the index showsa relatively strong trend (Table 2). As dis-cussed by Alroy (2000), the two statistics dif-fer substantially in that the simple proportion-al volatility index is strongly correlated withtaxonomic turnover, whereas the proportionalvolatility G-statistic is not. For this reason, theG-statistic curve seems to be far more infor-mative and our discussion will focus on it.

The G-statistic time series (Fig. 4F) suggestsfour distinct patterns. First, despite the lack ofa general correlation with the turnover ratedata, there still are instances in which highturnover at the species level results in highturnover at the ordinal level. For example, thePaleocene/Eocene transition shows unusualturnover at both levels.

Second, the rapid and near-total replace-ment of archaic groups like the multituber-culates and ‘‘condylarths’’ by the modern or-ders may largely be a side effect of generallyhigh Paleogene turnover rates. Some key stepsin this transition occur at times of little pro-portional volatility: multituberculates declinesteadily throughout the Paleocene, well beforethe modern groups establish themselves; and‘‘condylarths’’ lose their foothold during astretch of several million years in the early Eo-cene, well after the Paleocene/Eocene bound-ary and well before the massive mid-Eoceneradiation of artiodactyls.

Third, there is a weak trend of increasingproportional volatility, but it is not visible forthe 60 data points in the study interval (Table2; G vs. time: r 5 0.051; t 5 0.388; n.s.). Thelow points before 60 Ma cannot be explainedas a side effect of unusual turnover rates, notonly because secular variation in turnoverrates was accounted for in computing the G-

statistic (Alroy 2000), but because rates wereactually higher, not lower, in the latest Creta-ceous and early Eocene. Still, the persistentlyhigh G-values suggest the possibility of non-random replacement between pairs of ecolog-ically similar major groups, not just the sto-chastic loss of volatile groups. Testing for di-rect competitive replacement would be thesubject of another, much more complex anal-ysis.

Fourth and most obviously, a handful ofdata points stand out from the rest (Fig. 4).The second-highest marks the Clarkforkian/Wasatchian (Paleocene/Eocene) boundary at;55 Ma, which has been the focus of consid-erable paleoecological interest (e.g., Clyde andGingerich 1998). Surprisingly, there is no highpoint at the K/T boundary, even though highturnover rates and massive changes in ordinalcomposition are obvious and well known (e.g.,Alroy 1999a). Several other high points arescattered throughout the Oligocene and earlyMiocene, an interval where poor sampling(Alroy 2000: Fig. 4) often complicates anystraightforward biological interpretations ofturnover.

Perhaps the most interesting part of thetime series is a stretch in the mid-Eocene thatincludes four of the five highest G-values(46.5, 44.5, 43.5, and 41.5 Ma, i.e., Bridgerianand Uintan). This interval corresponds to theradiation of artiodactyls (and to some degreeperissodactyls), matched by the terminal de-cline of primates (and to some degree ‘‘con-dylarths’’). At 47 Ma, the two modern ungu-late orders account for 13.9% of standing di-versity, and the primates are near their all-time peak at 12.1%; by 44 Ma, these figures are35.6% and 5.1%. By 37 Ma, primates have gonetemporarily extinct in North America.

In light of the obvious evidence here for amajor ecological transition, it is almost dis-appointing to report our failure to find anymeaningful correlation between the propor-tional volatility data and the isotope data (Ta-ble 2). (1) As expected, the proportional vol-atility index does correlate significantly (if notvery strongly) with the midpoint d18O curve,because these two time series both show sec-ular trends. Therefore, this correlation must beput aside as being a potential statistical arti-


fact. (2) None of the correlations involving theproportional volatility statistic appear whenusing both the Pearson’s coefficient and theSpearman’s coefficient. The collapse of a cor-relation involving the d18O detrended stan-dard deviation and the G-statistic is particu-larly shocking (rP 5 10.379; rS 5 10.147). (3)The lagged correlations (Table 3) are every bitas uninteresting, with correlations involvingthe change in d18O variable and the propor-tional volatility index disappearing after de-trending the former (as discussed above).

Body Mass Distributions. The moment sta-tistics depict strong patterns of change in theoverall body mass distribution (Fig. 5). All ofthese individual statistics show strong serialcorrelation and strong trends through time(Table 2), making them unsuitable for beingcross-correlated with the autocorrelated iso-tope time series (i.e., midpoint value and stan-dard deviation), as discussed in the Introduc-tion. Therefore, after describing some majorfeatures of the body mass data, we will focusour discussion on comparisons with the re-maining three isotope data sets that lackstrong autocorrelation.

Mean body mass increases abruptly at theCretaceous/Tertiary boundary (Fig. 5A). Asdiscussed elsewhere (Alroy 1999a), some ofthis shift is attributable to differential immi-gration of relatively large species such as basalungulates, but most of it seems to be due to insitu evolution. The mean continues to increasethroughout most of the Cenozoic, but slowly.Most of the trajectory is attributable to strongevolutionary trends operating within medi-um- and large-sized lineages (Alroy 1998b),which could be explained by any number ofbiotic mechanisms: biomechanical or physio-logical optimality, escape from competitionwith diverse small-sized taxa, an evolutionaryarms race between predators and prey, or highspeciation and/or low extinction rates of larg-er species resulting from the scaling of de-mographic factors.

A relatively rapid drop in mean body massat around 7 Ma is too large to be a samplingartifact. One might think that the Miocenedata up to this point differentially samplelarge species. However, the remarkably stablestandard deviation values—which vary only

between 3.73 and 4.13 units between 18 and 1Ma—suggest that any size-related samplingbiases are essentially constant throughout thisentire interval. The pattern more likely reflectsbona fide differential extinction of large mam-mals in the latest Miocene (Alroy 1999b).

Like the somewhat noisier curve for themean, the standard deviation curve increasessteadily throughout the Cenozoic. The data doshow a major downward excursion betweenabout 56 and 49 Ma (Fig. 5B). The possible eco-logical significance of this drop is discussedbelow.

We employ skewness as a measure ofwhether faunas are dominated by small spe-cies (positive skewness) or large species (neg-ative skewness). The skewness curve shows anerratic drift toward negative values, meaningthat initially there is a long, thin tail of largerspecies, but that by the Miocene large mam-mals are dominant (Fig. 5C). The trend is re-versed in the latest Miocene. Brown and Ni-coletto (1991) and Marquet and Cofre (1999),who respectively studied Recent regional (bi-ome-scale) distributions in North and SouthAmerica, also found positive skews (althoughtheir values are higher than ours). Confirma-tion of their results is important because Re-cent distributions suffer from a clear historicalbias: they are influenced by a catastrophic ex-tinction of megafaunal species that was almostcertainly anthropogenic, had no clear ante-cedent in the Tertiary record, and had majorramifications for local, regional, and continen-tal-scale body mass distributions (Alroy1999b). Marquet and Cofre (1999) also arguedfor the importance of historical factors in gov-erning these distributions. Thus, the currentdata suggest that even if positive skewness inthe Recent biota is exaggerated, the patternstill reflects a remarkable late Miocene rever-sal in the overall Cenozoic trend that domi-nated before about 7 Ma.

The most important observation for ourpurposes is that skewness did generally dropthrough the Tertiary. The overall trend makessense given a dual-equilibrium pattern: thedistribution around the small-size equilibri-um point was constant and well filled fromthe very start, but only a few rapidly evolvinglineages were able to approach the large-size


equilibrium point prior to the late Tertiary(Alroy 1998b). Filling of the upper size rangeresulted in the distribution’s becoming moreevenly balanced, with lower (and eventuallyeven negative) skewness.

The last statistic is kurtosis, a measure ofwhether a distribution has more than the ex-pected number of species in the mid-sizerange (positive, or leptokurtic, values) or few-er, in which case a mid-sized gap may be vis-ible (negative, or platykurtic, values). Kurtosisshows an even more interesting pattern thanskewness (Fig. 5D). Values are slightly nega-tive in the Late Cretaceous and early Paleo-cene. They rise quickly around 54 Ma and driftdownwards until finally dropping to nearly21 by 45 Ma, where they largely remainthroughout the rest of the Cenozoic. Hence, alarge gap in the body mass distribution opensin the mid-Eocene and remains unfilled (Al-roy 1998b: Fig. 1). Alroy (2000: Fig. 9D)showed that exactly the same bimodal patternis seen in a majority of diverse quarry-scalesamples younger than 45 Ma.

The kurtosis pattern has three importantimplications. First, the Paleocene/Eocene im-migration pulse (Gingerich 1989; Clyde andGingerich 1998) registers not just in taxonomicturnover data, but in body mass data: a dropin the standard deviation and rise in kurtosisindicate the rapid filling of the middle sizerange by small ungulates, carnivores, and pri-mates. Second, the primate/ungulate transi-tion, which has such a remarkable impact onthe proportional diversity of major orders, isalso expressed as a substantial increase in thestandard deviation and decrease in kurtosisduring the Bridgerian (50.3–46.2 Ma [Alroy2000]), and arguably continuing into the Uin-tan (46.2–42.0 Ma). Hence, the mid-Eoceneecological transition easily ranks as one of themost important of the entire Tertiary. Third,the fact that kurtosis hovers around 21, evi-dencing no strong trend after 45 Ma—despiteepisodic drops in mean temperature and in-creases in seasonality—suggests that gaps inthe mammalian body mass distribution can-not be linked to climate change in a simpleway. If a link is indicated here, it is in the formof a nonlinear threshold effect whereby the

middle size range becomes emptied once cli-mate deteriorates past a certain point.

The lack of any simple relationship betweenclimate and body mass distributions is sup-ported by the correlation analyses. We find aseries of significant but potentially artifactualcross-correlations involving midpoint isotopevalues and the assorted body mass measures(Table 2). All of these variables have strongsecular trends, so the correlations are inevi-table and, therefore, uninformative.

For the remaining 16 comparisons we findexactly one case of significance at the p , 0.05level that is suggested by both the Pearson’sand Spearman’s coefficients. Of course, 16comparisons frequently should yield one suchcase just at random. The relevant correlationinvolves standard deviation of body mass andrate of change of d18O. Unfortunately, we findthat removing a single outlier changes the re-sult. The change in d18O of 20.350 units goinginto the 52.5-Ma bin is the second highest inthe time series; this bin’s body mass standarddeviation of 2.327 is the fourth highest. With-out this point, the correlations are insignifi-cant (rP 5 20.232; n.s.; rS 5 20.236; n.s.). Thelagged correlations (Table 3) are even less im-pressive. Apart from a similar correlation in-cluding this pair of variables, which again dis-appears once the isotopic data are detrended,not one of them approaches the p , 0.05 levelof significance.

Critical Intervals

Our exhaustive comparisons of isotopic andbiotic records provide substantial evidencethat mammal evolution and extinction are notlinearly forced by global climate change. Thefew cases of apparent cross-correlation are allattributable either to the presence of outlyingdata points or to the presence of strong, mis-leading autocorrelation in the time series. Ourresults should not be misinterpreted as merelyshowing that the data are noisy. We do see ro-bust patterns in the mammalian fossil record,but most of them can be attributed to biolog-ical processes such as ecological release in thewake of the K/T mass extinction (Alroy1999a), equilibrial diversity dynamics later onin the Cenozoic (Alroy 1998d), and evolution-ary trends within individual taxonomic line-


FIGURE 6. Frequency distributions of statistics describing benthic isotope records. Black boxes and numbers in-dicate the five critical intervals of climate change discussed in the text. A, Estimated midpoint d18O value for binbased on linear regression of values against time. B, Change in midpoint d18O value from preceding bin to currentbin. C, Isotopic volatility (absolute value of change). D, Standard deviation of residual d18O values (variability). E,Generalized differences of standard deviations (detrended variability).


ages (Alroy 1998b), all of which are better ex-plained by intrinsic factors like ecologicalcompetition than by extrinsic factors likemean temperature and precipitation. Similar-ly, the highly averaged isotopic records usedin our analysis do show major features thathave been interpreted in the past as evidencefor global climatic change, such as the Paleo-cene/Eocene boundary event, the Eocenethermal maximum, warming/ice volume de-crease in the early Miocene, and shifts towardcooler climates and/or greater ice volume atthe Eocene/Oligocene boundary, in the lateMiocene, and in the Plio-Pleistocene.

Even though our analyses failed to uncoverstrong evidence of linear forcings, they dosuggest an intriguing pattern: a handful ofcases in which a correlation results from oneor two highly anomalous data points. Per-haps, then, climate does have an influence onmammalian evolution—but only in the formof occasionally and unpredictably producingunique, one-time-only biotic responses. To testthis hypothesis more rigorously, here we ex-amine the state of the climate system duringcritical intervals documented in the biotic re-cords.

This exercise is substantively different fromthe analyses undertaken by Alroy (1998d,1999b) and Prothero (1999). In those studies,the authors first subjectively identified inter-vals of rapid change in the climate record andthen examined mammalian responses duringthose intervals. In some sense, this is equiva-lent to hypothesizing linear forcing; the exer-cise only makes sense if one expects every ma-jor climate event to instigate some sort of bi-otic response. The test conducted here de-pends on a less restrictive view of the impactof climate on mammalian evolution: we mere-ly consider whether the climate system was inan atypical state during time periods forwhich we have objective evidence of majorchanges in the biota.

There are six such biotic events in our re-cords, most of which correspond to generallyrecognized boundaries in the traditionalNorth American land mammal age system(Woodburne 1987; Alroy 1998a, 2000). Theyare the Tiffanian/Clarkforkian boundary(;57 Ma), the Clarkforkian/Wasatchian (i.e.,

Paleocene/Eocene) boundary (;56 to 55 Ma),the early Uintan (;45 to 44 Ma), the mid-Ol-igocene diversification (;31 to 28 Ma), the lat-est Miocene and possibly earliest Pliocene (;7to 4 Ma), and the Pleistocene/Recent bound-ary (1 to 0 Ma).

The massive faunal reorganization associ-ated with the late Pleistocene extinction was adramatic and highly selective catastrophe thatfocused almost exclusively on large mammals(Alroy 1999b). Because we consider human–faunal interaction the most likely cause of thisevent, we preclude it from further discussionhere. Our data for the 0.99 m.y. immediatelypreceding the extinction do suggest a net di-versification with high volatility and othersubtle shifts, like a decrease in the standarddeviation of body mass. However, these statis-tical wobbles are most likely attributable to re-sidual sampling artifacts created by the latePleistocene’s truly exceptional coverage—interms of geography, taphonomy, and sheerquantity of data. For the other five events, wewill briefly describe the biotic data that defineeach one, and then turn to an examination ofthe globe’s climatic state at the time.

Before proceeding, we will note that severalother events may merit attention at a futuredate. Currently, however, we are not confidentthat they are anything more than statisticalanomalies. A typical case is the subtle faunaltransition around the very end of the Eocene(Chadronian/Orellan boundary: 33.9 Ma). Di-versity drops slightly in the wake of elevatedextinction rates for the 34.5-Ma bin, and yetproportional volatility is truly unremarkableand shifts in the body mass distribution aresmall and seemingly aimless. The vast major-ity of intervals are marked by similar patterns,with no concordance among statistical mea-sures and data points that all fall comfortablywithin two or even 1.5 standard deviations ofthe mean. The few exceptions—especially forbody mass distributions—seem to relate to re-sidual sampling artifacts, with some periodsfailing to sample either large or (more com-monly) small mammals (e.g., data for 32–29Ma).

Our climatic analysis is simple. In Figures6–8, we present histograms respectively sum-marizing the benthic isotope, taxonomic turn-


FIGURE 7. Frequency distributions of turnover rates over the last 60 Ma. All rates are instantaneous and apply toa single 1.0-m.y.-long sampling interval. Black boxes and numbers indicate critical climate change intervals. A,Instantaneous rates of origination. B, Instantaneous rates of extinction. C, Net diversification rates. D, Diversificationvolatility. E, Total turnover rates. F, Proportional volatility G-statistic.

over, and body mass distributions. The bodymass data have been transformed into firstdifferences (changes between consecutivebins) in order to remove strong autocorrela-tion (see Table 2). If biotic events in the mam-

mal record are associated with unusual cli-mates, we would expect them to occur in, orimmediately after, intervals with climatic pa-rameter values (Fig. 6) more than two stan-dard deviations from typical Cenozoic values.


FIGURE 8. Frequency distributions of changes in body mass moment statistics over the last 60 Ma. Black boxes andnumbers indicate critical climate change intervals. A, Changes in the mean. B, Changes in the standard deviation.C, Changes in skewness. D, Changes in kurtosis.

These limits are 20.409 to 10.509 for changein midpoint d18O value, zero (the lowest pos-sible value) to 10.478 for isotopic volatility,10.025 to 10.395 for standard deviation ofisotope value residuals, and 20.161 to 10.164for detrended isotopic standard deviation. Bythis standard, the only significant climateevents are in the following five bins: 55.5 Ma(high standard deviation and detrended stan-dard deviation), 33.5 Ma (rise in midpointd18O, high isotopic volatility), 28.5 Ma (highdetrended standard deviation), 25.5 Ma (dropin midpoint d18O, high isotopic volatility), and0.5 Ma (high standard deviation and detrend-ed standard deviation). As we will argue, justtwo of these episodes also correspond to oneof the five intervals of major biotic change—even though we defined the intervals ratherbroadly. However, one other biotic event is as-sociated with a longer run of unusual climatic

values, perhaps indicating a nonlinear re-sponse to gradual climatic forcing.

1. The Tiffanian/Clarkforkian (Ti/Cf) tran-sition, which essentially falls in the 57.5-Mabin, is marked by a sudden drop in diversityfrom ;52 to 38 species (sampling-standard-ized data; see Fig. 3). The extinction rate(0.666) is the most extreme in our entire studyinterval. As a result, the volatility and totalturnover rate values are the highest and sec-ond-highest in the data set (0.327, 1.004), andthe net diversification value is the lowest(20.327). Sampling intensity is uniformthroughout this interval, so this drop cannotbe attributed to variation in sampling per se.

Because the Ti/Cf boundary occurs so nearthe start of our isotopic time series, it is diffi-cult to evaluate the role of climate change inthis event. The benthic marine d18O recordreached an early Cenozoic maximum at 60


Ma, then declined steadily for 10 m.y. (Table1). This trend has been interpreted as a sign ofgradual global warming (Miller et al. 1987;Zachos et al. 1994). While the Ti/Cf boundaryoccurs very near the inflection point in thebenthic curve (i.e., very close to the pointwhere temperatures begin to rise), it is notclear that the two precisely coincide and nei-ther the change in midpoint d18O value nor themeasure of d18O variability is at all unusualnear the boundary.

Rose (1981) argued that Tiffanian as well asClarkforkian alpha diversity was aberrantlylow. If this were true, it would make moresense in light of evidence that a shift to coolerclimates occurred in the early Paleocene, be-fore the Tiffanian. Maas et al. (1995) con-curred, arguing that regional diversity alsowas essentially constant during the middleand late Paleocene (i.e., Tiffanian–Clarkforki-an). Gunnell et al. (1995) thought that Clark-forkian faunas evidenced cooler, drier habitatsthan later, Wasatchian faunas, and went on toargue that Clarkforkian diversity may be un-derrepresented because of sampling biasesthat exclude many small species.

A simple relationship between climate anddiversity would predict low diversity in thecooler Tiffanian and steadily rising diversityafterwards. In our data, though, diversitycrashes suddenly after the Tiffanian—whichraises reasonable doubts about the reliabilityof both our biotic and our climatic data sets.However, our marine isotope data are stronglysupported by leaf-margin analyses (Wing etal. 1995; Wilf 1997, 2000), which show clear ev-idence for warming between the Tiffanian andClarkforkian in the same northern RockyMountains region as the mammal faunas stud-ied by Rose (1981), Gunnell et al. (1995), andMaas et al. (1995).

As for the diversity data: (1) a drop goinginto the Clarkforkian is present in all earlierversions of our data set (Alroy 1996, 1998d),even including one that was not corrected forsampling effects (Wing et al. 1995); (2) severalhigh-quality Clarkforkian faunas such asthose of Rose (1981) are included in our anal-yses; (3) there is no evidence for undersam-pling of small species in the form of any large,sudden shift in any of the body mass moment

statistics between the 58.5- and 57.5-Ma bins;and (4) likewise, proportional volatility is lowthroughout the late Tiffanian and Clarkforki-an, and small groups like the Insectivora donot experience a major drop in relative diver-sity—at 57 Ma they actually constitute 12.9%of the fauna, which is a bit higher than theirCenozoic mean of 9.9%.

If our data are meaningful, then how coulda gradual warming trend have resulted in asudden, dramatic diversity crash? One possi-ble scenario is that warming may have led tothe northward shift of a mammal communitythat heretofore was restricted to the verysouthern margin of North America. Perhapsthis subtropical community was depauperatebecause of the small geographic area of the bi-ome it occupied prior to the Clarkforkian(most of Central America would not emergefor another 55 m.y.). We find this argument adhoc. Furthermore, it has been argued thatsouthern limits of Recent mammals are set inlarge part not by climatic conditions, but bybiotic interactions (Kaufman 1995). If thisspeculation is correct, then Tiffanian holdoverspecies might have persisted in situ even as aset of more warm-adapted species immigrat-ed from the south—so the addition of even adepauperate subtropical fauna could have in-creased, not decreased, standing diversity. Insummary, we believe that the Clarkforkian di-versity crash is a legitimate biological mysterythat remains to be solved.

2. The Clarkforkian/Wasatchian (Cf/Wa)boundary is marked by a major ordinal re-placement event: true primates, hyaenodontidcreodonts, artiodactyls, and perissodactyls allmake their first appearance in North America(Gingerich 1989; Clyde and Gingerich 1998).The proportional volatility G-statistic (Fig. 4F)is one of two truly extreme values in the dataset and shows clearly that this event goes be-yond the limits of background turnover. In ad-dition, the body mass data show that theboundary is close to a large drop in the stan-dard deviation (20.301: 54.5-Ma bin) and thelargest increase in kurtosis (11.478: 53.5-Mabin) in the entire record (Fig. 5B,D). These sta-tistics record the filling of the middle bodysize range by members of each of the newgroups.


The Cf/Wa boundary coincides with themarine bin (55.5 Ma) that has the second high-est standard deviation (0.467, which is morethan two standard deviations above the mean)and by far and away the highest detrendedstandard deviation (10.307). This portion ofthe Paleogene is well sampled in the marinerecord, so it is very unlikely that the high val-ue is an artifact of insufficient sampling. Rath-er, it reflects the extremely unusual d18O val-ues associated with a warm climatic excursionat 55 Ma (Kennett and Stott 1991). Our mil-lion-year binning is too coarse to illustrate theevent, but the climatic transient is largeenough to increase observed variability for theentire million-year block. Highly resolved bio-stratigraphic, chronostratigraphic, and paleo-climatic analyses from the western UnitedStates show that changes in the relative diver-sity of orders and in the body size distributionare precisely coincident with the climatic tran-sient (Koch et al. 1992; Clyde and Gingerich1998). However, even at this coarse temporalscale the relationship between climatic changeand faunal response is obvious.

The proximate links between climatechange and turnover at the Paleocene/Eoceneboundary remain obscure. The warming atthis boundary is extremely rapid (,30,000years [Bains et al. 1999; Norris and Rohl1999]), and some of the mammalian first ap-pearances are tightly coupled to the warming(Koch et al. 1992). As a consequence, manyworkers have focused on immigration, ratherthan in situ evolution, as a primary factor inthis turnover (Gingerich 1989; Krause andMaas 1990; Beard 1998; Clyde and Gingerich1998). Under this scenario, the appearanceevent at the Paleocene/Eocene boundary inthe Holarctic continents is thought to reflectrapid faunal homogenization via high-lati-tude land bridges that is facilitated by extremehigh-latitude warming, though the ultimatesource of these immigrants is debated (Gin-gerich 1989; Koch et al. 1992; Beard 1998;Hooker 1998).

Despite the addition of these potential im-migrant taxa, the biotic transition at the Paleo-cene/Eocene boundary in North America isactually dominated by the products of in situcladogenesis immediately following the cli-

matic transient. Sampling-standardized datashow that primates, artiodactyls, and peris-sodactyls (the three new orders) together con-stitute 14.3% of the fauna by 55 Ma and 18.6%by 54 Ma, and raw data show that at least 121and 117 species existed at these two times.Thus, four or five founding species in thesegroups quickly gave rise to dozens of others.If cladogenesis in these groups had proceededat background rates instead, the immigrationevents would have appeared to be completelyunremarkable.

3. The early Uintan, and to some extent thepreceding Bridgerian, is marked by yet anoth-er major ordinal shift, as primates and ‘‘con-dylarths’’ decline while artiodactyls and pe-rissodactyls increase. The clearest evidencehere is a series of elevated proportional vola-tility G-values throughout the mid-Eocene,with particularly high values for the 46.5-,44.5-, 43.5-, and 42.5-Ma bins. With respect topatterns in body size, the key 44.5 early Uin-tan bin includes the third-largest increase inthe mean (11.102), the fifth-largest standarddeviation increase (10.307), and the fifth-big-gest drop in skewness (20.407), all of whichindicate a trade-off between medium- andlarge-sized mammals. Turnover rates per seare not remarkable, but the data set’s second-highest net diversification value is in the 49.5-Ma bin (i.e., earliest Bridgerian), which putsdiversity at the levels it maintained through-out most of the Eocene. Many of these quan-titative measures track the loss of primates,which creates a gap in the middle of the bodysize distribution. The unusual pattern of tax-onomic turnover and body mass changearound 45–44 Ma qualifies as a bona fide eco-logical transition, one with few or no parallelselsewhere in the record. Whether the transi-tion corresponded to a single, abrupt extinc-tion event or a gradual replacement lastingseveral million years is not yet determinable.

At first inspection, the isotopic standard de-viation and detrended standard deviation val-ues for this interval seem to be absolutely typ-ical. The rate of change is one standard devi-ation higher than the mean for the two blocksbetween 48.5 and 46.5 Ma, and is positive, butmuch closer to the mean in the temporalblocks bracketing this interval. In addition to


these slightly higher than normal rates of d18Oincrease, this portion of the record is conspic-uous for being the first long interval after theearliest Paleocene (immediately prior to ourfirst isotopic records at 60 Ma) in which d18Ovalues steadily increase. In other words, thetime period from ;49.5 to 44.5 Ma representsthe first sustained, significant pulse of globalcooling experienced by mammals in the Ce-nozoic. While no single 1.0-m.y.-long blockwas highly unusual, the aggregate effect of cli-mate change in this interval was to present thepresumably warm/wet adapted faunas of thelatest Paleocene–early Eocene with a coolerworld. A plausible argument could be madethat this trend included an increase in season-ality, a decrease in precipitation and temper-ature, or both.

In the Recent, primates and mammalian ar-boreal folivores/frugivores are most diversein tropical areas with low seasonality andhigh mean annual precipitation and temper-ature, whereas tropical ungulates dominate inareas with greater seasonality and lower pre-cipitation (Gunnell et al. 1995; Gagnon 1997).The fact that mammalian data for just a few1.0-m.y. intervals signal such a major transi-tion suggests that if environmental factorswere important, the biotic response involveda nonlinear threshold effect: perhaps a criticalamount of environmental deterioration result-ed in primates no longer being able to prosperand artiodactyls and perissodactyls suddenlybeing able to radiate.

4. The mid-Oligocene is a period of sub-stantial diversification following a long inter-val, going back arguably to the end of the mid-Eocene upheaval at about 41 Ma, that wit-nessed exceptionally low regional diversity(Alroy 1996). Although visually dramatic, themid-Oligocene diversification is hard to pindown to a particular bin. Instead, modest butconsistent net diversification in each bin from31 to 28 Ma boosts diversity by some 49%.Apart from this run, late Oligocene origina-tion, extinction, volatility, and total-turnoverrates are not very remarkable. However, the28.5-Ma bin does have the highest proportion-al volatility G-statistic in the study interval(33.964). Body mass data record nothing ofgreat interest, with all of the small shifts dur-

ing the late Oligocene being rendered dubiousby persistently low counts of measured spe-cies. Thus, the shifts may reflect variable re-porting of small mammals like insectivoransand small rodents.

There is strong evidence for significant cli-mate change in this interval. The 28.5-Ma binrecords the third-highest detrended standarddeviation value (10.173), and the standard de-viation seems high in general throughout thelate Oligocene (Fig. 1D, E). The single largestdecrease in the midpoint d18O value separatesthe 26.5- and 25.5-Ma bins. Unfortunately,poor faunal correlations make it hard to saywhich of these isotopic shifts, if either, corre-lates with the mammalian diversification. Inany event, the implied melting of ice sheetsand/or global warming event that is indicatedby these data marks the beginning of an iso-tope plateau that persists until perhaps themid-Miocene, at which point isotope valuesagain begin to climb steadily.

Here, as across the Paleocene/Eoceneboundary, there is evidence for both an ame-liorating climate and an increase in diversity.However, the mechanism is profoundly differ-ent. This time there is no evidence for the im-migration of important new taxonomicgroups, and shifts in ordinal dominance areshort lived: a relative increase in rodent andcarnivoran diversity at the expense of insec-tivorans, perissodactyls, and arguably artio-dodactyls, all of which is reversed within afew million years. These shifts could conceiv-ably relate to the monographic bias that is sug-gested by the body mass data. Another sourceof worry is the fact that the late Oligocene datainclude extensive faunal lists from the WestCoast (i.e., the John Day area) in addition tothe northern Great Plains, whereas the earlyOligocene data are heavily concentrated in theGreat Plains region. Despite these concernsabout data quality, we do believe that the eas-ily visible, half-again increase in regional di-versity between the early and late Oligoceneis real. Understanding the exact nature of thisbiotic response will require obtaining muchbetter paleoecological and taxonomic datathan are currently available in the publishedliterature.

5. The last conspicuous set of mammalian


events occurred in the late Miocene and Plio-cene, from ;7 to 4 Ma. Here it is hard to tellwhether one or more distinct events are in-volved. A very important shift in body massdistributions occurs going into the 6.5-Ma bin,with the time series’ third-largest drop in themean (20.955) and biggest increase in skew-ness (10.488); the preceding bin witnesses an-other large drop in the mean (20.898) and thesecond-largest decrease in kurtosis (20.661).Some of these patterns may reflect samplingbiases—small mammal faunas are unusuallypoor during the preceding several millionyears. However, the drop in the mean and in-crease in skewness both mark long-term tran-sitions between the first and second halves ofthe Neogene, and are therefore likely to be bi-ologically meaningful.

A second pattern involves high turnoververy close to the Miocene/Pliocene boundary,which may or may not be independent. Thelast two Miocene bins (6.5 and 5.5 Ma) witnessa pair of high extinction values (0.284, 0.316),and diversity crashes quite noticeably from 64species at 7 Ma to 50 at 5 Ma. Immediatelyafterwards there is a sharp recovery to 67 spe-cies, marked by the data set’s second-highestorigination value (10.476) and a high propor-tional volatility G-statistic (17.336). Althoughanother spike in diversity at the very end ofthe time series is visible, this may be attrib-utable to a ‘‘pull of the Recent’’ or some otherresidual bias.

Essentially, the data suggest that somethingfundamental sets off the large mammal-richfaunas of the late Miocene from the Plioceneand Pleistocene. The exact timing and natureof this transition remain to be documented inmore detail.

Here the marine isotope records are trulyunexceptional. Values for rate of change arequite low before 3 Ma, and both versions ofthe standard deviation values are also com-pletely typical. The only marine ‘‘event’’ is arapid increase in midpoint d18O at 13.5 Ma,well before diversity starts to decline. Afterthis event, the entire late Miocene was markedby steadily increasing d18O values.

Given available data from benthic forami-nifera, there is no reason to suppose that thiswas an interval of sudden change in the phys-

ical environment: d18O values do rise through-out the late Miocene as they did during themid-to-late Eocene, but in general more slow-ly. Unlike the latter situation, a large fractionof the late Miocene rise almost certainly re-flects an ice volume increase in addition tocooling. Interestingly, the late Miocene didwitness the global expansion of C4 plants inlow-to-middle terrestrial ecosystems. Cerlinget al. (1997) have argued that this expansionwas linked to a decline in pCO2 levels belowsome critical threshold, but several lines ofgeochemical and paleobotanical data havefailed to support their conjecture (van derBurgh et al. 1993; Palmer et al. 1998; Pagani etal. 1999). Whatever its source, however, the ex-pansion of C4 plants may have had a negativeimpact on mammal faunas. C4 plants havelower protein levels, are less digestible, andare richer in phytoliths than C3 plants (seediscussions in Koch 1998 and Stanley 1998).Several authors have suggested that one or allof these factors may have contributed to ex-tinctions and faunal change in the late Mio-cene (Cerling et al. 1998; Koch 1998; Stanley1998), although no rigorous tests of these hy-potheses have been conducted.

In summary, we found an association be-tween unusual climatic states and unusual bi-otic states at two times: across the Paleocene/Eocene boundary and in the mid-Oligocene.One other critical interval in the biotic record(early Uintan) occurs during a time of pro-longed and somewhat more rapid climate de-terioration, but there is no clear link to anytruly severe climate event. The two remainingcritical biotic intervals (Tiffanian/Clarkforki-an; late Miocene/Pliocene) show no clear as-sociation with unusual climate states at all.

Discussion

Our results are clear in demonstrating thatmajor changes in the mammalian biota, asmeasured by origination and extinction rates,proportional taxonomic turnover, and bodysize, are not linearly forced by the changes inglobal climate recorded in benthic isotopedata. We see evidence for an association be-tween climate and only two of the five criticaltransitions in the mammalian biota: the Paleo-cene/Eocene reorganization documented by


Gingerich (1989) and Clyde and Gingerich(1998), and the mid-Oligocene diversificationthat we illustrated above. One other importantepisode of mammalian turnover—also in theEocene—appears to occur near the beginningof a long-term, unidirectional shift in climate.These three intervals show no consistent pat-tern. One involves diversification withoutmarked immigration (mid-Oligocene), anoth-er both diversification and immigration (Pa-leocene–Eocene), and the third shifts in bodymass distributions and taxonomic composi-tion that don’t relate to long-term changes intaxonomic diversity (early Uintan).

Most importantly, these isolated events failto match up with our isotope records in anysimple way. The presumed warming events(Paleocene/Eocene; mid-Oligocene) matchwith increases in diversity, but the basic mech-anisms are fundamentally different: immigra-tion and an attendant pulse of cladogenesis inthe first case, simple cladogenesis in the sec-ond. The presumed mid-Eocene cooling eventhad a very different impact—a permanent andprofound shift in the biota’s ecomorphologicalcharacter (Uintan).

Despite the fact that both the isotope andmammal data sets are robust, we acknowl-edge that future research might show moresubtle connections between climate and evo-lution than we have been able to prove. Themajor reason for concern is that our data donot directly address the key climate variablesthat structure terrestrial ecosystems. To beginwith, there is a reasonable concern that marineisotope data may do a poor job of recordingmean annual temperature trends in continen-tal interiors, or even in ocean basins (Lear etal. 2000). The decoupling of the marine iso-tope record from continental climate changewas likely to have been more severe in theNeogene because of the growing impact ofcontinental ice sheets on the isotope records.Thus, events like the mid-Oligocene diversi-fication could in theory be tied to continentalclimatic changes that are not reflected, or areonly very weakly reflected, in the marine data.

We believe, however, that the use of marinedata as a proxy is fairly well justified, espe-cially in the Paleogene—which contains mostof the critical biotic intervals. Several studies

have shown that similar isotope signals areseen in both continental and marine recordsfor narrowly defined intervals of Cenozoictime (e.g., around the Paleocene/Eoceneboundary [Fricke et al. 1998; Bao et al. 1999]).Furthermore, the existing terrestrial climateproxy data (Wolfe 1994; Wing et al. 1995; Baoet al. 1999; Wilf 2000) seem to show a reason-able match to the marine records, with key cli-mate shifts like the late Eocene deteriorationturning up in both arenas.

Another concern is our lack of a marine re-cord that in any way serves as a quantitativeproxy for mean annual precipitation, whichmight be very important in structuring mam-malian communities. Increasingly sophisticat-ed analyses of leaf physiognomic data (Wilf etal. 1998) should eventually make it possible toget at this issue. For the moment, we will notemerely that available paleobotanical dataseem to point to a crude correlation betweenmean annual temperature and mean annualprecipitation: early Cenozoic climates werewarm and wet, late Cenozoic climates colderand drier. Seasonality of temperature and pre-cipitation also may be captured in part bymean temperature records. Therefore, we sus-pect that a good precipitation record wouldnot change our results substantially, but westrongly encourage this kind of future re-search.

The crudeness of using isotope data as oursole climate indicator is not the only potentialshortcoming of our analysis: we would be thefirst to admit that our mammalian time seriesdo not necessarily capture every important as-pect of paleoecological change. For example,we have not been able to examine changes inalpha (local-scale) diversity, beta (among-re-gion) diversity, and ecomorphological diver-sity. Stucky (1990) suggested that a majordrop in alpha diversity took place somewhereclose to the Eocene/Oligocene boundary,which also marks a major global climate shift.Van Valkenburgh and Janis (1993) made a rea-sonable case for gradual decreases in beta di-versity through time. Although there are someconcerns that their approach might be influ-enced by spatial variation in sampling inten-sity and other effects, it is likely that a moredetailed study would yield a statistically in-


formative beta diversity time series. Janis andWilhelm (1993) showed quantitatively that lo-comotor adaptations in ungulates and carni-vores have evolved greatly during the Tertiary,with ungulates quickly adopting their moderncursorial strategy but carnivores lagging farbehind. Hunter and Jernvall (1995) and Jern-vall et al. (1996) showed that dental morphol-ogy evolved quickly in the early Paleogeneand remained largely static through the mid-dle and late Cenozoic, which might relate toincreasing dietary specialization as mamma-lian lineages abandoned generalized omni-vory in favor of herbivory or carnivory. All ofthese patterns could be influenced by climatetrends.

Additional ecological indicators could andshould be analyzed in future studies. How-ever, we have reason to believe that few sur-prises would result. Stucky (1990) did not at-tempt to illustrate variation in alpha diversitywithin the Paleocene–Eocene, or the Oligo-cene–Neogene. Preliminary data of the samekind suggest that very little such variation ex-ists, and therefore that the Eocene/Oligocenedrop in alpha diversity is another singular pa-leoecological transition of the same kind asthe mid-Eocene changeover of ordinal groupsand opening of a gap in the body size distri-bution. Therefore, a general correlation withlong-term climate change is unlikely to bedemonstrated. We are similarly skepticalabout being able to demonstrate fine-scale var-iation in beta diversity; most samplingthroughout the Tertiary is restricted to theWestern Interior of the United states, an areahardly large enough to encompass significantamounts of biogeographic turnover.

Finally, ecomorphological shifts such as in-creasing dietary and locomotor specializationare of great interest, but we suspect that ouranalysis of proportional volatility has cap-tured the key ecomorphological transitionthat is to be found in the western North Amer-ican record: the loss of the arboreal frugivore/folivore guild and greatly increased richnessof the terrestrial large herbivore guild in themiddle Eocene. This interpretation is consis-tent with the data of Janis and Wilhelm (1993),Hunter and Jernvall (1995), and Jernvall et al.(1996), all of which suggest rapid ecomor-

phological transitions during the Eocene.Thus, the mid-Eocene diversification of un-gulates was probably related to their cursoriallocomotor adaptations (Janis and Wilhelm1993), well-developed hypocones (Hunter andJernvall 1995), and selenodont and lophodontdentitions (Jernvall et al. 1996). The climaticdeterioration following the Eocene thermalmaximum probably played a part in this di-versification, but the actual dynamics mayhave been rooted in evolutionary and ecolog-ical interactions among component taxa.

Conclusion

The idea that organisms ride passively onan evolutionary vehicle driven by global cli-mate change has pervaded the paleontologicalliterature for two centuries. Nothing in paleo-biology seems to be much harder than testingsuch a hypothesis rigorously. Taxonomic rich-ness is notoriously hard to quantify, with sam-pling biases potentially obscuring any realtrends. Turnover rates turn out to be concep-tually slippery, with most commonly usedmetrics having serious methodological short-comings (Foote 2000). Ecomorphologicaltrends cannot be studied objectively withoutobtaining exhaustive, hard-won morphomet-ric data sets. Temporal correlations in the ter-restrial realm are difficult and traditionaltimescales are so coarse as to be almost use-less. Finally, despite decades of work collect-ing isotopic data we are only now beginningto understand the intimate details of climatetrends throughout the entire Cenozoic.

In light of these problems, it is not reallysurprising that our efforts have yielded nostrong evidence in support of the traditionalclimate-evolution scenario. Still, though, wefeel that we have done everything imaginableto make our analysis rigorous and quantita-tive, and to remove every important statisticaland conceptual bias from our representationof the data. Even the fact that we have workedmostly at one spatial scale is simply a neces-sary consequence of (1) the dense geographicconcentration of the data and (2) the difficultyof computing precise statistics, such as mo-ments of body mass distributions, using localassemblage data (Alroy 2000).

More importantly, this and other studies


(Alroy 1996, 1998b,d) have shown that muchof mammalian evolution can be explained byintrinsic dynamics: species richness tracks anequilibrium throughout most of the Cenozoic;extinction events are rare; major orders main-tain roughly proportionate diversity levels fortens of millions of years; and body mass dis-tributions slowly move to equilibrium points.All of these features suggest the importance ofbiological factors like competition, escapefrom predation, and perhaps biomechanicaland physiological optimality over and abovethe more unpredictable influences of climate.We therefore would be very surprised to seeour results completely overturned by a newanalysis comparing terrestrial vertebrate datawith quantitative climate indicators, even ifthe climate data were derived solely from con-tinental records. Thus, the key question raisedby our analyses is not whether data qualityproblems may have caused us to overlooksome hidden climatic effect, but rather whypaleobiologists have traditionally been sowilling to embrace climate-driven evolution-ary scenarios.

Acknowledgments

We thank M. Foote, D. Fox, and J. Hunter forcomments on the manuscript, and M. Paganifor assistance in compiling and interpretingthe benthic marine isotope records. This workwas conducted while J. A. was a postdoctoralassociate at the National Center for EcologicalAnalysis and Synthesis, a center funded bythe National Science Foundation (grant DEB-94-21535); the University of California, SantaBarbara; the California Resources Agency;and the California Environmental ProtectionAgency.

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