The million-year wait for macroevolutionary burstsJosef C. Uyedaa,1, Thomas F. Hansenb, Stevan J. Arnolda, and Jason Pienaarc

aDepartment of Zoology, Oregon State University, Corvallis, OR 97331; bDepartment of Biology, Centre for Ecological and Evolutionary Synthesis, Universityof Oslo, 0316 Oslo, Norway; and cDepartment of Genetics, University of Pretoria, Pretoria, South Africa 0002

Edited by Mark A. McPeek, Dartmouth College, Hanover, NH, and accepted by the Editorial Board July 22, 2011 (received for review October 11, 2010)

We lack a comprehensive understanding of evolutionary patternand process because short-term and long-term data have rarelybeen combined into a single analytical framework. Here we testalternative models of phenotypic evolution using a dataset ofunprecedented size and temporal span (over 8,000 data points).The data are body-size measurements taken from historicalstudies, the fossil record, and among-species comparative datarepresenting mammals, squamates, and birds. By analyzing thislarge dataset, we identify stochastic models that can explainevolutionary patterns on both short and long timescales andreveal a remarkably consistent pattern in the timing of divergenceacross taxonomic groups. Even though rapid, short-term evolutionoften occurs in intervals shorter than 1 Myr, the changes areconstrained and do not accumulate over time. Over longerintervals (1–360 Myr), this pattern of bounded evolution yieldsto a pattern of increasing divergence with time. The best-fittingmodel to explain this pattern is a model that combines rare but-substantial bursts of phenotypic change with bounded fluctua-tions on shorter timescales. We suggest that these rare burstsreflect permanent changes in adaptive zones, whereas the short-term fluctuations represent local variations in niche optima due torestricted environmental variation within a stable adaptive zone.

microevolution | stasis | macroevolution | evolutionary rate |phylogenetic signal

Evolutionary biologists working at different timescales oftenadopt dramatically different perspectives on the pace and

process of phenotypic evolution. For example, the norm formicroevolutionary studies is to observe high levels of heritablegenetic variation (1, 2), strong selective pressures (3, 4), and thefrequent occurrence of substantial phenotypic change on atimescale of a few to a few dozen generations (5–8). However,paleontologists working on much longer timescales have recog-nized an overwhelming prevalence of evolutionary stasis (9–11),although other patterns are known (12–14). On even longertimescales, comparative studies of extant species routinely recordsubstantial divergence (15, 16). These different perspectives havegenerated controversy about the ability of microevolutionaryprocess to explain macroevolutionary patterns (4, 9–10, 17–21).To resolve this debate we need models that can simultaneouslyaccount for evolutionary change across a range of timescales.Here, we make a step toward that goal by assembling and ana-lyzing a dataset of body-size evolution across an unprecedentedtemporal span.Gingerich (7) compiled a large dataset representing a collec-

tion of evolutionary rates measured over 100–107 generations inthe fossil record. Analyzing this dataset, Estes and Arnold (21)found a striking pattern of bounded fluctuations in phenotype,which implies that the expected magnitude of phenotypic changeis about the same regardless of whether two samples are sepa-rated by 10 generations or 1 million generations (see also ref.22). In other words, short-term, fluctuating evolution occurs, butthe changes fail to accumulate with time. This pattern predictsthat closely related species should be as different as less relatedspecies, a conclusion seriously at odds with comparative studies,which often detect strong phylogenetic signal for traits related toorganism size (23–26). This incongruence suggests that we need

a more extensive compilation of data to get a full picture of howevolutionary patterns scale up over time.Many studies have examined large-scale patterns of body-size

evolution using either fossil (7, 21, 27, 28) or comparative data(15, 16, 29). Such studies have yielded many important insights,but no studies have yet combined paleontological and compar-ative data in the same modeling framework, and the puzzlinginconsistencies that seem to exist between these types of studiesremain. Resolving these inconsistencies is made more challeng-ing by the different timescales, traits, and taxa analyzed in dif-ferent studies. To achieve a much needed synthesis, we combinemicroevolutionary and fossil time series data with phylogeny-based comparative data and analyze these data with a set ofevolutionary models that extends the analysis of Estes andArnold (21). We base our analysis on a dataset that spans thebroadest range of timescales yet examined (0.2 y to 357 Myr) bycombining historical and contemporary field studies, fossil timeseries, and comparative data.

Results and DiscussionConsistent with previous studies (21, 22) we find a completeabsence of a time-span effect up tow1 Myr, but this pattern thenyields to a pattern of increasing divergence on timescales above1–10 Myr (Fig. 1). Whereas the dominant pattern of bounded,but fluctuating changes on shorter timescales is consistent witha common paleobiological concept of stasis (9, 14), the long-termevolutionary pattern is consistent with observations of phyloge-netic correlation and cumulative evolutionary change. The unionof these seemingly contradictory patterns generates a remarkablycontinuous visual pattern reminiscent of the flared barrel ofa blunderbuss firearm. We show that this “blunderbuss pattern”is consistent regardless of the method of trait standardizationand whether timescale is expressed in generations or years (SIText and Figs. S1 and S2). Because biases introduced by in-cluding different taxa and traits at different timescales may cloudour interpretation of the pattern, we examined subsets of data ondivergence in the body size of mammals, squamates, and birds, aswell as molar dimensions in primates (Fig. 2). The general pat-tern and timing are strikingly consistent across traits and taxa.Although the continuity of pattern is clear, it is less obvious whatevolutionary processes can account for divergence across alltimescales.To describe these patterns more precisely, we fitted four sto-

chastic models to the data. The first model describes boundedevolution (BE) and was designed to fit the pattern of short-termfluctuations observed in the data. This model assumes that the

Author contributions: J.C.U., T.F.H., and S.J.A. designed research; J.C.U. and J.P. per-formed research; J.C.U. and J.P. analyzed data; and J.C.U., T.F.H., and S.J.A. wrote thepaper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission. M.A.M. is a guest editor invited by the EditorialBoard.

Data deposition: The data reported in this paper have been deposited in the Dryad re-pository http://datadryad.org/ (doi:10.5061/dryad.7d580).1To whom correspondence should be addressed. E-mail: uyedaj@science.oregonstate.edu.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1014503108/-/DCSupplemental.

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amount of trait divergence over any time interval is an independentdraw from a normal distribution with mean zero and variance, σ2P.Because this model does not allow for increasing divergence onlonger timescales, we combined it with three other time-dependentstochastic models that capture this aspect of divergent evolution.The first of these unbounded model components is the well-knownBrownian-motion (BM) model, which is often used to describephylogenetic correlations. In this model the variance in trait meansamong replicate lineages increases linearly with time. In the single-burst (SB) model, we assume that the optimum can undergoa single large normally distributed change after a random (expo-nentially distributed) time interval. A special case of this model, inwhich the change was immediate, had the best fit to the data inEstes and Arnold (21). Finally, in the multiple-burst (MB) model,we allow multiple normally distributed changes in the optimum tooccur over time according to a Poisson process.The multiple-burst model was the best-fitting model, although

all unbounded models capture the expansion of variance thatoccurs after 1 Myr of stationary fluctuations (Figs. 1 and 3 andTable 1). The multiple-burst model was preferred over theBrownian-motion model primarily because it better explainedthe overdispersion of divergence values found in the data at in-termediate time intervals (106–108 y) in both the fossil data andthe phylogenetic data. The three models including unboundedcomponents (BM, SB, and MB) all estimate σ̂pz0:10; whichmeans that 1 SD in the central band of data corresponds to anw10% difference in linear size traits. Some of this changereflects measurement error, but much of it probably reflectsevolutionary change (SI Text). The time-dependent componentof the models leads to noticeable departures from the centralband only after w1 Myr of evolution (Table 1 and Fig. 3). Forexample, the expected waiting time to a displacement of the

optimum in the multiple-burst model is >10 Myr (107.3976). Thisresult implies that the distribution of divergence changes verylittle over the first million years, with only a modest 10% increasein the width of the 95% prediction interval for the central bandoccurring over this interval. By contrast, the prediction intervaldoubles after 5 Myr. For each displacement of the optimum, theestimated burst-size distribution predicts a size ratio betweenancestor and descendant population means of 1.28.The patterns we observe are not simple consequences of

sampling bias introduced by using different data sources.Whereas fossil data could be biased by the hesitancy of pale-ontologists to assign ancestor–descendant relationships to highlydivergent samples, we observe the opposite pattern in the data-set. When we fitted models to microevolutionary and fossil dataalone and compare these with models fitted to phylogenetic data,we find that the fossil series begin to diverge more rapidly thanthe phylogenetic data, with otherwise remarkably similar pa-rameter estimates (Table 1, Table S1, and Fig. 3). This pattern isnot expected if fossil series are biased against evolutionarychange, but may be explained, for example, by increasing prob-ability of extinction in more rapidly evolving lineages. Alterna-tively, this pattern could be a consequence of the knowntendency of molecular phylogenies to estimate older divergencetimes than the fossil record (30, 31).The transition from bounded evolution to steadily increasing

divergence is illuminated by using linear regressions to modelthe relationship between absolute divergence and time. Wecompared a segmented regression with a single breakpoint to amodel with separate regressions for each of the three subsets ofdata (Fig. 4 and SI Text). A segmented regression with a break-point at 66,000 y has a lower Akaike’s information criterion(AIC) than a model in which independent regressions are fittedto each of the three major subsets of the data. This successindicates that the change in slope is not an artifact arising fromdifferences in data sources, but instead indicates a pattern

Fig. 1. The “blunderbuss pattern”, showing the relationship betweenevolutionary divergence and elapsed time. Divergence is measured as thedifference between the means of log-transformed size in two populations(ln za and ln zb) standardized by the dimensionality, k. Intervals represent thetotal elapsed evolutionary time between samples. Microevolutionary datainclude longitudinal (allochronic) and cross-sectional (synchronic) fieldstudies from extant populations. Paleontological divergence is measuredfrom time series, including both stratigraphically adjacent (autonomous)populations and averaged longer-term trends (nonautonomous). We sup-plement these data with node-averaged divergence between species withintervals obtained from time-calibrated phylogenies. Pairwise comparisonsbetween species (small points) are also presented to give a visual sense of therange of divergence values across taxonomic groups. Dotted lines indicatethe expected 95% confidence interval for the multiple-burst model fitted tothe microevolutionary, fossil, and node-averaged phylogenetic data.

Fig. 2. Divergence patterns are similar across major groups of vertebrates.Taxonomic levels are denoted by color. For comparative data, smaller pointsindicate pairwise divergence measures and larger points are node-averageddivergence. Data for primates are first molar lengths and widths only.

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common to both phylogenetic and paleontological data (Fig. 4,Fig. S3, and SI Text).One potential explanation for a central, bounded band of di-

vergence that lasts 1 Myr is that the tendency to study rapidevolution on microevolutionary timescales might mask a patternof ever-increasing divergence in the data. In particular, evolu-tionary responses to disturbances such as introductions, anthro-pogenic disturbance, or island isolation may be especially rapidand bias microevolutionary data toward higher divergence val-ues. To test for such bias, we examined the evolution of body sizeaccording to whether a particular study represented disturbance-mediated evolution or in situ divergence (defined in ref. 8).Disturbance-mediated evolution is clearly more prevalent in fieldand historical studies (Fig. 5) and also appears elevated in twofossil time series that are arguably influenced by novel selectivefactors: the transition of Bison antiquus to Bison bison, which ishypothesized to have been driven by community change andanthropogenic selection (31), and the evolution of a dwarf formof Cervus elaphus on the Isle of Jersey (32). Clearly, we can oftenidentify the many causal processes that generate divergence inbody size, and these are likely to be overrepresented in our mi-croevolutionary dataset. Although these types of causal phe-

nomena may be overrepresented in intervals spanning 1–100 y,these same phenomena are likely to occur naturally over time-scales of 1,000–100,000 y, and yet we see little accumulation ofdivergence across these timescales.We have taken a phenomenological approach to modeling the

stable, central band of data apparent in Fig. 1 and have notattempted to account for that band with alternative models.Nevertheless, because that band is similar to a stable band an-alyzed by Estes and Arnold (21), we can conclude that none ofthe several alternative models considered by Estes and Arnold(21) can fully account for the band in Fig. 1. Those models in-clude Brownian motion of the trait mean, Brownian and white-noise motion of an intermediate optimum (including a stationaryoptimum as a special case), steady directional movement of anintermediate optimum, and shifts of the trait mean between al-ternative adaptive peaks. All of these models fail either becausethey require unrealistic values for microevolutionary processesor because bounded evolution is difficult to achieve under anyset of parameter values. We conclude that some unspecifiedprocess of bounded evolution is responsible for the band weobserve in our data (Fig. 1). This process may include short-termmovements of adaptive peaks corresponding to more or less

A B C

Fig. 3. Best-fitting time-dependent stochastic models determined by fitting by maximum likelihood. Each model was fitted to the complete dataset, as wellas to a subset including only microevolutionary and fossil data and a subset including only node-averaged phylogenetic data. Lines show the 95% confidenceintervals for the model fits using the estimated parameters presented in Table 1. (A) Multiple-burst (MB) model. (B) Single-burst (SB) model. (C) Brownian-motion (BM) model. Also included is the expected 95% confidence interval for a Brownian-motion model of body mass evolution fitted to the mammalianphylogenetic data, accounting for simulated measurement error (SI Text). Although the confidence intervals for both the MB and the BM model appear verysimilar, the MB is a better fit to the overdispersed distribution of divergence values that occurs at intervals >1 Myr (SI Text).

Table 1. Parameter estimates and AIC scores for four model fits to the complete dataset andsubsets

All datasets: microevolutionary, fossil, and phylogenetic

Model Parameter estimates Inverse of rate parameters AIC

Bounded evolution σ̂p ¼ 0:2026 −2940.53Brownian motion σ̂p ¼ 0:1072 σ̂bm ¼ 5:82× 10− 5 −7877.97Single-burst σ̂p ¼ 0:0965 σ̂D ¼ 0:418 1=λ̂ ¼ 107:4438 −9018.03Multiple-burst σ̂p ¼ 0:0958 σ̂D ¼ 0:272 1=λ̂ ¼ 107:3976 −9142.54

Multiple-burst model fit to subsets of the data

Dataset Parameter estimates

Microevolutionary and fossil σ̂p ¼ 0:0874 σ̂D ¼ 0:249 1=λ̂ ¼ 106:1642

Phylogenetic σ̂p ¼ 0:0857 σ̂D ¼ 0:217 1=λ̂ ¼ 107:3375

In all models, SDs are in units of the natural log size difference. The inverse of the rate parameters (1/λ) for theexponential distribution and Poisson distribution in the single-burst and multiple-burst models, respectively, canbe interpreted as the average number of years until a displacement. The lowest AIC score was for the multiple-burst model.

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regular, recurring fluctuations in the local environment (cf. Fig. 5and ref. 33) as well as bounded displacements of adaptive peakswithin adaptive zones. The process resembles Simpson’s de-piction of the bounded evolution of lineages as they radiatewithin an adaptive zone (34, 35). Under this interpretation, theslower time-dependent component of divergence commonly es-timated from phylogenetic comparative data (14, 15) could thenbe due to the accumulation of rare, dramatic changes in theniche (or “primary”) optimum (18, 34, 36, 37). However, thisinterpretation does not address the issue of what controls themacroevolutionary dynamics of niches and results in departuresfrom bounded evolution over longer timescales (19, 21, 37, 38).It is tempting to turn to climate for an explanation of evolu-

tionary bursts and suppose that the 1-Myr boundary on boundedevolution reflects limits on long-term rates of climatic and en-vironmental change. However, substantial changes in global cli-mate over timescales of <<1 Myr appear to result in boundeddivergence characteristic of microevolutionary timescales, ratherthan dramatically hastening phenotypic evolution (39). Althoughhabitat tracking by migration may mitigate the effects of suchclimate shifts, the data nonetheless do not strongly supporta primary role for climate in driving phenotypic change.What then, allows divergence to accumulate above 1 Myr, but

not below? A particularly elegant explanation is provided byFutuyma’s ephemeral-divergence model. Futuyma argues thatalthough continuous, rapid evolution often occurs in local pop-ulations, the mosaic of niches and diverse adaptive optima ofwide-ranging species prevents local evolutionary changes fromspreading across the entire range (9, 40–44). Consequently, thevariance of the stationary fluctuations, σ2P, that we estimate in our

models could be interpreted as measuring the among-populationgeographic variation that results from ephemeral divergence inphenotypes responding to local selective pressures. Selectivepressures that cause displacement of the optimum at the specieslevel could reflect the same kind of disturbances that we observeoccurring at the population level, but spread across a species’entire range. Such significant, range-wide changes in selectiveoptima may be sufficiently rare to explain the observed pattern ofbounded evolution on timescales <1 Myr. Note that range-widechanges in adaptive optima can be accomplished by two means:either by the global spread of a selective factor across a species’range or by the contraction of the species’ range itself (9, 41).Consequently, any process that reduces the range of a species,including speciation and taxon cycles, can potentially result ina displacement in phenotype by subsampling from the set ofpreviously occupied adaptive niches (e.g., sampling from thedistribution estimated by σ2P). Species life spans are typicallyidentified as spanning 1–5 Myr (28, 45–47) and taxon cycles havebeen described as spanning from 10,000 y to 10 Myr (48, 49),providing a suggestive correspondence to the rate of accumula-tion in phenotypic evolution that we observe in the data.Our results are qualitatively consistent with recent analyses of

body-size evolution that have fitted phenomenological modelsto data on a more limited timescale and with more taxonomicconstraint than the data that we examine here. Gillman (27)identified the striking regularity with which body-size rangeincreases with time on macroevolutionary timescales, but did notobserve this phenomenon’s relationship to bounded microevo-lutionary divergence due to limited sampling on short timescales.Other studies used various large comparative datasets to com-pare the fit of Brownian motion, an Ornstein–Uhlenbeck pro-cess, and an early-burst model in which a Brownian motion rate

A

B

Fig. 4. Linear regressions of interval on the logarithm of absolute di-vergence, ln(jdivergencej + 0.001). A positive linear relationship is predictedfrom Brownian-motion models of evolution. (A) AIC scores for the fit of themicroevolutionary, fossil, and node-averaged phylogenetic data to linearregressions. The fit of a single linear regression to the entire dataset is themost poorly fitting model (green dashed line, AIC = 79,520). We then per-formed a segmented regression to find the optimal breakpoint by fitting themodel iteratively while increasing the breakpoint from 0 to 8.5 log10 y witha step size of 0.01 (solid black line). The AIC for this model reaches a mini-mum with a breakpoint of 104.82 years (AIC = 79,059). Subsetting by datasetsand fitting a regression independently to each did not improve the fit rel-ative to the segmented regression (red dashed line, AIC = 79,062). (B) Best-fitsegmented regression model provides a better fit to the data (solid line) thana model where independent linear regressions are fitted to each dataset(dashed lines). Datasets and the corresponding regression lines are indicatedby color (microevolutionary, yellow; fossil, green; and phylogenetic, blue).

Fig. 5. Divergence identifiable as natural in situ variation vs. disturbance-mediated community change demonstrates that the majority of cases ofrapid evolution over microevolutionary timescales are from identifiablecauses such as introductions, anthropogenic disturbances, and island iso-lation. Highlighted examples include (clockwise, starting from left) in situevolution of Geospiza fortis in response to natural climate variation, di-vergence in Nucella lapillus in response to an introduced predator, in-troduction of Gambusia affinis to Nevada and Hawaii, island–mainlanddivergence in Crotalus mitchelli, Holocene dwarfing of Bison antiquus to B.bison, dwarfing of Cervus elaphus on Jersey Island, and the introduction ofPasser domesticus to North America and New Zealand. Most fossil time seriescannot be assigned to either group, but are expected to record primarily insitu evolution of wide-ranging species. Dotted lines indicate the 95% con-fidence interval for simulated measurement error given equal means, av-erage within-population variance, and a distribution of sample sizesmatching those found in the data (SI Text).

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parameter declined exponentially with time (15, 16). The early-burst model fitted best on large groups such as mammals or birdstaken as a whole (16). This success indicates that the rate ofevolution may be faster early in a radiation, but within subcladesthe early-burst model was usually outcompeted by the othermodels. Although Ornstein–Uhlenbeck models often are thebest-fitting models in these studies in some clades and subclades,the restraining force is generally very weak (15, 16). Conse-quently, the qualitative picture of linearly increasing variancewe observe over most macroevolutionary timescales is consistentwith these results (15, 16, 27). Our analysis and treatment of thedata do not allow us to make inferences about the possible roleof speciation and extinction events. Those processes may or maynot be important components in generating the patterns weobserve. In other words, our models and conclusions allow forthe possible existence of a correlation between evolutionarychange and speciation and extinction events (29).We believe the path forward will involve explicit microevolu-

tionary interpretations of the phenomenological stochastic modelsused in this and similar studies (15, 16, 29). In addition, combiningdata across micro- and macroevolutionary timescales should facil-itate interpretation of model results in terms of adaptive landscapesand ecological processes. Finally, understanding how landscapedynamics scale across species ranges is a neglected step that needsto be taken. We may need more sophisticated models that bridgebetween population- and range-wide evolution to understand thestriking patterns of divergence that we have documented.

Materials and MethodsMeasurement of Divergence and Interval. We log-transformed all trait meas-urements so that divergence between any two samples is a unitless measureof the proportional change in a phenotypic trait in factors of e. Divergencebetween the means of two samples a and b is then measured as

d ¼ ðln zb − ln zaÞ=k;

where za and zb are untransformed observations in each sample. Althoughthe difference in mean log-scaled trait values is unitless, it is not di-mensionless. Consequently, we divided by k, where k is the dimensionality ofthe data (e.g., k = 3 for mass, k = 2 for area, and k = 1 for linear measure-ments). We calculated divergence from time series data, tree-based com-parative data, and longitudinal and cross-sectional microevolutionarystudies and calculated the total time for evolution as the total duration ofindependent evolutionary change separating population samples (SI Text).To minimize potential biases in trait representation across different data-sets, we examine only a single trait class: morphometric traits correlatedwith body size on the log-linear scale. Therefore, the entire datasetapproximates the evolution of a single trait: body size. Alternative stand-ardizations are analyzed in SI Text (Fig. S1).

For each measure of divergence, we calculated a corresponding time in-terval. A generation timescale for these intervals is natural in the sense thatmany evolutionary models predict evolutionary change in generations. Onthe other hand, long-term trends in divergence may reflect responses tonatural events that occur on timescales that cut across differences in gen-eration time (e.g., tectonic processes, climate change). Consequently, di-vergence is of interest on both timescales. Preliminary analysis indicated thatdivergence patterns are more coincident on the absolute timescale and thatestimation of generation times apparently adds some systematic bias to theoverall pattern (Fig. S2). Consequently, we primarily present figures usingthe absolute timescale and provide generation scaling in SI Text.

Database. We compiled datasets that measure evolutionary divergence insize-related traits from three types of data: (i) contemporary field and his-torical studies, (ii) fossil time series, and (iii) phylogenetic comparative data.For the first two categories, we have drawn from the original databases ofGingerich (7) and Hendry et al. (8), which also include the entirety of thesize-related data used in Estes and Arnold (21). We also added 29 additionalmicroevolutionary and paleontological studies to the dataset (SI Text andTable S2). We have supplemented these with comparative data by usingdatabases of bird, mammal, and squamate body sizes and obtained timeintervals from time-calibrated phylogenies by summing the branch lengthsseparating species (SI Text and Table S3). The final database includes 6,053

morphometric divergence measurements from 169 microevolutionary andpaleontological studies and 2,627 node-averaged divergence estimatesobtained from 37 time-calibrated phylogenies. The total time span of thecomplete dataset ranges from 0.2 y to 357 Myr.

Because the datasets combine many types of data across many differenttaxa, we risk comparing traits and taxa for which the evolutionary process isnot comparable. Consequently, we examined patterns in the dataset forspecific taxonomic groups (mammals, birds, squamates, and primates). Forsquamates, we used data on body-size divergence between mainland andland-bridge island populations, using the age of last connection betweenpopulations to estimate the time interval. For primates, we examined a singletrait, first-molar size. By measuring a homologous trait in a single clade acrossthe range of timescales included in the full dataset, we reduce the compli-cations resulting from standardization. The first-molar size is ideal for thispurpose as it is among the most abundant fossilized remains in primates andhas one of the lowest sampling variances among dental traits (50).

To visualize the effect of time on evolutionary divergence in each dataset,we plotted divergence against time interval. We scaled the interval on thelog10 scale to obtain resolution from microevolutionary to macroevolu-tionary timescales.

Stochastic Model Fitting.We fitted four stochastic evolutionary models to thecombinedmicroevolutionary, fossil, and node-averaged phylogenetic data bymaximum likelihood. These models are (i) BE, (ii) BM, (iii) SB, and (iv) MB(Fig. S4). In the bounded-evolution model, divergence is modeled as in-dependent draws from a stationary normal distribution, N(0, σ2P ), so thatthere is no time-span effect on the size of evolutionary changes. All three ofthe remaining models include this time-independent component of di-vergence, as well as a process that causes cumulative evolutionary change,resulting in increasing variance in divergence among lineages with time. Inthe Brownian-motion model, the distribution of replicate trait means isa normally distributed random deviate, N(0, σ2bmt), where t is the length ofthe interval. In the single-burst model, evolution is episodic. The optimum isdisplaced from its original position just once with a displacement magnitudethat is a normally distributed deviate, N(0, σ2D). The timing of the displace-ment is not constrained as in ref. 21, but instead is modeled with an expo-nential distribution with rate parameter λ. In the multiple-burst model, weallowed multiple displacements to occur according to a Poisson process withrate parameter λt (as in ref. 17). As in the single-burst model, we modeledthe magnitude of individual displacements as a normally distributed randomdeviate, N(0, σ2D). The distribution of phenotypes for a given number ofdisplacements, m, is then N(0, σ2P + mσ2D). Note that all models includea randomly distributed normal deviate that is time independent, σ2P . For thebest-fitting model, we bootstrapped over studies (2,000 replicates) to eval-uate the sensitivity of the parameter estimates to overrepresented studies(SI Text and Fig. S5). More detail on models is provided in SI Text.

For each model, we derived a likelihood equation and estimatedparameters using the functions nlm and nlminb in R (SI Text) (51). In dataanalysis, we assumed independence of the data, common parameters, andno autocorrelation. Developing models to deal with the complex covariancestructure of this diverse dataset is beyond the scope of this paper. However,although these assumptions are clearly violated in our dataset, the excep-tional size of the database should allow us to determine what types ofmodels can explain the pattern and the associated parameter values, even ifthe exact differences in AIC between models are inaccurate (SI Text). Wecompared parameter estimates and AIC scores across models fitted to thefull dataset with models fitted to subsets of data including (i) microevolu-tionary and fossil data only and (ii) phylogenetic data only to determine towhat extent the different datasets differ in pattern. To compare our resultsto phylogeny-based model fitting, we fitted Brownian-motion models to thelargest comparative dataset in our database (mammals) using the fitCon-tinuous function in the Geiger package (52).

To determine how much of the estimated time-independent variancecould be due to sampling error, we simulated comparisons between pop-ulations with equal means, a within-population SD of 0.055, and sample sizesdrawn from a geometric distribution to match the sampling distribution oftypical studies found in the database (SI Text).

Linear Regressions. We calculated linear regressions of divergence on time.We log-transformed the absolute value of divergence, d, and regressed thisvalue against the log10 time interval using the combined dataset of micro-evolutionary, fossil, and node-averaged phylogenetic data. Each of the fol-lowing regressions was fitted to these data: (i) a single linear regression tothe entire dataset, (ii) separate linear regressions for each dataset (micro-evolutionary, fossil, and phylogenetic), and (iii) a segmented regression with

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a single breakpoint. We compared the fits of these regressions using AIC todetermine the best fitting model and whether different patterns exist be-tween datasets (SI Text).

ACKNOWLEDGMENTS. We thank Phil Gingerich for access to and help withhis evolutionary-rate database and two anonymous reviewers for comments.We thank Lee Hsiang Liow, Trond Reitan, and Tore Schweder for helpful

discussions. J.C.U. thanks the Centre for Ecological and EvolutionarySynthesis at the University of Oslo for hosting his visit. We also thank SonyaClegg for providing unpublished data. We thank Hal and Dee Ann Story forpermission to use Mr. Story’s artwork and Jesse Meik, A. Michelle Lawing,and Andre Pires-da Silva for use of their photograph. This research wassupported by a joint research grant from the National Science Foundation(DGE-0802268) and the Research Council of Norway (194945/V11) (to J.C.U.).

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6 of 6 | www.pnas.org/cgi/doi/10.1073/pnas.1014503108 Uyeda et al.

Supporting InformationUyeda et al. 10.1073/pnas.1014503108SI TextMeasures of Divergence and Time Intervals. We compiled datasetsthat measure evolutionary divergence in phenotypic traits fromthe following types of data: (i) contemporary field and historicalstudies, (ii) microgeographic divergence data where it can beinferred that there has been little to no gene flow betweenpopulations, (iii) fossil time series, and (iv) pairwise divergencebetween species on a phylogenetic tree. In each case, we stan-dardized measures of divergence to compare data across traits,taxa, and time. We log-transformed all trait measurements sothat divergence between any two samples is a unitless measure ofthe proportional change in a phenotypic trait in factors of e.Divergence between the means of two samples a and b is thenmeasured simply as

d ¼ ðln zb − ln zaÞ=k;where ln zi is the mean of sample i. We corrected for di-mensionality by dividing the difference in mean of the log-scaledtrait values by k, where k is the dimensionality of the data (e.g.,k = 3 for mass, k = 2 for area, and k = 1 for linear measure-ments). Time series data are commonly in the form

½ðln z1; t1Þ; ðln z2; t2Þ;.; ðln zn− 1; tn− 1Þ; ðln zn; tnÞ�;where the subscripts denote samples from earliest (i = 1) tothe last (i = n), and ti is the time elapsed between the ith and(i + 1)th sample. We measured autonomous divergence (1) as thedifference between successive means in the series,

d ¼ ðln ziþ1 − ln ziÞ=k:The corresponding time interval is of length ti. Some informationis lost if only autonomous divergence is plotted, as longer trendsin time series will not be represented. Consequently, we alsocalculated nonautonomous divergence (1) as the difference be-tween sample means farther apart in the series, so that

d ¼ �ln ziþj − ln zi

��k

is associated with a time interval of length

Xiþj

l¼i

tl;

where 1 < j < n. Nonautonomous divergence measures from thesame series are not independent because they may be nestedwithin one another or overlap, but they have the virtue of re-vealing trends in the mean over longer time intervals. Althoughthis nonindependence can affect the significance of our modelfits, it is unlikely to introduce a systematic bias in our parameterestimates or the visual appearance of the pattern given the largenumber of studies used. Consequently, whenever raw measure-ments were available, we included all pairwise comparisons be-tween samples for a given time series, resulting in n(n − 1)/2measures of nonautonomous divergence for a time series with nsamples. We then averaged divergence values by binning thetime series into n – 1 equally spaced intervals spanning the entirelength of the series and averaging divergence values within eachbin. Consequently, a maximum of n – 1 averaged nonauton-omous data points were plotted for each time series and usedin subsequent model fitting.

For the tree-based data, divergence was measured as

d ¼ ðln zb − ln zaÞ=k;where ln za and ln zb are the log-transformed means for speciesa and b. Associated with d is the time interval, tab, calculated asthe sum of the branch lengths from the most recent commonancestor to species a and b. We calculated d for all pairwisecomparisons of species on the tree to give a visual sense of therange of divergence values. Because of the nonindependence ofpairwise measures, we also averaged d and tab over comparisonsspanning each node on the tree to reduce the influence of outlierspecies. In the case of contemporary longitudinal data (allo-chronic), we calculated d, where a and b represent two samplesfrom a lineage separated by some known interval of time, tab. Forcontemporary cross-sectional data (synchronic), we measuredd for two population samples and measured tab as twice the timesince the most recent common ancestor of both populationsa and b. We include only data in which we can infer limited to nogene flow between populations.In many cases only trait means on an arithmetic scale were

available. In those cases we approximated the mean of meas-urements on the log scale by taking the natural logarithm of themean on the arithmetic scale. This approximation is good forsymmetric distributions such as the normal distribution when thecoefficient of variation is small, as is expected for most body sizetraits on the log scale. Furthermore, even if the distribution of log-scaled measurements is nonsymmetric and/or the SD is large, thedistribution of divergence values will still closely approximate thetrue divergence value as long as the distributions of the traits inthe two populations are similar.An alternative measure of divergence is calculated as h = d/σab

(corresponding to the haldane numerator), where σab is thepooled within-population standard deviation (SD) of the log-transformed measurements from samples a and b, which can beapproximated by the coefficient of variation. Gingerich (2) arguedfor standardization by σab to remove the dimensionality of the dataeven for traits with unknown allometric scaling (e.g., shape traits,behavioral traits, and life-history traits), because σab is itself pro-portional to the dimensionality of the data whereas standardizationby k assumes a constant proportionality. However, standardizationby σab comes at the cost of standardization by an evolving andoften poorly estimated quantity, and the exact dimensionalitycorrection factor depends on the covariance structure of the lower-dimensional measurements (2, 3). Furthermore, for most mor-phometric variables proportionality changes are expected to beminimal for within-genus comparisons. Because linear divergencein size-related traits used in fossil time series and contemporarydata reflect primarily a change in body size, the entire datasetapproximates the evolution of a single trait (linear body mass), andthe drawbacks of standardization by k are minimal. For simplicity,we present only data measured by divergence in d (Figs. 1 and 2)and present divergence in h for all traits in Fig. S1.

Datasets. We used the databases of Gingerich (3) and Hendryet al. (4), which included all of the data points used in Estes andArnold (5), as well as additional studies (Table S2). We includedthe Gingerich (1) dataset, which measures standardized, auton-omous divergence, ha, in units of change per generation overtimescales spanning a single generation to 10 million gen-erations. Because we wanted to avoid biasing patterns by in-cluding traits observed over only one timescale and not the

Uyeda et al. www.pnas.org/cgi/content/short/1014503108 1 of 14

other, we restricted our analysis to only traits related to body sizeof known dimensionality. In some instances we were able toconvert some time series in this dataset to full sets of autono-mous and nonautonomous divergence by using published rawdata. However, because some of the time series in the Gingerichdataset were available only in terms of h, we had to approximateσab to convert these values to d to obtain autonomous divergencevalues (for these datasets we did not estimate nonautonomousdivergence). We estimated σab for log-scaled linear measure-ments related to body size across mammalian taxa to determinethe range of biologically realistic values. We collected meas-urements of variation from both fossil time series and contem-porary populations to determine whether there are systematicdifferences between the estimates of variation in the two types ofdata. To supplement the fossil data, we used an online paleon-tology database (www.paleodb.org) and searched for mammaliantaxa for which measures of variation were available. Estimatedwithin-population SDs did not differ between population samplesof extant species (mean SD ± 1 SD = 0.059 ± 0.03; 446 pop-ulations, 63 species) and fossil populations (mean SD ± 1 SD =0.055 ± 0.03; 592 populations, 44 species), indicating that po-tential bias introduced by the different population samplingmethods is minimal. We used these estimates to convert betweenthe two standardizations for time series and comparative data forwhich measured SDs were not obtainable using a median valueof 0.055. Although ideally measurements would be obtainedfrom the actual populations for which the trait was measured, ithas long been known that these values do not vary considerablyfor functional traits across mammalian taxa, even when evolu-tionary rates differ (6). Furthermore, the general pattern andidentity of outlier taxa are consistent whether or not datasets arestandardized by σab or k (Fig. 1 and Fig. S1).We supplemented these data with comparative, tree-based data

on body-size divergence in mammals, birds, and squamates (TableS3). Measurements on body mass were taken from databases ofbody masses for extant birds and mammals to be matched to time-calibrated phylogenies (7, 8). Where multiple measurementswere available for a single species, these were averaged to obtaina species-wide mean value. Divergence times for pairs of extantspecies were estimated as the sum the branch lengths separatingtaxa from their most recent common ancestor. For mammals, weused Bininda-Emonds et al.’s (9, 10) time-calibrated phylogeny tomeasure divergence time intervals. To obtain divergence betweenmammals in terms of generations rather than years, we obtainedaverage generation times for 923 species from the PanTHERIAdatabase and converted branch lengths by the mean of the gen-eration time for the two species being compared (11). We alsoused a comparative dataset of molar size in 52 species of extantprimates to compare with microevolutionary and paleontologicalstudies of the same traits (mesio-distal length and trigonidbreadth of the first molar) (12). When data on both male andfemale trait values are available, we assumed equal proportionsof males and females to obtain an estimate of the species mean.For birds, we obtained intervals from phylogenies from McPeek’scompilation of family- and genus-level time-calibrated phyloge-nies (13) and a supertree of the order Charadriiformes (14). Forhigher-level comparisons, we used the family-level phylogeny ofSibley and Ahlquist (15) scaled to a root age of 90 Myr. We thenaveraged body masses of all bird species within each family to useas the tip values and calculated the node-averaged divergence ateach node in the phylogeny, which is equivalent to averaging allpairwise divergences for species means in monophyletic group-ings. For squamate comparative data, we used Wiens et al.’stime-calibrated phylogeny and snout-to-vent length (SVL) meas-urements for a sample of 259 species (16).We present divergence on the generation timescale (Fig. S2) to

compare with divergence plotted on an absolute timescale (Fig. 1).Althoughqualitatively thepattern is consistent regardless ofwhether

generations or years are used, the pattern of divergence is moreconsistent across taxa whenmeasured on the raw timescale (Fig. 1),rather than generations (Fig. S2). There is a systematic bias forlonger-lived organisms to diverge faster on the generation timescalethan shorter-lived organisms (Fig. S2). However, there is no suchobvious relationship between generation time and divergence pat-terns on the raw timescale. These results suggest that divergenceover longer intervals scales with years rather than generations.

Stochastic Model Fitting. We fitted stochastic-process models tothe combined datasets of node-averaged divergence values, theautonomous and averaged nonautonomous divergence valuesfrom fossil time-series data, and synchronic and allochronic mi-croevolutionary divergence data. In addition, all models werefitted to subsets of the data including (i) microevolutionary andfossil data and (ii) phylogenetic data only. Our intent is toquantitatively elucidate features of the overall pattern by (i)evaluating the types of models that can explain the pattern and(ii) determining what parameter estimates are needed to explainthe pattern. Accounting for the complex covariance structure ofthe data is beyond the scope of this paper and consequently wetreated all data as independent. Violations of the assumption ofindependence are unlikely to systematically bias the conclusionswe drew given the large and diverse nature of the dataset, al-though they will affect the magnitude of differences in AIC valuesfor each model, and consequently these differences should beinterpreted with caution. We further assume that all taxa have thesame parameter values for each model. Although this assumptionis clearly unrealistic, this preliminary modeling exercise is pri-marily aimed at identifying key general patterns that futuremodels should account for and, as with Estes and Arnold (5), canbe thought of as a screening procedure to synthesize data acrossa broad range of timescales and sources. The four models wetested are as follows.1) Bounded-evolution (BE) model. We fitted a bounded-evolutionmodel in which evolutionary changes are modeled as the dif-ferences between independent variables drawn from a normaldistribution with zero mean and a constant variance, ðσ2pÞ, cor-responding to a Gaussian white-noise process. This model is aspecial case of the models that follow and also corresponds to aspecial case of an Ornstein–Uhlenbeck process with an infinitelystrong restraining force resulting in no serial autocorrelationbetween samples. Ornstein–Uhlenbeck processes are commonlyused in comparative methods to model evolution toward an in-termediate optimal state (17, 18). The probability distribution ofdivergence (x) contains only a single parameter, the variance ofthe stationary normal distribution ðσ2pÞ,

PðxÞ ¼ 1ffiffiffiffiffiffiffiffiffiffi2πσ2p

q e− x22σ2p :

2) Brownian-motion (BM) model combined with white noise. This modeldescribes the evolution of mean phenotypes by a random walk,but also has a time-independent component of variance, σ2p, asin the bounded evolution model. This time-independent variancecould have contributions from multiple sources, including mea-surement error, phenotypic plasticity, genetic drift around astationary optimum, or fluctuating selective pressures. The addi-tional component of a random walk is modeled as Brownianmotion with a stepwise infinitesimal variance parameter, σ2bm.The variance among replicate lineages of the Brownian motionprocess increases linearly with time according to the equation

σ2t ¼ σ2bmt;

where t is elapsed time. Under the influence of both constantwhite noise and random walk, the probability of a given level of

Uyeda et al. www.pnas.org/cgi/content/short/1014503108 2 of 14

divergence after elapsed time t is a Gaussian probability densityfunction with variance σ2bmtþ σ2p. The likelihood for this modelthen follows as the product of independent normal distributions,which yields the log-likelihood equation

lnðLÞ ¼Xn¼N

n¼1

ln

− x2ne2ðσ

2pþtσ2bmÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

2πðσ2p þ tσ2bmÞq

0BB@

1CCA:

3) Single-burst (SB) model with white noise. This model describes theprocess of evolution as a step function in which the mean ofa lineage closely tracks an optimum that is displaced once andremains stationary thereafter. Under this model, most evolutionoccurs under a regime of stasis. We included this model becausea displaced-optimum model was the best of several models ex-amined by Estes and Arnold (5). In their model, the optimum wasdisplaced in the first generation and remained stationary there-after. We relaxed the constraint that the displacement occurs inthe first generation and instead model the waiting time to dis-placement as an exponential distribution with parameter λ.Under this generalization of the model, displacements of theoptimum are time dependent. Longer intervals are more likely toexperience a displacement of the optimum, and therefore thevariance in the magnitude of divergence values increases withtime, as we now show. Let I be an indicator variable so that I =0 when no displacement has occurred, and I = 1 when a dis-placement has occurred. Thus, for a single lineage the proba-bility that a displacement has occurred in elapsed time t is givenby the cumulative probability distribution of an exponentialdistribution:

PðI ¼ 1Þ ¼ 1− e− λt:

Once the displacement occurs, the magnitude of the optimum’sdisplacement, D, is drawn from a normal distribution with mean0 and variance σ2D. Mean phenotypes are normally distributedabout the expected optimum with variance σ2p. Consequently, thedistribution of divergence values can be obtained by conditioningon I:

PðxÞ ¼ PðxjI ¼ 1Þ þ PðxjI¼ 0Þ

PðxÞ ¼�1− e− λt

�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2πðσ2p þ σ2DÞ

q e− x2

2ðσ2pþσ2DÞ þ�e− λt

�ffiffiffiffiffiffiffiffiffiffi2πσ2p

q e− x22σ2p :

The likelihood for this model is calculated as the product of themarginal densities, resulting in the log-likelihood equation

lnðLÞ ¼Xn¼N

n¼1

ln

�1− e− λt

�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2πðσ2p þ σ2DÞ

q e− x2n

2ðσ2pþtσ2DÞ þ�e− λt

�ffiffiffiffiffiffiffiffiffiffi2πσ2p

q e− x2n2σ2p

0B@

1CA:

4) Multiple-bursts model with white noise. This model relaxes theassumption of a single displacement of the single-burst model andallows displacements to occur according to a Poisson processwith rate parameter λ. According to this model, evolution con-sists predominantly of stasis interspersed with burst-like evolu-tionary events. If these burst events are sufficiently frequent overthe interval examined, this model resembles the Brownian-mo-tion model. If bursts are infrequent enough that the expectednumber of displacements is <1, then this model resembles thesingle-burst model. Under this model, the expected number of

displacements, m, increases linearly with time and is equal to λt.The magnitudes of the displacements are drawn from N(0, σ2D).As with the other models, we allowed for time-independent,bounded evolution that follows a normal distribution with vari-ance, σ2p. Consequently, the probability distribution of divergenceafter m displacements is itself a normal distribution with mean0 and variance, σ2p þmσ2D. The probability distribution functioncan be obtained for this model by conditioning on the number ofdisplacements, m, which follows a Poisson distribution:

PðxÞ ¼Xm¼N

m¼0

PðxjmÞ ¼Xm¼N

m¼0

e

�− x2

2ðσ2pþmσ2DÞ�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2πðσ2p þmσ2DÞ

q pðmÞ

¼Xm¼N

m¼0

e

�− x2

2ðσ2pþmσ2DÞ�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2πðσ2p þmσ2DÞ

q ðλtÞme− λt

m!:

The likelihood function is then

lnðLÞ ¼Xn¼N

n¼1

lnXm¼N

m¼0

ðλtnÞme�

− x2n2ðσ2pþmσ2DÞ

− λtn�

m!ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2πðσ2p þmσ2DÞ

q

0BB@

1CCA:

Each model was fitted to the data by minimizing the negativelog-likelihood function using the function nlm or nlminb inthe R statistical computing environment (19). Because thenumber of data points provided by different studies varieswidely and a single well-sampled study could substantially alterthe overall model fit and parameter values, we bootstrappedover studies with 2,000 replicates for the best-fitting model (themultiple-burst model) to obtain a distribution of parametervalues (Fig. S5).

Results and Interpretation of Model Fitting. For all datasets, thebest-fitting model was the multiple-burst model. Note that thismodel is very similar to a Brownian-motion model for most of thetime period examined. For the parameters examined, both theBrownian-motion and multiple-burst models predict nearlyidentical normal distributions of divergence measures up untilw1 Myr. Furthermore, the two processes have the same co-variance structure (20). Consequently, the signal driving theimproved support for the multiple-burst model in both the fossiland the comparative data is the overdispersed distribution ofdivergence between 1 Myr and 100 Myr. However, a Brownian-motion model could potentially produce such a distribution ifmodeled with a distribution of parameter values rather than asingle parameter value. The single-burst model performs betterthan the Brownian-motion model for the same reason. However,this fitted single-burst model bears little resemblance to the best-fitting displaced-optimum model of Estes and Arnold (5). Thedifference arises because in their model, displacement of theoptimum was constrained to occur in the first generation; there-after the optimum remains stationary. In contrast, our model fitestimates that the mean time to displacement is over 25 Myr. Inother words, the two models capture different phenomena in thedata. The displaced-optimum model of Estes and Arnold (5)explains the central band of data that we model here as a con-sequence of a white-noise process and not the pattern of di-vergence observed on longer timescales that was fitted by ourmultiple-burst model (these longer timescales were not visible inthe dataset examined by Estes and Arnold). In fact, when fittedto only the data with intervals <500,000 y, our displaced opti-mum model estimates the expected time to displacement asw200 y and is the best fitting model among the four models weexamined (Table S1). It is worth noting that Estes and Arnold

Uyeda et al. www.pnas.org/cgi/content/short/1014503108 3 of 14

(5) reject a white-noise process for their data because the level ofstochasticity in the optimum needed to obtain a reasonable fitwould likely drive a population to extinction. Consequently, weuse the white-noise process as a phenomenological model for themore complex processes that rapidly result in a static boundeddistribution of divergence over microevolutionary timescales (<1Myr). The Ornstein–Uhlenbeck process is an obvious modelingalternative that does not require high levels of stochasticity in theoptimum (17, 18).

Measurement Error. We obtained reasonable estimates of theexpected variance resulting from measurement error by using themedian value for within-population SDs for linear body size traitsand the sample sizes taken from the data. Sample sizes, however,were not available for most of the data. Consequently, we sim-ulated sample sizes from a shifted geometric distribution withparameter 0.1 (giving a mean sample sample size of 10). We thendrew sample means for two populations from a normal distri-bution with mean 0 and SD= 0.055. The 95% confidence intervalwas then obtained from the simulated distribution of measure-ment error. Our simulated distribution of sample sizes is a con-servative estimate for microevolutionary studies, but a reasonablefit to the fossil data sample sizes. Although very few samples arerepresented by a single specimen, none of the divergence valueswe used were obtained from less than four total specimens. Weobtained an estimate of measurement error of σp = 0.04, givingmeasurement variance of 0.0016. This value is nearly an order ofmagnitude less than the time-independent variance estimatedfrom the data (σ̂2pz0:01, Table 1). To obtain a variance of 0.01,assuming equal means, samples would have to consist of a singleindividual with within-population SDs of 0.07, a value higherthan what is observed for most populations (median = 0.055).Because none of the data are represented by comparisons ofsuch small samples, we reject the notion that measurement erroralone is responsible for this significant time-independent com-ponent to variation in divergence.Systematic bias resulting from differences in measurement

error among data sources is unlikely to affect the observed patternand alter our conclusions. As already noted, the variations in errorfrom fossil and contemporary samples are often quite similardespite the diversity of taxa examined and the effects of time andgeographic averaging, as has been found by previous authors(21–23). Consequently, differences in measurement error amongsources will result primarily from systematic differences insample sizes. For example, it is possible that measurement errorcould result in the appearance of stasis if there is an inverse

relationship between the amount of measurement error and thelength of the interval, where measurement error decreases withincreasing intervals. Such an inverse relationship is unlikely be-cause contemporary field studies have the highest sample sizes inthe dataset and are least affected by measurement error. Simi-larly, the expansion of variance that occurs after 1 Myr couldresult if phylogenetic comparative data were significantly morevariable than paleontological data. However, this difference islikewise highly unlikely because the magnitude of the effect is solarge, and estimates of divergence are based on contemporarymeasurements that have reasonable sample sizes [median n = 12and n = 11 per species for reported values in Dunning (8) andSwindler (12), respectively]. Furthermore, variance in divergencein phylogenetic data is less that in than paleontological datacollected over the same time intervals (Fig. S3).

Linear Regressions of Absolute Divergence on Time. To determinewhether the pattern between datasets was better explained bya subdividing by dataset or by designating a specific breakpoint,we compared separate linear regressions fitted to each datasetwith a segmented regression with a single breakpoint. We log-transformed the absolute value of the response variable, jdj andadded a small fixed deviate (0.001) to obtain an approximatelynormal distribution of divergence values. All of the data pointsincluded in the stochastic modeling analysis were also analyzedhere. The transformed data are expected to have a linear re-lationship with log interval under a Brownian-motion model. Wethen compared three models: (i) a single linear regression fit tothe combined dataset (two parameters), (ii) a model in whicheach dataset was fitted independently (resulting in three in-dependent linear regressions and six parameters), and (iii)a segmented regression model with a single breakpoint (fourparameters). The segmented regression model allowed fora change in slope, but constrained the lines to connect, resultingin four parameters (two slope parameters for before and afterthe breakpoint, the initial intercept, and the breakpoint itself).We determined the optimal breakpoint by iteratively fitting thesegmented regression model to the data by increasing thebreakpoint value from 0 to 8.5 log10 y, with a step value of 0.01.The lowest AIC value is obtained at a breakpoint of w66,000 y(Fig. 4). Models were compared using AIC calculated from theresidual sum of squares. Care should be taken in interpreting theAIC scores, as violations of independence in the data will ex-aggerate the differences between models. Nonetheless, we foundthat the hybrid nature of the dataset contributes less to thechange in pattern of divergence than the change in timescale.

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geography of extant and recently extinct mammals. Ecology 90:2648.12. Swindler DR (2002) Primate Dentition (Cambridge Univ Press, Cambridge, UK).13. McPeek MA (2008) The macrocecological dynamics of clade diversification and

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16. Wiens JJ, Brandley MC, Reeder TW (2006) Why does a trait evolve multiple timeswithin a clade? Repeated evolution of snakelike body form in squamate reptiles.Evolution 60:123e141.

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20. Hansen TF, Martins EP (1996) Translating between microevolutionary process andmacroevolutionary patterns: The correlation structure of interspecific data. Evolution50:1404e1417.

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23. Hunt G (2004) Phenotypic variation in fossil samples: Modeling the consequences oftime-averaging. Paleobiology 30:426e443.

Uyeda et al. www.pnas.org/cgi/content/short/1014503108 4 of 14

Fig. S1. Divergence between populations in all types of traits standardized by their pooled within-population SD for log-scaled trait values (corresponding tothe Haldane numerator). Size traits are indicated by circles, and all others are indicated by triangles (including shape, behavior, life history traits, coloration,etc.). Datasets are colored according to data type: microevolutionary, yellow; fossil, green; and comparative, blue. All measurements of divergence forcomparative data are standardized by a median value of the SD of log-scaled linear body size traits of σab = 0.055.

Fig. S2. Body-size divergence as a function of generations rather than years. Colors are the same as in Fig. S1. The size of the points is proportional to the logof generation time. Generation times for comparative data are estimated as the mean generation time of the two species being compared (available formammals only, pairwise only). Note that in all datasets, there is a tendency for more rapid divergence in organisms with longer generation times and delayeddivergence for organisms with shorter generation times. This apparently systematic difference in divergence patterns suggests that divergence does not scalewith generations, but rather scales with years (compare with Fig. 1).

Uyeda et al. www.pnas.org/cgi/content/short/1014503108 5 of 14

A B

Fig. S3. (A) Among-lineage variance through time plot for each dataset individually (microevolutionary, yellow; fossil, green; phylogenetic, blue) and all threecategories combined (black line). Variance is calculated from the data binned at every 0.1 unit on the log10 interval scale. The size of the data points isproportional to the natural log of the number of data points included in that bin. Note that the fossil data appear to accumulate variance faster than thephylogenetic data. (B) Same plot as before, but variance is ln-transformed. Note the nearly linear accumulation of variance after w105–106 y.

BE BE

SB SB

MB MB

BM BM

Time Log Time

Div

erge

nce

Fig. S4. Simulated realizations of each model that we fitted to the data displayed on both the raw timescale (Left) and the log-transformed timescale(Right). The models are a bounded-evolution model (BE), a Brownian-motion model with white noise (BM), single-burst model (SB), and a multiple-burstmodel (MB). Shaded lines are the bounded-evolution process (BE) around each underlying process model, which is the solid line. Parameter values chosenfor these simulations are arbitrary, but a common white-noise parameter, σ2p, is used in each model. Note that when time is on the log scale, divergence isprimarily described by the white-noise parameter over much of the timespan, whereas at longer timescales it is primarily described by the underlyingstochastic process model.

Uyeda et al. www.pnas.org/cgi/content/short/1014503108 6 of 14

Fig. S5. Parameter distributions from the Poisson process model (MB) obtained by bootstrapping over studies (2,000 replicates). Dashed lines indicate theposition of the estimated parameter from the full dataset (Table 1). Strong positive correlations exist between all parameter values, with correlations rangingfrom 0.68 to 0.87.

Uyeda et al. www.pnas.org/cgi/content/short/1014503108 7 of 14

Table S1. Parameter estimates and AIC scores for three model fits to the data

Dataset Model Parameter estimates AIC

Microevolution and fossil BE σ̂p ¼ 0:1417 −5740.28BM σ̂p ¼ 0:0974 σ̂bm ¼ 1:60×10− 4 −8298.53SB σ̂p ¼ 0:0885 σ̂D ¼ 0:396 1=λ̂ ¼ 106:2990 −8687.00MB σ̂p ¼ 0:0874 σ̂D ¼ 0:249 1=λ̂ ¼ 106:1642 −8793.06

Phylogenetic only BE σ̂p ¼ 0:2986 1106.31BM σ̂p ¼ 0:1000 σ̂bm ¼ 4:61×10− 5 0.66SB σ̂p ¼ 0:1182 σ̂D ¼ 0:4451 1=λ̂ ¼ 107:7344 −171.30MB σ̂p ¼ 0:0857 σ̂D ¼ 0:2166 1=λ̂ ¼ 107:3375 −363.26

All data <500,000 y BE σ̂p ¼ 0:0976 −8493.74BM σ̂p ¼ 0:0976 σ̂bm ¼ 1:94×10− 7 −8491.74SB σ̂p ¼ 0:0260 σ̂D ¼ 0:106 1=λ̂ ¼ 102:276 −8960.72MB σ̂p ¼ 0:0872 σ̂D ¼ 0:327 1=λ̂ ¼ 106:337 −8758.38

All data >500,000 y BE σ̂p ¼ 0:2997 1417.48BM σ̂p ¼ 0:1946 σ̂bm ¼ 3:99×10− 5 599.30SB σ̂p ¼ 0:1558 σ̂D ¼ 0:508 1=λ̂ ¼ 107:8724 105.76MB σ̂p ¼ 0:1480 σ̂D ¼ 0:361 1=λ̂ ¼ 107:7482 45.82

Models tested include a bounded-evolution model (BE), a Brownian-motion model (BM), a single-burst model (SB), and a multiple-burst model (MB). In all models, SDs are in units of the natural log size difference. The inverse of the rate parameters (1/λ) for theexponential distribution and Poisson distribution in the single-burst and multiple-burst models, respectively, can be interpreted as theaverage number of years until a displacement. Details of each model can be found in SI Text. Best-fitting model for each dataset isindicated in bold.

Uyeda et al. www.pnas.org/cgi/content/short/1014503108 8 of 14

Table S2. Data sources for microevolutionary and paleontological data used in this study

Taxa Source SpeciesOriginaldatabase

Type ofstudy

No. ofdivergencepoints,

d (h only)

No. ofmeasured

traits in study,d (h only)

No. ofpopulations,d (h only)

Aves Baker, 1980 Passer domesticus (1) Field-syn 312 2 13Aves Baker, 1990 Fringilla coelebs (1) Field-syn 336 12 8Rodentia Berry, 1964 Mus musculus (1) Field-syn 2 (1) 2 (1) 2Salmonidae Bielak and Powers, 1986 Salmo salar (1) Field-allo 2 1 4Salmonidae Bigler et al., 1996 Oncorhynchus

gorbuscha(1) Field-allo 55 (11) 2 (1) 64 (22)

Insecta Carroll et al., 1997 Jadera hematoloma (1) Field-syn 50 (16) 3 (1) 9Insecta Carroll et al., 1998 J. hematoloma (1) Field-syn 20 (16) 2 (2) 9Aves Clegg et al., 2002 Zosterops lateralis (1) Field-syn 40 10 5Salmonidae Cox and Hinch, 1997 Oncorhynchus nerka (1) Field-allo 20 1 20Poecilidae Endler, 1980 Poecilia reticulata (1) Field-syn 2 (2) 2 (2) 1Aves Grant and Grant, 1995 Geospiza fortis (1) Field-allo 12 6 4Salmonidae Haugen and Vøllestad,

2001Thymallus thymallus (1) Field-syn 36 (18) 12 (6) 3

Salmonidae Haugen, 2000 T. thymallus (1) Field-syn 25 (23) 4 (3) 15 (5)Salmonidae Hendry and Quinn, 1997 Oncorhynchus nerka (1) Field-syn 16 2 3Salmonidae Hendry et al., 1998 O. nerka (1) Field-syn 0 (2) 0 (2) 0 (2)Insecta Hill et al., 1999 Pararge aegeria (1) Field-syn 4 1 4Insecta Huey et al., 2000 Drosophila

subobscura(1) Field-syn 2 1 2

Aves Johnston and Selander,1964

Passer domesticus (1) Field-syn 126 3 17

Salmonidae Kinnison, 1998 Oncorhynchustshawytscha

(1) Field-syn 6 (6) 3 (6) 7

GasterosteodaeKlepaker, 1993 Gasterosteusaculeatus

(1) Field-syn 44 1 (21) 1 (2)

Aves Larsson et al., 1998 Branta leucopsis (1) Field-allo 8 2 4Poecilidae Magurran et al., 1992 Poecilia reticulata (1) Field-syn 0 (2) 0 (1) 0 (2)Poecilidae Magurran et al., 1995 P. reticulata (1) Field-syn 0 (2) 0 (1) 0 (2)Mollusca McMahon, 1976 Physa virgata (1) Field-syn 0 (3) 0 (3) 0 (2)Rodentia Pergams and Ashley,

1999Peromyscus maniculatus (1) Field-allo 48 16 6

Poecilidae Reznick and Bryga, 1987 P. reticulata (1) Field-syn 3 (2) 2 (2) 2Poecilidae Reznick et al., 1990 P. reticulata (1) Field-syn 8 (11) 6 (6) 4Poecilidae Reznick et al., 1997 P. reticulata (1) Field-syn 6 (6) 1 (1) 5Aves Smith et al., 1995 Vestiaria coccinea (1) Field-allo 5 5 2Aves St.Louis and Barlow,

1991Passer domesticus (1) Field-syn 32 16 2

Poecilidae Stearns, 1983b Gambusia affinis (1) Field-syn 45 (30) 2 (1) 1Poecilidae Stearns, 1983a G. affinis (1) Field-syn 808 (277) 3 (1) 36Poecilidae Stockwell and Leberg,

2000G. affinis (1) Field-syn 12 (6) 2 (1) 4

Mollusca Trussell and Smith, 2000 Littorina obtusata (1) Field-syn 10 2 8Mollusca Vermeij, 1982 Nucella lapillus (1) Field-allo 8 2 8Lagomorpha Williams and Moore,

1989aOryctolagus cuniculus (1) Field-syn 0 (24) 0 (4) 0 (3)

Lagomorpha Williams and Moore,1989b

O. cuniculus (1) Field-syn 27 9 3

Aves Zink, 1983 Passerella iliaca (1) Field-allo 31 31 2GasterosteodaeBell et al., 2004 Gasterosteus

aculeatus(1) Field-allo 0 (4) 0 (1) 0 (5)

Diptera Bradshaw andHolzapfel, 2001

Wyeomyia smithii (1) Field-allo 0 (2) 0 (1) 0 (4)

Squamata Campbell andEchternacht, 2003

Anolis sagrei (1) Field-allo 10 2 6

Insecta Carroll et al., 2001 Jadera hematoloma (1) Field-syn 3 (2) 2 (1) 2Insecta Carroll et al., 2005 J. hematoloma (1) Field-syn 14 4 2Artiodactyla Coltman et al., 2003 Ovis canadensis (1) Field-allo 2 2 2Aves Conant, 1988 Telespyza cantans (1) Field-syn 18 3 3Aves Cooch et al., 1991 Anser caerulescens (1) Field-allo 4 3 8

Uyeda et al. www.pnas.org/cgi/content/short/1014503108 9 of 14

Table S2. Cont.

Taxa Source SpeciesOriginaldatabase

Type ofstudy

No. ofdivergencepoints,

d (h only)

No. ofmeasured

traits in study,d (h only)

No. ofpopulations,d (h only)

Diptera Gilchrist et al., 2001 Drosophilasubobscura

(1) Field-allo 48 3 16

Diptera Gilchrist et al., 2004 D. subobscura (1) Field-syn 6 3 2Salmonidae Handford et al., 1977 Coregonus clupeaformis (1) Field-allo 2 (1) 2 (1) 2Centrarchidae Holland et al., 1974 Lepomis macrochirus (1) Field-syn 0 (9) 0 (1) 0 (9)Salmonidae Kinnison et al., 2003 Oncorhynchus

tsawytscha(1) Field-syn 5 4 2

Oligochaeta Levinton et al., 2003 Limnodrilushoffmeisteri

(1) Field-allo 0 (1) 0 (1) 0 (2)

Poecilidae Meffe et al., 1995 Gambusia holbrooki (1) Field-syn 0 (2) 0 (2) 0 (2)Artiodactyla Milner et al., 1999 Ovis aries (1) Field-allo 12 3 6Aves Moller and Szep, 2005 Hirundo rustica (1) Field-allo 2 1 2Rodentia Pergams and Ashley, 2001 Mus musculus (1) Field-syn 29 13 8Anura Phillips and Shine, 2005 Bufo marinus (1) Field-allo 2 1 (1) 1 (1)Aves Postma and van

Noordwijk, 2005Parus major (1) Field-syn 0 (2) 0 (2) 0 (2)

Aves Rasner et al., 2004 Junco hyemalis (1) Field-syn 4 2 2Cichlidae Streelman et al., 2004 Cynotilapia afra (1) Field-syn 0 (15) 0 (1) 0 (6)Crustacea Tessier et al., 1992 Daphnia galeata

mendotae(1) Field-allo 4 (3) 4 (3) 2

Aves Clegg et al., 2008, Zosterops lateralis (1) Field-syn 7 7 2Artiodactyla Smith et al., 2003 Introduced Australian

artiodactylsThis paper Field-syn 13 1 4

Carnivora Simberloff, 2000 Herpestes javanicus This paper Field-syn 98 2 8Xenarthra Anderson and Handley,

2002Bradypus This paper Field-syn 7 1 8

Rodentia Smith et al., 1998 Neotoma This paper Field-allo 8 1 1Primates Cuozzo and Sauther,

2006Lemur catta This paper Field-allo 27 9 1

Primates DeGusta et al., 2003 Alouatta palliata This paper Field-allo 6 1 4Rodentia Milien, 2004 Apodemus argentatus This paper Field-syn 5 1 6Primates O’Rourke and Crawford,

2004Homo sapiens This paper Field-syn 52 26 2

Squamata Pregill, 1986 Anolis bimaculatis This paper Field-syn 6 6 2Squamata Meiri, 2007* Island-mainland

lizardsThis paper Field-syn 25 1 29

Squamata Meik et al., 2010 Crotalus mitchelli This paper Field-syn 12 1 14Insecta Santos et al., 1992 Drosophila buzzatii This paper Field-allo 8 2 4Rodentia Bouteiller-Reuter and Perrin,

2005Crocidura russula This paper Field-allo 6 2 3

Amphibia Wagner and Sullivan,1995

Bufo valliceps This paper Field-allo 3 1 3

Squamata Olsson and Madsen,2001

Lacerta agilis This paper Field-allo 1 1 2

Squamata Herrel et al., 2008 Podarcis sicula This paper Field-syn 20 10 2Condricthyes DiBattista et al., 2007 Negaprion brevirostris This paper Field-allo 0 (22) 4 6Rodentia Hester, n.d. Peromyscus (2) Field-allo 9 1 10Perissodactyla Gingerich, 1991 Hyracotherium grangeri (2) Fossil ts 42 2 22Perissodactyla Forsten, 1990 Equus germanicus (2) Fossil ts 204 34 7Rodentia Lich, 1990 Cosomys primus (2) Fossil ts 27 3 10Proprimates Gingerich and Gunnell,

1995Phenacolemur

praecox(2) Fossil ts 40 2 21

Primates Gingerich and Gunnell,1995

Tetonius steini–T. homunculus

(2) Fossil ts 26 2 14

Primates Gingerich and Gunnell,1995

Teilhardina amer.–T. tenuicula

(2) Fossil ts 18 2 10

Primates Clyde and Gingerich,1994

Cantius torresi–C. trigonodus

(2) Fossil ts 78 2 40

Uyeda et al. www.pnas.org/cgi/content/short/1014503108 10 of 14

Table S2. Cont.

Taxa Source SpeciesOriginaldatabase

Type ofstudy

No. ofdivergencepoints,

d (h only)

No. ofmeasured

traits in study,d (h only)

No. ofpopulations,d (h only)

Creodonta Gingerich and Gunnell,1995

Arfia junnei–A.opisthotoma

(2) Fossil ts 24 2 13

Condylarthra Gingerich, 1994 Haplomylus speir.–H. scott

(2) Fossil ts 70 2 36

Condylarthra Gingerich, 1994 Hyopsodus loomisi (2) Fossil ts 52 2 27Condylarthra Gingerich, 1994 Hyopsodus latidens (2) Fossil ts 32 2 17Condylarthra Gingerich and Gunnell,

1995Hyopsodus lo:la (2) Fossil ts 2 2 2

Condylarthra Gingerich and Gunnell,1995

Thryptacodonantiquus

(2) Fossil ts 28 2 15

Condylarthra Gingerich and Gunnell,1995

Ectocion osbornianus (2) Fossil ts 46 2 24

Condylarthra Gingerich and Gunnell,1995

Phenacodus vortmani (2) Fossil ts 42 2 22

Condylarthra Gingerich and Gunnell,1995

Phenacodus n. sp. (2) Fossil ts 52 2 27

Condylarthra Gingerich and Gunnell,1995

Phenacodusintermedius

(2) Fossil ts 22 2 12

Tillodontia Gingerich and Gunnell,1995

Azygonyx xenicus–A. grangeri

(2) Fossil ts 22 2 12

Tillodontia Gingerich and Gunnell,1995

Esthonyx spat.–E. bisulcatus

(2) Fossil ts 36 2 19

Artiodactyla Gingerich and Gunnell,1995

Diacodexis metsiacus (2) Fossil ts 58 2 30

Perissodactyla Gingerich and Gunnell,1995

Cardiolophusradinskyi

(2) Fossil ts 24 2 13

Perissodactyla Gingerich and Gunnell,1995

Homogalaxprotapirinus

(2) Fossil ts 20 2 11

Rodentia Jacobs and Lindsay, n.d. Potwarmus prim.–Mus auctor

(2) Fossil ts 54 2 28

Rodentia Flynn, 1986 Kanisamys indicus–K. sival.

(2) Fossil ts 38 2 20

Rodentia Jacobs, n.d. Karnimata sp.–K. huxleyi

(2) Fossil ts 18 2 10

Rodentia Jacobs, n.d. Karnimata sp.–Parapelomys rob.

(2) Fossil ts 12 2 7

Artiodactyla Morgan, n.d. Bramatheriummegacephalus

(2) Fossil ts 12 1 13

Artiodactyla Morgan, n.d. Giraffokeryxpunjabiensis

(2) Fossil ts 15 1 16

Condylarthra Gingerich, 1994 Apheliscus chydaeus (2) Fossil ts 26 2 14Proprimates Gingerich, 1996 Pronoth. jepi–

Ples. churchilli(2) Fossil ts 6 2 4

Proprimates Gingerich, 1996 Ples. churchilli–Ples. dubius

(2) Fossil ts 18 2 10

Proprimates Gingerich, 1996 Ples. churchilli–Ples. cookei

(2) Fossil ts 24 2 13

Proprimates Bloch and Gingerich,1998

Carpolestes spp. (2) Fossil ts 24 2 13

Proprimates Bloch and Gingerich,1998

Carpolestes spp. (2) Fossil ts 26 2 14

Proprimates Bloch and Gingerich,1998

Carpolestes spp. (2) Fossil ts 24 2 13

Perissodactyla Gingerich, 1991 Hyracotheriumaemulor

(2) Fossil ts 22 2 12

Perissodactyla Gingerich, 1991 Hyracotherium pernix (2) Fossil ts 6 2 4Perissodactyla Gingerich, 1991 Hyracotherium

sa:gr:ae:pe(2) Fossil ts 6 6 2

Proboscidea King and Saunders, 1984 Mammut americanum (2) Fossil ts 8 4 3

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Table S2. Cont.

Taxa Source SpeciesOriginaldatabase

Type ofstudy

No. ofdivergencepoints,

d (h only)

No. ofmeasured

traits in study,d (h only)

No. ofpopulations,d (h only)

Artiodactyla McDonald, 1981 Bison antiquus–B.bison

(2) Fossil ts 171 74 3

Artiodactyla Lister, 1989 Cervus elaphus (2) Fossil ts 10 10 2Primates Clyde and Gingerich,

1994Cantius torresi–

C. trigonodus(2) Fossil ts 22 2 12

Mammalia Gingerich, 1994 Haplomyous palust.–H. simpsoni

(2) Fossil ts 2 2 2

Mammalia Gingerich, 1994 Haplomyous si:sp (2) Fossil ts 8 1 9Foraminifera Malmgren et al., 1983 Globorotalia

plesiotumida(2) Fossil ts 8 1 9

Foraminifera Malmgren et al., 1983 G. plesiotumida (2) Fossil ts 43 1 44Foraminifera Malmgren et al., 1983 Globorotalia tumida (2) Fossil ts 43 1 44Foraminifera Malmgren et al., 1983 G. tumida (2) Fossil ts 29 1 30Foraminifera Malmgren et al., 1983 G. tumida (2) Fossil ts 29 1 30Foraminifera Malmgren et al., 1983 G. tumida (2) Fossil ts 11 1 12Foraminifera Malmgren et al., 1983 G. tumida (2) Fossil ts 11 1 12Foraminifera Malmgren et al., 1983 G. tumida (2) Fossil ts 16 2 9Artiodactyla Klein, 1995 Gazella sp. (2) Fossil ts 7 1 8Artiodactyla Klein, 1995 Gazella sp. (2) Fossil ts 96 (26) 41 4Proboscidea Maglio, 1973 Primeleph. gom.–

Loxodonta afr.(2) Fossil ts 50 (37) 20 (15) 5

Proboscidea Maglio, 1973 P. gom.–Elephasiolen.

(2) Fossil ts 31 (23) 15 (11) 4

Proboscidea Maglio, 1973 P. gom.–Elephashysud.

(2) Fossil ts 71 (53) 24 (18) 5

Proboscidea Maglio, 1973 P. gom.–Mammuth.prim.

(2) Fossil ts 12 1 13

Artiodactyla Prothero and Heaton,1996

Miniochoerus chad.–M. gracilis

(2) Fossil ts 57 1 58

Rodentia Heaton, 1993 Ischyromys parvidens–I. typus

(2) Fossil ts 70 1 71

Rodentia Heaton, 1993 I. parvidens–I. typus (2) Fossil ts 42 2 22Carnivora Polly, 1998 Viverravus acutus (2) Fossil ts 158 1 (11) 1 (15)Mollusca Geary, 1990 Peromyscus m. gracilis (2) Fossil ts 9 1 10Mollusca Geary, 1990 Melanopsis impressa (2) Fossil ts 7 1 8Mollusca Geary, 1990 Melanopsis fossilis (2) Fossil ts 1 1 2Perissodactyla Haldane, 1949 Melanopsis impressa:

fossilis(2) Fossil ts 6 2 4

Perissodactyla Haldane, 1949 Hyracotherium–

Neohipparion(2) Fossil ts 0 (3) 0 (1) 0 (4)

Dinosauria Colbert, 1948 Hyracotherium–

Neohipparion(2) Fossil ts 2 1 3

Dinosauria Colbert, 1948 Protoceratops–Triceratops

(2) Fossil ts 1 1 2

Dinosauria Colbert, 1948 Camptosaurus–Trachodon

(2) Fossil ts 1 1 2

Dinosauria Colbert, 1948 Polacanthus–Ankylosaurus

(2) Fossil ts 1 1 2

Dinosauria Colbert, 1948 Coelophysis–Tyrannosaurus

(2) Fossil ts 1 1 2

Dinosauria Colbert, 1948 Scelidosaurus–Stegosaurus

(2) Fossil ts 1 1 2

Hominidae Ruff et al., 1997 Homo (2) Fossil ts 36 4 40Rodentia Barnosky, 1990 Microtus

pennsylvanicus(2) Fossil ts 7 1 8

Rodentia Barnosky, 1990 M. pennsylvanicus (2) Fossil ts 8 1 9Rodentia Barnosky, 1990 M. pennsylvanicus (2) Fossil ts 5 1 6Radiolaria Kellogg, 1975 Pseudocubus verna This paper Fossil ts 33 1 34Carnivora Kurten, 1959 Ursus sp. This paper Fossil ts 10 1 11

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Table S2. Cont.

Taxa Source SpeciesOriginaldatabase

Type ofstudy

No. ofdivergencepoints,

d (h only)

No. ofmeasured

traits in study,d (h only)

No. ofpopulations,d (h only)

Carnivora Kurten, 1959 Felis silvestris ssp. This paper Fossil ts 4 1 5Carnivora Kurten, 1959 Felis lynx This paper Fossil ts 1 1 2Carnivora Kurten, 1959 Vulpes vulpes This paper Fossil ts 2 1 3Carnivora Kurten, 1959 Canis lupus This paper Fossil ts 1 1 2Carnivora Kurten, 1959 Putorius putorius This paper Fossil ts 1 1 2Carnivora Kurten, 1959 Martes martes This paper Fossil ts 3 1 4Carnivora Kurten, 1959 Gulo gulo This paper Fossil ts 1 1 2Carnivora Kurten, 1959 Meles meles This paper Fossil ts 2 1 3Carnivora Kurten, 1959 Lutra lutra This paper Fossil ts 2 1 3Rodentia Kurten, 1959 Apodemus sylvaticus This paper Fossil ts 1 1 2Total 5,087 (663) 645 (137) 1,631 (96)

Most data come from Hendry et al. (1) and Gingerich (2). A “field study” is defined as any study involving the collection of data on extant organisms.Synchronic studies are cross-sectional studies (“field-syn”) whereas allochronic studies are longitudinal (“field-allo”). Number of divergence points is the totalnumber of autonomous data points that were plotted for each type of divergence measure, with those data points for which h alone was measured inparentheses. Number of traits is the total number of different measurements that were used to obtain divergence (autonomous divergence only), and numberof populations is the number of samples. Original databases indicate either Hendry et al. (1) or Gingerich (2). n.d., not determined.*Dates for land-bridge islands are taken from Lu et al., 2002; Boback, 2003; Foufopoulos, 1999; Castilla, et al., 2008; Podner et al., 2004; Foufopolous and Ives,1999; Villagran, 1988; and Case and Schwaner, 1993.

1. Hendry AP, Farrugia TJ, Kinnison MT (2008) Human influences on rates of phenotypic change in wild animal populations. Mol Ecol 17:20e29.2. Gingerich PD (2001) Rates of evolution on the time scale of the evolutionary process. Genetica 112–113:127e144.

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Table S3. Data sources for across-species comparative data

Taxa Interval source Divergence source Original database No. of taxa No. of nodes Trait

Squamates Wiens et al., 2006 Wiens et al., 2006 This paper 259 258 SVLMammalia Bininda-Emonds et al., 2007 Smith et al., 2004 This paper 3,264 1,770 (Mass)^1/3Primates Bininda-Emonds et al., 2007 Swindler, 2002 This paper 47 42 M/1 (MD)Primates Bininda-Emonds et al., 2007 Swindler, 2002 This paper 47 42 M/1 (TriB)Aves Sibley and Ahlquist, 1990 Dunning, 2008 This paper 121* 119 (Mass)^1/3Aves Thomas et al., 2004 Dunning, 2008 This paper 286 217 (Mass)^1/3Aves Filardi and Smith, 2005 Dunning, 2008 McPeek, 2008 12 11 (Mass)^1/3Aves Pérez-Emán, 2005 Dunning, 2008 McPeek, 2008 5 4 (Mass)^1/3Aves Eberhard and Bermingham, 2005 Dunning, 2008 McPeek, 2008 4 3 (Mass)^1/3Aves Eberhard and Bermingham, 2005 Dunning, 2008 McPeek, 2008 10 9 (Mass)^1/3Aves Lijtmaer et al., 2004 Dunning, 2008 McPeek, 2008 20 13 (Mass)^1/3Aves Austin, J. J., 1996 Dunning, 2008 McPeek, 2008 10 9 (Mass)^1/3Aves Chesser, R. T., 2000 Dunning, 2008 McPeek, 2008 7 6 (Mass)^1/3Aves Garcia-Moreno et al., 2001 Dunning, 2008 McPeek, 2008 20 17 (Mass)^1/3Aves Garcia-Moreno et al., 1999 Dunning, 2008 McPeek, 2008 9 8 (Mass)^1/3Aves Groombridge et al., 2004 Dunning, 2008 McPeek, 2008 7 6 (Mass)^1/3Aves Joseph et al., 2004 Dunning, 2008 McPeek, 2008 11 8 (Mass)^1/3Aves Klicka et al., 2003 Dunning, 2008 McPeek, 2008 6 5 (Mass)^1/3Aves Lee et al., 2003 Dunning, 2008 McPeek, 2008 3 2 (Mass)^1/3Aves Lucchini et al., 2001 Dunning, 2008 McPeek, 2008 12 11 (Mass)^1/3Aves Omland et al., 1999 Dunning, 2008 McPeek, 2008 22 18 (Mass)^1/3Aves Randi, 1996 Dunning, 2008 McPeek, 2008 5 4 (Mass)^1/3Aves Randi et al., 2001 Dunning, 2008 McPeek, 2008 5 4 (Mass)^1/3Aves Ribas and Miyaki, 2004 Dunning, 2008 McPeek, 2008 5 4 (Mass)^1/3Aves Weibel and Moore, 2002 Dunning, 2008 McPeek, 2008 19 18 (Mass)^1/3Aves Whittingham et al., 2002 Dunning, 2008 McPeek, 2008 8 7 (Mass)^1/3Aves Sorenson et al., 2004 Dunning, 2008 McPeek, 2008 18 11 (Mass)^1/3Aves Kimball et al., 2001 Dunning, 2008 McPeek, 2008 4 3 (Mass)^1/3Aves Cheviron et al., 2005 Dunning, 2008 McPeek, 2008 6 5 (Mass)^1/3Aves Gill et al., 2005 Dunning, 2008 McPeek, 2008 23 21 (Mass)^1/3Aves Given et al., 2005 Dunning, 2008 McPeek, 2008 9 7 (Mass)^1/3Aves Lovette and Bermingham, 1999 Dunning, 2008 McPeek, 2008 23 22 (Mass)^1/3Aves Mooers et al., 1999 Dunning, 2008 McPeek, 2008 11 10 (Mass)^1/3Aves Price et al., 2000 Dunning, 2008 McPeek, 2008 3 1 (Mass)^1/3Aves Ruolonen et al., 2000 Dunning, 2008 McPeek, 2008 7 6 (Mass)^1/3Aves Weckstein, 2005 Dunning, 2008 McPeek, 2008 6 5 (Mass)^1/3Aves Sato et al., 1999 Dunning, 2008 McPeek, 2008 12 10 (Mass)^1/3

*Taxa for this phylogeny are the family means rather than species-level means, with average values being calculated from Dunning(2008) for all taxa assigned to a given family. The phylogeny was scaled to a root age of 90 Myr.

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