This document presents a new method for estimating divergence times between populations based on quantitative traits like cranial measurements. The authors develop a phenotypic divergence time (PTD) estimator modeled after genetic divergence time estimators. They apply their PTD estimator to cranial measurements from over 2,500 modern humans and 20 Neandertals. Their analysis estimates the Neandertal-modern human divergence at either 311,000 years ago or 435,000 years ago, depending on assumptions. These dates are similar to estimates from ancient DNA, implying cranial and genetic divergence largely track population history through neutral evolution.

1. Close correspondence between quantitative- and
molecular-genetic divergence times for Neandertals
and modern humans
Timothy D. Weaver*†‡, Charles C. Roseman§, and Chris B. Stringer¶
*Department of Anthropology, University of California, One Shields Avenue, Davis, CA 95616; †Department of Human Evolution, Max Planck Institute for
Evolutionary Anthropology, Deutscher Platz 6, D-04103 Leipzig, Germany; §Department of Anthropology, University of Illinois at Urbana–Champaign,
109 Davenport Hall, 607 South Matthews Avenue, Urbana, IL 61801; and ¶Department of Palaeontology, Natural History Museum,
London SW7 5BD, United Kingdom
Edited by Erik Trinkaus, Washington University, St. Louis, MO, and approved January 17, 2008 (received for review September 27, 2007)
Recent research has shown that genetic drift may have produced cranial differences between Neandertals and modern humans,
many cranial differences between Neandertals and modern hu- even though the tests look reasonably powerful (12). Further-
mans. If this is the case, then it should be possible to estimate more, within-population cranial diversity seems to decrease with
population genetic parameters from Neandertal and modern hu- geographic distance from subSaharan Africa (13). This decrease
man cranial measurements in a manner analogous to how esti- may mirror a decrease in molecular diversity (14–17), but the
mates are made from DNA sequences. Building on previous work strength of the cranial relationship is much weaker.
in evolutionary quantitative genetics and on microsatellites, we If neutral evolution is responsible for cranial differences
present a divergence time estimator for neutrally evolving mor- among human populations and between Neandertals and mod-
phological measurements. We then apply this estimator to 37 ern humans, then it should be possible to estimate population
standard cranial measurements collected on 2,524 modern humans genetic parameters from cranial measurements in a manner
from 30 globally distributed populations and 20 Neandertal spec- analogous to how estimates are made from DNA sequences.
imens. We calculate that the lineages leading to Neandertals and Building on previous work in evolutionary quantitative genetics
modern humans split 311,000 (95% C.I.: 182,000 to 466,000) or (18–21) and on microsatellites (22–24), we present a divergence
435,000 (95% C.I.: 308,000 to 592,000) years ago, depending on time estimator for neutrally evolving morphological measure-
assumptions about changes in within-population variation. These ments. We then apply this estimator to cranial measurements to
dates are quite similar to those recently derived from ancient infer when Neandertals and modern humans diverged, and we
Neandertal and extant human DNA sequences. Close correspon- compare our results with those from ancient Neandertal and
dence between cranial and DNA-sequence results implies that both extant human DNA sequences.
datasets largely, although not necessarily exclusively, reflect neu-
tral divergence, causing them to track population history or phy- Morphological Divergence Time Estimator
logeny rather than the action of diversifying natural selection. The Divergence Time. To estimate the divergence time of two popu-
cranial dataset covers only aspects of cranial anatomy that can be lations (or species), we adapt the TD estimator that was originally
readily quantified with standard osteometric tools, so future re- developed for microsatellites (23). Microsatellites are rapidly
search will be needed to determine whether these results are evolving blocks of DNA for which a simple DNA sequence is
representative. Nonetheless, for the measurements we consider repeated multiple times, and individuals vary in their number of
here, we find no conflict between molecules and morphology. repeats. So, like morphological measurements (metric charac-
teristics), microsatellites are quantitative characters that change
craniometrics evolutionary quantitative genetics by lengthening and shortening (24–26), making the adaptation
microsatellites population genetics human evolution fairly straightforward. We call the new estimator PTD for phe-
notypic TD and to distinguish it from TD for microsatellites. By
divergence time, we mean when the two populations last shared
L ately, evidence has been accumulating for the importance of
neutral evolution in producing cranial differences among
human populations and between Neandertals and modern
a randomly mating common ancestor.
We define PTD as follows. For two daughter populations at
mutation drift equilibrium (balance between the addition of
humans. Under neutral evolution, genetic drift provides the
variation by mutation and the removal of variation by genetic
mechanism, and mutation provides the raw material for diver-
drift), the between-population variance for a measurement is
gence between groups, with natural selection being relegated to
expected to increase at the rate of 2 Vm per generation (20, 21),
a role of slowing down divergence (1–3). Lynch (4) and Releth-
where Vm is the average amount of new additive genetic variance
ford (5) provided some of the first evidence of the importance
introduced by mutation per zygote per generation in each
of neutral evolution for understanding human cranial differ-
ANTHROPOLOGY
population. This result holds for many different underlying
ences. Lynch (4) found that cranial distances among human genetic models (20) as long as the divergence is by genetic drift
populations corresponded well with relative and absolute rates rather than by natural selection. Let x1 and x2 be measurement
of divergence predicted by neutral evolution. Relethford (5)
showed that estimates of FST (a measure of among-population
differentiation) from human cranial measurements were similar Author contributions: T.D.W., C.C.R., and C.B.S. designed research; T.D.W. and C.C.R.
to those from presumably neutral genetic loci. Further work performed research; C.B.S. contributed new reagents/analytic tools; and T.D.W., C.C.R., and
established that cranial and molecular distances among human C.B.S. wrote the paper.
populations tend to be significantly associated with each other The authors declare no conflict of interest.
(6–9), both cranial and molecular distances are correlated with This article is a PNAS Direct Submission.
geographic distances among globally distributed human popu- ‡To whom correspondence should be addressed. E-mail: tdweaver@ucdavis.edu.
lations (10, 11), cranial measurements appear to fit neutral Because of a spelling change in German, there are two acceptable spellings for the name
expectations as well as microsatellites for humans (12), and of the group. “Neanderthal” rather than “Neandertal” is the preferred spelling of C.B.S.
statistical tests fail to detect deviations from neutrality for © 2008 by The National Academy of Sciences of the USA
www.pnas.org cgi doi 10.1073 pnas.0709079105 PNAS March 25, 2008 vol. 105 no. 12 4645– 4649

2. means for populations nos. 1 and 2, respectively. An estimator large effective sizes, at first they will remain homogeneous, but
for the time in generations when the two populations diverged, over time, mutations will continue to introduce variation until a
under the assumption of mutation drift equilibrium, is: new equilibrium is reached. In the initial generations after the
split, the morphological divergence will be very slow, because
x1 x2 2 genetic drift will be very weak. This is because in a large
PTDMDE . [1]
4V m population, the chance effects of sampling are small, and if the
population is homogeneous, it does not matter much which
Note that (x1 x2)2 equals twice the between-population vari- individuals give rise to the next generation. As the populations
ance, which is the quantity most commonly used in the evolu- become less homogeneous with the addition of mutational
tionary quantitative genetics literature (21). Also note that the variance over time, the rate of divergence will increase until the
numerator in Eq. 1 is mathematically analogous to the expression mutation-drift-equilibrium rate is reached. Because the diver-
for ( )2, a genetic distance for microsatellites (22, 23), if a gence is slow initially, assuming that the populations were always
measurement is equated to a single microsatellite. The denom- at mutation, drift equilibrium will underestimate the actual
inator in Eq. 1, or the expected rate of increase, is four times the divergence time. The three additional variance terms correct for
mutation parameter, Vm, whereas for ( )2, it is twice the mu- this bias.
tation parameter (22, 23). This is because of differences in the
definitions of the mutation parameters. By necessity, all within- Effective Population Size. If the amount of additive genetic vari-
population and mutational variances in the quantitative genetics ance introduced by mutation per generation, Vm, is known, then
literature are zygotic, whereas they are gametic for microsatel- it should be possible to estimate the effective population size of
lites. Gametic variances include differences both among a particular group (populations or species) from the amount of
individuals and among the paired chromosomes of a given additive genetic variation found within that group. Let Ne be the
individual; zygotic variances only include among-individual dif- effective size of a population. Following Lynch and Hill (20), at
ferences. At Hardy–Weinberg equilibrium, a gametic variance mutation drift equilibrium, the expected amount of additive
should be twice a zygotic variance (27), hence the difference by genetic variance, V, found within the population is
a factor of two between the quantitative genetic and microsat-
ellite formulas. EV 2NeVm. [7]
Following results for microsatellites (23), if the assumption of
mutation drift equilibrium is relaxed, three additional variance Eq. 7 has been tested empirically, and it appears to hold
terms must be added to the numerator (with modifications to reasonably well, at least on average, in inbreeding experiments
account for zygotic vs. gametic variances as before). These terms on Drosophila melanogaster (30). Substituting V for V1 and for
are measures of the degree of departure from mutation drift 1 in Eq. 3, combining Eqs. 3 and 5 with Eq. 7, and solving for
equilibrium. Departures could happen with population expan- N results in an estimator for the effective size of the population
sions or migration between populations. Let V1 and V2 be the given by
additive genetic variances for the measurements for populations
nos. 1 and 2, respectively. Let V0 be the additive genetic variance h2 2
ˆ
Ne 2 2 2. [8]
in the ancestral population before subdivision into two daughter 2m P 2m Ph
populations. Under a more general model, an estimator for the
time in generations when the two populations diverged is: Statistical Analyses
Data. Our analyses are based on 37 standard cranial measure-
2
x1 x2 2V 1 2V 2 4V 0 ments (Fig. 1) collected on 2,524 modern humans from 30
PTD . [2] globally distributed populations and 20 Neandertal specimens.
4V m
More details about the sample and measurements can be found
Let h2 be the narrow-sense heritability for the measurement in elsewhere (12, 31–33). We have previously shown that these 37
both populations and 2 and 2 be the phenotypic variances for
1 2 measurements appear to be evolving neutrally in Neandertals
populations nos. 1 and 2, respectively. Following Falconer (28), and modern humans (12), making them candidates for use in
2
estimating divergence times.
V1 h2 1 [3]
Treatment of Multiple Measurements. Divergence time can be
V2 h2 2
2. [4] —
estimated from multiple measurements as PTD, the mean of
Let m be a mutation parameter and 2 be the pooled within PTD estimates for individual measurements. The expected
P
population phenotypic variance. Following Lynch (29), value for PTD for each measurement is the divergence time, so
—
the expected value for PTD is also the divergence time,
Vm m 2
P m 2 2
Ph . [5] regardless of whether the measurements are correlated with
each other. If the measurements are completely indepen-
Combining Eqs. 3, 4, and 5 with Eq. 2 results in dent (uncorrelated within and between groups), bootstrapping
—
(34) can be used to estimate the variance of PTD, but this
—
2 2 2
x1 x2 2h 2 1 2h 2 2 4V 0 procedure will underestimate Var {PTD} if the measurements
PTD 2 2 2 . [6] are not independent.
4m P 4m Ph
It is always possible, however, to find a basis for which the
Setting V0 0 provides a maximum estimate of divergence time. measurements are uncorrelated within groups as the eigenvec-
Using V0 (V1 V2)/2 reduces Eq. 6 to a mutation-drift- tors of the pooled within group variance–covariance matrix.
equilibrium model (Eq. 1), which provides a minimum estimate There are as many eigenvectors as original measurements. Each
unless there was a decline in population size (23). eigenvector (sometimes called a principal component) repre-
The rationale behind the three additional variance terms can sents a new measurement that is a linear combination of the
be illustrated with an example. Imagine two daughter popula- original measurements and is uncorrelated with the other eig-
tions with very small effective population sizes that are at envectors within groups. For neutral divergence, the elements of
mutation drift equilibrium. Because of their small sizes, these the between-group variance–covariance matrix are expected to
populations will be very homogeneous. If they expand rapidly to be proportional to the elements of the within-group variance–
4646 www.pnas.org cgi doi 10.1073 pnas.0709079105 Weaver et al.

3. with other studies. This divergence time estimate is almost
certainly too recent, because the mutation-drift-equilibrium
model assumes that there was no postdivergence gene flow
between subSaharan African and other human populations,
and that human populations have not expanded in size recently.
However, by calibrating to a divergence time based on a
mutation-drift-equilibrium model, we are just assuming that the
morphological and microsatellite estimates should match up
under the same model, not that this is the most realistic model
to use to infer the actual divergence time. In other words,
because the mutation-drift-equilibrium model is expected to
underestimate the actual divergence time between subSaharan
African and other human populations by the same amount for
morphology and microsatellites, using 30,000 years ago as the
calibration point will not result in an underestimate of the
divergence time between Neandertals and modern humans.
The—second reference point is the effective population
size, PN e, under a mutation–drift–equilibrium model for sub-
Saharan African human populations. Zhivotovsky and col-
—
leagues (17) estimated N e from 271 microsatellites using an
equation equivalent to our Eq. 7 as 2,700 individuals. Once
again, we are just assuming that the morphological and micro-
satellite estimates should match up under the same model, not
that this is the most realistic model to use to infer the actual
effective population size. Using V0 (V1 V2)/2 in Eq. 8 for
— —
mutation drift equilibrium and setting PT D
— — T D in Eq. 6 and
PN e N e in Eq. 8 produces two equations that can be solved for
h2 and m, the two remaining unknown parameters. Following
Zhivotovsky (23), we use a generation length of 25 years for all
our calculations.
Confidence Limits. We use bootstrapping (34) to calculate approx-
—
imate 95% confidence limits for PT D. We resampled with
replacement 10,000 times from the PTD estimates — the indi-
for
vidual eigenvectors and calculated an estimate of PT D for each
—
resample, producing a distribution of PT D estimates. The lower
and upper confidence limits are the 2.5% and 97.5% quantiles
respectively of this distribution. These confidence limits account
for evolutionary stochasticity in the amount of mutational
variance actually introduced per generation, but they do not
account for uncertainty in the calibration. Because uncertainty
in the calibration is difficult to quantify accurately, it is not
usually included in confidence limits for divergence times esti-
mated from DNA sequences. We follow this practice here, but
Fig. 1. The approximate locations of the cranial measurements used in the
it is important to point out that this additional uncertainly can
analyses are superimposed as red lines on lateral (A), anterior (B), and inferior
(C) views of a human cranium. Note that when the endpoints of a measure-
often be quite large.
ment are not visible, the line is projected into a plane situated in front of the
cranium. Calculations. We wrote scripts in MATLAB (Mathworks) to
perform all of the calculations, making use of the statistical
toolbox and Richard E. Strauss’ MATLAB function package.
covariance matrix (35–37), so the eigenvectors should be ap-
proximately uncorrelated between groups as well. Eq. 8 for Results
effective population size can be extended to multiple measure- Calibration. From our calibration, we estimate h2 0.37. Studies
ANTHROPOLOGY
ments in a similar manner. of human cranial measurements commonly use h2 0.55 (5, 6,
38, 39), but this value actually derives from soft-tissue head
Calibration. As with divergence time estimates from molecular measurements, which appear to have higher heritabilities than
data, to estimate an ‘‘unknown’’ divergence time, we must first skeletal measurements (40). In a recent study of skeletal mea-
calibrate certain parameters using ‘‘known’’ reference points. In surements collected on a pedigreed human sample, Carson (40)
our case, we need to calibrate m and h2. We pick two ‘‘known’’
— estimated heritabilities for 21 of the 37 measurements we use
reference points. The first is PT D under a mutation-drift- here with mean h2 0.36. The sample sizes were small for three
equilibrium model for the split between subSaharan African and measurements, potentially making the h2 estimates unreliable
other human populations. This divergence is the oldest among (40). For the remaining 18 measurements, mean h2 0.31. Both
human populations, so it is the most appropriate calibration estimates are quite close to our calibration-based estimate,
point for estimating even older divergence times. Zhivotovsky especially considering the considerable uncertainty in h2 esti-
—
(23) estimated T D as 30,000 years ago based on 131 autosomal mates. Additionally, we do not expect an exact match, because
and four Y-chromosomal microsatellites and from comparisons the populations are different, and our calibration-based estimate
Weaver et al. PNAS March 25, 2008 vol. 105 no. 12 4647

4. reflects average h2 over hundreds to thousands of generations Our PTD results are estimates of when the ancestral Nean-
(evolutionary time) rather than over just a few generations. dertal and modern human populations last shared a randomly
From our calibration, we estimate m 1.20 10 4. Exper- mating common ancestor (split time), whereas most molecular
imental studies of a number of different taxa for a variety of traits estimates are DNA sequence coalescence times. As long as the
(21, 29, 41) suggest a rough range of 10 4 to 10 2 for m. Our mutation rate is correct, coalescence times will equal or predate
calibration-based estimate is at the lower end of the range, which the split time by an amount that depends, on average, on
is expected, because most experimental values for m are over- ancestral effective population size (50). For example, if the
estimates. Experimental estimates consider all mutations, not ancestral population had a constant effective size of 2,500
just neutral ones, and over evolutionary time stabilizing selection individuals, an autosomal coalescence time based on one Ne-
will remove some mutations from the population. The overes- andertal and one extant human sequence would be expected to
timation may sometimes be substantial, because the experimen- predate the split time by 125,000 years, assuming a generation
tal populations have low effective sizes, which would weaken length of 25 years. Point estimates for the coalescence of ancient
stabilizing selection (1). A similar overestimation problem is Neandertal and extant human sequences for both mitochondrial
documented for molecular evolution where mutation rates es- and nuclear DNA range from 300,000 to 800,000 years ago (42,
timated from pedigrees are much higher than those estimated 51–55). Additionally, Noonan and colleagues (53) estimated that
from phylogenetic calibration points (42, 43). the Neandertal and modern human lineages split 370,000 years
ago based on comparisons at 36,000 autosomal DNA sites. This
Neandertal and Modern Human Divergence. We estimate that Ne- split time is very similar to 373,000 years ago, the average of our
andertals and modern humans diverged 311,000 years ago mutation-drift-equilibrium and V0 0 point estimates.
(95% C.I.: 182,000–466,000) assuming mutation drift equilib- The divergence time estimates could change somewhat if the
rium or 435,000 years ago (95% C.I.: 308,000–592,000) assuming separation between Neandertals and modern humans was actu-
V0 0. For both estimates, we added 25,000 years to account for ally more complicated than a simple splitting of populations.
the fact (averaging dates) that Neandertals lived 50,000 years Additionally, although the ancestors of Neandertals and modern
ago. When we compare Neandertals with only male recent humans may have split 400,000 years ago, modern humans are
humans, the point estimates and C.I.s decrease by 10,000 years, sometimes thought to have originated with a subsequent spe-
so our estimates would not be strongly biased, even if the entire ciation event 150,000 years ago. It is unclear what this view
Neandertal sample were male. implies demographically, but it could be taken to mean that the
It is difficult to decide which V0 model is most appropriate. The emergence of modern humans involved a bottleneck, which is a
V0 0 result is probably an overestimate for at least two reasons. sharp reduction followed by a rapid expansion in population size.
(i) Because the Neandertal sample is too small to accurately If such a bottleneck occurred, the mutation-drift-equilibrium
estimate within-population variation in Neandertals, we used the result would likely be an underestimate, and the V0 0 estimate
human value for both V1 and V2. If Neandertals were actually less would be closer to the actual split time.
variable than present-day human populations, the V0 0 result Regardless of these potential complications, the close corre-
would be an overestimate (i.e., the Neandertal lineage would spondence between the cranial and DNA-sequence estimates
maximally deviate from mutation drift equilibrium less than the implies that both datasets largely, although not necessarily
modern human lineage). (ii) The additive genetic variance in the exclusively, reflect neutral divergence, causing them to track
last common ancestor of Neandertals and modern humans must population history or phylogeny rather than the action of
have been greater than zero, making the V0 0 result an overes- diversifying natural selection. The overall pattern for the mea-
timate. In contrast, the mutation-drift equilibrium, V0 (V1 surements considered here appears to be neutral divergence, but
V2)/2, result could be an underestimate for at least two reasons. (i) as is the case among human populations (6–8, 38), a few
Human populations have grown in size recently, which would make measurements could still have diverged by diversifying natural
the mutation-drift-equilibrium result an underestimate as long as selection. Additionally, future research will be needed to deter-
this growth in census size corresponds to growth in effective size. (ii) mine if this pattern is representative of Neandertal and modern
Postdivergence gene flow between Neandertals and modern hu- human cranial divergence in general, or whether it applies only
mans would make the mutation-drift-equilibrium result an under- to the measurements included in our study. In particular, more
estimate (23). Given this uncertainty, the mean of the two estimates, detailed or internal cranial structures and other aspects of
373,000 years ago, seems to be a reasonable point estimate. cranial anatomy that are difficult to quantify with standard
osteometric tools many have been shaped by diversifying natural
Discussion selection.
If we consider the maximum extent of the 95% confidence limits Brain size relative to body size appears to have increased in
for both the mutation-drift equilibrium and the V0 0 estimates, both the Neandertal and the modern human lineages (56, 57).
then the Neandertal and modern human lineages split between These parallel trajectories may indicate that directional natural
182,000 and 592,000 years ago. Although this range is quite large, selection was acting on both lineages independently, resulting in
it still allows for some observations with respect to the human differently shaped but similarly sized brain cases (58). To the
fossil record. First, even the lower limit is within the Middle extent that the measurements considered here reflect these
Pleistocene, suggesting a relatively deep divergence of Neander- changes, our results would imply that although natural selection
tals and modern humans, which is consistent with the presence may have produced the similarities in size, genetic drift lead to
of derived Neandertal features on Middle Pleistocene fossils the differences in shape. We are not arguing that natural
from Europe (44–47). Second, recent dates suggesting that the selection had no effect, just that it appears not to have played a
Sima de los Huesos site is 530,000 years old (48) would put the dominant role in producing differences.
fossils from this site, which appear to have multiple derived One misconception about neutral evolution is that it is slow,
Neandertal features (46), at or potentially before the split of the because it is driven by genetic drift rather than by natural
Neandertal and modern human lineages. Third, although the selection. However, if stabilizing natural selection is more prev-
800,000-year-old Atapuerca-TD6 humans (49) could be an- alent than directional natural selection, then neutral evolution
cestral to Neandertals and modern humans, their morphology will actually be comparatively fast. Lynch (59) estimated that
may not be representative of the source population that actually human cranial evolution was rapid relative to morphological
gave rise to Neandertals and modern humans, because they date evolution in other mammals, but the absolute rate was consistent
from, at minimum, 200,000 years before the split time. with neutral evolution. It follows from these results and ours that
4648 www.pnas.org cgi doi 10.1073 pnas.0709079105 Weaver et al.

5. Neandertal and modern human crania may have been released nial divergence and the amount of DNA sequence divergence
from the constraints of stabilizing natural selection that limit the between Neandertals and modern humans.
rates of morphological evolution in other mammals.
Perhaps the most significant implication of our results is that ACKNOWLEDGMENTS. We thank D. DeGusta, R. Fournier, B. Henn, J.-J. Hub-
there is no conflict between molecules and morphology. This lin, K. A. Horsburg, R. Klein, J. Mountain, N. Rosenberg, T. Steele, M. Stonek-
contrasts with a common characterization of debates about the ing, and two anonymous reviewers for valuable comments on drafts or
feedback; the late W. W. Howells for making his raw data publicly available;
origins of modern humans as molecules vs. morphology (60). In the institutes that made their fossil material available for study; M. v. Harling
fact, at least for the measurements considered here, there is a for the CT scans used to create Fig. 1; and the Max Planck Society for financial
close quantitative correspondence between the amount of cra- support.
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