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Estimating the distribution of probable age-at-death from dental remains of immature human fossils.

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AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 147:227–253 (2012)
Estimating the Distribution of Probable Age-at-Death
From Dental Remains of Immature Human Fossils
Laura L. Shackelford,* Ashley E. Stinespring Harris, and Lyle W. Konigsberg
Department of Anthropology, University of Illinois at Urbana-Champaign, Urbana, IL 61801
KEY WORDS
Neandertals; early modern humans; teeth
ABSTRACT
In two historic longitudinal growth studies, Moorrees et al. (Am J Phys Anthropol 21 (1963) 99108; J Dent Res 42 (1963) 1490-1502) presented the
‘‘mean attainment age’’ for stages of tooth development
for 10 permanent tooth types and three deciduous tooth
types. These findings were presented graphically to
assess the rate of tooth formation in living children and
to age immature skeletal remains. Despite being widely
cited, these graphical data are difficult to implement
because there are no accompanying numerical values for
the parameters underlying the growth data. This analysis generates numerical parameters from the data
reported by Moorrees et al. by digitizing 358 points from
these tooth formation graphs using DataThief III, version 1.5. Following the original methods, the digitized
points for each age transition were conception-corrected
and converted to the logarithmic scale to determine a
median attainment age for each dental formation stage.
These values are subsequently used to estimate age-atdeath distributions for immature individuals using a single tooth or multiple teeth, including estimates for 41
immature early modern humans and 25 immature Neandertals. Within-tooth variance is calculated for each age
estimate based on a single tooth, and a between-tooth
component of variance is calculated for age estimates
based on two or more teeth to account for the increase in
precision that comes from using additional teeth. Finally,
we calculate the relative probability of observing a particular dental formation sequence given known-age reference information and demonstrate its value in estimating age for immature fossil specimens. Am J Phys
Anthropol 147:227–253, 2012. V 2011 Wiley Periodicals, Inc.
The determination of age in immature populations is
important in multiple contexts. In a clinical setting, it
may be necessary to compare physiological age with
chronological age to determine if normal growth is occurring in an individual; in forensic or archeological contexts, age may be an unknown variable that is necessary
for identification. Physiological age can be estimated
based on the maturation of tissue systems, and multiple
physiological assessors can be used to determine chronological age in juveniles, including skeletal markers,
height, and weight. The emergence and formation of
teeth is a particularly reliable tissue system on which to
base age assessments because it is comparable in accuracy to other skeletal growth markers but it is less
affected by environmental insults to the individual than
these other systems. Dental formation is superior to
emergence for estimating age because emergence is a
very short-phase phenomenon in the longer formation
and eruption process, and emergence may be influenced
by environmental factors such as the loss of deciduous
teeth or space in the dental arch. Because teeth begin
calcifying early in the fetal period and become increasingly numerous as a child ages, they create a relatively
complete chronology from fetal life to adulthood, allowing a greater range for age estimation.
The accuracy of determining chronological age using
dental development depends on the ability to accurately
assess tooth formation and, for deciduous teeth, root
resorption in an appropriate reference sample. To this
end, multiple methods for quantifying the rate of crown
and root growth have been proposed (Kronfeld, 1935;
Schour and Massler, 1940; Gleiser and Hunt, 1955; Fanning, 1961; Lysell et al., 1962; Moorrees et al., 1963a,b;
Haavikko, 1970; Demirjian et al., 1973; Demirjian and
Goldstein, 1976; Sunderland et al., 1987). This study
evaluates one such method of determining chronological
age using dental formation and its application to anthropological samples (Moorrees et al., 1963a,b). Data from
these historic studies have been widely cited, but it is
difficult to apply because it was presented only graphically and the original data have been lost.
In their 1963 studies, Moorrees et al. (1963a,b) analyzed radiographs from children of all ages to determine
the stages of dental development for 10 permanent tooth
types (maxillary incisors and all mandibular teeth) and
three deciduous tooth types (mandibular canine, first
and second molars). Maxillary and mandibular incisors
were analyzed for 99 children (48 males and 51 females)
using intraoral radiographs; the remaining teeth were
studied using lateral jaw radiographs from 246 children
(136 males and 110 females). Degree of tooth formation
and root resorption was determined by examining dental
radiographs and assigning a rating based on 14 arbitrarily defined stages. The children in their studies were
Caucasian, North American children growing up in Boston, Massachusetts, as well as a subset from Yellow
Springs, Ohio. To date, this is the only longitudinal chronology of dental growth that extends to birth.
C 2011
V
WILEY PERIODICALS, INC.
C
*Correspondence to: Laura L. Shackelford, Department of Anthropology, University of Illinois at Urbana-Champaign, 607 S. Mathews
Ave., 109 Davenport Hall, Urbana, IL 61801.
E-mail: llshacke@illinois.edu
Received 8 March 2011; accepted 11 October 2011
DOI 10.1002/ajpa.21639
Published online 21 December 2011 in Wiley Online Library
(wileyonlinelibrary.com).
228
L.L. SHACKELFORD ET AL.
A cumulative percentage frequency (i.e., percentage of
children having attained or passed each of the 14 stages)
was obtained for each stage of tooth formation. From
these values, mean attainment ages for each stage were
determined, which could then be transformed into chronological ages. The findings from these studies were presented graphically to assess the rate of tooth formation
in living children and to age immature skeletal remains.
The graphs presented in these articles have been
widely cited (for example, Smith, 1991b; Saunders et al.,
1993; Cardoso, 2007; Sciulli, 2007), but unfortunately
the information they contain is difficult to implement in
age estimation without numerical parameters. Smith
(1991b) converted the graphs to actual mean attainment
ages by hand measuring the points in each figure, but
variance data surrounding these age estimates were difficult to assess. Understanding how these graphs were
constructed makes it possible to more effectively convert
the graphical information into parameters that are useful for age estimation.
Fanning (1961) described much of the basis for the
production of these graphs. In her original study, she
scored longitudinal dental formation in 48 males and 51
females, and fit individual probit models to these data
using the logarithm of conception-corrected age (calendar
age plus 0.75 years). These probit models were calculated by the ordinary linear regression of the z-scores for
percentage attainment at particular ages on the log, conception-corrected ages. As is true in probit analysis, the
inverse of the slope of the line can be interpreted as the
standard deviation for the ages at which individuals
move from one stage to the next higher stage. Similarly,
the mean log age at which individuals move to the next
higher stage (or, similarly, the mean age of attainment
for the next higher stage) is the intercept divided by the
slope of the probit regression line. Fanning used these
relationships to draw graphs of the mean and plus and
minus one and two standard deviations for attainment
ages after back-transforming to the original scale and
subtracting the 0.75 years used to correct for conception.
Although she referred to the central points in the graphs
as ‘‘mean attainment ages,’’ they are in fact median
attainment ages when back-transformed to this original
scale.
Moorrees et al. (1963a,b) built on Fanning’s original
work by assuming that there was a common slope for all
probit regression lines, an assumption that they indicate
was ‘‘confirmed by plotting the cumulative frequencies of
the present data on arithmetic probability paper’’ (Moorrees et al., 1963b: 1493). They further state in both studies that the log-scale, conception-corrected standard
deviation (inverse of the probit regression slope) used
was 0.042. The ability to assume a common standard
deviation throughout is one of the primary reasons that
a logarithmic scale for age was used in the Moorrees et
al.’s studies, as the logarithmic scale allows for increasing variance in ages of attainment for stages that occur
later in development. Although Moorrees et al. never
state the basis for the 0.042 value, it was presumably
found by averaging across the many individual probit
analyses they calculated. Despite this omission, the logarithmic scale explains the asymmetry in the graphs,
such that the spans in standard deviation units below
the ‘‘mean’’ (actually, the median) are less than the
spans in standard deviation units above the mean.
Although they did not indicate whether the 0.042 value
was on a natural or a base-10 log scale, it is clear from
American Journal of Physical Anthropology
the value itself that their analyses were done using
base-10 logarithms.
Smith’s (1991b) translation of the graphical information on permanent tooth formation from Moorrees et al.
(1963b) into data for age estimation has been widely
cited and applied. About a decade later, Harris and Buck
(2002) also made a conversion of the Moorrees et al.’s figures from the permanent dentition into data for age estimation. Unfortunately, they neglected the fact that the
logarithmic scale explains the asymmetry in the graphs;
instead, they appear to have measured the length of
each bar from minus and plus two standard deviations
and then divided by four to estimate the standard deviation (which is known to be 0.042 on the common log
scale or 0.0967 on the natural log scale, where ln(10) 3
0.042 5 0.0967 for every graph). They (Harris and Buck,
2002: 16) stated that ‘‘Positions of the means and lengths
of the error bars were obtained with drafting instruments and sliding calipers.’’ In point of fact, some algebra shows that Harris and Buck’s estimates of ‘‘standard
deviations’’ are estimates of the ‘‘mean attainment ages.’’
Specifically, 10.33(SD) 20.75 is approximately equal to
the associated ‘‘mean’’ (actually, median) attainment age.
Harris (2010) used Photoshop CS3 to measure the deciduous dental charts (Moorrees et al., 1963a), but again he
lists the ‘‘standard deviations’’ measured on the straight
scale. Again, these appear to have been obtained by
measuring the length of each bar from minus and plus
two standard deviations and then dividing by four.
Unfortunately, he apparently inadvertently divided by
five for the ‘‘standard deviations’’ from Figures 6 and 7
in Moorrees et al. (1963a), which cover root resorption
and exfoliation. This error also appears to have been
made for the ‘‘root three-quarters’’ complete stage for the
male second deciduous molar. Millard and Gowland
(2002: 202) have also used the Moorrees et al. graphs to
obtain transition ages, writing that: ‘‘the data were
degraphed to obtain mean ages of transition. . .’’ Millard
and Gowland recognized that the standard deviation is
known on the logarithmic scale; however, they neither
indicated how the data were ‘‘degraphed’’ nor provided a
tabling of their obtained values.
This analysis translates the graphical information
from Moorrees et al. (1963a,b) to more usable data for
determining ages of tooth formation. These data are
then applied to dental remains of early modern human
and Neandertal juveniles as a demonstration of how the
Moorrees et al.’s studies can be used both for age estimation and for testing sequencing variation between these
fossil groups and modern humans. It is necessary before
undertaking this study to briefly review some of the
issues surrounding age estimation from dental stages.
Definition of ordered stages
As Roberts et al. (2008) have noted, there is a considerable range in the number of ordered stages defined for
dental formation. For molars, excluding an initial stage
of ‘‘no calcification,’’ there is a three-stage definition
(Garn et al., 1959), a four-stage definition (Gustafson
and Koch, 1974), a five-stage definition (Harris and
Nortje, 1984), a seven-stage definition (Kullman et al.,
1992), an eight-stage definition (Demirjian et al., 1973),
a 10-stage definition (Gunst et al., 2003), a 12-stage definition (Haavikko, 1970), a 14-stage definition (Moorrees
et al., 1963b), a 16-stage definition (Gleiser and Hunt,
ESTIMATING AGE-AT-DEATH FROM DENTAL REMAINS
1955), and a 19-stage definition (Fanning, 1961). In general, these different systems can be viewed as ‘‘collapsed
versions’’ of Gleiser and Hunt’s earlier scoring, though
Fanning’s scoring represents the addition of three root
apex stages to Glesier and Hunt’s system. Two of these
root apex stages were eventually eliminated for the
Moorrees et al.’s studies. The rationale given for collapsing scores in any of the newer systems is to decrease
intraobserver and/or interobserver error in scoring, and
usually Cohen’s kappa coefficient is presented as a measure of repeatability for any scoring used in a given
study (Dhanjal et al., 2006; Liversidge et al., 2006;
Cameriere et al., 2008; Roberts et al., 2008; Butti et al.,
2009; AlQahtani et al., 2010; Blenkin and Evans, 2010;
Liversidge and Marsden, 2010; Maia et al., 2010; Thevissen et al., 2010; Galić et al., 2011). Weighted (also known
as generalized) kappa (Landis and Koch, 1977) is an
appropriate measure of repeatability for ordinal categorical traits, but as Harris (2007) has observed, repeatability is only one of the considerations in choosing a scoring
system. To quote at length from Harris (2007: 99) in this
journal:
Some recent studies suggest that using fewer grades
increases within- and between-observer repeatability.
This doubtlessly is true, but increased repeatability
occurs at the expense of precision. One can easily
appreciate that repeatability is enhanced by reducing
the number of grades because the gaps between adjacent grades become so large that there is little opportunity to confuse the well-separated stages. But, fewer
grades causes each one to encompass greater intervals
of growth and development—and more time (age)
between the grades—so the sample variance, confidence limits, and all other measures of dispersion of
each grade increase, which would appear to be selfdefeating if the (forensic) purpose is to optimize precision of the age estimation.
Harris’ comments were specifically directed in support
of his using the Moorrees et al.’s 14-stage system.
Statistical analysis of ordered stages
Smith (1991b) presented a cogent review of the various
analytical methods available for dental age estimation
based on tooth stages. It is important in looking at any
particular method to dissociate the scoring system used
from the statistical approach, as both the Moorrees et
al.’s and Demirjian et al.’s scoring systems have been
used with a number of different analytical methods. The
Demirjian et al.’s scoring has often been used with a
‘‘maturity scale’’ approach or ‘‘Method F’’ in Smith’s
(1991b) classification. This approach has limited utility
except in the living, where all teeth are available for
study, and it is not generally capable of pin-pointing
deviations in dental formation sequences. The original
maturity scale approach used by Demirjian et al. (1973)
was based on the work of Tanner et al. on skeletal maturity of the hand and wrist, the latest edition of which
was published in 1983 (Tanner et al., 1983). Interestingly, in that last edition, Tanner et al. dispatched with
the use of probit or logit models because of the problem
of potentially nonparallel lines. They (Tanner et al.,
1983: 3) wrote that ‘‘the probit or logit model is not suitable . . . unless the lines for all the stages of each bone
are parallel, and it is found that this is not the case for
229
many bones of the hand and wrist, even when log age or
log postconception age . . . is used.’’
The problem of nonparallel lines in probit or logit
analysis was addressed in two important volumes on
skeletal maturity (Roche et al., 1975, 1988). In these volumes, Roche et al. used cumulative logit regression for
each staged indicator with three or more stages, and
they assumed that each regression within an indicator
had a common slope. Aitchison and Silvey (1957) had
described such a model using cumulative probit regression four years before Fanning’s (1961) publication of
graphs and summary statistics that presaged the Moorrees et al.’s publications. Although a statistical test for
the assumption of parallel lines was not available at the
time of the Moorrees et al.’s publications (they commented that they did a visual comparison of plotted
lines), such a test is now available (Johnson, 1996;
Glewwe, 1997; Weiss, 1997). In the absence of applications of this test to known-age dental data, we have followed Moorrees et al.’s original assumption of a common
slope for all teeth. Boldsen et al. (2002), in what they
refer to as ‘‘transition analysis,’’ used a continuation
ratio model for the cumulative logit that removes the
assumption of parallel lines.
Since the Moorrees et al.’s publications, Anderson et
al. (1976) published a longitudinal study of permanent
tooth formation in 121 boys and 111 girls using the
Moorrees et al.’s stages. Although the total sample size
for the Anderson et al.’s study was actually slightly less
than in the Moorrees et al.’s studies (they used data
from 136 boys and 110 girls, except for the permanent
incisors where they had data from only 48 boys and 51
girls), the Anderson et al.’s study is often used preferentially over the Moorrees et al.’s studies. In large measure, this may be due to the ready availability of summary statistics in the Anderson et al.’s study. Unfortunately, the summary statistics in the Anderson et al.’s
publication are of questionable value because the
authors used what Smith (1991b) has referred to as
‘‘Method B.’’ In ‘‘Method B,’’ interval-censored longitudinal data are analyzed by assuming that events occurred
at the midpoint of the interval or evenly spaced within
the interval if more than one event occurred within an
observation window. This approach to analyzing interval-censored data is well known to be problematic
(Lindsey and Ryan, 1998), and more appropriate methods are available that have been applied to longitudinal
data on dental emergence (Holman and Jones, 1998;
Parner et al., 2001; Bogaerts et al., 2002; Holman and
Jones, 2003; Leroy et al., 2003; Holman and Yamaguchi,
2005; Yamaguchi and Holman, 2010).
Recently, Bayesian analysis has been offered as an advantageous method both for determining dental ages
and for testing for sequence differences against modern
human dental formation schedules (Braga et al., 2005;
Braga and Heuzé, 2007; Heuzé and Braga, 2008; Bayle
et al., 2009a,b). To date, these analyses have used age
categories rather than ages, an approach that Konigsberg and Frankenberg (2002) referred to as ‘‘contingency
table paleodemography’’ because it uses the cross tabulation of skeletal (or in this case dental) stages against age
categories. Although there is a long history of using this
approach, ‘‘contingency table paleodemography’’ has
largely been supplanted by methods that treat age as
continuous. In the Materials and Methods section, we
present the use of parameters from the Moorrees et al.’s
studies in a non-Bayesian setting to estimate probabilAmerican Journal of Physical Anthropology
230
L.L. SHACKELFORD ET AL.
ities of particular dental sequences. We do not present a
Bayesian method for age estimation, as it could be
obtained directly by combining a prior age distribution
with the likelihoods that we obtain from the Moorrees et
al.’s data. In the absence of a reasonable prior distribution, we use a uniform prior so that the resulting posterior age estimates for individuals are maximum likelihood estimates. This is also the approach used by Braga
et al. (2005) who do refer to their age estimates as
‘‘Bayesian predictions.’’
MATERIALS AND METHODS
One of the primary goals of this article was to generate numerical parameters from the graphical data
reported by Moorrees et al. (1963a,b). For this analysis,
all points from all charts in Moorrees et al. (1963a,b)
were digitized using DataThief III, version 1.5
(Tummers, 2006). Usually, five points are available for
each transition, with these being the mean age and plus
and minus one and two standard deviations on the log10
scale, which Moorrees et al. transformed back to the
straight scale. For transitions near birth, it is sometimes
the case that points to the left of the mean are not
included on the graphs, whereas for a few extreme cases
only plus one and plus two standard deviations are
given. Indexing the five points as x[1..5] we have:
lnðx½1 þ 0:75Þ ¼ l 230:0967
lnðx½2 þ 0:75Þ ¼ l 0:0967
lnðx½3 þ 0:75Þ ¼ l
lnðx½4 þ 0:75Þ ¼ l þ 0:0967
lnðx½5 þ 0:75Þ ¼ l þ 230:0967;
ð1Þ
where l is the natural logarithm of the conception-corrected mean attainment age, and 0.0967 is the standard
deviation on the natural log scale. The value of l was
then estimated by least squares for every transition.
Specifically, the digitized points for each transition were
conception-corrected and converted to the logarithmic
scale; subsequently, the right sides of the Eq. (1) were
used as estimates of these points dependent on l, and
the sum of squares for the predicted points around the
digitized points was minimized. We estimated 358 mean
ages of attainment from the Moorrees et al.’s charts.
These ages are available in Table A1.
These updated parameters allow us to estimate age-atdeath of juvenile individuals by using one tooth or multiple teeth as well as examine sequence patterns of dental
development. We assess the efficacy of these parameters
by estimating the age-at-death for four contemporary
human juveniles of known age taken from the literature
(Anderson et al., 1976). We also estimate age-at-death
for several Neandertal and early modern human fossils
and demonstrate how to assess the probability of a dental formation sequence.
Stages of dental development were determined for 66
immature fossil specimens (25 Neandertals and 41 early
modern humans, Table A2) following the methods of
Moorrees et al. (1963a,b). The permanent maxillary incisors and all permanent mandibular dentition as well as
the deciduous mandibular canines and the first and second molars were evaluated using radiographs for each
specimen, as available. Maxillary tooth scores for the canine, premolars, and molars were substituted for manAmerican Journal of Physical Anthropology
Fig. 1. Plot of the digitized ‘‘mean attainment ages’’ from
this study against the estimated mean attainment ages where
the estimate is from a least squares fit of digitized points from
Moorrees et al. (1963a,b) that does not include the mean. The
diagonal line is the line of identity.
dibular scores if the mandibular scores were unavailable.
Each tooth was assigned to a formation stage using the
diagrams provided by Moorrees et al. (1963a,b). The
stages were ‘‘cusp initiation,’’ ‘‘cusp coalescence,’’ ‘‘cusp
outline complete,’’ ‘‘crown half complete,’’ ‘‘crown threequarters complete,’’ ‘‘crown complete,’’ ‘‘root initiation,’’
‘‘root cleft initiation,’’ ‘‘root one-quarter complete,’’ ‘‘root
half complete,’’ ‘‘root three-quarters complete,’’ ‘‘root complete,’’ ‘‘apex half complete,’’ ‘‘apex complete,’’ ‘‘root onequarter resorbed,’’ ‘‘root half resorbed,’’ and ‘‘root threequarters resorbed.’’ Resorption stages are only scored for
deciduous teeth, and cleft initiation applies only to
molars that show no signs of ‘‘taurodontism.’’ The mesial
and distal roots of all molars were scored individually
and, when different, the more advanced score was used.
Radiographs are from Tompkins (1991). In some cases,
comparable dental scores were available from the literature (Skinner and Sperber, 1982). When available, the
scores were compared to those gathered by the authors.
See Table A2 for our final scores, which also includes
scores for 11 fossils from the supplemental materials to
Smith et al. (2010), scores in Bayle et al. (2009b) for the
Roc de Marsal fossil, and scores for four known-age modern humans from Anderson et al. (1976).
RESULTS AND DISCUSSION
Application to known-age individuals
Assessing the accuracy of the Moorrees et al.’s parameters. As all further analyses in this article depend
on the quality of our numerical estimates of ‘‘mean
attainment ages’’ from the Moorrees et al.’s graphs, we
must first examine the quality of our estimates. One
way to do this is to compare our raw digitization of the
‘‘mean attainment ages’’ with our estimates of those
attainment ages. To avoid circularity in this comparison,
we use Eq. (1) for our estimates, but we exclude the
third point (the mean) and use only the plus and minus
one and two standard deviation points. Figure 1 shows a
plot of the digitized mean attainment ages against the
ESTIMATING AGE-AT-DEATH FROM DENTAL REMAINS
Fig. 2. Plot of Harris and Buck’s (2002) mean attainment
ages measured from the Moorrees et al.’s graphs against our
estimates from least squares (including the mean). This graph
is restricted to the range from 7 to 12 years to better show the
erroneous point for the three-quarters root length stage of the
third premolar in girls from Harris and Buck’s study. The original point is shown as a filled circle, whereas the arrow points to
the position that would be estimated from Harris and Buck’s
measure of the ‘‘standard deviation.’’
231
estimated mean attainment age (with the mean itself
excluded from the estimates). The diagonal line in Figure 1 is the line of identity, and the correlation between
the digitized means and the estimated means is 1.0000.
We can also compare Harris and Buck’s (2002), Harris’s (2010), and Smith’s (1991b) measurements of the
mean ages of attainment to our final estimates including
the digitization of the mean attainment ages. In making
this comparison, we found one value from Harris and
Buck’s (2002) Table 2 that was erroneous. For the threequarters root length stage of the third premolar in girls,
Harris and Buck (2002) had a value of 8.8 years versus
Smith’s (1991b) value of 9.2 years and our value of 9.25
years from digitization. Figure 2 shows the erroneous
value from Harris and Buck where we have restricted
the plot to the 7- to 12-year age range. The filled dot
shows the original position of 8.8 years, whereas the tip
of the arrow shows the position of the mean attainment
age if we estimate it from Harris and Buck’s measurement of the ‘‘standard deviation.’’ This value was listed
in their table as 0.97, which gives an estimate (to one
significant digit) when multiplied by 10.3 (and corrected
by 0.75 years for conception) of 9.2 years, identical with
Smith’s (1991b) value. We also found three minor errors
in Smith’s (1991b) Table 8, where she had listed mandibular lateral incisor ages of attainment in girls for ‘‘root
one-half,’’ ‘‘root two-thirds,’’ and ‘‘root three-quarters’’
that were actually for ‘‘root one-third,’’ ‘‘root one-half,’’
and ‘‘root two-thirds.’’ Figure 3 shows a plot of mean
Fig. 3. Lower triangular scatter plot matrix of Smith’s (1991b), Harris and Buck’s (2002), Harris’s (2010), and this study’s
‘‘mean attainment ages’’ obtained from the Moorrees et al.’s charts. The diagonal shows a bar graph giving counts of attainment
ages within single year ‘‘bins.’’ This study has greater counts because it includes both mesial and distal roots for molars and
because it includes both deciduous and permanent teeth. Smith’s study does not include deciduous teeth.
American Journal of Physical Anthropology
232
L.L. SHACKELFORD ET AL.
attainment ages from Harris and Buck (with the one correction cited above) and Harris (2010), from Smith (with
the three ages shifted into their appropriate spots), and
from this study. All studies show good agreement. The
scatter plots for the Smith (1991b) and Harris and Buck
(2002) studies show no points beyond about 14.2 years
because Smith used the distal molar roots from the
Moorrees et al.’s (1963b) graphs, whereas Harris and
Buck (2002) used the mesial molar roots. The scatter
plots comparing this study to the two previous studies
do extend through the full range of dental development
because we included both mesial and distal molar roots
from the Moorrees et al.’s graphs. Also, note that the histogram of attainment ages for this study and for the
combined Harris and Buck (2002) and Harris (2010)
studies shows stronger representation at younger ages
than in the Smith’s (1991b) study. This is because the
deciduous dentition charts from Moorrees et al. (1963a)
are not included in Smith’s study.
Estimating age-at-death from a single tooth using
the Moorrees et al.’s parameters. To motivate this section, we use the stage of the mandibular fourth premolar
from Anderson et al.’s (1976) ‘‘Subject A,’’ which was
scored as ‘‘crown half complete.’’ Subject A was a Canadian boy who was 5 years of age at the time that a cephalogram was made. Table 1 gives the mean (conceptioncorrected) ages of attainment on the natural logarithmic
scale for males and for females at each of 13 formation
stages for the mandibular fourth premolar. The first column of numbers was estimated using the least squares
method described in the previous section. The following
three columns in Table 1 list the mode, median, and
mean attainment ages on the straight scale, less 0.75
years to return the ages to decimal years since birth.
Although they refer to them as ‘‘mean ages of attainment,’’ the median ages of attainment are the values
plotted in the Moorrees et al.’s (1963a,b) articles, as
exponentiating the log mean age of attainment returns
the median, not the mean, on the straight scale. The
mode, median, and mean are found as:
mode ¼ 0:99073 expðlÞ 0:75
median ¼ expðlÞ 0:75
mean ¼ 1:00473 expðlÞ 0:75;
ð2Þ
where the multiplicative constants for the mode and the
mean are found from the known standard deviation of
0.042 on the log10 scale (0.0967 on the natural log scale)
for conception-corrected age. We list these numbers separately for males and for females, but we also average the
male and female log means to apply them to cases where
sex is not known. We use the log-mean conception ages
(‘‘Ln mean’’ from Table 1) for all further work here, and
only provide the mode, median, and mean on the original scale to show the result of Moorrees et al. assuming
a (nonsymmetric) logarithmic distribution for attainment
ages. When we present ages converted to the original
scale (for example, in Table 2) these are always listed for
the median age. The other conversions shown in Eq. (2)
can be used if a researcher wants the modal or mean
ages. Smith (1991b) analyzed the data from Subject A,
as well as B to D, under both the correct sex and the
incorrect sex. As we are ultimately considering a relatively large number of fossils for whom sex is not known,
we simplify by averaging attainment ages.
American Journal of Physical Anthropology
TABLE 1. Attainment ages in years for 13 stages of formation
in the fourth premolar, taken from graphs in Moorrees et al.
(1963b) and listed for males, females, and the average of male
and female values
Stage
Ln mean
Males
C.i
1.2776
C.co
1.4063
C.oc
1.5719
Cr.5
1.6703
Cr.75
1.7858
Cr.c
1.9206
R.i
2.0103
R.25
2.1259
R.5
2.3037
R.75
2.4314
R.c
2.5039
A.5
2.5885
A.c
2.7031
Females
C.i
1.2557
C.co
1.4709
C.oc
1.6041
Cr.5
1.7191
Cr.75
1.8251
Cr.c
1.9340
R.i
2.0245
R.25
2.1198
R.5
2.2638
R.75
2.3854
R.c
2.4439
A.5
2.5535
A.c
2.6745
(Male 1 Female)/2
C.i
1.2667
C.co
1.4386
C.oc
1.5880
Cr.5
1.6947
Cr.75
1.8055
Cr.c
1.9273
R.i
2.0174
R.25
2.1229
R.5
2.2838
R.75
2.4084
R.c
2.4739
A.5
2.5710
A.c
2.6888
Mode-0.75
Median-0.75
Mean-0.75
2.80
3.29
4.02
4.51
5.16
6.01
6.65
7.55
9.17
10.52
11.37
12.44
14.04
2.84
3.33
4.07
4.56
5.21
6.07
6.72
7.63
9.26
10.63
11.48
12.56
14.18
2.85
3.35
4.09
4.59
5.24
6.11
6.75
7.67
9.31
10.68
11.54
12.62
14.25
2.73
3.56
4.18
4.78
5.40
6.10
6.75
7.50
8.78
10.01
10.66
11.98
13.62
2.76
3.60
4.22
4.83
5.45
6.17
6.82
7.58
8.87
10.11
10.77
12.10
13.75
2.78
3.62
4.25
4.86
5.48
6.20
6.86
7.62
8.91
10.16
10.82
12.16
13.82
2.77
3.43
4.10
4.64
5.28
6.06
6.70
7.53
8.97
10.26
11.01
12.21
13.83
2.80
3.46
4.14
4.69
5.33
6.12
6.77
7.60
9.06
10.37
11.12
12.33
13.96
2.82
3.48
4.17
4.72
5.36
6.15
6.80
7.64
9.11
10.42
11.17
12.39
14.03
‘‘Ln mean’’ is the natural logarithm of the conception-corrected
age, whereas the next three columns are the modal, median,
and mean ages of attainment on the original scale.
Using the average of the male and female values in
the first column of Table 1, and knowing that Subject A’s
mandibular fourth premolar has a crown that is half
formed, we can find the probability at any given age that
this individual would have a fourth premolar in
this stage. Realizing that the Moorrees et al.’s studies
used a cumulative probit model, the probability at
any age that an individual would be in stage ‘‘Cr.5’’ can
be expressed as:
pðCr:5jageÞ ¼ /ðage; 1:6947; 0:0967Þ /ðage; 1:8055; 0:0967Þ;
ð3Þ
where / is the lower tail of a normal integral, age is
measured in the natural log, conception-corrected scale,
and we are using the average of the male and female
values for the mean attainment ages. It is generally simpler to work directly with the cumulative log-normal dis-
233
ESTIMATING AGE-AT-DEATH FROM DENTAL REMAINS
TABLE 2. Estimated values for four known age individuals from Anderson et al. (1976) and for the Roc de
Marsal fossil (Bayle et al., 2009b)
Individual and teeth
Subject ‘‘A’’ (5 years)
P4
P4 and M1
P4 to M2
P3 to M2
C to M2
I2 to M2
I1 to M2
Subject ‘‘B’’ (10 years)
I1 to C
P3 to M3
I1 to M3
Subject ‘‘C’’ (4.3 years)
I2 to P4, M2
I1 to M2
Subject ‘‘D’’ (7 years)
I1, I2, C
P3, P4, M1, M2
I1 to M2
Roc de Marsal
M1
M1, dm2
M1, dm2, dc
C, P3
dm1
C, P3, dm1
dc, dm2, C, P3, M1
Mean Var. within Var. between
P(seq.)
P(max)
P prop.
22 SD 21 SD Median 11 SD 12 SD
1.750
1.736
1.719
1.743
1.722
1.710
1.713
0.0104
0.0051
0.0034
0.0025
0.0021
0.0019
0.0016
0.0004
0.0010
0.0030
0.0049
0.0049
0.0039
0.4331
0.1382
0.0427
0.0140
0.0049
0.0032
0.0015
0.4331
0.1382
0.0458
0.0220
0.0085
0.0072
0.0032
1.0000
0.9323
0.6364
0.5765
0.4444
0.4688
3.94
4.14
4.14
4.18
3.98
3.94
4.03
4.45
4.52
4.47
4.56
4.40
4.34
4.40
5.00
4.92
4.83
4.96
4.85
4.78
4.80
5.62
5.36
5.21
5.40
5.33
5.25
5.22
6.31
5.83
5.62
5.88
5.86
5.77
5.68
2.279
2.385
2.348
0.0042
0.0023
0.0012
0.0024
0.0020
0.0052
0.0420
0.0022
\0.0001
0.2209
0.0077
0.0030
0.1901
0.2857
0.0134
7.55
8.77
8.17
8.25
9.42
8.91
9.02
10.11
9.71
9.84
10.85
10.59
10.74
11.63
11.53
1.535
1.568
0.0027
0.0019
0.0043
0.0100
0.0250
0.0017
0.0950
0.0473
0.2632
0.0359
3.18
3.11
3.52
3.55
3.89
4.05
4.30
4.60
4.74
5.22
2.141
1.987
2.054
0.0034
0.0026
0.0019
0.0027
0.0039
0.0100
0.0253
0.0223
\0.0001
0.0700
0.0275
0.0071
0.3614
0.8109
0.0110
6.53
5.46
5.52
7.12
5.98
6.24
7.76
6.54
7.05
8.45
7.16
7.95
9.20
7.82
8.95
1.137
1.056
1.028
1.389
1.938
1.567
1.157
0.0118
0.0053
0.0034
0.0068
0.0180
0.0039
0.0022
0.6279
0.0776
0.0186
0.4888
0.9039
0.0008
\0.0001
0.6279
0.2313
0.3355
0.1278
0.1455
0.4888
1.0000
0.9039
0.2732
0.0029
0.0864 \0.0001
1.76
1.49
1.51
2.57
4.56
1.77
1.33
2.05
1.79
1.77
2.90
5.32
2.72
1.82
2.37
2.12
2.05
3.26
6.19
4.04
2.43
2.72
2.51
2.36
3.66
7.19
5.86
3.18
3.12
2.94
2.70
4.10
8.33
8.37
4.12
0.0103
0.0077
0.0022
0.0995
0.0431
For the known age individuals, ages are given within parentheses. ‘‘Mean’’ is the estimated mean age on a natural log, conceptioncorrected scale, whereas the ‘‘var. within’’ and ‘‘var. between’’ are the estimated components of variance in age within and between
teeth. ‘‘P(seq.)’’ is the probability of the tooth sequence at the estimated age, ‘‘P(max)’’ is the probability of the most likely sequence
at the estimated age, and ‘‘P prop.’’ is the proportion of ‘‘P(seq.)’’ out of ‘‘P(max).’’ The remaining columns give the estimated median
age and plus and minus one and two standard deviations on the straight scale not corrected for conception. For Subjects ‘‘A’’ to ‘‘D,’’
the bold values are for all available teeth.
tribution, which can be obtained in Excel C using
LOGNORMDIST or in ‘‘R’’ using plnorm. If we assume
an uninformative prior (in other words, all ages are
equally likely), then we can use Bayes’ theorem to invert
this probability into a probability density function for
age, which gives:
(natural log scale, conception-corrected) age, we can
search either Eq. (3) or (4) across age for their maxima.
To find the variance from Eq. (4), we have:
var ¼
Z h
ðmean ageÞ2 3 f ðagejCr:5Þ
i
ð5Þ
age
pðCr:5jageÞ
f ðagejCr:5Þ ¼ R
:
pðCr:5jageÞ
ð4Þ
age
Note that although we use Bayes’ theorem here, our
estimate will not be Bayesian because we have assumed
a uniform prior. In other words, we have assumed that
the likelihood completely dominates the prior, so that
our age estimate will be a maximum likelihood estimate.
Box and Tiao (1973: 73) make this point writing that ‘‘if
the likelihood function can be plotted in an appropriate
metric, it is identical with the posterior distribution
using a noninformative prior.’’
Because Eq. (3) is a difference of two normal cumulative densities, it follows that the density function in Eq.
(4) should also specify a normal density, an assumption
we examine in the next section. Figure 4 shows a plot of
Eq. (4) as a solid line and a fitted (log)-normal density as
a series of filled points. These curves are indistinguishable. Figure 4 was drawn using an ‘‘R’’ script called
‘‘get.age,’’ which is available from https://netfiles.uiuc.edu/lylek/www/SSK2011.htm. This site provides all of
the scripts for various calculations in this article as well
as scripts to draw all of the figures. To find the mean
From Table 2 we have the (natural) log scale, conception-corrected mean and variance of age for Subject A
from the fourth premolar alone listed as 1.75 and
0.0104, respectively. These correspond to 2.3, 50, and
97.7% percentiles of age of 3.94, 5.00, and
6.31 years,
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
respectively, calculated as expð1:75 2 0:0140Þ 0:75
for the 2.3 and 97.7% points and exp(1.75)20.75 for the
50% (median) point. This median age of 5.0 years agrees
with the known age of 5.0 years.
Some comments are in order here concerning the earliest (cusp initiation) and latest (apex closure) stages. As
we have previously mentioned, Table 1 lists the mean
log conception-corrected ages of attainment for 13 stages
of the fourth premolar. To have estimated attainment
age for cusp initiation, there would had to have been
another radiographic stage, which is the presence of a
dental crypt with the absence of any tooth calcification
(a ‘‘stage 0’’ if we were to number stages with cusp initiation being stage 1). Although this stage can be scored
on radiographs of living children, we do not score ‘‘stage
0’’ in fossils because of uncertainty over whether fragile
cusp tips have preserved. In contrast, apex closure can
be, and often is, scored on fossil teeth. We refer to this
American Journal of Physical Anthropology
234
L.L. SHACKELFORD ET AL.
Fig. 4. Probable age distribution for Anderson et al.’s (1976)
Subject ‘‘A’’ based solely on the fourth premolar (observed to
have a crown that was half complete). The solid curve is drawn
using the likelihood from a cumulative log-probit, whereas the
filled circles are from the log-normal that best fits the solid
curve. The vertical line shows the known age of 5.0 years.
as ‘‘stage 14’’ on all teeth to account for a ‘‘stage 8’’ (root
cleft initiation) that can only be scored on molars. Consequently, our stage numbering scheme for permanent uniradicular teeth is 1–7 and 9–14, a system that appears
to deviate slightly from Anderson et al. (1976) where all
teeth are scored on a scale of 1 to 14. A tooth that is in
its final stage provides an age density which is open to
the right.
The assumption of a (log)-normal distribution for
an estimated age. Our assumption that a log normal
can be used to model the distribution of estimated age
for an individual is based on the idea that mean ages of
attainment within a tooth are not widely separated. For
‘‘Subject A’’ this was the case, as the median age of
attainment for the fourth premolar half-crown stage is
4.69 years and for the three-quarters stage is 5.33 years
(a difference of 0.64 years). When attainment ages for
adjacent stages are widely separated, the assumption of
a log-normal distribution for the estimated age is unreasonable. We show this for a second deciduous molar that
has the apex of its roots complete (such as is the case for
Skhul I), which has a median age of attainment at 2.94
years, but where the roots have not begun to resorb,
which has a median age of attainment at 6.33 years for
one-quarter resorption. This is a difference of 3.39 years,
which leads to the cumulative probit giving a very platykurtotic curve relative to the log-normal distribution.
This is shown in Figure 5 where the platykurtotic curve
from the cumulative probit is a solid line, whereas the
log-normal distribution that best fits the cumulative
probit is shown as a dashed line. To check the assumption that the estimated age follows a log-normal distribution, we always make a visual inspection, such as
those shown in Figures 4 and 5, before accepting age
estimates.
Estimating age-at-death from multiple teeth using
the Moorrees et al.’s parameters. Continuing with the
example of ‘‘Subject A,’’ scores are available for all of the
American Journal of Physical Anthropology
Fig. 5. Probable age distribution for an individual whose
second deciduous molar is in the ‘‘apex complete’’ stage. The
solid line is the likelihood curve, whereas the dashed line is the
best-fitting log-normal distribution.
mandibular permanent dentition except for the third
molar. Figure 6 (drawn using the ‘‘R’’ script plot.teeth)
shows a plot of the ‘‘normed likelihoods’’ (Lindsey, 1995:
73) for the observed teeth on a plot that we use to assess
all individuals. The normed likelihood is determined by
scaling Equation (4) so that the likelihood function at
the maximum likelihood (for each tooth) is equal to 1.0.
As a consequence, the curves shown for the teeth in Figure 6 have the same height. From Moorrees et al.
(1963b), the first stage within the mandibular incisors
that has an attainment age is ‘‘root one-quarter complete.’’ As a consequence, for the first lower incisor from
‘‘Subject A’’, which was in the ‘‘root one-quarter complete’’ stage, the age distribution is bounded on the left
and on the right. For the second mandibular incisor,
which was in the ‘‘root initiation’’ stage, the age distribution is open to the left. To convert the estimates from all
teeth to a single age estimate, we assume conditional independence (Lucy et al., 2002) and multiply the raw likelihoods together. We then divide by the integral of this
product to convert the quantity to a proper probability
density function. Figure 7 shows the probability density
function as a solid line and the fitted log-normal curve
as filled points. Again, these curves are indistinguishable. Figure 7 also shows a dashed curve, which is
drawn using the sum of within-tooth and between-tooth
variances, as we describe below.
When an age estimate is based on a single tooth, there
is a single variance term that represents uncertainty in
age due to variance in age of attainment and to separation of the mean attainment ages for entering a stage as
versus leaving a stage. We refer to this as the withintooth component of variance. When an age estimate is
based on two or more teeth, the within-tooth variance
component remains, but it decreases with the addition of
information from each additional tooth. The easiest way
to see this relationship is to consider the precision of the
final estimate, which is formally defined as the inverse
of the variance of the estimate. Because we have
assumed conditional independence between all teeth, the
ESTIMATING AGE-AT-DEATH FROM DENTAL REMAINS
Fig. 6. Plot of ‘‘normed’’ likelihoods (Lindsey, 1995: 73) for
all mandibular teeth observed in Anderson et al.’s (1976)
Subject ‘‘A,’’ a 5-year-old boy. The vertical line represents the
known age.
sum of the individual tooth precisions is equal to the
overall precision, which is the inverse of the total
within-tooth variance component. For example, in Figure
4, the precision of age from the mandibular fourth premolar is calculated (rounding to two digits) at 96.39. The
inverse of 96.39 is 0.0104, which is the variance of
the log-normal distribution represented in Figure 4. For
the remaining teeth, the precision from the first incisor
is 94.43, from the canine it is 89.54, from the third premolar it is 94.99, from the first molar it is 101.00, and
from the second molar it is 100.63 (see Table 5 for all
precision values). Summing these precisions gives a total
of 576.98, and taking the inverse of that value gives an
overall within-tooth variance component of 0.0017, which
agrees well with the value of 0.0016 given in Table 2.
The proportion of individual tooth precisions out of the
total precision can also be used as weights to find the
overall (log-scale) mean age. For ‘‘Subject A,’’ we have
(94.43 3 1.72 1 89.54 3 1.63 1 94.99 3 1.82 1 96.39 3
1.75 1 101.00 3 1.72 1 100.63 3 1.69)/576.98 (see
Table 6 for log-scale means) which equals 1.7223 (4.85
years). This agrees well with the value from Table 2 of
1.713 (4.80 years), and both agree well with the true age
of 5.0 years.
There are two potential problems with this approach.
First, we have the problem of the effects of violation of
conditional independence on the estimated log-mean age
and its variance. Although violation of conditional independence (i.e., having nonzero residual covariances
between tooth formation stages after removing the effect
of age) should not cause bias in estimation of the logmean age, it will cause underestimation of the variance
of the age estimate. As a consequence, any residual correlation between teeth after partialing out the effect of
age will lead to interval estimates for age that are too
narrow. Thevissen et al. (2010) have presented an analysis that does not assume conditional independence, but
235
Fig. 7. Probable age distribution for Anderson et al.’s Subject ‘‘A’’ based on the teeth shown in Figure 6. The solid line is
the combined likelihood curve across the teeth, whereas the
filled circles show the best-fitting log-normal distribution.
The dashed line shows the final age distribution, which includes
the between-tooth component of variance. The vertical line at 5
years represents the actual age of the individual.
in the absence of the raw data or any of the covariances
from Moorrees et al.’s studies, we cannot address the
problem of assuming conditional independence. The second problem with our approach so far is that the
increase in precision that comes from using additional
teeth does not take into account the between-tooth component of variance in the age estimates. In the calibration literature (see Brown, 1982; Brown and Sundberg,
1987; Brown, 1993), this problem is handled so that the
variance in the final estimate increases if the individual
estimators give disparate answers. To account for this
additional component of variance, we calculate the
between-tooth component of variance as the variance
between the log mean conception-corrected ages from
individual teeth (see Table 6 for these values). The
dashed line in Figure 7 shows the within-tooth plus the
between-tooth components of variance around the median age estimate. From Table 2, we can calculate the
estimated age plus or minus half a standard deviation
using all available teeth from the four known-age individuals in Anderson et al. (1976). If we do so, the actual
age is within plus or minus a half standard deviation of
the estimated age for all four individuals if we use the
combined within- and between-tooth components of variance to get the standard deviation. Using only the
within-tooth component of variance, the estimated age
plus or minus a half standard deviation includes the
actual age for Subject ‘‘D’’ but not for the remaining
three known-age individuals.
Application to fossil specimens of unknown age
Estimating age-at-death from multiple teeth using
the Moorrees et al.’s parameters. Table 3 contains age
estimates for the fossils in Smith et al.’s (2010) study,
whereas Table 4 contains estimates from radiographs
used in this study. It will be useful to look in detail at
one particular fossil, for which we use the Roc de Marsal
American Journal of Physical Anthropology
236
L.L. SHACKELFORD ET AL.
TABLE 3. Estimated values for 11 fossils from Smith et al. (2010)
Fossil
Mean
Var. within
Var. between
P prop.
22 SD
21 SD
Median
11 SD
12 SD
Engis 2 (3.0 years)
Gibraltar 2 (4.6 years)
Irhoud 3 (7.8 years)
Krapina Max B (?)
Krapina Max C (?)
La Quina H18 (?)
Le Moustier (11.6–12.1 years)
Obi Rakhmat (6.0–8.1 years)
Qafzeh 10 (5.1 years)
Qafzeh 15 (?)
Scladina (8.0 years)
1.711
1.734
2.008
1.937
2.319
1.905
2.837
2.197
1.783
2.059
2.412
0.0023
0.0013
0.0016
0.0017
0.0045
0.0017
0.0064
0.0022
0.0012
0.0017
0.0022
0.0441
0.0110
0.0032
0.0091
0.0186
0.0055
1.0000
0.5014
0.7770
0.0387
0.4122
0.0819
0.0188
0.0100
0.0073
0.0054
0.0522
0.1006
0.0636
0.2779
2.85
3.79
5.73
4.89
6.75
4.92
13.79
5.98
4.06
5.73
8.62
3.71
4.32
6.20
5.50
7.98
5.42
15.00
7.03
4.60
6.38
9.47
4.78
4.91
6.70
6.19
9.42
5.97
16.31
8.25
5.20
7.09
10.41
6.11
5.58
7.23
6.95
11.08
6.56
17.74
9.65
5.86
7.87
11.42
7.76
6.32
7.81
7.79
13.03
7.21
19.28
11.27
6.60
8.73
12.53
See Table 2 for explanation of column headings. Ages in parentheses are Smith et al.’s histological ages (from their Table 1),
whereas the tooth scores used here are from Smith et al.’s supplemental materials, with the exception that scores of ‘‘8’’ for uniradicular teeth were adjusted to ‘‘7’’ or ‘‘9’’ (see Table A2). This table excludes the third molar of Scladina from the estimate. The
means and variances are in log (conception-corrected) years, whereas the median and plus/minus one and two standard deviations
are in decimal years since birth.
Neandertal as it is included both in our radiographs from
Tompkins and is the basis for a recent study (Bayle et al.,
2009b). Our scoring of the teeth from this fossil is quite
similar to the published scoring (Bayle et al., 2009b), with
the exception of the score for the second deciduous molar.
We scored this tooth as being in the ‘‘root complete’’ (but
apex open) stage, whereas Bayle et al. (2009b) scored the
tooth as being in a root resorption stage. In the next section of this article, we examine this scoring issue as part
of a presentation of results from calculating relative probabilities of dental formation sequences. In this section of the
article, we use our scores from Tompkins’ radiographs
rather than Bayle et al.’s scores from microtomography.
The mandibular second deciduous molar and the mandibular first permanent molar were scored as having the ‘‘root
apex complete’’ and ‘‘crown complete,’’ respectively. Figure
8 (drawn using the ‘‘R’’ script plot.teeth) shows a plot of
the ‘‘normed likelihoods.’’ We again assume conditional independence and convert the estimates from both teeth to a
single age estimate by multiplying the raw likelihoods together. Dividing by the integral of this product converts
the quantity to a proper probability density function (Fig.
9). In this figure, the probability density function is shown
as a solid line, and the fitted log-normal curve is shown as
filled points with the curves indistinguishable.
We can assess the overall precision of the final estimate, which is the inverse of the total within-tooth variance component. The sum of the precision values (from
Table 5) for each tooth is 440.35 (102.03 from the deciduous canine, 15.47 from the deciduous first molar, 93.17
from the deciduous second molar, 62.89 from the canine,
82.30 from the third premolar, and 84.49 from the first
molar). The reciprocal of the total precision value of
440.35 is 0.002, which agrees with the within-tooth
variance from Table 4. The individual tooth precisions
can also be used as weights to find the overall (log-scale)
mean age, where the individual tooth log-scale mean
ages are from Table 6. For Roc de Marsal, we have
102.03 3 0.977 1 15.47 3 1.370 1 93.17 3 1.082 1
62.89 3 1.160 1 82.30 3 1.179 1 84.49 3 1.137, which
equals 487.74. Dividing this sum by the total precision,
we have 487.74/440.35 1.108, which agrees well with
the mean from Table 4 of 1.100. The between-tooth variance we have already explained is the variance of the
mean attainment ages across teeth, which is 0.017.
Therefore, for Roc de Marsal, we have an estimated log
conception-corrected age of 1.108 with a total variance of
0.019. These values convert to ages on the original scale
American Journal of Physical Anthropology
that differ from the last five columns in Table 4 by a
maximum of only 11 days. In general, Tables 5 and 6
can be used to estimate the full distribution of age-atdeath without having to resort to the likelihood calculations that underlie both the ‘‘plot.age’’ graphs and the
exact values shown in Table 4.
Relative probability of a dental formation
sequence. An additional problem that has recently
received considerable attention in the literature is the calculation of the probability of observing particular dental
sequences given known-age reference information (Braga
and Heuzé, 2007; Heuzé and Braga, 2008; Bayle et al.,
2009a,b; Bayle et al., 2010). The Roc de Marsal Neandertal serves as a useful example, as Bayle et al. (2009b)
have examined this probability using synchrotron radiation microtomography, while we can also assess the probability of the dental sequence using Tompkins’ radiographs. Bayle et al. scored the mandibular first permanent molar as being in a Demirjian et al. (1973) stage
‘‘D,’’ which is equivalent to Moorrees et al.’s ‘‘root initiation’’ stage (Liversidge and Marsden, 2010). We scored
this same tooth from Tompkins’ radiographs at the
slightly earlier ‘‘crown completion’’ stage. To find the probability of obtaining the observed configuration of six permanent teeth for the Roc de Marsal fossil, Bayle et al.
used the frequency data from a reference sample after
conditioning on various combinations of teeth. There are
2622 5 62 ways to partition six teeth into a dependent
set and an independent set on which to condition.
For their analysis, Bayle et al. (2009b: 71) evaluated
47 of these ‘‘62 theoretically possible probabilities.’’
Although not specifically mentioned here, elsewhere
Braga and Heuzé (2007) described a bootstrap that they
applied to sample the probabilities from their reference
data. Considering the last of the 47 probabilities, Bayle
et al. (2009b) evaluated in their Figure 3, and following
Braga and Heuzé (2007), we have:
PrðDjC; C; C; B; 0Þ
PrðC; C; C; B; 0jDÞ3 PrðDÞ
P
¼
;
PrðC; C; C; B; 0jiÞ3 PrðiÞ
PrðC; C; C; B; 0jDÞ3 PrðDÞ þ
i6¼D
ð6Þ
where the mandibular first incisor through the canine
were in stage ‘‘C’’ of Demirjian et al.’s (1973) scoring, the
third premolar was in stage ‘‘B,’’ the fourth premolar
237
ESTIMATING AGE-AT-DEATH FROM DENTAL REMAINS
TABLE 4. Estimated values for 66 fossils in this study
Mean Var. within Var. between P(seq.) 22 SD 21 SD Median 11 SD 12 SD
Fossil
AbriPataud 26.230 B
AbriPataud 26.236
AreneCandide (young prince)
AreneCandide VB
AreneCandide VIII
AreneCandide XI
Atapuerca 2
Badegoule #3
Barma Grande adolescent 3, 4
Barma Grande child
Brillenhöhle
Chateauneuf-sur-Charente 2
CombeGrenal I
Ehringsdorfjuvenile
Fontéchevade 1957-53
Grotte du Rousset
Hohlenstein infant #1
Hortus 2
Isturitz III (1937) 1950-7
Isturitz III 1937—5-1
Isturitz III 1950-6
Kostenki XVIII
Kostenski XV
Krapina #45 and 45.1 (Max A)
Krapina #46 (Max B)
Krapina #47 (Max C)
Krapina #51 (M and A)
Krapina #52 (M and B)
Krapina #53 (M and C)
Krapina #54 (M and D)
Krapina #55 (M and E)
La Ferrassie 8
La Genière #3 1926
La Madeleine child (#4)
La Quina H18 (75372)
La Quina Q-761 (child)
La Chaud 3
Laugerie-Basse 1
Laugerie-Basse 2
Laugerie-Basse 3
Laugerie-Basse 6
Laugerie-Basse teen
Le Fate II
Le Placard 56029
Le Placard 61397
Le Placard 61401 (D.G. #31/32)
Le Placard 61401 (D.G. #40)
Le Placard 61401-61397
Mal’ta child (older)
Mal’ta child (younger)
Mas d’Azil
Montgaudier 3
Paglicci adolescent (2)
Parpallo I
Pech de l’Aze
Qafzeh 11
Qafzeh 4
Qafzeh 10
Roc de Marsal
Rochereil 1945-18
Saint Germain La Rivière 1970-8
Saint Germain La Rivière 1970-8
Saint Germain La Rivière 1970-8
Saint Germain La Rivière 1970-8
Skhul I
Skhul X
B3
B4
B5
B6
1.760
1.935
2.853
1.252
1.900
0.999
2.634
1.550
2.734
2.390
2.017
1.872
1.944
2.540
1.734
1.750
0.710
2.188
0.999
1.854
1.716
2.388
1.859
2.101
1.843
2.396
1.898
2.185
2.464
2.669
2.549
0.753
1.862
1.317
1.833
1.861
2.824
1.817
1.447
1.813
1.227
2.364
2.090
1.988
2.791
2.305
1.526
2.100
0.783
0.361
1.720
2.144
2.573
2.705
0.817
2.354
1.949
1.845
1.100
0.856
1.964
2.060
1.746
and B7 1.814
1.269
1.595
0.005
0.002
0.008
0.004
0.001
0.003
0.010
0.003
0.004
0.003
0.002
0.001
0.002
0.003
0.003
0.010
0.003
0.003
0.004
0.002
0.002
0.002
0.001
0.003
0.003
0.010
0.002
0.002
0.003
0.004
0.003
0.004
0.002
0.004
0.002
0.003
0.008
0.002
0.005
0.002
0.003
0.002
0.002
0.002
0.007
0.003
0.005
0.003
0.003
0.005
0.004
0.002
0.003
0.006
0.003
0.002
0.001
0.003
0.002
0.004
0.003
0.003
0.002
0.003
0.006
0.005
0.029
0.010
0.318
0.116
0.018
0.010
0.040
0.279
0.256
0.456
0.007
0.010
0.005
0.007
0.007
0.008
0.009
0.003
0.531
0.282
0.099
0.169
0.215
0.793
0.193
1.000
0.014
0.010
0.017
0.014
0.014
0.001
0.010
0.015
0.001
0.342
0.201
0.181
0.222
0.228
0.568
0.310
0.141
0.682
0.029
0.004
0.014
0.201
0.845
0.195
0.008
0.018
0.005
0.007
0.005
0.009
0.558
0.188
0.147
0.778
0.687
0.254
0.015
0.020
0.014
0.012
0.001
0.005
0.003
1.000
0.695
1.000
0.472
0.268
0.337
0.898
0.008
0.004
0.012
0.010
0.012
0.013
0.008
0.013
0.444
1.000
1.000
0.324
0.163
1.000
0.169
0.213
0.012
0.008
0.006
0.002
0.017
0.006
0.011
0.008
0.026
0.006
0.123
0.044
0.199
0.274
0.543
0.593
0.223
0.837
0.225
0.100
0.530
0.924
0.305
0.641
3.26
4.80
13.77
1.86
4.68
1.05
10.69
3.09
11.40
8.44
5.47
4.68
4.96
9.47
4.12
3.94
0.82
6.39
1.28
4.20
3.56
8.97
4.46
5.51
4.81
8.27
3.92
6.90
8.31
11.95
9.66
0.83
4.69
2.26
4.53
4.45
13.41
4.00
2.34
3.99
1.92
8.76
6.04
5.64
13.01
7.36
3.04
5.62
1.00
0.35
3.57
6.24
9.45
12.03
1.02
7.83
5.13
4.68
1.53
1.18
4.89
5.62
3.34
4.35
0.98
2.41
4.08
5.45
15.11
2.27
5.28
1.46
11.87
3.50
12.93
9.27
6.08
5.19
5.57
10.63
4.50
4.45
1.04
7.23
1.60
4.87
4.15
9.54
5.03
6.40
5.18
9.20
4.84
7.50
9.57
12.78
10.79
1.08
5.17
2.60
5.00
5.03
14.69
4.65
2.87
4.64
2.27
9.31
6.66
6.08
14.22
8.27
3.42
6.46
1.21
0.51
4.16
6.97
10.81
13.08
1.25
8.76
5.68
5.11
1.87
1.38
5.59
6.32
4.09
4.84
1.73
3.20
5.06
6.17
16.58
2.75
5.94
1.96
13.17
3.96
14.65
10.16
6.76
5.75
6.24
11.92
4.91
5.00
1.28
8.17
1.97
5.64
4.81
10.14
5.67
7.43
5.57
10.23
5.92
8.14
11.00
13.68
12.04
1.37
5.69
2.98
5.50
5.68
16.10
5.40
3.50
5.38
2.66
9.89
7.33
6.55
15.54
9.28
3.85
7.41
1.44
0.68
4.83
7.78
12.36
14.20
1.51
9.78
6.27
5.58
2.25
1.60
6.38
7.10
4.98
5.38
2.81
4.18
6.25
6.98
18.19
3.30
6.67
2.58
14.61
4.47
16.58
11.13
7.51
6.36
6.98
13.36
5.36
5.62
1.56
9.22
2.39
6.50
5.57
10.77
6.38
8.59
5.98
11.37
7.22
8.84
12.64
14.63
13.43
1.71
6.25
3.40
6.05
6.40
17.62
6.25
4.24
6.21
3.11
10.50
8.07
7.05
16.98
10.40
4.32
8.49
1.70
0.89
5.60
8.68
14.11
15.42
1.81
10.92
6.93
6.08
2.70
1.85
7.26
7.96
6.03
5.97
4.34
5.40
7.68
7.88
19.94
3.94
7.49
3.35
16.19
5.03
18.77
12.20
8.33
7.03
7.81
14.97
5.83
6.31
1.88
10.39
2.88
7.49
6.44
11.45
7.16
9.93
6.42
12.62
8.78
9.60
14.50
15.64
14.97
2.10
6.86
3.87
6.65
7.20
19.29
7.22
5.10
7.16
3.61
11.15
8.88
7.59
18.54
11.65
4.84
9.71
1.99
1.12
6.47
9.67
16.10
16.74
2.14
12.17
7.64
6.62
3.21
2.12
8.26
8.92
7.28
6.62
6.55
6.93
See Table 2 for explanation of column headings. The third molar scores were dropped for ‘‘Laugerie-Basse teen’’ and Qafzeh 11. The
means and variances are in log (conception-corrected) years, whereas the median and plus/minus one and two standard deviations
are in decimal years since birth.
American Journal of Physical Anthropology
238
L.L. SHACKELFORD ET AL.
Fig. 8. Plot of ‘‘normed’’ likelihoods for the Roc de Marsal
Neandertal child. Scoring of each tooth is shown to the right of
the graphs.
was in stage ‘‘0’’ (no calcification), and the first molar, as
previously mentioned, was in stage D. The sum across
i = D is for stages 0, A, B, C, E, F, G, and H of the first
molar. Braga and Heuzé (2007: 254) state: ‘‘we assume
that each mineralization stage has the same prior probability to be observed’’ and as they further note the prior
probabilities cancel so that
PrðDjC; C; C; B; 0Þ
is just the frequency of individuals in the reference sample who have the C, C, C, B, 0, D sequence out of the
individuals in the reference sample who have the C, C,
C, B, 0, — sequence without regard to the score for the
last tooth (the mandibular molar). Note that if a
sequence in the denominator does not exist then the
probability is undefined (the reason that Bayle et al.
(2009b) are missing 15 of 62 possible combinations), and
that if the denominator sequence exists but the numerator sequence does not then the probability is 0.0. Bootstrapping will have no effect on either situation. Bootstrap sampling for a nonzero probability will recover the
standard error for the estimate of the probability, but
this could also be approximated using the binomial distribution.
Using the Moorrees et al.’s (1963a,b) parameters we
take a different approach from Braga and Heuzé (2007)
for calculating sequence probabilities. First, note that in
Braga and Heuzé’s method the reference sample need
not be from known-age individuals, so their method does
not benefit from the known ages. Also, note that their
(Braga and Heuzé, 2007: 254) assumption ‘‘that each
mineralization stage has the same prior probability to be
observed’’ is difficult to support. If we assume a uniform
age distribution then the probability of being in each
mineralization stage is determined by the separation in
mean attainment ages. As an example, integrating
across a uniform age distribution from conception to age
American Journal of Physical Anthropology
Fig. 9. Probable age distribution for the Roc de Marsal
Neandertal child based on the teeth shown in Figure 8. The
solid line is the combined likelihood curve across the teeth,
whereas the filled circles show the best-fitting log-normal distribution. The dashed line shows the final age distribution, which
includes the between-tooth component of variance.
25, we find that for the third molar a person is about
three and two-thirds times more likely to be in the ‘‘apex
half complete’’ than in the ‘‘cusp initiation’’ stage.
In our analysis, we have already found the probability
of obtaining the observed dental sequence by: 1) assuming conditional independence and 2) estimating age as
that point which gives the highest likelihood of obtaining
the observed dental stages. This likelihood is the probability of obtaining the observed dental sequence in someone at the (exact) stated age point, and it is monotonically decreasing with increases in the number of
observed teeth. This means that for any individual with
more than a few teeth observed, the probability of the
observed sequence will be small. This can be clearly seen
for ‘‘Subject A’’ in Table 2, where the ‘‘P(seq.)’’ value
decreases with the addition of more teeth in the analysis.
We further demonstrate this principal using Bayle et al.’s
(2009b) scores for Roc de Marsal, where we have converted those scores that we could directly to Moorrees et
al.’s scoring system and read the remaining scores from
the images in Bayle et al.’s (2009b) Table 1. Figure 10
shows the ‘‘plot.teeth’’ view for Roc de Marsal using this
scoring. There is a script to produce all of the ‘‘plot.teeth’’
views of fossils and individuals discussed in this article at
https://netfiles.uiuc.edu/lylek/www/SSK2011.htm. We will
focus first on three of the earlier forming teeth: the deciduous canine, the deciduous second molar, and the first
permanent molar. Using only the permanent first molar
score of ‘‘crown complete,’’ our point estimate of age would
be 2.37 years, and the probability of getting a ‘‘crown
complete’’ score for this tooth in someone 2.37 years old is
0.6279. If we add the second deciduous molar to the analysis, then our estimated point age would be 2.12 years
and the probability of getting a ‘‘crown complete’’ score for
the permanent first molar and ‘‘root three-quarters complete’’ for the second deciduous molar is 0.0776. Now, add-
239
ESTIMATING AGE-AT-DEATH FROM DENTAL REMAINS
TABLE 5. Precisions (for log conception-corrected ages in years) for teeth within particular stages
Score
C.i
C.co
C.oc
Cr.5
Cr.75
Cr.c
R.i
Cl.i
R.25
R.5
R.75
R.c
A.5
A.c
Res.25
Res.5
dc
78.09
101.16
81.61
87.85
97.07
97.17
89.00
74.62
102.03
85.56
90.13
32.97*
55.67
88.34
dm1
55.75
108.55
91.48
88.49
106.22
103.20
91.54
91.37
102.47
93.41
94.17
15.47*
55.60
81.16
dm2
68.47
104.60
80.21
84.61
90.57
106.11
82.61
96.49
92.68
104.73
93.17
86.99
22.38*
67.04
83.28
UI1
UI2
LI1
85.87
85.87
91.64
91.64
100.90
92.29
102.83
104.07
101.62
92.13
100.25
106.48
LI2
94.43
86.70
101.91
98.99
105.50
85.73
92.79
99.88
103.15
103.86
C
P3
P4
79.84
61.99
52.08
62.89
67.80
89.54
91.49
80.47
82.30
82.90
85.32
91.59
94.99
94.16
84.63
89.19
97.07
96.39
94.43
99.71
97.28
62.48
88.45
103.98
94.71
96.69
77.92
93.68
103.92
95.23
98.44
86.88
93.91
102.99
98.64
95.16
M1
M2
M3
53.20
61.24
73.45
64.07
84.49
77.25
68.41
101.00
103.99
104.13
92.83
80.89
103.73
91.05
100.63
99.29
93.93
98.21
97.41
91.01
102.08
102.97
105.54
101.45
89.63
104.83
104.35
104.27
105.09
105.28
104.66
103.94
101.42
104.91
105.31
106.17
103.39
101.39
Stages marked with asterisks do not follow a log normal distribution and consequently should only be used in combination with
other teeth.
TABLE 6. Mean log conception-corrected ages in years for teeth within particular stages
Score
C.i
C.co
C.oc
Cr.5
Cr.75
Cr.c
R.i
Cl.i
R.25
R.5
R.75
R.c
A.5
A.c
Res.25
Res.5
dc
20.244
20.045
0.107
0.278
0.410
0.516
0.644
0.830
0.977
1.097
1.253
1.576*
1.988
2.225
dm1
dm2
20.250
20.054
0.052
0.199
0.289
0.335
0.435
0.573
0.677
0.775
0.901
1.370*
1.938
2.193
20.240
20.035
0.105
0.288
0.446
0.531
0.637
0.783
0.904
0.994
1.082
1.227
1.632*
2.087
2.305
UI1
UI2
1.848
1.848
1.945
1.945
1.972
2.079
2.179
2.240
2.052
2.157
2.268
2.322
LI1
1.725
1.867
1.985
2.069
2.136
LI2
1.838
1.987
2.097
2.173
2.234
C
P3
P4
0.294
0.534
0.848
1.160
1.428
1.629
1.772
0.992
1.179
1.361
1.536
1.689
1.816
1.938
1.353
1.513
1.641
1.750
1.866
1.972
2.070
1.982
2.199
2.304
2.392
2.507
2.101
2.267
2.358
2.445
2.553
2.203
2.346
2.441
2.522
2.630
M1
M2
M3
0.090
0.406
0.663
0.913
1.137
1.327
1.556
1.723
1.791
1.847
1.940
2.100
1.475
1.575
1.687
1.775
1.884
1.996
2.098
2.220
2.327
2.396
2.448
2.506
2.619
2.340
2.390
2.443
2.492
2.535
2.581
2.633
2.701
2.763
2.807
2.842
2.888
2.967
Stages marked with asterisks do not follow a log normal distribution and consequently should only be used in combination with
other teeth.
ing in the deciduous canine score the estimated age is
2.05 years and the probability of getting the three
observed tooth scores has decreased to 0.0186.
As we have just shown, the probability of getting a
particular dental sequence conditional on age will
decrease as the number of teeth included in the
sequence increases. As a consequence, the probability of
a given sequence conditional on a fixed age must be
scaled, for which we use the probability of the most
likely sequence that would have arisen at the fixed age.
At 2.05 years the most likely scores for the deciduous canine, deciduous second molar, and permanent first molar
are ‘‘root complete,’’ ‘‘root complete,’’ and ‘‘crown threequarters complete,’’ respectively. This sequence has a
0.1278 probability of occurrence in a 2.05-year old. The
observed sequence of ‘‘root three-quarters complete,’’
‘‘root three-quarters complete,’’ and ‘‘crown complete’’
had a probability of only 0.0186, but when divided by
the probability for the most likely sequence at this age
the relative probability is 0.1454. We can continue this
example for the later forming teeth. If we use the permanent canine and third premolar scores, the estimated
point age is 3.26 years, and the probability of the
sequence (‘‘crown three-quarters complete’’ and ‘‘cusp
outline complete’’) is 0.4888. This is the most likely
sequence for someone at 3.26 years of age, so the relative
probability is 1.0.
We have not discussed the incisor or deciduous first
molar scores for Roc de Marsal (see Fig. 10). The incisors
do not contribute to the likelihood, whereas the deciduous first molar appears to have been scored incorrectly.
Bayle et al. (2009b) scored the tooth as being in resorption. If we use the earliest resorption stage in the Moorrees et al.’s system (one-quarter) for this tooth alone the
estimated age is 6.19 years, which is clearly too old. If
we add this tooth into the later forming set of teeth the
relative probability of occurrence is only 0.0029. We also
have not discussed combining the earlier and later forming teeth to estimate the relative probability of the
sequence. The relative probability for all of the teeth in
Figure 8 (with the exception of the incisors and the first
deciduous molar) is \0.0001. This would appear to be
evidence for an increased rate of dental development in
this individual, as it has resulted in the later forming
American Journal of Physical Anthropology
240
L.L. SHACKELFORD ET AL.
Fig. 10. Plot of ‘‘normed’’ likelihoods for the Roc de Marsal
Neandertal child using the micro-CT scores from Bayle et al.
(2009b).
teeth looking ‘‘old’’ given the earlier forming teeth. However, it is not unusual to find individuals who have some
acceleration or deceleration within parts of a sequence.
For example, Anderson et al.’s (1976) ‘‘Subject D’’ who
was a 7-year-old girl has an age estimate from the anterior dentition (incisors and canine) of 7.76 years and
from the posterior dentition of 6.54 years (see Table 2).
The relative probability of occurrence for the anterior
dentition is 0.3614 and for the posterior dentition is
0.8109, but taken together the entire dentition has a relative probability of occurrence of only 0.0110. Subjects
‘‘B’’ and ‘‘C’’ also show similar departures.
Application of modern human standards to Neandertal and early modern human specimens. Using
these newly generated parameters to estimate age-atdeath for fossil Neandertals and early modern humans
raises questions about the appropriateness of applying
modern human dental formation standards to these
fossil groups. Neandertals and early modern humans
have traditionally been aged according to modern
human standards; however, this is only appropriate if
they are shown to fit within modern human variation
for dental formation. Evidence has both supported and
challenged the use of these modern growth standards
on these groups, with controversy surrounding the
dental development in these fossils ongoing for decades
(reviewed in Thompson and Nelson, 2000; GuatelliSteinberg, 2009).
Differences in the pattern and rate of dental formation
and calcification based on macroscopic observations have
been noted for Neandertals, but these findings are not
always consistent. For instance, the formation of Neandertal incisors has been reported as both advanced
(Thoma, 1963; Legoux, 1966) and delayed (Tompkins,
1996b; Bayle et al., 2009b) relative to modern humans.
Incisors are highly variable teeth in modern humans
and this may account for the disagreement among
researchers (Braga and Heuzé, 2007). The formation of
American Journal of Physical Anthropology
the second and third molars has consistently been
reported as advanced for Neandertals (Wolpoff, 1979;
Dean et al., 1986; Tompkins, 1996b; Bayle et al., 2009b).
In a large-scale comparison, Tompkins (1996b) found
that early modern humans shared this pattern of dental
formation; thus, it is not unique to Neandertals. His
findings also revealed that neither fossil group was statistically different from modern South Africans. These
results support Smith’s (1991a) finding that Neandertal
dental development fell within the modern human range
of variation.
Studies of developmental differences between Late
Pleistocene and recent human samples in incremental
structures also present a complex picture of fossil dental
development (methodological review in Smith, 2008).
Many authors support the idea that Neandertals were
characterized by significantly advanced dental development (Ramirez Rozzi and Bermudez de Castro, 2004;
Smith et al., 2007b), whereas others argue that they fall
within the range of modern human variation (Dean et
al., 1986; Mann et al., 1991; Dean et al., 2001; GuatelliSteinberg et al., 2005; Macchiarelli et al., 2006). The few
studies that have focused on early modern humans have
placed them within the range of modern human dental
development (Ramirez Rozzi and Bermudez de Castro,
2004; Smith et al., 2007a). It should also be noted that
incremental structures can be used to calculate age-atdeath in immature individuals (for example, Bromage
and Dean, 1985; Dean et al., 1986; Stringer et al., 1990;
Stringer and Dean, 1997; Smith et al., 2007a). However,
this method requires either cross sectioning or virtual
sectioning (Tafforeau and Smith, 2008) teeth from every
individual to be aged. Although accurate, these methods
are more time intensive than radiographic aging techniques and are not always feasible, especially when dealing with large sample sizes.
Smith et al. (2010) have recently published a detailed
study using virtual sectioning, which shows that Neandertals formed their teeth on an accelerated schedule
relative to both early modern and extant humans. This
study presented a regression of ages estimated from
tooth formation and modern standards for six Neandertals onto the ‘‘actual’’ ages from counting incremental
lines. The method Smith et al. used for estimating ages
from tooth formation did not take into account any of
the sources of variation we have referred to in this article, so it is worth returning to their study and reestimating the dental formation ages. We have done this
using tooth formation scores from Smith et al.’s (2010)
supplemental materials (SI Table 7) and provide these
scores as part of Table A2. It was necessary in doing
this analysis to convert their scores of ‘‘8’’ for uniradicular teeth to either ‘‘7’’ or ‘‘9,’’ which is why we provide
the scores used in this analysis in Table A2. Using the
‘‘get.age’’ script, we estimated the 95% region for ageat-death for each fossil and plotted these against Smith
et al.’s histological ages (see Fig. 11 and Table 3 for the
estimates). Note that for two of the fossils (Obi Rakhmat and Le Moustier), Smith et al. listed a range for
the actual ages as these were estimated from ‘‘long increment’’ counts. Looking at the line of identity in Figure 11, only two fossils (Scladina and Le Moustier)
have ‘‘actual’’ ages that are outside of the 95% regions
of estimated age from tooth formation. Le Moustier’s
dental formation age is entirely based upon the third
molar, as this tooth has the root half formed, whereas
all other teeth are fully formed. Given the considerable
ESTIMATING AGE-AT-DEATH FROM DENTAL REMAINS
241
Fig. 11. Plot of the 95% interval for estimated age from the
Moorrees et al.’s parameters against ‘‘known’’ ages from Smith
et al.’s (2010) histological study of six Neandertals. The diagonal
line shows age identity. Obi Rakhmat and Le Moustier have
error bars for ‘‘known’’ age based on values stated in Smith et
al. (2010).
Fig. 13. Plots of the probable age distribution for Scladina,
where the solid line is the combined likelihood curve across the
teeth, the filled circles show the best-fitting log-normal distribution, and the dashed line shows the final age-at-death distribution, which includes the between-tooth component of variance.
Panel ‘‘A’’ shows the age distribution with the third molar
included, whereas Panel ‘‘B’’ excludes the third molar.
Fig. 12. Plot of ‘‘normed’’ likelihoods for the Scladina fossil,
with the ‘‘known’’ age of 8.0 years plotted as a vertical line. The
dental formation scores and known age are from Smith et al.
(2010).
evidence that third molars do form on an advanced
scale in Neandertals and early modern humans relative to recent modern humans, this result is not particularly surprising. However, the Scladina results
merit further examination. Figure 12 shows the ‘‘plot.teeth’’ view for this fossil, where the histological age of
8.0 years is marked with a vertical line. With the
exception of the lower central incisor and the first
molar, the remainder of the teeth from the Scladina
fossil appear to have formed at an accelerated pace
relative to the modern human standards. Not surprisingly, the third molar is particularly accelerated. In
Figure 13, we consequently show the estimated dental
formation age distribution both with and without the
third molar.
As supplemental materials to their publication on
the Scladina fossil, Smith et al. (2007b) also provided
information on the number of days after birth (read
from the ‘‘neonatal’’ line) for cusp initiation and crown
completion. These data can be compared to the log-normal distributions for attainment that we have
extracted from Moorrees et al. (1963b). Figure 14
shows this comparison for the maxillary canine and
the three molars from Smith et al. (2007b), whereas
American Journal of Physical Anthropology
242
L.L. SHACKELFORD ET AL.
Fig. 14. A: Plot of cusp initiation age (dotted vertical line) and crown completion age (dashed vertical line) from Smith et al.
(2007b) for the Scladina upper canine. The solid vertical line shows the ‘‘known’’ age-at-death of 8.0 years from Smith et al. (2010),
whereas the curves are the log-normal distributions for attainment ages (labeled below the curves) from Moorrees et al. The final
two curves (A.5 and A.c) are shown because the tooth had the root apex half completed. B: The Scladina first molar drawn as in
Figure 14A, but with cusp initiation not shown as the distribution for attainment age is not given in Moorrees et al. C: The Scladina second molar drawn as in Figure 14A. D: The Scladina third molar drawn as in Figure 14A. Crown completion is not shown
as the individual died before completion of the third molar crown.
the Moorrees et al.’s standards are shown for the
equivalent mandibular teeth. In each graph, the
observed age for cusp initiation from Smith et al.
(2007b) is shown as a vertical dotted line, the observed
age for crown completion is shown with a dashed vertical line, and the age at death is shown (at 8 years)
with a solid vertical line. The log-normal distributions
for attainment ages from Moorrees et al. (1963b) are
labeled across the bottom of each figure. For the canine, Figure 14A shows that although cusp initiation
is slightly advanced for Scladina relative to the modern standards, crown completion is essentially on tarAmerican Journal of Physical Anthropology
get, and the root development is very advanced. For
the first molar (Fig. 14B), crown completion is slightly
delayed in Scladina relative to the modern human
standard, whereas the root formation (with the apex
complete) is on target relative to modern humans.
Macchiarelli et al. (2006) showed that this was also
the case for La Chaise with an apex closure age that
they estimated at 8.7 years. Cusp initiation is not
shown in Figure 14B as the distribution of attainment
ages is not available for this stage/tooth in the Moorrees et al.’s publication. The second molar (Fig. 14C)
provides a situation very similar to the canine, in that
ESTIMATING AGE-AT-DEATH FROM DENTAL REMAINS
cusp initiation and crown completion are on target in
Scladina relative to modern human standards,
whereas the root development is markedly accelerated. Finally, for the third molar (Fig. 14D), cusp initiation is very advanced in Scladina relative to the
modern human standards, and the formation stage of
the tooth at the time of death (crown three-quarters
complete by the age of 8.0 years) is very advanced.
These findings from the third molar are in keeping
with other studies that have suggested an accelerated
rate of development for the third molar relative to
the rest of the posterior dentition. However, the
results from the remainder of the teeth shown in Figure 14 are perplexing. The first molar appears to be
essentially on target given modern human standards,
though this may be explicable because this tooth is
the first of the permanent dentition to form. The
results from the canine and second molar may suggest that Neandertals formed permanent dental
crowns on a modern human schedule, but that their
tooth root development was accelerated relative to
modern humans. Again, it may be that there is an
advanced rate of dental formation in Neandertals
throughout the dentition, but this advanced rate can
only be demonstrated for the latter forming part of
each tooth. Alternatively, as the results from the dental roots appear advanced while the results from the
crowns do not, there may be some systematic error
specific to the dentine that does not affect the
enamel.
It is also useful to look at the Scladina fossil results
from Smith et al. (2007b) in light of the Moorrees et al.’s
(1963b) standards and of arguments most clearly articulated by Beynon et al. (1998). Beynon et al. (1998)
pointed out that there are strong developmental and
imaging reasons that would explain the common finding
that cusp initiation viewed radiographically will generally postdate the correct initiation time viewed histologically. In contrast, crown completion viewed radiographically will generally precede the correct completion time
viewed histologically. In a comment on Beynon et al.,
Kuykendall (2001) demonstrated that although early
crown completion times from radiography relative to the
correct completion times from histology could be demonstrated in the literature, the difference in initiation
times viewed radiographically versus histologically generally were not apparent in the literature. In any event,
these effects are not demonstrable in comparing the
Scladina histological data to the Moorrees et al.’s (1963b)
standards. Although the modern human radiographic
standards are slightly ‘‘late’’ for cusp initiation and early
for crown completion in the upper canine relative to the
Scladina values, the Scladina values are still well within
the modern human standards as far as enamel formation
is concerned. For the first molar, the modern human
cusp initiation detected radiographically actually
appears to predate the Scaldina fossil, though again
Scladina falls well within the distribution. Crown completion for the first molar as well as cusp initiation and
crown completion for the second molar are quite similar
for the Scladina fossil and for the modern human radiographic standards. We have already commented on the
acceleration of the third molars in Neandertals, as well
as on the fact that viewed against modern human radiographic standards as a whole, it is root development and
not crown formation that appears accelerated in the
Scladina fossil.
243
A consensus has not yet been reached regarding dental development in Neandertals and early modern
human fossils. Fossil specimens display a high amount
of variability relative to one another, which presents
challenges for both locating standardized differences
between these groups and modern humans as well as
constructing reliable group-specific growth standards
(Bayle et al., 2009b). Further, we still have much to
learn about the patterns of variation displayed among
modern human groups in several aspects of dental development before we can truly understand the extent to
which closely related fossil groups resemble them.
Although a complete review of variation in modern
human dental development is beyond the scope of this
article, it is worth pointing to a few salient examples.
For instance, we know that there are differences in dental formation between Native Americans, French Canadians, and South Africans (Tompkins, 1996a); however,
population-specific growth standards are not readily
available in the literature. Reid and Dean (2006) have
shown a considerable amount of similarity in crown formation times for Southern African and Northern European samples. However, their study cannot address the
effects of variation in cusp initiation age either within
samples or across them, and as they pointed out, there
are some perplexing differences between the Moorrees et
al.’s (1963b) study and other radiographic studies of
tooth formation. Finally, and importantly, we do not yet
have enough information about root formation in recent
humans and its role in the process of dental eruption,
which is itself highly variable (root formation reviewed
in Dean and Vesey, 2008; Smith and Buschang, 2009;
variation in eruption reviewed in Guatelli-Steinberg,
2009). As highlighted in this study, the rate of root
rather than crown formation may be driving the variation seen between Neandertals and modern humans.
However, this pattern will become clearer in the light of
future studies on modern human variation.
CONCLUSION
The method put forward by Moorrees et al. (1963a,b)
has been widely used for estimating age-at-death from
dental remains. Unfortunately, the traditional application of this method required that dental scores be compared to graphical representations of their data. This
is difficult to accomplish with large datasets, and less
precise than utilizing numerical values. The purpose of
this study was to transform these graphical reports of
‘‘mean attainment age’’ for dental development stages
into more usable parameters. The data published in
this study will allow more accurate application of the
Moorees et al.’s method and more reliable estimation
of age-at-death. We have applied the newly generated
parameters by estimating the probable age-at-death
from the dental remains of immature Neandertals and
immature early modern humans. We have made both
the age estimates and our scores available for future
use.
ACKNOWLEDGMENTS
The authors thank Erik Trinkaus, Robert Tompkins,
and Libby Cowgill for making data available to us. We
are grateful to three anonymous reviewers whose comments significantly improved the quality of this manuscript.
American Journal of Physical Anthropology
244
L.L. SHACKELFORD ET AL.
TABLE A1. Digitized values in years for minus two standard deviations (L2SD), minus one standard deviation (L1SD),
the mean, plus one standard deviation (U1SD), and plus two standard deviations (U2SD) attainment ages for tooth scores
from Moorrees et al.’s (1963a,b) charts
Sex
Tooth
Stage
L2SD
L1SD
Mean
U1SD
U2SD
Without mean
With mean
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
F
F
F
F
F
F
F
F
F
F
F
F
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
m1
m1
m1
m1
m1
m1
m1
m1
m1
m1
m1
m1
m1m
m1m
m1m
m1d
m1d
m1d
m1d
m2
m2
m2
m2
m2
m2
m2
m2
m2
m2
m2
m2
m2
m2m
m2m
m2m
m2d
m2d
m2d
m2d
c
c
c
c
c
c
c
c
c
c
c
c
Cco
Coc
Cr1/2
Cr3/4
Crc
Ri
R1/4
R1/2
R3/4
Rc
A1/2
Ac
Res1/4
Res1/2
Res3/4
Exf
Coc
Cr1/2
Cr3/4
Crc
Ri
Rcleft
R1/4
R1/2
R3/4
Rc
A1/2
Ac
Res1/4
Res1/2
Res3/4
Res1/4
Res1/2
Res3/4
Exf
Cco
Coc
Cr1/2
Cr3/4
Crc
Ri
Rcleft
R1/4
R1/2
R3/4
Rc
A1/2
Ac
Res1/4
Res1/2
Res3/4
Res1/4
Res1/2
Res3/4
Exf
Coc
Cr1/2
Cr3/4
Crc
Ri
R1/4
R1/2
R3/4
Rc
A1/2
Ac
Res1/4
–
0.01
0.10
0.26
0.42
0.54
0.68
0.95
1.38
1.48
1.94
2.39
4.87
6.80
7.97
8.64
–
0.01
0.05
0.21
0.33
0.39
0.47
0.61
0.82
0.94
1.22
1.47
4.32
6.11
7.61
5.07
6.74
8.12
8.74
–
0.01
0.09
0.27
0.46
0.63
0.68
0.93
1.16
1.43
1.55
1.87
2.39
5.30
6.93
8.44
5.97
7.69
8.97
9.42
–
0.07
0.25
0.43
0.57
0.74
0.95
1.33
1.56
1.94
2.32
3.91
–
0.08
0.18
0.37
0.55
0.68
0.82
1.11
1.60
1.72
2.21
2.70
5.46
7.57
8.84
9.61
–
0.08
0.13
0.31
0.45
0.50
0.59
0.75
0.99
1.11
1.42
1.71
4.85
6.81
8.47
5.71
7.50
9.02
9.73
–
0.09
0.18
0.38
0.56
0.77
0.81
1.14
1.36
1.65
1.79
2.15
2.71
5.93
7.70
9.38
6.67
8.54
9.98
10.47
0.06
0.15
0.36
0.55
0.71
0.89
1.13
1.55
1.79
2.21
2.63
4.39
–
0.16
0.27
0.47
0.68
0.83
0.98
1.29
1.84
1.96
2.49
3.05
6.10
8.43
9.80
10.67
–
0.18
0.21
0.41
0.56
0.63
0.73
0.92
1.17
1.31
1.65
1.95
5.43
7.59
9.40
6.36
8.34
10.00
10.79
–
0.18
0.27
0.49
0.71
0.92
0.97
1.33
1.58
1.90
2.05
2.44
3.06
6.61
8.59
10.41
7.46
9.48
11.06
11.62
0.14
0.25
0.47
0.68
0.85
1.05
1.30
1.77
2.05
2.51
2.98
4.92
0.00
0.25
0.38
0.60
0.82
0.98
1.16
1.50
2.10
2.24
2.83
3.44
6.80
9.39
10.89
11.84
20.02
0.26
0.31
0.53
0.71
0.77
0.88
1.05
1.36
1.51
1.89
2.23
6.06
8.47
10.45
7.09
9.29
11.13
11.96
20.01
0.27
0.38
0.62
0.86
1.10
1.16
1.53
1.82
2.17
2.34
2.77
3.45
7.39
9.51
11.54
8.28
10.53
12.30
12.92
0.23
0.35
0.59
0.82
1.01
1.24
1.52
2.04
2.33
2.84
3.35
5.47
0.07
0.36
0.49
0.75
0.98
1.17
1.34
1.73
2.39
2.54
3.20
3.86
7.55
10.41
12.07
13.11
0.06
0.37
0.43
0.68
0.86
0.94
1.05
1.27
1.58
1.74
2.16
2.53
6.73
9.40
11.58
7.88
10.30
12.33
13.25
0.06
0.38
0.49
0.76
1.02
1.29
1.35
1.78
2.08
2.46
2.65
3.12
3.88
8.21
10.55
12.80
9.16
11.70
13.59
14.28
0.33
0.48
0.73
0.98
1.20
1.44
1.74
2.33
2.65
3.21
3.77
6.07
20.2900
20.0892
0.0270
0.2079
0.3536
0.4545
0.5467
0.7180
0.9513
0.9975
1.1801
1.3348
1.9223
2.2170
2.3580
2.4348
20.2900
20.0837
20.0334
0.1553
0.2781
0.3242
0.3927
0.5015
0.6498
0.7189
0.8724
0.9935
1.8193
2.1217
2.3182
1.9606
2.2080
2.3771
2.4453
20.2900
20.0793
0.0201
0.2159
0.3761
0.5163
0.5479
0.7274
0.8448
0.9736
1.0295
1.1601
1.3387
1.9971
2.2315
2.4122
2.1009
2.3268
2.4697
2.5156
20.1165
0.0007
0.1943
0.3585
0.4721
0.5926
0.7232
0.9292
1.0298
1.1825
1.3156
1.7306
20.2900
20.0894
0.0260
0.2055
0.3544
0.4546
0.5466
0.7171
0.9514
0.9971
1.1793
1.3349
1.9228
2.2170
2.3577
2.4349
20.2900
20.0819
20.0348
0.1547
0.2770
0.3236
0.3925
0.5031
0.6502
0.7192
0.8727
0.9932
1.8196
2.1215
2.3181
1.9608
2.2078
2.3766
2.4454
20.2900
20.0776
0.0192
0.2156
0.3766
0.5162
0.5473
0.7281
0.8447
0.9737
1.0292
1.1601
1.3385
1.9969
2.2321
2.4122
2.1017
2.3265
2.4696
2.5155
20.1173
0.0000
0.1950
0.3583
0.4716
0.5919
0.7220
0.9286
1.0296
1.1822
1.3158
1.7314
American Journal of Physical Anthropology
245
ESTIMATING AGE-AT-DEATH FROM DENTAL REMAINS
TABLE A1. (Continued)
Sex
Tooth
Stage
L2SD
L1SD
Mean
U1SD
U2SD
Without mean
With mean
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
c
c
c
m1
m1
m1
m1
m1
m1
m1
m1
m1
m1
m1
m1m
m1m
m1m
m1d
m1d
m1d
m1d
m2
m2
m2
m2
m2
m2
m2
m2
m2
m2
m2
m2m
m2m
m2m
m2d
m2d
m2d
m2d
UI1
UI1
UI1
UI1
UI1
UI1
UI2
UI2
UI2
UI2
UI2
UI2
LI1
LI1
LI1
LI1
LI1
LI1
LI2
LI2
LI2
LI2
LI2
LI2
LI2
LI2
C
C
C
C
C
Res1/2
Res3/4
Exf
Cr1/2
Cr3/4
Crc
Ri
Rcleft
R1/4
R1/2
R3/4
Rc
A1/2
Ac
Res1/4
Res1/2
Res3/4
Res1/4
Res1/2
Res3/4
Exf
Cr1/2
Cr3/4
Crc
Ri
Rcleft
R1/4
R1/2
R3/4
Rc
A1/2
Ac
Res1/4
Res1/2
Res3/4
Res1/4
Res1/2
Res3/4
Exf
Crc
R1/4
R1/2
R2/3
R3/4
Rc
Crc
R1/4
R1/2
R2/3
R3/4
Rc
R1/2
R2/3
R3/4
Rc
A1/2
Ac
R1/4
R1/3
R1/2
R2/3
R3/4
Rc
A1/2
Ac
Ci
Cco
Coc
Cr1/2
Cr3/4
5.84
7.04
7.71
–
0.08
0.15
0.34
0.35
0.41
0.63
0.80
0.93
1.09
1.33
3.93
5.81
7.11
4.08
6.16
7.59
8.18
0.07
0.25
0.45
0.63
0.67
0.95
1.15
1.41
1.50
1.80
2.21
4.85
6.69
8.13
5.57
6.96
8.04
8.99
4.27
5.07
5.57
6.06
6.49
7.01
4.74
5.56
6.10
6.49
7.06
7.79
4.23
4.72
5.18
5.63
6.19
6.55
4.29
4.51
5.01
5.49
5.96
6.42
6.94
7.46
0.26
0.47
0.90
1.63
2.28
6.53
7.82
8.57
0.08
0.16
0.24
0.45
0.45
0.52
0.75
0.96
1.09
1.28
1.56
4.39
6.48
7.92
4.59
6.90
8.41
9.09
0.15
0.35
0.57
0.78
0.82
1.14
1.33
1.63
1.74
2.07
2.49
5.42
7.43
8.99
6.22
7.73
8.93
9.97
4.80
5.65
6.21
6.78
7.23
7.78
5.31
6.24
6.78
7.23
7.86
8.67
4.75
5.28
5.78
6.29
6.92
7.30
4.81
5.04
5.60
6.14
6.64
7.18
7.70
8.32
0.37
0.63
1.07
1.90
2.58
7.24
8.70
9.51
0.16
0.25
0.34
0.57
0.58
0.66
0.89
1.14
1.26
1.49
1.79
4.90
7.23
8.82
5.17
7.66
9.36
10.10
0.25
0.46
0.70
0.93
0.97
1.32
1.55
1.88
1.99
2.35
2.83
6.08
8.28
10.01
6.94
8.60
9.93
11.09
5.34
6.30
6.91
7.53
8.05
8.62
5.90
6.91
7.57
8.04
8.72
9.62
5.29
5.88
6.45
7.00
7.69
8.11
5.39
5.62
6.27
6.82
7.40
7.96
8.56
9.25
0.49
0.76
1.21
2.13
2.91
8.07
9.68
10.60
0.24
0.35
0.46
0.70
0.70
0.79
1.07
1.32
1.47
1.72
2.05
5.50
8.04
9.77
5.76
8.52
10.41
11.22
0.36
0.58
0.84
1.09
1.15
1.53
1.78
2.14
2.27
2.68
3.19
6.75
9.19
11.14
7.69
9.55
11.00
12.31
5.95
7.03
7.71
8.39
8.94
9.57
6.59
7.73
8.41
8.95
9.66
10.66
5.91
6.55
7.19
7.78
8.55
9.00
6.03
6.28
6.98
7.62
8.20
8.84
9.50
10.26
0.61
0.92
1.46
2.44
3.31
8.98
10.74
11.75
0.35
0.46
0.58
0.84
0.85
0.96
1.26
1.53
1.71
1.96
2.33
6.11
8.93
10.85
6.41
9.46
11.52
12.43
0.46
0.72
1.01
1.29
1.34
1.76
2.04
2.43
2.56
3.01
3.59
7.54
10.23
12.37
8.56
10.61
12.26
13.65
6.64
7.79
8.55
9.27
9.91
10.64
7.30
8.57
9.31
9.93
10.71
11.85
6.59
7.29
7.98
8.65
9.47
9.95
6.69
7.00
7.75
8.46
9.09
9.81
10.55
11.41
0.74
1.06
1.64
2.72
3.72
2.0805
2.2469
2.3305
20.0972
20.0008
0.0904
0.2737
0.2819
0.3403
0.5061
0.6335
0.7061
0.8057
0.9318
1.7349
2.0758
2.2567
1.7731
2.1292
2.3137
2.3839
20.0033
0.1895
0.3720
0.5170
0.5449
0.7272
0.8308
0.9641
1.0062
1.1328
1.2753
1.9180
2.2005
2.3775
2.0378
2.2355
2.3683
2.4713
1.8075
1.9533
2.0375
2.1138
2.1737
2.2398
1.8957
2.0391
2.1165
2.1741
2.2478
2.3389
1.7995
1.8919
1.9738
2.0473
2.1322
2.1800
1.8135
1.8536
1.9465
2.0263
2.0955
2.1645
2.2317
2.3020
0.2071
0.4069
0.6912
1.0609
1.3028
2.0800
2.2467
2.3302
20.0973
20.0013
0.0903
0.2739
0.2820
0.3404
0.5044
0.6338
0.7043
0.8057
0.9317
1.7343
2.0761
2.2570
1.7740
2.1292
2.3137
2.3839
20.0028
0.1891
0.3721
0.5172
0.5447
0.7274
0.8311
0.9648
1.0063
1.1328
1.2751
1.9188
2.2004
2.3772
2.0382
2.2354
2.3683
2.4714
1.8072
1.9533
2.0372
2.1138
2.1739
2.2393
1.8953
2.0385
2.1169
2.1739
2.2478
2.3390
1.7994
1.8917
1.9739
2.0473
2.1324
2.1803
1.8138
1.8532
1.9469
2.0259
2.0961
2.1644
2.2316
2.3021
0.2089
0.4082
0.6879
1.0604
1.3016
American Journal of Physical Anthropology
246
L.L. SHACKELFORD ET AL.
TABLE A1. (Continued)
Sex
Tooth
Stage
L2SD
L1SD
Mean
U1SD
U2SD
Without mean
With mean
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
C
C
C
C
C
C
C
C
PM3
PM3
PM3
PM3
PM3
PM3
PM3
PM3
PM3
PM3
PM3
PM3
PM3
PM4
PM4
PM4
PM4
PM4
PM4
PM4
PM4
PM4
PM4
PM4
PM4
PM4
M1
M1
M1
M1
M1
M1
M1
M1m
M1m
M1m
M1m
M1m
M1m
M1d
M1d
M1d
M1d
M1d
M1d
M2
M2
M2
M2
M2
M2
M2
M2
M2m
M2m
M2m
M2m
M2m
M2m
M2d
M2d
M2d
Crc
Ri
R1/4
R1/2
R3/4
Rc
A1/2
Ac
Ci
Cco
Coc
Cr1/2
Cr3/4
Crc
Ri
R1/4
R1/2
R3/4
Rc
A1/2
Ac
Ci
Cco
Coc
Cr1/2
Cr3/4
Crc
Ri
R1/4
R1/2
R3/4
Rc
A1/2
Ac
Cco
Coc
Cr1/2
Cr3/4
Crc
Ri
Rcl
R1/4
R1/2
R3/4
Rc
A1/2
Ac
R1/4
R1/2
R3/4
Rc
A1/2
Ac
Ci
Cco
Coc
Cr1/2
Cr3/4
Crc
Ri
Rcl
R1/4
R1/2
R3/4
Rc
A1/2
Ac
R1/4
R1/2
R3/4
3.18
3.81
4.62
6.53
7.85
8.33
9.62
10.67
1.17
1.65
2.07
2.68
3.37
3.96
4.57
5.38
6.77
7.89
8.31
9.58
10.75
2.20
2.58
3.19
3.60
4.15
4.84
5.37
6.13
7.47
8.60
9.29
10.18
11.53
–
0.15
0.61
0.99
1.51
2.00
2.66
3.66
4.00
4.29
4.60
5.48
6.84
3.51
3.99
4.55
4.94
6.04
7.52
2.75
2.97
3.67
3.94
4.39
5.07
5.61
6.37
7.45
8.12
8.71
9.04
9.80
11.47
7.52
8.14
8.95
3.58
4.29
5.19
7.29
8.72
9.24
10.66
11.81
1.41
1.89
2.40
3.07
3.82
4.45
5.14
6.02
7.55
8.80
9.27
10.62
11.93
2.48
2.96
3.61
4.07
4.66
5.44
6.02
6.85
8.31
9.55
10.35
11.34
12.81
20.01
0.26
0.77
1.19
1.78
2.30
3.02
4.12
4.49
4.80
5.15
6.11
7.63
3.94
4.46
5.13
5.51
6.77
8.36
3.13
3.36
4.12
4.42
4.92
5.68
6.27
7.10
8.32
9.01
9.70
10.06
10.89
12.71
8.38
9.05
9.92
4.03
4.82
5.77
8.09
9.68
10.23
11.82
13.09
1.63
2.20
2.73
3.48
4.31
5.02
5.73
6.71
8.43
9.80
10.28
11.80
13.29
2.84
3.33
4.08
4.57
5.22
6.07
6.72
7.61
9.28
10.63
11.49
12.56
14.17
0.09
0.36
0.94
1.41
2.05
2.63
3.40
4.64
5.03
5.37
5.75
6.84
8.51
4.45
5.03
5.70
6.17
7.52
9.28
3.52
3.78
4.62
4.93
5.51
6.33
6.96
7.91
9.21
9.97
10.71
11.19
12.07
14.09
9.28
10.04
11.01
4.50
5.40
6.44
9.00
10.71
11.38
13.10
14.50
1.91
2.51
3.12
3.92
4.85
5.62
6.43
7.52
9.36
10.89
11.44
13.13
14.71
3.21
3.76
4.57
5.13
5.83
6.80
7.49
8.49
10.30
11.79
12.72
13.94
15.68
0.22
0.51
1.13
1.61
2.36
2.98
3.84
5.19
5.63
6.01
6.42
7.61
9.44
4.96
5.62
6.37
6.89
8.38
10.28
3.96
4.24
5.19
5.53
6.15
7.05
7.77
8.80
10.21
11.09
11.88
12.37
13.40
15.64
10.30
11.13
12.23
5.03
6.01
7.16
9.97
11.88
12.58
14.50
16.04
2.17
2.87
3.52
4.41
5.44
6.29
7.16
8.36
10.44
12.10
12.70
14.53
16.29
3.64
4.23
5.13
5.72
6.51
7.58
8.33
9.47
11.43
13.10
14.14
15.43
17.40
0.33
0.64
1.31
1.83
2.66
3.35
4.32
5.79
6.29
6.73
7.17
8.48
10.49
5.54
6.26
7.11
7.67
9.27
11.43
4.45
4.74
5.76
6.18
6.85
7.85
8.63
9.78
11.36
12.28
13.20
13.71
14.82
17.30
11.43
12.36
13.52
1.5616
1.7155
1.8758
2.1800
2.3436
2.3982
2.5317
2.6277
0.8682
1.0786
1.2463
1.4390
1.6205
1.7506
1.8708
2.0118
2.2154
2.3553
2.4021
2.5307
2.6390
1.2775
1.4065
1.5714
1.6702
1.7856
1.9209
2.0101
2.1265
2.3033
2.4314
2.5038
2.5885
2.7031
20.1479
0.1168
0.5197
0.7562
1.0258
1.2135
1.4256
1.6817
1.7549
1.8136
1.8728
2.0254
2.2232
1.6442
1.7511
1.8660
1.9342
2.1122
2.3057
1.4514
1.5093
1.6812
1.7402
1.8332
1.9568
2.0446
2.1583
2.2993
2.3748
2.4413
2.4769
2.5515
2.6982
2.3065
2.3790
2.4652
1.5624
1.7161
1.8756
2.1799
2.3438
2.3978
2.5316
2.6277
0.8679
1.0792
1.2462
1.4397
1.6206
1.7511
1.8704
2.0114
2.2157
2.3555
2.4017
2.5306
2.6396
1.2776
1.4063
1.5719
1.6703
1.7858
1.9206
2.0103
2.1259
2.3037
2.4314
2.5039
2.5885
2.7031
20.1548
0.1142
0.5208
0.7589
1.0262
1.2145
1.4249
1.6824
1.7549
1.8131
1.8725
2.0257
2.2236
1.6452
1.7517
1.8657
1.9344
2.1123
2.3056
1.4513
1.5094
1.6810
1.7397
1.8334
1.9567
2.0440
2.1584
2.2991
2.3742
2.4408
2.4774
2.5514
2.6980
2.3063
2.3788
2.4651
American Journal of Physical Anthropology
247
ESTIMATING AGE-AT-DEATH FROM DENTAL REMAINS
TABLE A1. (Continued)
Sex
Tooth
Stage
L2SD
L1SD
Mean
U1SD
U2SD
Without mean
With mean
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
M2d
M2d
M2d
M3
M3
M3
M3
M3
M3
M3
M3
M3m
M3m
M3m
M3m
M3m
M3m
M3d
M3d
M3d
M3d
M3d
M3d
UI1
UI1
UI1
UI1
UI1
UI1
UI1
UI2
UI2
UI2
UI2
UI2
UI2
UI2
UI2
LI1
LI1
LI1
LI1
LI1
LI1
LI1
LI2
LI2
LI2
LI2
LI2
LI2
LI2
LI2
C
C
C
C
C
C
C
C
C
C
C
C
C
PM3
PM3
PM3
PM3
Rc
A1/2
Ac
Ci
Cco
Coc
Cr1/2
Cr3/4
Crc
Ri
cleft
R1/4
R1/2
R3/4
Rc
A1/2
Ac
R1/4
R1/2
R3/4
Rc
A1/2
Ac
Crc
R1/4
R1/2
R2/3
R3/4
Rc
A1/2
Cr2/3
Crc
R1/4
R1/2
R2/3
R3/4
Rc
A1/2
R1/4
R1/2
R2/3
R3/4
Rc
A1/2
Ac
R1/4
R1/3
R1/2
R2/3
R3/4
Rc
A1/2
Ac
Ci
Cco
Coc
Cr1/2
Cr3/4
Crc
Ri
R1/4
R1/2
R3/4
Rc
A1/2
Ac
Ci
Cco
Coc
Cr1/2
9.46
10.39
12.05
7.44
7.82
8.36
8.79
9.38
9.75
10.29
11.07
11.88
12.31
13.00
13.37
14.40
15.67
11.78
12.30
13.14
13.61
14.82
16.37
3.86
4.79
5.25
5.72
6.09
6.58
7.20
3.62
4.52
5.25
5.73
6.22
6.69
7.32
7.73
3.59
4.09
4.49
4.87
5.31
5.97
6.17
3.73
4.14
4.72
5.08
5.38
6.09
6.52
6.85
0.22
0.44
0.84
1.44
2.26
3.12
3.72
4.25
5.77
6.75
7.19
8.10
9.23
1.31
1.73
2.24
2.80
10.45
11.54
13.39
8.30
8.70
9.24
9.80
10.41
10.82
11.45
12.28
13.22
13.65
14.42
14.76
15.94
17.37
13.08
13.67
14.56
15.07
16.40
18.12
4.35
5.37
5.88
6.39
6.80
7.32
8.01
4.06
5.07
5.89
6.41
6.94
7.45
8.16
8.61
4.03
4.60
5.02
5.44
5.93
6.68
6.89
4.19
4.63
5.29
5.70
6.02
6.82
7.27
7.65
0.35
0.56
1.04
1.67
2.58
3.51
4.16
4.78
6.41
7.52
8.03
9.00
10.26
1.55
1.97
2.60
3.18
11.62
12.80
14.81
9.21
9.66
10.27
10.85
11.54
11.98
12.67
13.62
14.61
15.12
15.91
16.35
17.67
19.22
14.49
15.09
16.08
16.70
18.16
20.05
4.85
5.97
6.54
7.09
7.56
8.16
8.92
4.54
5.67
6.57
7.14
7.70
8.29
9.03
9.55
4.52
5.12
5.60
6.08
6.62
7.42
7.68
4.70
5.17
5.92
6.34
6.70
7.60
8.10
8.50
0.46
0.71
1.19
1.93
2.93
3.94
4.67
5.32
7.14
8.33
8.89
9.98
11.39
1.76
2.23
2.90
3.59
12.87
14.19
16.38
10.20
10.71
11.41
12.02
12.81
13.32
14.06
15.06
16.14
16.72
17.66
18.12
19.51
21.22
16.03
16.73
17.82
18.47
20.09
22.20
5.39
6.69
7.30
7.91
8.43
9.07
9.90
5.10
6.33
7.29
7.92
8.59
9.21
10.05
10.61
5.09
5.73
6.29
6.79
7.37
8.28
8.55
5.27
5.80
6.61
7.08
7.45
8.41
9.00
9.43
0.58
0.86
1.39
2.21
3.29
4.45
5.22
5.94
7.94
9.28
9.88
11.08
12.62
2.03
2.54
3.28
3.99
14.29
15.70
18.13
11.35
11.88
12.63
13.34
14.17
14.74
15.56
16.68
17.91
18.50
19.49
20.04
21.59
23.47
17.75
18.50
19.72
20.43
22.20
24.42
6.06
7.47
8.13
8.78
9.34
10.04
10.98
5.70
7.05
8.13
8.79
9.52
10.21
11.17
11.75
5.67
6.41
7.00
7.55
8.20
9.17
9.48
5.88
6.49
7.34
7.84
8.30
9.31
9.97
10.45
0.70
1.03
1.60
2.45
3.70
4.96
5.82
6.64
8.80
10.28
10.96
12.27
13.96
2.31
2.88
3.67
4.48
2.5153
2.6060
2.7443
2.2980
2.3422
2.4005
2.4512
2.5095
2.5461
2.5975
2.6641
2.7315
2.7638
2.8153
2.8402
2.9120
2.9931
2.7232
2.7639
2.8250
2.8588
2.9395
3.0342
1.7223
1.9089
1.9883
2.0614
2.1182
2.1858
2.2679
1.6687
1.8584
1.9886
2.0631
2.1363
2.2010
2.2834
2.3325
1.6643
1.7730
1.8524
1.9215
1.9966
2.1014
2.1310
1.6962
1.7817
1.8959
1.9586
2.0085
2.1173
2.1788
2.2233
0.1816
0.3732
0.6657
0.9787
1.2990
1.5484
1.6894
1.8053
2.0657
2.2084
2.2671
2.3737
2.4952
0.9247
1.0972
1.2959
1.4618
2.5153
2.6061
2.7443
2.2982
2.3422
2.4004
2.4511
2.5094
2.5456
2.5973
2.6644
2.7316
2.7639
2.8148
2.8399
2.9123
2.9933
2.7233
2.7637
2.8247
2.8590
2.9395
3.0343
1.7224
1.9080
1.9878
2.0610
2.1179
2.1862
2.2682
1.6682
1.8584
1.9889
2.0635
2.1358
2.2011
2.2828
2.3324
1.6639
1.7722
1.8517
1.9213
1.9966
2.1012
2.1311
1.6961
1.7809
1.8962
1.9587
2.0085
2.1182
2.1791
2.2236
0.1834
0.3744
0.6651
0.9802
1.2996
1.5479
1.6894
1.8050
2.0658
2.2080
2.2668
2.3736
2.4954
0.9236
1.0965
1.2959
1.4631
American Journal of Physical Anthropology
248
L.L. SHACKELFORD ET AL.
TABLE A1. (Continued)
Sex
Tooth
Stage
L2SD
L1SD
Mean
U1SD
U2SD
Without mean
With mean
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
PM3
PM3
PM3
PM3
PM3
PM3
PM3
PM3
PM3
PM4
PM4
PM4
PM4
PM4
PM4
PM4
PM4
PM4
PM4
PM4
PM4
PM4
M1
M1
M1
M1
M1
M1
M1
M1m
M1m
M1m
M1m
M1m
M1m
M1d
M1d
M1d
M1d
M1d
M1d
M2
M2
M2
M2
M2
M2
M2
M2
M2m
M2m
M2m
M2m
M2m
M2m
M2d
M2d
M2d
M2d
M2d
M2d
M3
M3
M3
M3
M3
M3
M3
M3
M3m
Cr3/4
Crc
Ri
R1/4
R1/2
R3/4
Rc
A1/2
Ac
Ci
Cco
Coc
Cr1/2
Cr3/4
Crc
Ri
R1/4
R1/2
R3/4
Rc
A1/2
Ac
Cco
Coc
Cr1/2
Cr3/4
Crc
Ri
cleft
R1/4
R1/2
R3/4
Rc
A1/2
Ac
R1/4
R1/2
R3/4
Rc
A1/2
Ac
Ci
Cco
Coc
Cr1/2
Cr3/4
Crc
Ri
cleft
R1/4
R1/2
R3/4
Rc
A1/2
Ac
R1/4
R1/2
R3/4
Rc
A1/2
Ac
Ci
Cco
Coc
Cr1/2
Cr3/4
Crc
Ri
Rcl
R1/4
3.40
4.05
4.65
5.28
6.63
7.50
8.09
9.07
9.98
2.12
2.87
3.34
3.85
4.38
4.95
5.50
6.15
7.19
8.22
8.75
9.86
11.23
0.06
0.49
0.70
1.09
1.65
2.07
2.71
3.67
4.09
4.36
4.63
5.25
6.44
3.66
4.13
4.60
4.87
5.74
7.11
2.72
2.95
3.35
3.84
4.30
4.94
5.64
6.27
7.31
7.93
8.50
8.88
9.69
11.35
7.36
7.95
8.76
9.08
10.17
11.86
7.76
8.22
8.63
9.16
9.49
9.96
10.49
11.02
12.11
3.84
4.55
5.21
5.86
7.37
8.35
8.98
10.06
11.06
2.41
3.22
3.77
4.32
4.87
5.54
6.15
6.82
8.00
9.13
9.73
10.92
12.41
0.16
0.61
0.89
1.26
1.92
2.37
3.07
4.14
4.60
4.89
5.18
5.84
7.17
4.10
4.66
5.15
5.45
6.42
7.93
3.09
3.32
3.80
4.31
4.79
5.54
6.29
6.98
8.16
8.79
9.45
9.86
10.75
12.60
8.21
8.82
9.70
10.10
11.31
13.15
8.63
9.12
9.60
10.17
10.52
11.09
11.64
12.23
13.43
4.29
5.07
5.82
6.53
8.21
9.25
9.95
11.15
12.24
2.74
3.59
4.22
4.84
5.47
6.17
6.82
7.57
8.86
10.09
10.75
12.11
13.74
0.26
0.76
1.04
1.47
2.19
2.70
3.45
4.62
5.13
5.48
5.77
6.50
7.98
4.60
5.19
5.75
6.10
7.07
8.77
3.48
3.74
4.26
4.80
5.36
6.18
6.99
7.77
9.05
9.78
10.46
10.93
11.93
13.93
9.09
9.79
10.76
11.18
12.51
14.58
9.60
10.09
10.64
11.30
11.66
12.25
12.92
13.52
14.87
4.82
5.68
6.49
7.29
9.13
10.27
11.05
12.38
13.58
3.17
4.02
4.74
5.40
6.08
6.87
7.57
8.40
9.83
11.23
11.92
13.40
15.23
0.35
0.89
1.22
1.67
2.47
3.02
3.88
5.18
5.73
6.08
6.44
7.28
8.86
5.16
5.76
6.41
6.78
7.94
9.78
3.91
4.18
4.75
5.39
5.96
6.88
7.79
8.64
10.03
10.82
11.60
12.08
13.20
15.41
10.10
10.84
11.93
12.41
13.87
16.10
10.63
11.23
11.77
12.54
12.92
13.58
14.25
15.00
16.45
5.39
6.33
7.20
8.10
10.06
11.40
12.23
13.69
15.00
3.55
4.51
5.27
6.00
6.76
7.62
8.41
9.34
10.91
12.39
13.22
14.82
16.82
0.44
1.08
1.42
1.92
2.81
3.39
4.37
5.77
6.37
6.77
7.17
8.08
9.83
5.74
6.43
7.12
7.51
8.80
10.81
4.37
4.68
5.31
6.00
6.66
7.66
8.65
9.60
11.12
11.98
12.85
13.40
14.61
17.07
11.18
12.00
13.21
13.74
15.33
17.84
11.74
12.40
13.07
13.86
14.30
15.06
15.77
16.58
18.19
1.6199
1.7635
1.8811
1.9874
2.1912
2.3038
2.3715
2.4774
2.5652
1.2570
1.4715
1.6041
1.7188
1.8246
1.9339
2.0245
2.1201
2.2639
2.3860
2.4443
2.5534
2.6747
20.0098
0.4059
0.5795
0.7933
1.0738
1.2303
1.4368
1.6820
1.7714
1.8249
1.8761
1.9846
2.1660
1.6776
1.7795
1.8713
1.9203
2.0647
2.2564
1.4404
1.4999
1.6078
1.7179
1.8091
1.9349
2.0478
2.1425
2.2817
2.3522
2.4175
2.4572
2.5387
2.6867
2.2875
2.3545
2.4440
2.4801
2.5850
2.7283
2.3342
2.3859
2.4324
2.4884
2.5188
2.5664
2.6123
2.6596
2.7481
1.6194
1.7631
1.8813
1.9869
2.1914
2.3035
2.3713
2.4773
2.5650
1.2557
1.4709
1.6041
1.7191
1.8251
1.9340
2.0245
2.1198
2.2638
2.3854
2.4439
2.5535
2.6745
20.0052
0.4076
0.5797
0.7939
1.0747
1.2316
1.4365
1.6816
1.7714
1.8257
1.8760
1.9839
2.1662
1.6775
1.7799
1.8713
1.9210
2.0632
2.2558
1.4408
1.5002
1.6084
1.7172
1.8094
1.9352
2.0474
2.1425
2.2819
2.3527
2.4173
2.4573
2.5389
2.6866
2.2874
2.3546
2.4437
2.4799
2.5850
2.7286
2.3348
2.3854
2.4325
2.4886
2.5188
2.5661
2.6129
2.6594
2.7482
American Journal of Physical Anthropology
249
ESTIMATING AGE-AT-DEATH FROM DENTAL REMAINS
TABLE A1. (Continued)
Sex
Tooth
Stage
L2SD
L1SD
Mean
U1SD
U2SD
Without mean
With mean
F
F
F
F
F
F
F
F
F
F
F
M3m
M3m
M3m
M3m
M3m
M3d
M3d
M3d
M3d
M3d
M3d
R1/2
R3/4
Rc
A1/2
Ac
R1/4
R1/2
R3/4
Rc
A1/2
Ac
12.91
13.38
13.83
14.67
16.37
12.03
12.83
13.52
13.99
14.91
16.94
14.32
14.80
15.33
16.21
18.13
13.33
14.20
15.00
15.51
16.51
18.74
15.83
16.36
16.94
17.94
20.07
14.75
15.73
16.58
17.17
18.24
20.72
17.55
18.13
18.76
19.83
22.19
16.35
17.41
18.34
18.98
20.18
22.93
19.36
20.04
20.70
21.93
24.39
18.08
19.24
20.31
20.99
22.34
25.14
2.8090
2.8412
2.8736
2.9282
3.0340
2.7418
2.8021
2.8528
2.8852
2.9452
3.0654
2.8088
2.8409
2.8734
2.9282
3.0343
2.7416
2.8021
2.8527
2.8853
2.9449
3.0657
The ‘‘tooth’’ column uses lower case for mandibular deciduous teeth (c, m1, and m2) and upper case for permanent mandibular teeth
(C, PM3, PM4, M1, M2, and M3). Permanent maxillary and mandibular incisors are differentiated using ‘‘U’’ for ‘‘upper’’ and ‘‘L’’
for lower. Lowercase ‘‘d’’ and ‘‘m’’ at the end of molar root stages differentiate distal from mesial. Stages are as defined and abbreviated in Moorrees et al. (1963a,b). The final two columns are the natural log conception-corrected ages without the digitized mean
and with the digitized mean.
TABLE A2. Tooth scores for 82 records
Individual
c
m1
m2
UI1
UI2
LI1
LI2
C
PM3
PM4
M1
M2
M3
Abri Pataud
26.230 B
Abri Pataud
26.236
Arene Candide
(young
prince)
Arene Candide
VB
Arene Candide
VIII
Arene Candide
XI
Atapuerca 2
Badegoule #3
Barma Grande
adolescent 3,
4
Barma Grande
child
Brillenhöhle
Chateauneufsur-Charente
2
Combe-Grenal I
Ehringsdorf
juvenile
Fontéchevade
1957-53
Grotte du
Rousset
Hohlenstein
Infant #1
Hortus 2
Isturitz III
(1937) 1950-7
Isturitz III
1937–5-1
Isturitz III
1950-6
Kostenki XVIII
Kostenski XV
Krapina #45
and 45.1
(Max A)
Krapina #46
(Max B)
–
–
–
–
–
–
–
–
–
C.oc
–
Cr.75
–
–
Res.25
Res.25
–
Cr.c
–
–
R.i
R.i
Cr.c
–
–
–
–
–
–
A.c
A.c
–
–
–
–
–
A.c
A.c
R.75
–
A.c
A.5
Cr.75
–
R.i
Cr.c
Cr.75
–
–
Cr.c
–
–
Res.25
Res.25
A.c
Cr.c
Cr.c
R.5
R.25
R.25
R.i
Cr.c
R.75
Cr.75
–
R.75
A.c
R.5
Cr.75
Cr.5
–
–
Cr.5
–
–
Cr.75
–
–
–
–
–
–
–
–
–
A.c
–
–
–
A.c
–
–
A.c
–
–
A.c
–
Cr.c
A.c
–
Cr.75
–
–
Cr.5
A.c
–
C.oc
A.c
–
Cl.i
A.c
–
–
A.5
R.i
–
R.25
–
–
–
A.c
A.c
–
–
R.75
R.75
R.75
–
–
–
–
Res.25
Res.25
–
Res.25
–
–
R.25
–
R.i
A.5
–
–
–
R.25
R.i
–
Cr.c
Cr.c
Cr.75
R.c
R.5
–
Cr.75
–
–
Res.25
–
Res.25
–
Res.25
–
–
–
–
–
–
A.c
–
A.c
R.25
R.c
Cr.c
A.c
–
–
R.c
–
–
R.c
–
Cr.c
–
–
A.c
–
–
–
–
–
Cr.75
Cr.5
R.25
Cr.5
–
–
–
–
–
–
–
–
–
–
Cr.5
–
–
–
R.5
R.5
R.25
–
–
–
Cr.75
–
–
–
Cr.5
–
–
–
–
–
A.c
–
R.75
–
–
–
–
–
–
–
Cr.c
R.75
Cr.5
R.25
–
R.25
–
A.5
–
–
–
–
–
–
–
A.c
–
–
–
R.25
R.i
Cr.c
Cr.75
–
Cr.c
–
–
–
A.c
–
–
R.25
R.i
Cr.c
Cr.c
Cr.75
Cl.i
–
–
–
–
–
Res.75
Res.25
Res.5
Res.5
A.c
Res.25
A.c
R.25
–
A.c
R.i
–
A.c
R.5
–
A.c
R.25
–
–
R.i
R.5
R.75
Cr.c
–
R.5
Cr.75
–
A.c
R.5
R.c
R.5
–
–
–
–
–
–
–
–
–
–
–
–
–
Cr.c
Cr.75
R.75
–
–
American Journal of Physical Anthropology
250
L.L. SHACKELFORD ET AL.
TABLE A2. (Continued)
Individual
c
m1
m2
UI1
UI2
LI1
LI2
C
PM3
PM4
M1
M2
M3
Krapina #47
(Max C)
Krapina #51
(Mand A)
Krapina #52
(Mand B)
Krapina #53
(Mand C)
Krapina #54
(Mand D)
Krapina #55
(Mand E)
La Ferrassie 8
La Genière #3
1926
La Madeleine
child (#4)
La Quina H18
(75372)
La Quina Q761 (child)
La Chaud 3
Laugerie-Basse
1
Laugerie-Basse
2
Laugerie-Basse
3
Laugerie-Basse
6
Laugerie-Basse
teen
Le Fate II
Le Placard
56029
Le Placard
61397
Le Placard
61401 (D.G.
#31/32)
Le Placard
61401 (D.G.
#40)
Le Placard
61401-61397
Mal’ta child
(older)
Mal’ta child
(younger)
Mas d’Azil
Montgaudier 3
Paglicci
adolescent (2)
Parpallo I
Pech de l’Aze
Qafzeh 11
Qafzeh 4
Qafzeh 10
Roc de Marsal
Rochereil 194518
Saint Germain
La Rivière
1970-8 B3
Saint Germain
La Rivière
1970-8 B4
–
–
–
–
–
–
–
–
–
–
–
R.5
–
A.c
–
–
–
–
R.5
R.5
R.25
R.i
–
–
–
–
Res.5
–
–
–
–
–
R.75
R.5
R.25
R.25
A.c
–
–
–
–
–
–
–
–
A.c
–
–
R.5
A.c
R.75
Cr.c
–
–
–
–
–
–
A.c
A.c
A.c
A.c
A.c
R.c
–
–
–
–
–
–
A.c
A.c
A.5
R.c
A.5
A.c
A.5
–
–
–
R.75
–
R.5
–
–
–
–
–
–
–
–
R.5
–
R.i
–
Cr.c
–
Cr.75
Cr.5
R.75
–
Cr.75
–
–
–
A.c
A.5
–
–
R.i
Cr.c
Cr.75
–
–
R.i
–
–
–
–
–
–
–
–
–
R.i
Cr.c
Cr.75
R.c
Cr.5
–
–
–
–
–
–
–
R.5
R.i
Cr.c
Cr.75
–
–
–
–
–
–
Res.25
–
A.c
–
–
–
–
–
–
–
R.25
–
Cr.c
–
Cr.c
–
Cr.75
A.c
–
A.c
Cr.75
R.5
–
–
A.c
A.c
–
–
–
–
–
Cr.5
–
R.i
–
–
–
Res.25
A.c
–
–
R.5
R.25
Cr.c
Cr.c
Cr.75
–
–
–
–
A.c
A.5
–
Cr.75
–
–
Cr.5
C.oc
–
Cr.c
–
–
–
–
Res.5
A.c
A.c
–
–
R.75
R.75
R.5
A.c
R.5
Cr.75
–
–
–
–
–
Res.25
–
–
–
–
–
R.75
–
–
R.5
R.25
R.25
R.i
R.i
Cr.c
A.5
–
Cr.c
Cr.c
–
–
–
–
–
–
–
–
–
–
–
–
A.c
A.c
R.25
–
–
–
–
–
–
–
R.5
R.75
R.5
–
–
–
–
–
A.c
–
–
–
–
–
Cr.5
C.co
–
–
–
–
Res.25
Res.25
–
–
–
–
–
R.25
R.25
–
–
–
R.5
R.75
R.25
–
–
–
–
–
–
–
Cr.75
–
–
–
R.i
Cr.c
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
Res.5
–
R.i
–
A.c
–
–
A.c
–
–
A.c
–
–
A.c
Cr.c
R.5
A.5
Cr.75
R.25
–
–
R.i
–
–
A.5
A.c
–
R.i
R.c
–
–
Cl.i
–
R.5
–
–
–
R.75
–
–
R.75
–
–
–
A.c
R.c
–
R.5
–
Res.25
–
R.c
R.5
–
–
–
–
–
Cr.75
Cr.75
–
–
–
–
–
Cr.5
Cr.5
–
–
A.c
R.75
–
Cr.c
–
–
–
A.c
R.5
–
Cr.75
–
–
–
R.c
R.25
–
Cr.5
–
–
–
R.75
Cr.c
–
C.co
–
–
–
R.25
Cr.c
Cr.75
–
–
–
Cr.75
A.c
R.c
R.5
Cr.c
Cr.75
A.c
–
R.5
Cr.75
Cr.75
–
–
R.i
–
Cr.75
–
–
–
–
–
–
–
–
–
–
–
R.25
R.25
Cr.c
R.75
–
–
–
–
Res.25
–
–
–
–
R.5
R.i
R.i
A.5
Cr.c
–
American Journal of Physical Anthropology
251
ESTIMATING AGE-AT-DEATH FROM DENTAL REMAINS
TABLE A2. (Continued)
Individual
c
m1
m2
UI1
UI2
LI1
LI2
C
PM3
PM4
M1
M2
M3
Saint Germain
La Rivière
1970-8 B5
Saint Germain
La Rivière
1970-8 B6
and B7
Skhul I
Skhul X
Engis 2 (Smith
et al., 2010)
Gibraltar 2
(Smith et al.,
2010)
Irhoud 3
(Smith et al.,
2010)
La Quina H18
(Smith et al.,
2010)
Krapina Max B
(Smith et al.,
2010)
Krapina Max C
(Smith et al.,
2010)
Obi Rakhmat
(Smith et al.,
2010)
Qafzeh 10
(Smith et al.,
2010)
Qafzeh 15
(Smith et al.,
2010)
Scladina (Smith
et al., 2010)
Le Moustier
(Smith et al.,
2010)
Anderson et al.
(1976) ‘‘A’’
Anderson et al.
(1976) ‘‘B’’
Anderson et al.
(1976) ‘‘C’’
Anderson et al.
(1976) ‘‘D’’
Roc de Marsal
(Bayle et al.,
2009b)
–
A.c
A.c
–
–
R.25
R.25
Cr.c
Cr.c
–
R.5
–
–
–
Res.25
–
–
–
–
–
R.i
Cr.c
–
R.5
–
–
–
–
–
–
–
–
A.c
–
–
–
–
Cr.c
–
–
Cr.c
–
R.25
–
–
R.i
–
–
Cr.75
Cr.75
–
–
Cr.75
–
–
–
Cr.c
–
Cl.i
–
–
–
–
–
–
–
–
–
R.i
R.i
R.i
R.i
Cr.c
Cr.75
Cr.5
R.25
Cr.5
–
–
–
–
–
–
R.75
R.5
R.25
R.25
R.i
R.c
Cr.c
–
–
–
–
R.25
R.i
–
–
R.i
R.i
Cr.c
R.75
Cr.75
–
–
–
–
R.25
R.25
–
–
R.i
R.i
Cr.c
R.75
Cr.c
–
–
–
–
–
–
–
–
–
–
R.25
A.c
R.5
–
–
–
–
–
R.75
–
–
R.25
R.25
R.25
–
R.25
–
–
–
–
R.i
Cr.c
R.i
R.i
Cr.c
Cr.c
Cr.75
R.5
Cr.75
–
–
–
–
R.75
R.5
R.75
R.5
R.25
R.25
R.i
R.c
R.i
–
–
–
–
–
A.c
A.c
–
A.5
R.75
R.5
A.c
R.5
Cr.75
–
–
–
A.c
A.c
A.c
A.c
A.c
A.c
A.c
A.c
A.c
R.5
–
–
–
–
–
R.25
R.i
Cr.c
Cr.c
Cr.5
R.25
C.oc
–
–
–
–
–
–
A.c
A.5
R.75
R.75
R.75
A.c
R.5
C.i
–
–
–
–
–
R.i
Cr.c
Cr.c
Cr.5
C.co
R.25
C.i
–
–
–
–
–
–
A.5
R.75
R.5
R.i
R.i
R.c
Cr.c
–
R.75
Res.25
R.75
Cr.75
Cr.75
Cr.75
Cr.75
Cr.75
C.oc
–
Cr.c
–
–
Individuals 1–66 are our scores from radiographs taken by Robert Tompkins, individuals 67–77 are from our translation of numeric
scores in Smith et al. (2010), individuals 78–81 are from Anderson et al. (1976), and individual 82 is from Bayle et al. (2009b).
Abbreviations are as in Table A1.
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