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or less random sample of remains from those multiple individuals will produce an
extremely right-skewed frequency distribution. Rather, it is likely that few kinds of
skeletal element will be represented by just one specimen or one MNE but instead
most kinds of skeletal element will be represented by multiple specimens and MNE
will be > 1.
Whatever the reason for the distributions observed in Figures 6.3 and 6.4, what is
most important in the frequency distributions of NISP and MNE values of deer and
wapiti at the Meier site is that there are gaps between many of the NISP values and
particularly between the MNE values (Figures 6.3 and 6.4). Change in how the MNE
values were de¬ned may alter their ratio scale differences but is less likely to alter their
ordinal scale rank order abundances. The same is likely for variation in aggregation
and sample size. It is for these reasons that MNE values are ordinal scale. Their ratio
quantitative paleozoology

Table 6.4. Frequencies of major skeletal elements in a single
mature skeleton of several common mammalian taxa

Skeletal element Bovid/Cervid Equid Suid Canid
cranium 1 1 1 1
mandible 2 2 2 2
atlas 1 1 1 1
axis 1 1 1 1
cervical 5 5 5 5
thoracic 13 18 14 13
lumbar 6 (or 7) 6 6 (or 7) 7
sacrum 1 1 1 1
innominate 2 2 2 2
rib 26 36 28 26
sternum 1 1 1 1
scapula 2 2 2 2
humerus 2 2 2 2
radius 2 2 2 2
ulna 2 2 2 2
carpal 12 14 16 14
metacarpal 2 2 8 10
femur 2 2 2 2
patella 2 2 2 2
tibia 2 2 2 2
¬bula 2 2 2 2
astragalus 2 2 2 2
calcaneum 2 2 2 2
other tarsals 6 8 10 10
metatarsal 2 2 8 10
¬rst phalanx 8 4 16 20
second phalanx 8 4 16 16
third phalanx 8 4 16 20

scale abundances likely will vary with aggregation, de¬nition, and sample size, but
their ordinal scale abundances likely will not, though this should be evaluated for
each assemblage.
Much of the energy to develop and re¬ne a protocol for determination of MNE
values has been spent for little gain in mathematical or statistical resolution. Hours
of re¬tting fragments that are otherwise unidenti¬able would be better spent doing
other things. Increasing the accuracy of drawing skeletal specimens whether by hand
skeletal completeness, skeletal parts, and fragmentation 229

figure 6.5. Frequency distribution of skeletal parts in single skeletons of four taxa.

or with the assistance of computer-aided sophisticated technology for purposes of
detecting anatomical overlap is not a hoped for panacea.

A Digression on Frequencies of Left and Right Elements

Perhaps the simplest, as well as one of the earliest discussions of determining MNE
values (without using the term MNE), was provided by White (1953a:397), who not
only de¬ned MNI as the most frequent of either left or right elements of a species,
but also listed MNI values per skeletal part (e.g., proximal humerus, distal tibia).
Interestingly, he also sometimes listed the frequencies of both left and right skele-
tal parts (White 1952, 1953b, 1955, 1956). In the latter, he was using MNE values,
and importantly, he suggested that to divide [the total MNE, or sum of lefts and
quantitative paleozoology

Table 6.5. MNE frequencies of left and right skeletal
parts of pronghorn from site 39FA83. P, proximal;
D, distal. Original data from White (1952)

Skeletal part Left Right
Mandible 18 19
Innominate 13 19
Scapula 24 24
P humerus 3 0
D humerus 26 30
P radius 28 25
D radius 23 23
P ulna 23 22
P metacarpal 27 11
P femur 11 6
D femur 6 10
P tibia 9 9
D tibia 19 31
P metatarsal 22 15

rights per paired element or portion] by two would introduce great error because of
the possible differential distribution of the kill (White 1953a:397). He, like Voorhies
and Binford some years later, was interested in taphonomic questions regarding fre-
quencies of skeletal parts, and he observed that in most of the features in the sites
from which I have identi¬ed the bone the discrepancy between the right and left
elements of the limb bones was too great to be accounted for by accident of preser-
vation or sampling.... One should look for large discrepancies between the [frequen-
cies of] right and left elements. Small discrepancies are not necessarily signi¬cant
because they might be due to the accidents of sampling or preservation (White
1953b:59, 61).
White believed that human hunters, butchers, and consumers of animals might
distinguish between the left and right sides of an animal, and butcher, transport,
distribute, or discard the two sides of a large mammal differentially, yet he did
not attempt to ¬nd evidence for this in any of the bone assemblages he studied.
No one has, in the 50 years since White suggested it, sought such patterns in the
frequencies of bilaterally paired bones. It is easy to illustrate how this might be done
using data White (1952) published. The data involve MNE frequencies for pronghorn
(Antilocapra americana) from archaeological site 39FA83 in the state of South Dakota
(Table 6.5). If the MNE values were equivalent for left and right elements, then the
skeletal completeness, skeletal parts, and fragmentation 231

figure 6.6. Comparison of MNE of left skeletal parts and MNE of right skeletal parts in
a collection of pronghorn bones. Diagonal shown for reference. P, proximal; D, distal. Data
from Table 6.5.

points plotted in Figure 6.6 should all fall on or near the diagonal line. Many of those
points do not fall near the diagonal line. Do those points that do not fall on the line
not fall there because of statistically signi¬cant differences between the frequencies
of left and right specimens? Indeed, that seems to be the case for at least two, and
perhaps three, skeletal elements. The adjusted residuals for each category of skeletal
part indicate that there are more left proximal metacarpals (relative to few right
proximal metacarpals) and more right distal tibiae (relative to few left distal tibiae)
than chance alone would produce (Table 6.6; adjusted residuals are read as standard-
normal deviates [Everitt 1977]). There may also be more left proximal humeri (and
fewer right proximal humeri) than chance alone would produce, but the total small
sample size of proximal humeri may be in¬‚uencing the result.
Precisely this sort of analysis might be performed in order to accomplish what
White suggested to determine if there is a signi¬cant difference in frequencies of
left and frequencies of right elements. This could be important to assessing skeletal
completeness, and also to evaluating, say, frequencies of proximal and distal halves
of long bones. Both potentialities lead us to the next topic measuring the frequencies
of particular skeletal parts.
quantitative paleozoology

Table 6.6. Expected MNE frequencies of pronghorn skeletal parts at site 39FA83,
and adjusted residuals and probability values for each. Based on data in
Table 6.5

Adjusted Adjusted
Skeletal part Left residual p Right residual p
Mandible 18.8 0.26 0.397 18.2 0.28 0.390
Innominate 16.3 1.21 0.113 15.7 1.22 0.111
Scapula 24.4 0.12 0.452 23.6 0.12 0.452
P humerus 1.5 1.76 0.039 1.5 1.76 0.039
D humerus 28.5 0.71 0.239 27.5 0.73 0.233
P radius 27 0.29 0.386 26 0.30 0.382
D radius 22.9 0.03 0.492 22.1 0.03 0.488
P ulna 22.9 0.03 0.492 22.1 0.03 0.488
P metacarpal 19.3 2.61 0.004 18.7 2.62 0.004
P femur 8.7 1.13 0.129 8.3 1.16 0.123
D femur 8.1 1.07 0.142 7.9 1.09 0.138
P tibia 9.2 0.10 0.460 8.8 0.10 0.460
D tibia 25.5 1.95 0.026 24.5 1.98 0.024
P metatarsal 18.8 1.09 0.138 18.2 1.10 0.136


Other than Whites (1953b) suggestions regarding comparison of the frequencies
or the spatial distributions of right-side skeletal parts and left-side skeletal parts,
how have MNE data been used? As indicated earlier, they have been used largely by
taphonomists who seek to discern if, and why, frequencies of skeletal parts diverge
from a model of some number (usually the MNI of the collection under study) of
complete skeletons. They have also been used to measure the degree of fragmentation
evident in an assemblage. Procedures used to analyze skeletal-part frequencies are
discussed ¬rst. Throughout, it is assumed that the principle of anatomical overlap
or redundant skeletal parts has been used to measure MNE, and it is assumed that
all skeletal specimens (e.g., diaphysis and epiphysis fragments of long bones) have
been included.
Usually the number of complete skeletons to which observed skeletal-part frequen-
cies are compared is that expected given the MNI for the taxon of concern. If the MNI
is ten of an artiodactyl species, then there should be, for example, ten skulls, seventy
cervical vertebrae, twenty humeri (= 10 left + 10 right), eighty ¬rst phalanges, and so
on. Were one to graph the frequencies of the major categories of skeletal elements for
skeletal completeness, skeletal parts, and fragmentation 233

Table 6.7. Frequencies of skeletal elements in a single
generic artiodactyl skeleton

Skeletal element N Skeletal element N
Skull 1 Mandible 2
Cervical vertebra 7 Thoracic vertebra 13
Lumbar vertebra 6 Sacrum 1
Rib 26 Innominate 2
Scapula 2 Humerus 2
Radius 2 Ulna 2
Carpal 12 Metacarpal 2
Femur 2 Tibia 2
Tarsal 10 First phalanx 8
Second phalanx 8 Third phalanx 8

a single artiodactyl carcass (Table 6.7), a graph like the one shown in Figure 6.7 might
be the result. (This type of graph is very similar to the one used by many early workers
who had followed Whites [e.g., 1952] lead and interpreted skeletal-part frequencies.)
Comparing the frequency of skeletal parts of a taxon in a prehistoric collection to
that model would be dif¬cult visually (using the graph) and also statistically (using
a table of expected and observed frequencies). To simplify comparisons of observed
frequencies with those manifested in the model, the model (expected frequencies)
and the observed frequencies can be modi¬ed such that divergence of the latter from
the former is made obvious. That is precisely what several analysts did beginning in
the 1960s and 1970s.

Modeling and Adjusting Skeletal-Part Frequencies

Binford (1978, 1981, 1984; Binford and Bertram 1977) was not interested in the fre-
quencies of left and right elements in a collection, or in the frequencies of third
cervical and seventh thoracic vertebrae, or the like; such distinctions were unim-
portant to the questions he was asking of the remains of caribou (Ranifer tarandus)
exploited by his Inuit informants nor were they relevant to the Paleolithic assem-
blages of faunal remains he was studying. Rather, he was interested in whether humeri
preserved better than tibiae, whether Inuit hunters more often transported femora
from kill sites to camp/consumption sites than they transported phalanges, and the
like. Therefore, he divided MNE values for each anatomical part or portion by the
number of times that part or portion occurs in one complete skeleton. Skulls were
quantitative paleozoology

figure 6.7. Frequencies of skeletal elements per category of skeletal element in a single
artiodactyl carcass. Data from Table 6.7.

divided by one; mandibles and humeri and femora (etc.) by two; cervical vertebrae by
seven; and so on (see Table 6.4 for various divisors). This standardized (or normed)
the observed MNE counts to individual carcasses or skeletons. Each caribou skull
represented one skeleton or individual, every two femora represented the equivalent
of one skeleton whereas a single femur represented half of a skeleton or individual,
every eight ¬rst phalanges of caribou represented one skeleton but every single ¬rst
phalanx represented the equivalent of 1 /8 or 0.125 individuals, and so on through
the entire skeleton.
Binford (1984:50) ultimately referred to the skeletally standardized values as mini-
mum animal units, or MAU values. Typically, MAU values themselves were normed
by dividing all MAU values by the greatest observed MAU value in a particular collec-
tion and multiplying each resulting value by 100. Because the values produced ranged
between 0 and 100 and were similar to percentages, they were (and are) sometimes
referred to as %MAU values. Because the MNE values were all normed to the same
scale, samples of faunal remains of quite different sizes could be compared graph-
ically without fear of variation in sample size in¬‚uencing the results. Thus, White
skeletal completeness, skeletal parts, and fragmentation 235

figure 6.8. MNE and MAU frequencies for a ¬ctional data set. Data from Table 6.8.

(1955, 1956) normed some of the assemblages he studied, as did others after him (e.g.,
Gilbert 1969, Kehoe and Kehoe 1960; Wood 1962, 1968), long before Binford (1978,
1981, 1984) popularized this analytical protocol.
Norming makes graphs of skeletal-part frequencies easier to interpret. Figure 6.8
presents the data from Table 6.8 in the same format as that in Figure 6.7, but both
traditional MNE values per skeletal part or portion and MNE values standardized to
a single artiodactyl skeleton, or MAU values, are presented. The data in Table 6.8 are
¬ctional; a two-digit whole number was drawn from a table of random numbers and
served as the MNE for a skeletal part or portion. Those values were divided by the
values in Table 6.7 to generate the standardized, or MAU, values in Table 6.8. Notice
the difference in the two sets of values plotted in Figure 6.8. Converting MNE values
to MAU values mutes much of the variation between frequencies of skeletal parts
and portions that is due to variation in how frequently a kind of part or portion is
represented in a skeleton.
But the more important thing to realize is that a comparison of MNE values to
a model skeleton is dif¬cult to interpret, as exempli¬ed in Figure 6.9, where the
quantitative paleozoology

Table 6.8. MNE and MAU frequencies of skeletal parts and portions. MNE
frequencies were generated from a random numbers table

Skeletal element MNE MAU Skeletal element MNE MAU
Skull 24 24 Mandible 62 31
Cervical vertebra 42 6 Thoracic vertebra 12 0.9
Lumbar vertebra 21 3.5 Sacrum 39 39
Rib 89 3.4 Innominate 20 10
Scapula 5 2.5 Humerus 56 28
Radius 67 33.5 Ulna 10 5
Carpal 88 7.3 Metacarpal 79 39.5
Femur 32 16 Tibia 95 47.5
Tarsal 98 9.8 First phalanx 78 9.75
Second phalanx 13 1.6 Third phalanx 28 3.5

figure 6.9. MNE values plotted against the MNE skeletal model. Data from Tables 6.7
and 6.8.
skeletal completeness, skeletal parts, and fragmentation 237

figure 6.10. MAU values plotted against the MAU skeletal model (for forty-eight individ-
uals). Data from Table 6.8.

MNE values from Table 6.8 are compared to the MNE model skeleton from Table
6.7 (graphed in Figure 6.7). MAU values present a more readily interpretable result,
as exempli¬ed by Figure 6.10, where MAU values from Table 6.8 are compared to
the MAU model skeleton. Recall that MAU values are MNE values that have been
standardized to a complete skeleton. That standardization process makes comparison
of observed frequencies of skeletal parts and portions with a skeletal model more
comprehensible because the MAU skeletal model sets the frequency of all skeletal
parts and portions to the MNI observed in the total collection. If the MNI is seven, the
MAU skeletal model is set to seven across all skeletal parts; if the MNI is forty-three,
the MAU skeletal model is set to forty-three across all skeletal parts and portions;
and so on.
A means to standardize MNE values related to the one described by Binford (1978,
1981, 1984; Binford and Bertram 1977) was designed with a different analytical goal
in mind. Brain (1967, 1969, 1976) did not use the term MNE (nor did he use the term
quantitative paleozoology

MNI), though it is likely he used that quantitative unit to produce what he called the
%survivorship of skeletal parts (Lyman 1994a). Given his descriptions of how he
calculated %survivorship, Brain likely used the equation:

([MNEi ]100)/(MNI[number of times i occurs in one skeleton]), (6.1)

where i denotes a particular skeletal part or portion (e.g., proximal half of humeri,
thoracic section of vertebral column). The denominator in this equation is the num-
ber of each skeletal portion to expect if 100 percent of them are in the collection, in
light of the MNI for the collection. Thus, the denominator is equal to the maximum
MNE in the assemblage. If there is an MNI of ten mammals, we would expect to ¬nd
ten skulls, twenty humeri, and so on, depending on the taxon under consideration.
As it turns out, Brains %survivorship equation produces exactly the same value
as Binfords %MAU. The latter is calculated with the equation (Binford 1978, 1981,

([MAUi ]100)/maximum MAU in the assemblage, (6.2)

where i again denotes a particular skeletal part or portion. Note that MAUi is deter-
mined with the equation:

(MNEi )/number of times i occurs in one skeleton. (6.3)

Substituting Eq. 6.3 into Eq. 6.2,

([MNEi /number of times i occurs in one skeleton]100)/(maximum MNEi /
number of times maximumi occurs in one skeleton). (6.4)

Given that the /number of times i occurs in one skeleton in the numerator and
denominator cancel each other out, Eq. 6.4 is mathematically identical to Eq. 6.1 .
Binford and Brain each determined a means to quantify skeletal parts and to scale
them in such as manner as to allow graphing those values in forms that were easily
interpreted. Various paleontologists derived similar equations that are in fact math-
ematically identical (Andrews 1990; Dodson and Wexlar 1979; Korth 1979; Kusmer
1990; Shipman and Walker 1980). It suf¬ces here to describe one of them (see Lyman
[1994b] for detailed discussion). Andrews (1990:45) suggested the equation:

Ri = Ni /(MNI)Ei, (6.5)

where Ri is the relative (proportion) frequency of skeletal part i, Ni is the observed
frequency of skeletal part i in the assemblage, MNI is the minimum number of
individuals in the assemblage, and Ei is the frequency of skeletal part i in one
skeleton. (In practice, Andrews [1990] multiplies Ri by 100 to derive a percentage
skeletal completeness, skeletal parts, and fragmentation 239

Table 6.9. MAU and %MAU frequencies of bison (Bison bison) from two sites. Data
for 32SL4 from Wood (1962); data for 24GL302 from Kehoe and Kehoe (1960)

Skeletal part 32SL4-MAU 32SL4-%MAU 24GL302-MAU 24GL302-%MAU
Skull 9 60 16 43
Mandible 11 73 37 100
Atlas 2 13 20 54
Axis 5 33 16 43
Cervical 2 13 15 41
Thoracic 1 7 12 32
Lumbar 1 7 6 16
Sacrum 0 0 8 22
Humerus 7 47 7 19
Radius 7 47 13 35
Ulna 11 73 10 27
Metacarpal 3 20 18 49
Innominate 1 7 12 32
Femur 2 13 15 41

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