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Tibia 8 53 14 38
Astragalus 15 100 19 51
Calcaneum 8 53 18 49
Metatarsal 3 20 13 35
First phalanx 4 27 14 38
Second phalanx 9 60 18 49
Third phalanx 5 33 14 38



frequency.) Because Ni = MNEi, and because (MNI)Ei = the expected number of
parts were all of i present given MNI, then Eq. 6.5 is mathematically the same as
Eqs. 6.1 and 6.4.
Recall that norming MAU values to %MAU, or calculating %survivorship, allows
one to graphically compare samples of different sizes. Deciphering the signi¬cance of
a comparison of MAU values determined for one collection that contains remains of
¬ve individuals with another collection that contains remains of twenty individuals
would be dif¬cult without norming both to the same scale. Table 6.9 presents data
from two sites, one with remains of an MNI of ¬fteen bison (Bison bison) (Wood
1962) and the other with remains of an MNI of thirty-seven bison (Kehoe and Kehoe
1960). If the unnormed MAU values are graphed together, it is dif¬cult to discern
what is happening (Figure 6.11 ). But if both sets of MAU values are normed to %MAU
values and graphed, then it is much easier to discern similarities and differences in the
quantitative paleozoology
240




figure 6.11. MAU values for two collections with different MNI values. MNI at 32SL4 is
15; MNI at 24GL302 is 37. Compare with Figure 6.12. Data from Table 6.9.


frequencies of skeletal parts and portions (Figure 6.12). Such norming, however, gives
values that some statisticians suggest cannot be analyzed statistically; the in¬‚uence
of sample size is, for example, masked by such norming and will in¬‚uence statistical
results as a consequence.
MNE originally (if implicitly) formed the basis of the MNI quantitative unit. As
research interests shifted from taxonomic abundances to include consideration of
skeletal-part abundances, MNE became a unit in need of explicit recognition. And
that is in fact what it received beginning in the 1960s and especially the 1970s. With
explicit recognition came consideration of how to operationalize MNE. It would
be interesting to review the numerous discussions of how to determine MNI that
appeared in the 1950s through 1980s with the goal of ascertaining if the commentators
worried as much about operationalizing MNI as those who in the 1980s and 1990s
have worried about operationalizing MNE.
MNE became a very popular and much used quantitative unit after about 1980.
It was dif¬cult to read an article on paleozoology (especially in the zooarchaeology
skeletal completeness, skeletal parts, and fragmentation 241




figure 6.12. %MAU values for two collections with different MNI values. MNI at 32SL4
is 15; MNI at 24GL302 is 37. Compare with Figure 6.11 . Data from Table 6.9.


literature) without encountering it or one or more of its derivatives (MAU, %MAU,
%survivorship, etc.), likely because of the increased frequency of detailed tapho-
nomic analyses that centered around questions thought to be answerable by analyses
of skeletal-part frequencies. Interestingly, the quantitative units derived from MNE
may have a utility that could serve a long sought after analytical goal. That goal is to
measure the average or overall completeness of the skeletons represented in a collec-
tion. Are those skeletons all more or less complete, or are they relatively incomplete?
It is to measuring that variable that we next turn.



M E A S U R I N G S KE L E T A L CO M P L E TE N E S S


In the 1950s, Shotwell (1955, 1958) developed a method that he thought would allow
a paleozoologist to separate the remains of animals originating in one biological
community from the remains of animals that originated in another community. He
referred to the local community the one in which the collection locality was located
as the proximal community, and any other community that might have contributed
quantitative paleozoology
242


taxa (but nonlocal) as the distal community. Shotwell reasoned that members of the
proximal community would be more skeletally complete than members of the distal
community.
Commentators identi¬ed taphonomic dif¬culties with sorting out the members of
the two communities (e.g., Clark and Guensburg 1970; Dodson 1973; Voorhies 1969;
Wolff 1973). These included the assumption that skeletons of individuals originating
near the site of accumulation and deposition would be more complete than those of
individuals that originated some distance away. This assumption presumed that bone
accumulation processes (mechanisms, such as ¬‚uvial transport, and agents, such as
carnivores) would operate according to a principle of distance decay the greater
the distance away, the fewer of an organisms remains that would be transported
to and deposited at the (future) site of recovery. Shotwell (1958:272) stated that the
community with the greater relative [skeletal] completeness is the one nearest to
the site of deposition and is therefore referred to as the proximal community. We
now know that the mechanisms and agents that accumulate faunal remains display
no consistent or universal distancedecay pattern. Sometimes they do, sometimes
they do not. Shotwells suggestion is best considered as a hypothesis that warrants
examination on a case-by-case basis.
Shotwells method involves determination of MNI, and then calculating the cor-
rected number of specimens per individual (CSI). The CSI is the index used to deter-
mine whether a taxon represents a member of the proximal or distal community.
Although Shotwell (1955, 1958) used the terms specimens and elements interchange-
ably in his discussion, what he had in mind was MNE values rather than NISP values.
He wrote his formula as:

CSI = 100(NISP)/number of elements per skeleton, (6.6)

where CSI is the corrected number of specimens (per individual), and the number of
elements per skeleton is the number that could be identi¬ed in a complete skeleton,
excluding ribs and vertebrae. Because the average skeletal completeness per individual
per taxon is the desired measure, the denominator should be multiplied by the MNI
of the taxon under study. Because Shotwell was dealing with skeletal elements that
were anatomically complete, his formula for measuring skeletal completeness can be
rewritten more completely as:

CSIi = 100(MNE)/MNE per complete skeleton
(minus vertebrae and ribs)—[MNI]. (6.7)

For one standard artiodactyl skeleton as in Table 6.7, the denominator would be
sixty-¬ve. This step accounts for the fact that a standard artiodactyl, for instance,
skeletal completeness, skeletal parts, and fragmentation 243




figure 6.13. Relationship between Shotwell™s CSI (or skeletally normed NISP/MNI ratio)
per taxon and NISP per taxon for the Hemphill paleontological mammal assemblage. Taxa
assigned to the proximal community by Shotwell are represented by ¬lled squares; they
have high NISP/MNI ratios, but also greater sample size than taxa assigned to the distal
community (un¬lled squares). Simple best-¬t regression line (Y = 0.276X0.48 ) shown for
reference (r = 0.85, p < 0.001). Data from Shotwell (1958).



has a different number of identi¬able elements than a standard perissodactyl (fewer
phalanges than an artiodactyl), or a standard canid (more metapodials and phalanges
than an artiodactyl) (Table 6.4). It is important to note that in both the numerator
and the denominator, MNE is the total number of elements present in a collection
regardless of which elements are represented.
Grayson (1978b) argued that Shotwell™s method was ¬‚awed for statistical reasons,
regardless of the history of accumulation of faunal remains. Grayson showed that
the calculation of skeletal completeness using Shotwell™s method produces a mea-
sure of sample size. Using Shotwell™s original formula (Eq. 6.6), CSI is a skeletally
normed ratio of NISP/MNI. As Grayson (1978b) showed, the ratio NISP/MNI varies
with NISP. Figure 6.13 shows CSI and NISP values for one of Shotwell™s (1958)
assemblages plotted against one another. As NISP (sample size) increases, so too
does the value of the ratio of NISP/MNI. There is an autocorrelation between
quantitative paleozoology
244


the two variables because NISP occurs on both sides; taxa with larger samples
will appear to be more skeletally complete because of the relationship shown in
Figure 2.4.
Thomas (1971 ) adapted Shotwell™s method to an archaeological setting. Thomas
(1971:367) reasoned that the assumption of an archaeologist was not that the taxa
from a proximal community would be more skeletally complete than those from a
distal community, but rather that skeletons of taxa exploited by humans would be
more skeletally incomplete than skeletons of animals that died naturally on the site;
“The primary assumption for the [zoo]archaeologist to evaluate is that the dietary
practices of man tend to destroy and disperse the bones of his prey species.” This
may seem to be a reasonable assumption, but it is taphonomically na¨ve for the same
±
reasons that Shotwell™s method is. Thomas™s (1971 ) alteration of Shotwell™s method
is ¬‚awed for the same reason that Shotwell™s original method is ¬‚awed. Thomas did
not really modify Shotwell™s method, but instead used exactly the same reasoning
and formula to measure skeletal completeness; what he did different than Shotwell
was to argue that the least skeletally complete taxa (Shotwell™s distal community)
were the ones that humans had accumulated and deposited. Figure 6.14 is a graph of
the data from one site analyzed by Thomas (1971 ) in the same form as Shotwell™s data
is graphed in Figure 6.13. Again, the relationship between CSI (or the standardized
ratio of NISP/MNI) is strongly correlated with NISP. And, it is obvious that the least
skeletally complete taxa not only are the ones that Thomas suggests were accumulated
and deposited by human predators, but those same taxa have the smallest sample
sizes.



A Suggestion

Perhaps because of the serious statistical weaknesses of Shotwell™s method, whether
used as he originally intended or as Thomas (1971 ) modi¬ed it, no paleozoologist
has used it since the 1970s. Reitz and Wing™s (1999:255) nonjudgmental mention of
the method is the only reference to it published since 1980 of which I am aware.
Shotwell™s method failed for taphonomic reasons and also for statistical reasons.
What no one has previously noted is that the method did not directly take account
of variation in the frequencies of individual skeletal parts and portions; rather, it
merely calculated an average skeletal completeness based on whatever skeletal parts
and portions per individual were represented. The skeletal completeness index was
calculated the same way regardless of the skeletal parts and portions present in the
skeletal completeness, skeletal parts, and fragmentation 245




figure 6.14. Relationship between Thomas™s CSI per taxon and NISP per taxon for the
Smoky Creek zooarchaeological mammal collection. Taxa thought to be accumulated and
deposited by humans are represented by ¬lled squares; they have low NISP/MNI ratios,
but also smaller sample size than taxa thought to have been naturally accumulated and
deposited (un¬lled squares). Simple best-¬t regression line (Y = 0.262X0.564 ) shown for
reference (r = 0.93, p < 0.001). Data from Thomas (1971 ).


collection. (This is analogous to the ¬‚aw with skeletal mass allometry described in
Chapter 3.)
The manner in which MNE has been used to examine skeletal completeness sug-
gests a solution to some of the problems with Shotwell™s original method. Table 6.10
provides MNE values and MAU values for twenty skeletal parts and portions of
two taxa, each of which has an MNI of 10. Taxon 1 has relatively even skeletal-part
frequencies (after Faith and Gordon 2007) measured as MAU values (Shannon™s
e = 0.999), whereas taxon 2 has less even skeletal-part frequencies (e = 0.962). Indi-
viduals of taxon 1 are more skeletally complete, on average, than individuals of
taxon 2 (Figure 6.15). One might argue, then, that taxon 1 comprises the proxi-
mal community whereas taxon 2 comprises the distal community. If there are > 2
taxa, follow Shotwell™s lead (perhaps) and assign all taxa with e > average (or some
other value) to the proximal community and taxa with e < average to the dis-
tal community. This version as well as Shotwell™s original method assumes taxa
quantitative paleozoology
246


Table 6.10. Skeletal-part frequencies (MNE and MAU) for two taxa of
artiodactyl. MNI = 10 for both. Data are ¬ctional

Skeletal element Taxon 1 “MNE 1 “MAU Taxon 2“MNE 2“MAU
Skull 10 10 5 5
Mandible 19 9.5 8 4
Cervical vertebra 68 9.7 42 6
Thoracic vertebra 120 9.2 30 2.3
Lumbar vertebra 56 9.3 31 5.2
Sacrum 8 8 3 3
Rib 245 9.4 200 7.7
Innominate 18 9 2 1
Scapula 19 9.5 5 2.5
Humerus 20 10 18 9
Radius 18 9 16 8
Ulna 17 8.5 14 7
Carpal 115 9.6 42 3.5
Metacarpal 16 8 8 4
Femur 19 9.5 20 10
Tibia 19 9.5 15 7.5
Tarsal 92 9.2 65 6.5
First phalanx 78 9.8 44 5.5
Second phalanx 75 9.4 32 4
Third phalanx 72 9 16 2



will not occur in both the proximal and the distal communities, which may be
false.
In the preceding paragraph MAU values were used rather than MNE values to
measure the evenness of skeletal-part frequencies because the former provide the
model baseline. Any number of anatomically complete skeletons would produce a
Shannon™s e = 1.0 using MAU values; any number of anatomically complete skele-
tons would produce a Shannon™s e = 0.862 using MNE values (the MNE values in
Table 6.7 were used to generate this e value), making any observed value more dif¬-
cult to interpret (an observed e would range from 0 to 1.0 rather than from 0 to
0.862). The example in Table 6.10 and Figure 6.15 is ¬ctional. With real data, a critical
early step is to determine if the numbers of left and the numbers of right elements
of bilaterally paired bones are not signi¬cantly different (e.g., Table 6.6). If they are
signi¬cantly different, then measures of skeletal-part abundances calculated as MAU
skeletal completeness, skeletal parts, and fragmentation 247




figure 6.15. Bar graph of frequencies of skeletal parts (MAU) for two taxa. Data from
Table 6.10.



will be meaningless with respect to the completeness of individual skeletons. Recall
that MAU values ignore left and right distinctions and divide the observed MNE
by the number of times a skeletal part or portion occurs in one skeleton. If there
are major discrepancies in the frequencies of left and right elements, then the MNI
(maximum number of, say, left or right elements = number of skeletons) will be
considerably larger than any MAU value (say, [lefts + rights]/2).
The procedure of measuring skeletal completeness using the evenness of skeletal
parts measured as MAU values described in the preceding paragraph should not
be adopted uncritically (if at all). The evenness of skeletal parts may be a func-
tion of sample size (Chapter 5). And recall the other problems that attend MNE “
in¬‚uences of aggregation and de¬nition. These problems also in¬‚uence MAU and
%MAU values. Graphs such as that in Figure 6.15 may help evaluate the degree of
skeletal completeness. But if NISP and MNE (or MAU) per skeletal part are corre-
lated, then the two quantitative units provide redundant information on skeletal-part
quantitative paleozoology
248


frequencies. As we saw in Chapter 2, NISP is not af¬‚icted by problems of aggregation
or de¬nition, so evaluating skeletal completeness can be done with NISP to avoid
the problems with MNE and MAU (see Grayson and Frey [2004] for additional
discussion).
Whether taxa with complete skeletons derived from a local (proximal) commu-
nity, or were naturally deposited, and whether taxa with incomplete skeletons derived
from a distant (distal) community, or were deposited by particular bone accumu-
lating processes, are different questions. Deciding what that completeness (or lack
thereof) means in terms of taphonomy requires more actualistic research. If Shotwell
and Thomas were correct, and even if they were not, the concept of skeletal-part
frequencies suggests a technique to measure skeletal completeness in a much more
anatomically realistic way than that proposed by Shotwell. The new technique comes
from explicit recognition of MNE as a quantitative unit, second, that MNE is derived
(inherently problematic), and third, that NISP and MNE are often correlated. The
solution is to alter the value plotted on the horizontal axis of Figure 6.15 from MAU
to NISP.
Recall that the NISP and MNE value pairs for deer remains from the Meier site are
strongly correlated, as are those values for wapiti remains. The frequency distribu-
tions of each suggest that the NISP values provide ordinal scale data on skeletal-part
frequencies (Figures 6.3 and 6.4). Are deer or are wapiti more completely represented
skeletally? The Shannon evenness index for the NISP per skeletal part of the two taxa
are: deer, e = 0.993 (heterogeneity [H] = 3.114); wapiti, e = 0.925 (H = 2.901). Deer
skeletons are a bit more completely represented than are wapiti skeletons. This is
perhaps explicable by the fact that deer are smaller than wapiti and some carcasses of
adult deer might be transported as a single unit (they must be divided into smaller
parts [usually anatomical quarters] in many instances), wapiti are considerably larger
than deer and must always be divided into smaller portions for transport purposes.
Butchering (reduction) of carcasses for transport is likely to be more extensive and
result in more culling and discard of wapiti bones at a kill site than is butchering of
deer.
There is yet another possible way to compare frequencies of skeletal parts of two
assemblages (whether two different taxa in the same collection or the same taxon
in two different collections). The technique is to calculate a χ 2 statistic, and if it is
signi¬cant and thus indicates a signi¬cant divergence from random frequencies, then
calculate adjusted residuals for each value to determine which frequencies diverge
from randomness. Comparison of the NISP per skeletal-part data for deer and wapiti
in Table 6.3 indicates the two sets of values are signi¬cantly different (χ 2 = 90.41,
skeletal completeness, skeletal parts, and fragmentation 249


Table 6.11. Expected (EXP) frequencies of deer and wapiti remains at Meier,
adjusted residuals (AR), and probability values for each (p). Based on data
in Table 6.3

Skeletal part Deer EXP Wapiti EXP Deer AR Wapiti AR Deer p Wapiti p
’2.746 <0.01 <0.01
mandible 176.3 43.7 2.741
’2.324 <0.05 <0.05
atlas 37.7 9.3 2.316
’0.103 >0.1 >0.1
axis 19.2 4.8 0.102
’0.180 >0.1 >0.1
cervical 77.7 19.3 0.180
’1.597 >0.1 >0.1
thoracic 81.7 20.3 1.599
’1.604 >0.1 >0.1
lumbar 111.4 27.6 1.608
’0.778 >0.1 >0.1
rib 226.0 56.0 0.779
’0.280 >0.1 >0.1
innominate 131.4 32.6 0.281
’1.348 >0.1 >0.1
scapula 68.1 16.9 1.350
’1.744 >0.05 >0.05
humerus 141.0 35.0 1.743
’0.090 >0.1 >0.1
radius 163.5 40.5 0.090
’1.546 >0.1 >0.1
ulna 95.4 23.6 1.543
’0.159 >0.1 >0.1
metacarpal 133.8 33.2 0.159
’2.153 <0.05 <0.05
femur 95.2 24.8 2.101
’0.647 >0.1 >0.1
patella 12.0 3.0 0.649
’2.393 <0.05 <0.05
tibia 176.3 43.7 2.394
’2.297 <0.05 <0.05
astragalus 116.2 28.8 2.293
’3.313 <0.05 <0.05
calcaneum 141.9 35.1 3.301
’2.579 <0.05 <0.05
naviculo-cuboid 76.1 18.9 2.585
’1.880 >0.05 >0.05
metatarsal 153.1 37.9 1.888
’3.656 <0.01 <0.01
¬rst phalanx 248.5 61.5 3.662
’3.708 <0.01 <0.01
second phalanx 181.1 44.9 3.985
’1.298 >0.1 >0.1
third phalanx 80.1 19.9 1.296


p < 0.001). Calculation of expected values and adjusted residuals indicate that nine
of the twenty-three included skeletal parts differ signi¬cantly between the two taxa
in terms of their abundances (Table 6.11 ). Relative to wapiti remains, deer mandibles,
atlas vertebrae, tibiae, astragali, calcanei, and naviculo-cuboids are overrepresented
whereas deer femora, ¬rst phalanges, and second phalanges are under represented.
Why this is the case is a taphonomic question, but quantitative analysis has identi¬ed
the signi¬cant variation and indicates those aspects of the data requiring taphonomic
analysis. One of the analytical avenues that might be explored in trying to determine
why variation in NISP occurs between the two taxa is variation in fragmentation,
which brings us to methods for measuring fragmentation.
quantitative paleozoology
250


MEASURING FRAGMENTATION


Each distinct kind of skeletal element can be conceived as a model of how a particular
kind of “natural” biological thing looks. If a specimen of a skeletal element “ femur,
atlas vertebra, or third upper molar “ is anatomically incomplete, it is not biolog-
ically natural but instead is fragmentary (relative to the model). Even if the entire
element is represented, it may be in unnatural pieces or fragments (just as the bones
and teeth of a complete skeleton might be disarticulated and dispersed in a unnat-
ural arrangement). Thus, individual, anatomically complete skeletal elements can
be conceived of as not only whole or complete, but as single or individual discrete
entities (ignoring for sake of discussion whether a tooth embedded in a mandible
is a separate, distinct, discrete skeletal element or not). Given the model of natural
whole discrete skeletal elements, an obvious quantitative measure is the number of

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