. 7
( 10)


Taphonomists seek answers to questions that differ in kind and scale from those
traditionally asked by paleozoologists. (This is not meant to imply that paleozo-
ologists and taphonomists are two distinct sets of researchers; rather, it is meant
to underscore differences in the questions that are asked about a collection of fau-
nal remains.) Instead of asking how many or how much of each taxon contributed
to a collection what a paleozoologist would normally ask, although perhaps with
different target variables in mind (Figure 2.1 ) a taphonomist would ask why only
certain skeletal elements, individual organisms, or taxa are represented in a collec-
tion. Taphonomists attempt to measure and understand why paleozoologists do not
always ¬nd complete articulated skeletons. Rather, what they typically ¬nd are vari-
ously incomplete skeletons, often comprising broken skeletal elements. The questions
taphonomists ask, then, are focused more on the proximate causes for the existence
of a bone assemblage and why the assemblage is made up not only of the taxa that
it represents, but the skeletal parts and the taxonomic abundances that it is, as well
as such questions as why some bones are missing, others are broken, and still others
are abundant.
Taphonomists effectively shift the level of measurement from taxonomic abun-
dances to attributes of a collection of remains, such as skeletal-part frequencies, usu-
ally of a single taxon at a time (Lyman 1994c). Paleozoologists with taphonomic inter-
ests have an advantage over other scientists who study the past such as paleobotanists;
the former have a model of what a complete animal carcass consisted of skeletally. If
it was a mammal, then it had one skull, left and right mandibles, (most likely) thir-
teen left and thirteen right ribs, thirteen thoracic vertebrae, left and right humeri,
and so on. A paleobotanist has no such model of, say, an apple tree; the questions
How many leaves? How many apples? How many seeds? cannot be answered with any
con¬dence for want of a model of a standard apple tree with N1 leaves, N2 apples, and
N3 seeds. The model of a complete animal is where a paleozoological taphonomist
starts. Measuring how a collection of bones and teeth of a taxon differ from a col-
lection of complete skeletons of that taxon is the ¬rst step toward answering the
ultimate taphonomic question: How and why are these bones and teeth here and in
the condition that they are whereas other bones and teeth are missing or in different
condition (Lyman 1994c)?
Increasing demand to answer more taphonomically detailed questions in order to
build strongly warranted explanations of the paleozoological record in the 1960s and
1970s brought about a growth in the number of quantitative units used to measure
aspects of the record (Lyman 1994a). Perhaps not surprisingly, then, the ¬rst explicit
use of MNE is found in a seminal, explicitly taphonomic study. Voorhies (1969)
sought to understand the taphonomy of an early Pliocene paleontological site in
skeletal completeness, skeletal parts, and fragmentation 217

the state of Nebraska. He did not use the term MNE but listed what he termed the
number of individual skeletal elements represented for twenty-six different skeletal
elements of an extinct form of antelope the remains of which made up the bulk of
the collection he studied. Voorhies (1969:1718) described the quantitative unit as the
minimum number of elements (bones) represented by all identi¬able fragments of
the element in the collection, and distinguished it from the [minimum] number of
individual animals represented by nonserial paired [skeletal] elements.
Voorhies designed the MNE quantitative unit because he was concerned with why
some skeletal parts were very frequent in the collection whereas others were of mid-
level abundance and still others were rare. Observed MNE frequencies of skeletal
parts diverged from the model of a set of complete skeletons, and Voorhies wanted
to know why that divergence existed. He began by trying to determine if a pattern
in skeletal-part frequencies existed, and to do that required that he use an MNE-
type quantitative unit. He sought an answer to a question concerning taphonomy,
in particular a question concerning skeletal-part abundances. He found that skeletal
elements that were of light weight relative to their volume tended to be winnowed
out of a deposit by ¬‚owing water whereas bones that were heavy relative to their
volume lagged behind (were not removed by ¬‚owing water). His research resulted in
the designation of what came to be known as Voorhiess Groups distinctive groups
of particular skeletal elements that are variously winnowed, moved, or left behind
by the action of ¬‚owing water (e.g., Behrensmeyer 1975; Lyman 1994c; Wolff 1973).
About a decade after Voorhies (1969) used the MNE quantitative unit, zooar-
chaeologists seem to have independently invented the same unit. The question they
asked was ultimately the same one asked by Voorhies: Why were some skeletal parts
abundant and other parts rare in a collection? Binford (1978, 1981, 1984; Binford
and Bertram 1977) was interested in how hominids differentially dismembered and
transported portions of prey carcasses, and wanted to identify the effects of natural
attrition such as carnivore gnawing on frequencies of skeletal parts. Thus, Binford,
like Voorhies, started with the model of a complete carcass or skeleton (or multiple
complete carcasses or skeletons), and sought to explain why collections of prehis-
toric bones had, say, more thoracic vertebra than ribs, or more distal humeri than
proximal humeri. Binford initially de¬ned the quantitative unit he designed as the
minimum number of individual animals represented by each anatomical part and
referred to them as MNI values (Binford and Bertram 1977:79). Binford (1984:50)
made it clear that his MNI values were not the same as the traditional MNI values of
Stock (1929), White (1953a), and Chaplin (1971 ), when he stated that I have decided
to reduce the ambiguity of language by no longer referring to anatomical frequency
counts as MNIs.
quantitative paleozoology

Bunn (1982) is the ¬rst paleozoologist I know of to use the term MNE. Bunn
(1982:35) de¬ned the unit as the minimum number of elements, but he did not de¬ne
element. He, like Binford (1978, 1981 ; Binford and Bertram 1977) before him, used
MNE to signify not only anatomically complete skeletal elements (e.g., femora),
but anatomically incomplete skeletal parts (e.g., the distal half of humeri) and also
portions of a skeleton made up of multiple discrete skeletal elements (e.g., thoracic
portion of vertebral column). This makes MNE even more of a derived unit than
traditional MNI values. Both MNE and MNI might be determined with or without
consideration of age, sex, and size differences among specimens (is a particular frag-
ment of a proximal left humerus from a small female, 2-year-old deer, distinguished
from another fragment of a proximal left humerus from a large male, 5-year-old deer
that does not anatomically overlap the ¬rst?). But whereas an individual animal is a
natural, inherently bounded unit (its boundaries are its skin), a femur is a skeletal
element that is naturally bounded (it is discrete), but a distal femur is not naturally
bounded and a thoracic section of the vertebral column is not necessarily discrete.
These sorts of considerations in¬‚uence MNE values, and there are even more fun-
damental issues to contend with when it comes to deciding if femora outnumber
humeri and the like. There are other as yet unmentioned phases to the history of
MNE, but discussion of them is better served if they come up later. The next issue
that must be dealt with is how MNE values are determined.


Despite a relatively simple de¬nition of MNE as the minimum number of skeletal
elements necessary to account for the specimens under study, this quantitative unit
has seen more discussion and debate over how it is to be determined during the past
20 years or so than any one might have imagined. This is because MNE and two
quantitative units based on it (not including MNI) became extremely important to
answering taphonomic questions about skeletal-part abundances beginning in the
1970s (e.g., Andrews 1990; Binford 1981, 1984; Dodson and Wexlar 1979; Hoffman
1988; Klein 1989; Korth 1979; Kusmer 1990; Lyman 1984, 1985, 1994b, 1994c; Marean
and Spencer 1991 ; Shipman and Walker 1980; Turner 1989).
Many researchers suggested ways to determine MNE. For example, Klein and
Cruz-Uribe (1984:108) proposed that each specimen be recorded as a fraction using
common and intuitively obvious fractions (e.g., 0.25, 0.33, 0.5, 0.67) and not attempt-
ing great precision. The fractions were used to record how much of a category of
skeletal part (typically a proximal or distal half of a long bone) each specimen rep-
skeletal completeness, skeletal parts, and fragmentation 219

Table 6.1. MNE values for six major limb bones
of ungulates from the FLK Zinjanthropus site

Bunn (1986); Bunn
Skeletal element and Kroll (1988) Potts (1988)
Humerus 20 19
Radius 22 18
Metacarpal 16 14
Femur 22 8
Tibia 31 12
Metatarsal 16 16

resented; all recorded fractions were summed to estimate the MNE for a category of
skeletal part. Thus, if the category is proximal half of the femur, the analyst records
a specimen representing the proximal half of a femur as 1.0, a specimen representing
one half of a proximal femur is recorded as 0.5, and a specimen representing one
third of a proximal femur as 0.33. Adding those fractions produces an MNE of 1.83,
or an MNE of two proximal femora halves. This procedure does not, however, take
account of anatomical overlap. For example, what if the three specimens of proximal
femur all include the greater trochanter? If they do, the MNE is not two, but three.
Marean and Spencer (1991:649650) suggested measuring the percent of the com-
plete circumference represented by long-bone diaphysis specimens. Summing the
percentages recorded for each portion of the diaphysis measured say, proximal dia-
physis, middiaphysis, and distal diaphysis would provide an estimate of the MNE
of particular shaft portions. Again, the weakness is that anatomically overlapping
skeletal parts are ignored, potentially resulting in under estimates of MNE. Bunn
and Kroll (1986, 1988) described three ways to derive MNE values from a collection
of mammalian long bones. The analyst may determine (1) the minimum number
of anatomically complete limb skeletal elements necessary to account for only the
specimens with one or both articular ends, (2) the minimum number of complete
limb skeletal elements necessary to account for only the specimens of limb diaphyses
(without an articular end), and (3) the minimum number of complete limb skele-
tal elements necessary to account for both the specimens with one or both articular
ends and the diaphysis specimens lacking articular ends. These are labeled MNEends,
MNE shafts, and MNEcomp, respectively.
Underscoring that the quantitative unit is derived, if the method of determining
MNE varies, different MNE tallies are produced. Table 6.1 presents MNE values
for the six major limb bones of ungulates represented in the Plio-Pleistocene FLK
quantitative paleozoology

Zinjanthropus collection. MNE values were calculated by two researchers who used
different methods. Bunn (1991 ) used all specimens diaphysis fragments as well as
epiphyses whereas Potts (1988) focused mostly on articular ends. Given what we
have seen in preceding chapters and the consistently strong relationship between
NISP and MNI, and between sample size (however measured) and a variable of
interest, it should come as no surprise that if Bunn included more long-bone dia-
physis specimens in his derivation than did Potts, then Bunns MNE values would be
greater than Pottss.
MNE is de¬ned in precisely the same way that MNI is de¬ned but at the scale of
a partial skeleton (what I have been referring to as a skeletal part or portion) rather
than at the scale of a complete skeleton (Lyman 1994b). To reiterate using different
wording, MNE is de¬ned as the minimum number of skeletal elements necessary
to account for an assemblage of specimens of a particular skeletal element or part
(discrete item) or portion (multiple discrete items, such as all thoracic vertebrae in a
vertebral column) (Lyman 1994b:289). The de¬nition is operationalized by examining
specimens of each kind of skeletal element or part, say, left femora or distal right
humeri, for anatomical overlap (e.g., Bunn 1986; Morlan 1994). If three specimens
of left femora comprise the collection (assuming all are of the same taxon), then the
possible MNE represented by those specimens ranges from 1 to 3. If two specimens
represent the complete distal end and one represents the proximal end, then the
MNE of left femora is two. Just as when two left scapula and one right scapula are
said to represent a minimum of two individuals (MNI = 2), anatomically overlapping
skeletal specimens must represent unique individuals, whether these are individual
organisms or individual skeletal elements.
The techniques used to determine MNE have, in the past 15 years, become hotly
contested issues in paleozoology. Bunn (1991 ) and Potts (1988) used different methods
to determine MNE values; the difference was whether or not diaphysis fragments
were included in the tallies or only articular ends of long bones. That difference
alone spawned a huge debate, in the literature, on whether a tally of skeletal-part
frequencies was valid if diaphysis fragments were not included (e.g., Bartram and
Marean 1999; Marean and Frey 1997; Pickering et al. 2003; Stiner 2002). A recent effort
to bring all concerned parties together did not resolve the debate, though concessions
were made (e.g., Cleghorn and Marean 2004; Marean et al. 2004; Stiner 2004). The
debate originated in part with assumptions by some commentators regarding how
other researchers were thought to count skeletal-part frequencies. In particular, those
who advocate tallying diaphysis fragments have assumed that many have not counted
diaphysis fragments but instead tallied only taxonomically diagnostic articular ends
of long bones. This assumption is suspect given that ribs and many vertebrae are not
taxonomically diagnostic, yet these specimens were tallied by those who allegedly did
skeletal completeness, skeletal parts, and fragmentation 221

not tally nontaxonomically diagnostic long-bone diaphysis fragments. Whatever the
case, the important point is this: We must be explicit about how we count, whether
we count NISP, MNE, MNI, or any other measure. Many paleozoologists still do
not distinguish skeletal specimens, elements, parts, fragments, and the like, despite
numerous suggestions over the past several decades that they be distinguished via
explicit de¬nitions (e.g., Casteel and Grayson 1977; Grayson 1984; Lyman 1994a,
Assuming that all specimens in a collection, whether of articular ends or diaphysis
fragments, are included in MNE (and NISP) tallies, we are left with the question of
how to tally those specimens in order to derive an MNE value. The practical aspects of
operationalizing the de¬nition of MNE as based on anatomically overlapping speci-
mens became technologically more sophisticated when Marean et al. (2001 ) applied
GIS image software to the problem. They had found verbal descriptions and individ-
ual drawings of specimens that were anatomically incomplete skeletal elements to
be cumbersome to manipulate when determining MNE values. For them, computer
software provided a solution. Each specimen is outlined on a template of the skele-
tal element it represents; the template has previously been loaded into the software
program. The software allows the analyst to digitally overlay outlines of multiple
specimens. The maximum number of overlaps detected by the software indicates
the MNE. The key step to the process, whether using hard-copy drafting paper or
computer software, is drawing the specimens accurately. Marean et al. (2001 ) do not
address this most critical step. Efforts by a student in my zooarchaeology class to
replicate drawings of the same set of fragments of known (experimental) deriva-
tion found that the general shape of the fragment could be reproduced fairly con-
sistently, but its size and location varied from iteration to iteration. Thus, some
fragments that did not overlap in reality were sometimes drawn in such a way as
to overlap in the database, and other fragments that did overlap in reality were
sometimes drawn so as to not overlap. Errors increased in frequency and magnitude
(degree of overlap, or lack thereof) as specimens displayed fewer and fewer anatom-
ical landmarks. Tallies of MNE produced using the software varied from the actual
number of elements by anywhere from 0 to more than 50 percent greater than the
actual number across several trials.
The errors described in the preceding paragraph may be the result of inexperience,
but the student who performed them earns her living applying GIS to archaeological
problems, so degree of experience does not seem to be a signi¬cant factor. Additional
trials by others using specimens of known derivation (e.g., experimentally generated
from anatomically complete skeletal elements) might prove revealing, but I hazard
the guess that the smaller the fragments one tries to draw the more errors in tallying
MNE will result. Whether this is found to be true may be academic. This is so
quantitative paleozoology

because MNE is typically strongly correlated with NISP (Grayson and Frey 2004). This
should not be surprising at all given that we know NISP and MNI are often strongly
correlated, and we know that MNI is based on MNE. The relationship between
MNE and NISP is examined in a subsequent section on fragmentation. Several other
issues need to be dealt with ¬rst.

MNE Is Ordinal Scale at Best

Given the de¬nition of MNE as the number of skeletal parts or portions necessary to
account for the specimens under study, it should be clear that MNE is but MNI at a
less skeletally inclusive scale. Both are derived measures. Quite simply (and sadly) this
means that all of the problems that attend MNI must also attend MNE. Furthermore,
at best MNE can be only ordinal scale. To ensure these problems are appreciated,
lets quickly review the major bene¬t and the major problem with MNI, but in terms
of MNE.
MNI was designed to control for specimen interdependence when measuring tax-
onomic abundances. Thus, if two or more specimens came from the same individual,
NISP would tally that individual twice but MNI would tally that individual only once.
The same bene¬t attends MNE at the level of skeletal part or portion. Determination
of MNE ensures that each skeletal part (or portion) that contributed to a collection
will not be tallied, say, twice if represented by two specimens. This takes care of the
treacherous problem of differential fragmentation that causes some paleozoologists
to use MNI rather than NISP when measuring taxonomic abundances, and it takes
care of the same problem at the level of skeletal part or portion when tallying abun-
dances of ribs, cervical vertebrae, and tibiae. If humeri are broken into three pieces
(on average) but femora are broken into six pieces (on average), the NISP of humeri
will be half the value of the NISP of femora simply because of differential fragmen-
tation and the attendant specimen interdependence. MNE values circumvent these
problems. Varying degrees of interdependence of specimens representing a skeletal
part or portion such as proximal (half of the) humerus, left half of the rib cage,
or thoracic section of the vertebral column could in¬‚uence relative NISP values of
skeletal parts and portions. MNE might seem, therefore, to be a better unit than NISP
for quantifying the abundances of skeletal parts and portions because it controls for
specimen interdependence.
But, alas, MNE, like MNI, is subject to two serious problems. First, MNE is just that
it is a minimum. Therefore, one cannot statistically compare two minimum values
that might differentially range to some maximum value. Second, MNE is in¬‚uenced
skeletal completeness, skeletal parts, and fragmentation 223

Table 6.2. Fictional data showing how the distribution of specimens of two
skeletal elements across different aggregates can in¬‚uence MNE. Assuming
no anatomical overlap of specimens, if stratigraphic boundaries are
ignored, seven right and six left humeri, and fourteen right and nine left
femora are tallied. If stratigraphic boundaries are used to de¬ne
aggregates, nine right and eight left humeri, and fourteen right and ten left
femora are tallied. R, right, L, left; P, proximal, D, distal

Humerus Femur
Stratum 1 6 R P; 2 L P; 3 R D; 3 L D 4 R P; 1 L P; 4 L D
Stratum 2 1 R P; 4 L P; 1 R D; 1 L D 4 R P; 1 L P; 3 R D; 1 L D
Stratum 3 2 R D; 1 L D 6 R P; 5 L P; 4 R D; 4 L D

by sample size, aggregation, and de¬nition (are sex, age, size taken into account).
Different aggregates of specimens will often produce different MNE values, especially
as sample sizes grow larger. If a collection is treated as one aggregate, the MNE of
tibiae may be ¬ve, but if that collection is divided into three aggregates the MNE
of tibia will likely increase because the parts that are redundant may be proximal
ends in one aggregate, diaphyses in another, and distal ends in the third aggregate.
Consider the data in Table 6.2, which is based on Table 2.13 where the in¬‚uence
of aggregation on MNI is illustrated. To produce Table 6.2 from Table 2.13, Taxon
1 in the latter was converted to humerus and Taxon 2 to femur, and humerus in
Table 2.13 was converted to proximal in Table 6.2 and femur to distal. Assuming that
there is no anatomical overlap of the skeletal parts in Table 6.2, the ¬ctional data
there show that exactly the same sorts of in¬‚uence of aggregation can occur at the
scale of skeletal element, part, or portion (MNE), as occur at the scale of individual
animal (MNI). If stratigraphically de¬ned aggregates are ignored and specimens are
treated as one aggregate, there are seven right and six left humeri ( = 13 humeri) and
there are fourteen right and nine left femora ( = 23 femora) listed in Table 6.2.
If the remains in each stratum in Table 6.2 are treated as comprising distinct
aggregates, then the total number of humeri increases to nine right and eight left ( = 17
humeri) and the total number of femora increases to fourteen right and ten left ( = 24
femora). Note that if the remains are treated as one aggregate, the ratio of humeri to
femora is 13:23 (or 0.565), but if the remains are treated as three separate aggregates,
the ratio of total humeri to total femora is 17:24 (or 0.708). Just as with altering the
aggregates of most common (redundant) skeletal specimens alters the resulting MNI,
quantitative paleozoology

Table 6.3. NISP and MNE per skeletal part of deer and wapiti at the Meier site

Skeletal part Deer NISP Deer MNE Wapiti NISP Wapiti MNE
Mandible 192 58 28 9
Atlas 44 22 3 2
Axis 19 17 5 5
Cervical 77 22 20 12
Thoracic 75 53 27 20
Lumbar 104 32 35 18
Rib 221 110 61 35
Innominate 130 43 34 15
Scapula 73 45 12 6
Humerus 150 58 26 11
Radius 164 60 40 15
Ulna 102 60 17 10
Metacarpal 133 87 34 10
Femur 86 29 34 13
Patella 13 11 2 2
Tibia 190 88 30 11
Astragalus 127 118 18 18
Calcaneum 159 121 18 16
Naviculo-cuboid 86 75 9 9
Metatarsal 143 89 48 12
First phalanx 224 148 86 58
Second phalanx 158 109 68 47
Third phalanx 75 75 25 25

changing the aggregates of most common (redundant) skeletal specimens alters the
resulting MNE.
Sample size rendered as NISP also in¬‚uences MNE values, as recently shown by
Grayson and Frey (2004). Consider the deer (Odocoileus sp.) and wapiti (Cervus
elaphus) data from the Meier site (Table 6.3). For deer, the NISP and MNE data
are strongly correlated (Figure 6.1 , r = 0.883, p < 0.0001 ), and the same holds for
the wapiti data (Figure 6.2, r = 0.837, p < 0.0001 ). Grayson and Frey (2004) present
numerous other examples in which the NISP per skeletal part and the MNE of skeletal
parts are correlated. Their results and those for the Meier site deer and wapiti indicate
that MNE values are often strongly in¬‚uenced by sample size measured as NISP. The
larger the NISP value per skeletal part or portion, the larger the MNE value for that
part or portion. MNE is also in¬‚uenced by how it is de¬ned in the sense of whether
figure 6.1. Relationship of NISP and MNE values for deer remains from the Meier site.
Best-¬t regression line (Y = 0.126X0.807 ; r = 0.837) is signi¬cant (p = 0.0001). Data from Table

figure 6.2. Relationship of NISP and MNE values for wapiti remains from the Meier
site. Best-¬t regression line (Y = 0.063X0.692 ; r = 0.883) is signi¬cant (p = 0.0001). Data from
Table 6.3.

quantitative paleozoology

figure 6.3. Frequency distributions of NISP and MNE abundances per skeletal part for
deer remains from the Meier site. Data from Table 6.3.

or not size, ontogeny, and the like are taken into account when seeking to determine
if two or more nonanatomically overlapping specimens come from the same original
skeletal element.
Finally, MNE is at best ordinal scale. This can be shown using the same tech-
nique that was used to show that MNI is often at best ordinal scale (Chapter 2).
The NISP and MNE data from Table 6.3 for the Meier site deer and wapiti are
graphed in Figures 6.3 and 6.4, respectively. Note that the distributions of frequen-
cies are different than those across taxonomic abundances illustrated in Figures
2.132.16. This is likely because in any given skeleton, there is a standard frequency
of skeletal elements such that the frequency distribution is right skewed (like that
observed for taxonomic abundances) but the mode is not to the farthest left but
instead is slightly to the right (unlike that observed for taxonomic abundances)
skeletal completeness, skeletal parts, and fragmentation 227

figure 6.4. Frequency distributions of NISP and MNE abundances per skeletal part for
wapiti remains from the Meier site. Data from Table 6.3.

(Table 6.4, Figure 6.5). Given that most paleozoological samples derive from > 1
individuals the taphonomic starting point (prior to variation in accumulation,
preservation, and recovery) of a paleozoological collection it is unlikely that a more
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
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

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.


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

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
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

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

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

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
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

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
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
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


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
pieces (fragments) that each skeletal element has been broken into or is represen-
ted by.
Paleozoologists have worried about the degree of fragmentation of faunal remains
for decades, as evidenced by their worries about intertaxonomic variation in frag-
mentation differentially skewing NISP measures of taxonomic abundances (Chap-
ter 2). Tallying MNE frequencies per taxon escapes that problem, but introduces
the problems attending derivation of MNE (aggregation, sample size, de¬nition).
Taphonomic questions about fracturing agents and processes have resulted in some
innovations in measuring fragmentation. Simply because taxon A has a greater NISP
value than taxon B does not mean that the remains of taxon A are more fragmentary
than those of taxon B. How might we determine which taxon™s remains are the more
anatomically complete and less fractured, and which taxon™s are more anatomically
incomplete and more fragmentary?

Fragmentation Intensity and Extent

Klein and Cruz-Uribe (1984) use the ratio NISP/MNI per skeletal element to measure
fragmentation for each taxon, but there is a potential problem with this measure.
NISP is the number of identi¬ed specimens, and a specimen is a bone or tooth
or fragment thereof. The last two words are emphasized for one simple reason. If,
say, many of the skeletal elements of taxon A are anatomically complete but a few
of each were broken into many (small) fragments, then the ratio NISP/MNI for
that taxon may be the same as that for taxon B all the remains of which are (large)
fragments. This suggests that there are two dimensions of fragmentation. The extent
skeletal completeness, skeletal parts, and fragmentation 251

of fragmentation is the dimension that signi¬es the proportion or percentage of
specimens in a collection that are anatomically incomplete, or its complement, the
percent of NISP that comprise anatomically complete specimens, or %whole (Lyman
1994b, 1994c). The intensity of fragmentation signi¬es how small fragments are or how
many pieces a kind of skeletal element has been broken into on average (Lyman 1994b,
To calculate %whole or %fragmentary, tally up NISP for a taxon. Then, tally the
number that are anatomically complete or whole (how many are actually skeletal
elements rather than fragments of elements); this number will likely be (sometimes
quite signi¬cantly) smaller than the number of fragmentary specimens. Divide the
number of whole specimens by the total number of specimens (and multiply by 100)
to derive the %whole; or, subtract the number of whole specimens from the total
number of specimens, and divide the resulting number (number of fragments) by
the total NISP (and multiply by 100) to derive the %fragmentary.
In the collection of faunal remains from the sample of owl pellets (Table 2.9),
skulls of Microtus are not always complete. The total NISP of Microtus skulls is 110;
the number of complete skulls is 103; the %whole of Microtus skulls is 93.6 percent.
In that same collection, the total NISP of Peromyscus skulls is 206; the number of
complete skulls is 115; the %whole of Peromyscus skulls is 55.8 percent. The extent
of fragmentation of Microtus skulls is considerably less than is the extent of frag-
mentation of Peromyscus skulls. Why this difference should exist given the identical
taphonomic histories of the two may now be explored; it likely is a result of Peromyscus
skulls being much more fragile and of much more gracile structure than Microtus
skulls, which are larger and more robust.

The NISP:MNE Ratio

But what if, in a case like the skulls of the two taxa of rodents just described, the
specimens of the taxon with greater %whole are smaller than the fragments of the
taxon with lower %whole? This concerns fragmentation intensity and it is mea-
sured as the ratio of anatomically incomplete specimens to the MNE represented by
those specimens. (To calculate this ratio one must assume MNE values are not in¬‚u-
enced by aggregation, sample size, or de¬nition. Alternatively, one could assume the
in¬‚uences on MNE are randomly distributed across the collections compared such
that they do not skew the values in such a way as to in¬‚uence statistical interpreta-
tion.) Anatomically complete specimens are not included in the calculation because
(i) when they are included they decrease the ratio because they increase both values
quantitative paleozoology

Table 6.12. Ratios of NISP:MNE for four long bones of
deer in two sites on the coast of Oregon State. Data
from Lyman (1995b)

Skeletal element Umpqua/Eden site Seal Rock site
Humerus 1.14 1.75
Radius 2.00 1.89
Femur 1.50 2.67
Tibia 2.10 2.33

of the NISP:MNE ratio equally, and (ii) the intensity of fragmentation is meant to
capture the variable of fragment size. With respect to the ¬rst point, in an assemblage
of anatomically incomplete specimens, if NISP = 10 and MNE = 5, then the ratio is
2:1. If two anatomically complete specimens are included, NISP = 12, MNE = 7, and
the ratio is reduced to 1.71 :1. The more anatomically complete specimens, the less the
difference between NISP and MNE. With respect to the second point “ NISP:MNE
measures fragment size “ higher ratios suggest smaller fragments. A ratio of 2:1 sug-
gests elements were basically broken in half; a ratio of 15:1 suggests elements were
almost pulverized.
Let™s say we want to determine if the fragmentation of bones of a taxon differs
across two assemblages. (The remains of two taxa can be compared using the same
technique.) I did this for the four major long bones of deer (Odocoileus sp.) using the
remains from two sites on the coast of the state of Oregon (Lyman 1991 , 1995b). The
ratios (Table 6.12) suggest that, overall, long bones were less intensively fractured (bro-
ken into larger pieces) at the Seal Rock site than they were at the Umpqua/Eden site.
The average ratio at Seal Rock is 1.68 compared to an average ratio at Umpqua/Eden
of 2.16. Determination of the reason for this apparent difference in fragmentation
intensity requires other sorts of analyses. The NISP:MNE ratio allows one to rank-
order the elements from most intensively broken to least intensively broken. For Seal
Rock, that order is femur, tibia, radius, humerus; for Umpqua/Eden, that order is
tibia, radius, femur, humerus. Of course, variation in the NISP:MNE ratio can be
assessed and compared across different taxa as well.
Ratios of NISP:MNE have been used by zooarchaeologists in both the New World
(e.g., Wolverton 2002) and the Old World (e.g., Munro and Bar-Oz 2005) to measure
the intensity of fragmentation. But a property of the ratio needs to be identi¬ed.
The ISP of NISP concerns identi¬ed specimens, and to be identi¬ed a specimen
must retain suf¬cient anatomical and taxon-speci¬c features to be identi¬ed. As
skeletal completeness, skeletal parts, and fragmentation 253

figure 6.16. Model of the relationship between fragmentation intensity and NISP. The
value of Maximum and of N are unknown. Modi¬ed from Marshall and Pilgram (1993).

elements are broken into successively smaller and smaller fragments, the resulting
pieces become successively less likely to retain suf¬cient landmarks to permit their
identi¬cation. Thus, as Marshall and Pilgram (1993) pointed out some years ago,
fragmentation has the effect of ¬rst increasing the NISP represented by pieces of
any given skeletal element, but as fragmentation intensity increases beyond some
as yet unknown level of intensity, NISP will level off and then decrease because
the fragments are becoming so small as to be unidenti¬able (Figure 6.16). This
may be an interpretively treacherous property of fragmentation if some kinds of
skeletal elements are represented by only one identi¬able fragment and numerous
unidenti¬able small fragments. Each identi¬able fragment will represent an MNE of
1, and so the ratio for these would be 1 :1, or 1, but slightly larger and (thus) identi¬able
fragments will cause the ratio to be > 1.0.
The preceding leads to another observation. There is some threshold of fragment
size controlling whether or not a fragment is identi¬able. If the fragment is smaller
than the threshold size, it is not identi¬able. For the sake of illustration, grant the
(no doubt somewhat unrealistic) assumption that for any given skeletal element,
the element can be broken into some number of pieces of equal size. If we set that
threshold number of pieces at ¬fteen, such that if, say, a humerus is broken into ¬fteen
pieces, all can be identi¬ed (to skeletal element and to taxon), then if that humerus
is broken into sixteen pieces, none of them will be identi¬able (to skeletal element
or to taxon). The implication of this observation is graphed in Figure 6.17. That
quantitative paleozoology

figure 6.17. Model of the relationship between NISP and MNE. Observed values will
always fall on or below the diagonal (NISP ≥ MNE), but not in¬nitely far below the diagonal
because fragments that are too small will not be identi¬able. After Lyman (1994b).

graph suggests there will be a relatively strong correlation between MNE and NISP
per skeletal element simply because of constraints on the total NISP (identi¬able
fragments) that can be generated from any given set of fragments of multiple skeletal
elements. Again, that these two variables are often strongly correlated should come
as no great surprise given that whatever the greatest (left or right) MNE was for a
taxon, that value was the MNI for that taxon. Nevertheless, we need to examine the
relationship of these two variables in depth.


There have been subsequent phases to the history of MNE. One later phase was
the derivation of MAU and the related %MAU, along with the mathematically
equivalent %survivorship. Those units served as the basis for a large volume of
research on skeletal-part frequencies, and because they are ultimately based on MNE,
they also prompted a plethora of research projects on how to determine MNE in the
most accurate way possible. The former focused on what frequencies of skeletal
skeletal completeness, skeletal parts, and fragmentation 255

Table 6.13. African bovid size classes. After Brain (1974,
1981) and Klein— (1978, 1989)

Bovid size class Live weight
I (small) 0“23 kilograms (0“50 pounds)
II (small medium) 23“84 kilograms (50“200 pounds)
III (large medium) 84“296 kilograms (200“650 pounds)
>296 kilograms (>650 pounds)
IV (large)
V (very large)— ?

parts “ normed to the model of the MNI of complete skeletons “ meant with respect
to taphonomic agents and processes of dispersal (e.g., ¬‚uvial winnowing), accumu-
lation (e.g., nutritional value to carnivores and hominids), and destruction (e.g.,
carnivore gnawing) (see Lyman [1994c] for discussion of methods, and see the Jour-
nal of Taphonomy [2004: vol. 2] for more recent considerations). Earlier in this
chapter efforts to derive the most accurate MNE values possible were outlined.
Subsequent to those efforts, a new chapter or phase to the history of MNE was
Grayson and Frey (2004) recently showed that the relationship between NISP
per skeletal element and MNE per skeletal element is strong; the two variables are
often tightly correlated. As indicated earlier in this chapter, that a strong relationship
exists between these two variables shouldn™t really be a surprise, given that NISP
and MNI are often tightly correlated and that MNI is operationalized as the largest
value of MNE (of left or right specimens) per taxon, and given the model in Fig-
ure 6.17. But the fact that people grappled with MNE and its derivatives for more
than twenty-¬ve years before the statistical and analytical signi¬cance of the cor-
relation of MNE and NISP was identi¬ed suggests that this signi¬cance should be
illustrated. The relationship is shown in Figures 6.1 and 6.2, but it warrants additional
discussion given the analytical weight placed on MNE abundances over the past two
Researchers have published both NISP and MNE data for collections from diverse
geographic locations and temporal periods. In one such presentation, Marean and
Kim (1998) described frequencies of skeletal parts for an assemblage of remains
representing several species of medium-small (size class II [Brain 1981 ]) bovids
and cervids. (Bovid size classes used in much of the following are summarized in
Table 6.13.) The remains originate from a Mousterian (Middle Paleolithic) deposit
in Kobeh Cave, located in the Zagros Mountains of Iran. The data are summarized
quantitative paleozoology

Table 6.14. NISP and MNE frequencies of skeletal parts of
bovid/cervid size class II remains from Kobeh Cave, Iran.
Data from Marean and Kim (1998)

Skeletal part/portion NISP MNE
Horn 43 20.00
Skull 60 19.00
Mandible 75 22.00
Upper teeth 46 29.60
Lower teeth 82 21.86
Atlas 5 0.90
Axis 1 0.40
Cervical 24 8.35
Thoracic 28 11.30
Lumbar 28 8.60
Sacrum 2 1.90
Ribs 266 30.80
Humerus 404 63.80
Radius 336 47.25
Ulna 127 25.10
Carpal 14 11.50
Metacarpal 319 37.95
Innominate 53 11.30
Femur 478 62.90
Tibia 665 95.70
Astragalus 3 3.00
Calcaneum 13 4.90
Metatarsal 307 35.85
Tarsal 10 7.85
Phalange 102 24.90
Sesamoid 7 6.00

in Table 6.14, and graphed in Figure 6.18. The two variables are strongly correlated


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