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cut marks were randomly distributed across bone surfaces, but this is unlikely to be
true for many reasons and empirical data indicate it is not true. In short, we cannot
assume what we are trying to discover.


One driving force behind study of the frequencies of bone specimens displaying
butchery damage and frequencies of specimens displaying carnivore damage con-
cerns the roles of meat eating and of carcass acquisition (hunting or scavenging)
in hominid evolution (see Dom´nguez-Rodrigo [2002] and Lupo and O™Connell
[2002] for recent reviews). The underlying assumption comprises two interrelated
parts. First, if carnivores have access to a prey carcass before tool-carrying butch-
ers, prey bones will have many tooth marks but few butchering marks; if hominid
butchers have access to a prey carcass prior to access by a carnivore/scavenger, then
quantitative paleozoology

bones of prey will have many butchering marks (especially cut marks representing
de¬‚eshing of meat-rich proximal limb elements) and few tooth marks of carnivores.
Second, the more ¬‚esh on bones, the more cut marks are expected. Each of the pre-
ceding statements is carefully phrased; each refers to the frequency of marks, not the
frequency of marked skeletal elements or skeletal specimens. The target variable is
clear “ how many marks are there per specimen “ the signi¬cant assumption is that
more ¬‚esh results in more marks, whether cut marks or tooth marks. Variation in
the relative frequencies of the two kinds of marks depends on order of access and
the amount of ¬‚esh remaining that the second carnivore (whether a quadruped or
biped) can exploit.
The critical assumption is worded so as to emphasize that frequencies of marks “
whether butchering marks or tooth (gnawing) marks “ is the critical variable, that is
in fact also how individuals who have debated the issue phrase the assumption (e.g.,
Binford 1986, 1988; Bunn and Kroll 1986, 1988; Dom´nguez-Rodrigo 2002; Lupo and
O™Connell 2002; Pobiner and Braun 2005; Selvaggio 1994, 1998; Thompson 2005).
But almost without fail, paleozoologists involved in the discussion do not tally up cut
marks and tooth marks; instead they tally up cut marked bones and tooth marked
bones and analyze those frequencies. The relationship between the number of marked
bones (measured variable) and the property or process of interest (target variable)
is obscure. Furthermore, the target variable is inexplicit “ is it the amount of meat
associated with a bone, the size of the carcass, the size of the bone “ and this contributes
to the obscure relationship between it and the measured variable. Some examples
will make this clear.
Among the data in Table 7.5, the number of strokes necessary to de¬‚esh an indi-
vidual skeletal element is signi¬cantly correlated with the amount of meat removed
from the element (r = 0.365, p = 0.044), especially if both variables are log trans-
formed (r = 0.592, p = 0.0005; Figure 7.6). The number of cut marks per skeletal
part, however, is not correlated with the amount of meat removed from a bone (r =
“0.079, p = 0.67), and this holds true for the log transformed data as well (Figure 7.7).
These results suggest the interpretive assumption that more cut marks means there
was more meat on bones for stone-tool wielding butchers to remove is unfounded.
However, the data in Table 7.6 may support the assumption. Those data were gener-
ated by Pobiner and Braun (2005), who provided eighteen hindlimbs comprising the
femur and tibia to stone-tool wielding butchers. But, before the limbs were turned
over to the butchers, different amounts of ¬‚esh were removed by Pobiner and Braun
to simulate early access to fully ¬‚eshed limbs, later access to partially ¬‚eshed limbs (25
percent of ¬‚esh removed prior to butchery), and still later access to rather de¬‚eshed
limbs (50 percent of ¬‚esh removed prior to butchery).
figure 7.6. Relationship between number of arm strokes necessary to de¬‚esh a bone and
the amount of ¬‚esh removed (r = 0.592, p = 0.0005). Data from Table 7.5.

figure 7.7. Relationship between number of cut marks and the amount of ¬‚esh removed
from thirty-one limb bones (r = “0.035, p = 0.85). Data from Table 7.5.

quantitative paleozoology

Table 7.6. Number of cut marks generated and amount of meat
removed from eighteen mammal hindlimbs (femur + tibia) by
butchering. Data from Pobiner and Braun (2005)

Meat removed
Limb Taxon N of cut marks
1 cow (juvenile) 14.25 15
2 cow (juvenile) 12.00 14
3 cow (juvenile) 4.25 56
4 cow (juvenile) 3.25 15
5 cow (juvenile) 1.00 20
6 cow (juvenile) 0.50 69
7 goat 0.390 31
8 goat 0.538 14
9 goat 0.814 12
10 goat 0.786 8
11 goat 1.084 28
12 goat 1.010 53
13 zebra 23.0 73
14 zebra 23.5 67
15 zebra 13.5 90
16 zebra 14.0 160
17 zebra 23.0 95
18 zebra 23.0 45

Note, the amount of meat removed varies intrataxonomically because
of prebutchery meat removal aimed at testing the hypothesis that the
amount of meat remaining for removal would correlate with the
number of cut marks.

Pobiner and Braun (2005) conclude that there is no relationship between the
number of cut marks and amount of meat removed within each size class of butchered
animal. Their data on amount of meat removed and number of cut marks produced
per each of eighteen butchering experiments are plotted in Figure 7.8 by taxon. There
is no signi¬cant relationship between the two variables intrataxonomically for any of
the three taxa represented (goat, r = 0.62, p = 0.19; cow, r = “0.78, p = 0.065; zebra,
r = “0.48, p = 0.34). However, there is a positive relationship between carcass size and
number of cut marks when all carcasses were included and analysis is intertaxonomic
rather than intrataxonomic (Figure 7.9, r = 0.49, p = 0.039). It matters little which
analysis is correct. The varied results highlight a critical point. Target variables must
figure 7.8. Relationships between number of cut marks and the amount of ¬‚esh removed
from six hindlimbs in each of three carcass sizes. Simple best-¬t regression lines (dashed)
are shown for each carcass size. None of the relationships is statistically signi¬cant (goat,
r = 0.62, p = 0.19; cow, r = “0.78, p = 0.065; zebra, r = “0.48, p = 0.34). Data from Table 7.6.

figure 7.9. Relationship between number of cut marks and the amount of ¬‚esh removed
from eighteen hindlimbs (r = 0.49, p = 0.039). Data from Table 7.6.

quantitative paleozoology

be explicitly de¬ned, as must measured variables and the suspected relationship
between the two. Such speci¬cations will assist with determination of the appropriate
statistical tests.
With respect to quantifying cut marks, obscure target variables and poorly under-
stood relationships between target and measured variables are not the only aspects of
the quantitative data that are recorded, analyzed, and reported that likely contribute
to the lack of resolution of the debate whether early hominids hunted large game
or merely scavenged long-dead carcasses. Lupo and O™Connell (2002:102) correctly
note that analysts report tallies of cut marked specimens (and tooth marked speci-
mens) differently. Many analysts report the number of marked specimens per portion
(e.g., proximal, distal, shaft) per skeletal element (e.g., humerus, radius, femur) (e.g.,
Dom´nguez-Rodrigo 1997; Dom´nguez-Rodrigo and Pickering 2003); a few report
± ±
the number of marked specimens per skeletal element with no distinction of por-
tion of element (e.g., Dom´nguez-Rodrigo 1999a; Oliver 1994); and a few report
the number of marked specimens per portion (proximal, shaft, distal) of skeletal
element with no distinction of skeletal element (e.g., Blumenschine 1995; Capaldo
1997). It is these sorts of ambiguities that in part prompted a ¬‚urry of rebuttals
and responses regarding interpretations of the cut mark and tooth mark data (e.g.,
Dom´nguez-Rodrigo 1999b, 2003a, 2003b; Monahan 1999; O™Connell and Lupo 2003;
O™Connell et al. 2003). A major cause of the debate has been poorly developed and
weakly warranted methods that are incompletely described “ the problem identi-
¬ed by Dom´nguez-Rodrigo “ in conjunction with poorly worded and incompletely
developed theoretically informed interpretive models “ the problem identi¬ed by
O™Connell et al. (2003). In terms used throughout this volume, measured variables
are inexplicit and have at best a poorly understood relationship to target variables.


Discussions in other arenas summarize in somewhat different terms what has been
discussed in this chapter. With respect to attributes on prey remains created by preda-
tors, Kowalewski (2002:14) states that “the frequency of traces is arguably the most
important and widely used metric in quantitative analyses of the fossil record of
predation that estimates the frequency of predator“prey interactions and may serve
as a proxy for predation intensity.” But when he describes ways to tally the frequency
of traces, he in fact suggests the number of specimens with traces be tallied and thus
correctly notes that “the number of specimens with traces of predation is not synony-
mous with the total number of traces found in those specimens unless all specimens
tallying for taphonomy 297

bear singular traces. When computing predation intensity we should always use the
number of prey specimens attacked (i.e., the number of specimens with traces) and
not the number of attacks (i.e., the number of traces)” (Kowalewski 2002:15). This is
because the target variable is predation intensity, implied by Kowalewski to comprise
the fraction of the prey population that has in fact been preyed on. Tallying numbers
of predation marks would thus not measure the frequency or intensity of predation
but rather how often a particular prey organism was attacked.
Kowalewski (2002) is concerned with organisms that have single element skeletons,
and so he notes that measuring predation intensity may require modi¬cation to
measurement techniques if skeletons of prey comprise multiple elements. This is so
for the same reason that the number of traces would not measure the intensity of
predation but rather the frequency of attacks (individual prey may be attacked more
than once). Counting predation traces on multiple but different skeletal elements
introduces the problem of interdependence “ has one attack been counted more than
once because multiple elements of a single organism have been tallied? Measuring
the intensity of carnivore gnawing, corrosion, burning, and butchering, however,
because of how “intensity” is (typically implicitly) de¬ned, requires tally of those
potentially interdependent specimens.
Among other approaches to mapping predation traces on the anatomy of the prey
skeleton, Kowalewski (2002:25) distinguishes a “qualitative approach” and a “sector
approach.” The ¬rst involves mapping each trace on a single standard skeletal ele-
ment. Although this approach precludes statistical comparison of data sets and is
subject to mapping error based on operator error and morphological and allometric
variation among specimens, it does reveal anatomical areas that may have tapho-
nomic or biological signi¬cance. It has been used by various taphonomists. The
sector approach involves partitioning the skeleton or skeletal elements into sectors
and tallying the number of traces in each. This approach allows statistical compar-
ison of data sets, such as χ 2 analysis and calculation of evenness and heterogeneity
indices. This approach too has been used by various taphonomists. At the risk of
being redundant, the approach chosen should be dictated by the research question.
Discussion in this chapter is not to resolve debates over whether early hominids
were scavengers, hunters, or acquired meat using both techniques. Rather, the goals of
the chapter have been two. First, methods used to quantify various sorts of damage to
bones “ weathering, corrosion, gnawing, burning, butchering “ have been described.
Second, the critically signi¬cant nature of the relationship between a measured vari-
able and a target variable and the critically signi¬cant fact that each variable must be
explicitly de¬ned have been highlighted. Precisely the same (then ambiguous) rela-
tionship underpinned debates in the 1950s through 1980s regarding the relationship
quantitative paleozoology

between NISP, MNI, biomass, and other measures of taxonomic abundances, and a
target variable of abundances of taxa exploited by people or abundances of taxa on
the landscape (Chapters 2 and 3). Those debates were more or less resolved in the
1980s as two things became clear. First, any measure of taxonomic abundance was
found to be at best ordinal scale (or to be an estimate), and second, the relationship
between a chosen measured variable (NISP, MNI, biomass) and the target variable
was a taphonomic question. Many paleobiologists came to both conclusions using
“¬delity studies,” actualistic research on the relationship between recently formed
assemblages of faunal remains and the accuracy with which they re¬‚ect taxonomic
abundances in the faunas from which the collections derive (see Chapter 2 for a for-
mal de¬nition of ¬delity studies). The success of these studies resides in unambiguous
de¬nitions of measured and target variables. Ambiguity with respect to measured
variables and target variables permeates many modern taphonomic studies. It is no
wonder that we do not understand the relationship between two variables when one
or more of them is poorly de¬ned or is simply inexplicit.
Final Thoughts

In this volume, some of the most basic issues of quantifying different kinds of paleo-
zoological data have been explored. A bit more than two decades ago, Grayson (1984)
published a book-length treatment on the same general topic, and that seemed to
resolve many of the debates over how to quantify taxonomic abundances. Arguments
over whether NISP or MNI was the better measure nearly ceased to appear in the
literature. Yet, some individuals continue to report MNI values, either as the unit of
choice for quantifying taxonomic abundances (e.g., Avery 1991 , 1992; Landon 1996),
or apparently for the sake of complete descriptive reporting (e.g., Plug 2004; Stahl
and Athens 2001). A few continue to develop innovative ways of tallying MNI (e.g.,
Vasileiadou et al. 2007). The usual reason given for use of MNI is that NISP is subject to
intertaxonomic variation in fragmentation and so gives potentially biased estimates
of taxonomic abundances. Although it is true that NISP can in¬‚uence estimates of
taxonomic abundance, those who use the differential fragmentation argument as a
warrant to determine MNI values neither empirically evaluate the truthfulness of
this warrant in their particular instances nor fail to present NISP data. Why do they
present what they take to be biased data? Why do they not determine if in fact frag-
mentation varies intertaxonomically rather than simply assert that it does? Perhaps
they do not because of a lack of mathematical and statistical sophistication. That lack
of sophistication is a major reason for this book.
Some have argued on the basis of ethnoarchaeological (Hudson 1990) or histori-
cal (Breitburg 1991 ) data that MNI provides more accurate estimates of taxonomic
abundances than NISP. That may well be so in particular cases where aggregation
and derivation of MNI is not dependent on analytical choices; we must make these
choices when dealing with prehistoric materials. Reitz and Wing (1999:199) state
that MNI is the “only way to compare mammals, birds, reptiles, amphibians, ¬shes,
and mollusks,” but the arguments in Chapter 2 identify the fallacious nature of
this statement. Given the continued use and advocacy of MNI, arguments made
quantitative paleozoology

by Richard Casteel and Donald Grayson regarding the nature of MNI and its sta-
tistical relationship with NISP, as well as their characterizations of MNI and NISP
as quantitative units, have been reiterated for a new generation of paleozoologists.
This is not to say that MNI is always the wrong quantitative unit to use. Both logic
and empirical data indicate, however, that it typically is the wrong unit to use when
some measure of taxonomic abundances is needed. It has been argued that MNE is
not as good a quantitative unit as NISP when one needs a measure of skeletal part
Other methods of quantifying taxonomic abundances, such as estimating biomass,
have also been reviewed. Some analysts continue to calculate meat weight using
Theodore White™s method (references in Dean 2005b). (Ornithologists still use the
Whitean method of multiplying the MNI of prey evident in a sample of egested
pellets by the average weight of an individual prey to determine biomass [Leonardi
and Dell™Arte 2006].) The skeletal mass allometry technique is quite popular in some
areas, and it continues to be used today (e.g., Carder et al. 2004; Lapham 2005;
Pavao-Zuckerman 2007). Chapter 3 of this volume was written with the express
purpose of highlighting some of the weaknesses of estimating biomass. Because
many of the quantitative variables paleozoologists seek to measure are dependent on
sample size, Chapter 4 summarizes the various ways that sample-size effects might be
detected and analytically controlled. Chapter 5 covers a central issue in paleozoology “
quantifying and comparing the structure and composition of prehistoric faunas, and
monitoring trends in taxonomic abundances. Chapter 6 provides detailed coverage
of a quantitative unit that has been extensively used over the past 20+ years “ MNE “
even though it has been around virtually as long as MNI. And Chapter 7 describes
ways to tally and analyze quantitative variables that concern taphonomic agents and
processes. What could possibly be left to discuss?
There is one thing that warrants comment. This concerns the fact that statisticians
have found it necessary to comment on quantitative paleozoology. This commen-
tary began with Ringrose™s (1993) detailed discussion that is still quite worthwhile
to read. Pilgram and Marshall (1995) pointed out that Ringrose apparently had little
experience with faunal remains, and so some of his comments were a bit off base.
Ringrose (1995) responded that although he did not in fact know very much about
the realities of paleozoology, he commented in kind that Pilgram and Marshall (1995;
Marshall and Pilgram 1991 ) seemed to not be as statistically sophisticated as he (at
least) hoped paleozoologists might be. It was with that discussion ¬rmly in mind
that I have included minimal discussion of statistics and focused on what simple sta-
tistical analyses might reveal about the quantitative properties of a paleozoological
¬nal thoughts 301

collection. In an effort to make revelations clear, graphs of statistical relationships are
included, along with various statistical results attending the graphed relationships.
And, in most cases, the data underpinning the graphs and the statistics are included
to allow the interested reader to replicate analyses graphically and statistically. Repli-
cation will assist comprehension of an analytical technique, and it ensures correct
implementation of the technique. Hopefully, readers will ¬nd utility in the many
graphs and tables.
Paleozoologists who read this volume may well hope for more, or less, statistical
sophistication. Not being a statistician, I can only reply: Read a statistics book. But
in saying that, I also want to make the observation that, like Ringrose (1993), other
statisticians have contributed to the discussions on quantitative paleozoology. And
it is clear that at least some of those statisticians are, like Ringrose, not aware of the
practical realities of quantitative paleozoology. Thus, MNE is (incorrectly) de¬ned as
“the NISP calculated for each skeletal part” (Baxter 2003:212) by a statistician. Such
errors are not restricted to those who are not paleozoologists. NISP has been said
by paleozoologists to be the Number of Identi¬ed Skeletal Parts, or the Number of
Identi¬ed Skeletal Portions, yet they do not de¬ne skeletal part or skeletal portion.
Such loose use of key terms is commonplace in many scienti¬c endeavors, but that
does not make it acceptable. Explicitly de¬ned terminology is critical to the success of
any research; such is all the more critical with respect to quantitative units, whether
fundamental or derived. That NISP has various de¬nitions (or at least descriptions)
in the literature re¬‚ects poor understanding of the term “specimen” and how it
compares with “skeletal element” and the generic “bone.” Using the de¬nitions in
Chapter 1 of this book, or a similar set of de¬nitions that are explicitly stated by the
researcher, would help the discipline a lot.
This is not a book about terminology. It is instead a book about how to count
faunal remains “ bones, teeth, shells, and fragments thereof. To reiterate, one should
read a statistics book to learn about statistics; read Quantitative Paleozoology to
learn about counting faunal remains. In so doing, and putting the two together, a
paleozoologist may well conceive of a unique analysis that reveals something about
the behavior of a quantitative unit or gain insights to some aspect of a collection of
broken bones. In most chapters, knowledge about the relationship (or lack thereof)
between a target variable and a measured variable has been emphasized. In many
cases, such knowledge is crucial to valid interpretation, but it may not always be
required. In some cases, exploratory data analysis may suggest further analyses are
necessary because of a particular relationship between two variables. The nature of
the relationship between variables may suggest other sorts of variables that need to
quantitative paleozoology

be measured in order to understand the relationship. As a way to conclude this book,
I outline an example.


Grayson (1979, 1984) suggested that analyses of the relationship between NISP and
MNI might prove revealing. Such analyses might reveal something about the par-
ticular collections studied, something about the nature of the relationship between
these two most basic counting units, or both. Recall that Klein and Cruz-Uribe (1984)
noted that their results were different than Casteel™s (1977, n.d.) with respect to the
statistical relationship they found between NISP and MNI. Because of that difference,
Klein and Cruz-Uribe suggested that perhaps the set of assemblages they had used to
examine the relationship comprised remains that were much more fragmented than
those remains in the assemblages that Casteel had used. This was an astute obser-
vation to make, but it was also one that Klein and Cruz-Uribe could not evaluate
empirically given a lack of appropriate data. They did not have NISP:MNE data for
the various skeletal elements because the data they used (and those used by Casteel)
were derived from literature that did not present that data (it was not a target variable
of the analysts). About the same time that Klein and Cruz-Uribe (1984) presented
their conclusion, Bobrowsky (1982) pointed out that Casteel (1977, n.d.) had lumped
numerous taxa together, and that such lumping masked the in¬‚uence of intertaxo-
nomic variation in the number of identi¬able elements per individual skeleton. That
is, Bobrowsky identi¬ed a cause for variation in the relationship between NISP“MNI
data pairs that was different than the cause identi¬ed by Klein and Cruz-Uribe.
In a clever bit of analysis, Bobrowsky (1982) chose one stratum from one site and
compared the relationship of NISP to MNI across four taxonomic groups (birds,
mammals, reptiles, ¬sh) represented by the remains from that single stratum. His
results indicate that indeed, intertaxonomic variation in the number of identi¬able
elements per individual skeleton signi¬cantly in¬‚uenced the slope of the best-¬t
regression line described by the model in Figure 2.4. Thus, the line describing the
relationship between the NISP and MNI data from remains of birds had a steeper
slope and higher plateau (it leveled at a higher MNI) than did the line for mammals.
Bobrowsky (1982) found this relationship between the two lines expectable given that
each bird skeleton tended to provide fewer taxonomically identi¬able elements than
did each mammal skeleton. This simply meant that each additional NISP of birds was
more likely to contribute a new MNI than was each additional NISP of mammals.
I can identify to the genus or species level about forty-¬ve to forty-eight kinds of
¬nal thoughts 303

Table 8.1. Statistical summary of relationship between NISP and MNI in collections of
paleontological birds, paleontological mammals, archaeological birds, and
archaeological mammals. p < 0.0001 in all

N of N of data Y
assemblages pairs Pearson™s r r Slope intercept
Paleontological 7 265 0.8747 0.7651 0.483
Paleontological 11 360 0.8719 0.7586 0.5581

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