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¬‚esh removed from six hindlimbs in each of three carcass sizes. 295
7.9. Relationship between number of cut marks and the amount of ¬‚esh
removed from eighteen hindlimbs. 295
8.1. Relationship between NISP and MNI in seven paleontological
assemblages of bird remains from North America. 304
8.2. Relationship between NISP and MNI in eleven paleontological
assemblages of mammal remains from North America. 304
8.3. Relationship between NISP and MNI in twenty-two archaeological
assemblages of bird remains from North America. 305
8.4. Relationship between NISP and MNI in thirty-¬ve archaeological
assemblages of mammal remains from North America. 306

1.1. An example of the Linnaean taxonomy. page 6
1.2. Fictional data on the absolute abundances of two taxa in six
chronologically sequent strata. 15
1.3. Description of the mammalian faunal record at Meier and at
Cathlapotle. 19
2.1. Fictional data on abundances of three taxa in ¬ve strata. 32
2.2. Data in Table 2.1 adjusted as if each individual of taxon A had ten
skeletal elements per individual, taxon B had one skeletal element per
individual, and taxon C had ¬ve skeletal elements per individual. 33
2.3. The differential exaggeration of sample sizes by NISP. 36
2.4. Some published de¬nitions of MNI. 40
2.5. A ¬ctional sample of seventy-one skeletal elements representing a
minimum of seven individuals. 45
2.6. Statistical summary of the relationship between NISP and MNI for
mammal assemblages from Meier and Cathlapotle. 53
2.7. Statistical summary of the relationship between NISP and MNI for
mammal assemblages from fourteen archaeological sites in eastern
Washington State. 55
2.8. Maximum distinction and minimum distinction MNI values for six
genera of mammals in a sample of eighty-four owl pellets. 55
2.9. Adams™s data for calculating MNI values based on Odocoileus sp.
remains. 57
2.10. Differences in site total MNI between the MNI minimum distinction
results and the MNI maximum distinction results. 59
2.11. The most abundant skeletal part representing thirteen mammalian
genera in two (sub)assemblages at Cathlapotle. 62

xviii list of tables

2.12. Fictional data showing how the distribution of most abundant
skeletal elements of one taxon can in¬‚uence MNI across different
aggregates. 63
2.13. Fictional data showing how the distribution of skeletal elements of
two taxa across different aggregates can in¬‚uence MNI. 64
2.14. Fictional data showing that identical distributions of most common
skeletal elements of two taxa across different aggregates will not
in¬‚uence MNI. 65
2.15. Ratios of abundances of pairs of taxa in eighty-four owl pellets. 72
3.1. Biomass of deer and wapiti at Cathlapotle. 86
3.2. Meat weight for deer and wapiti at Cathlapotle, postcontact
assemblage. 90
3.3. Comparison of White™s conversion values to derive usable meat with
Stewart and Stahl™s conversion values to derive usable meat. 91
3.4. Variation by age and sex of wapiti butchered weight as a percentage
of live weight. 92
3.5. Weight of a 350-kilogram male wapiti in various stages of butchering. 93
3.6. Descriptive data on animal age, bone weight per individual, and
soft-tissue weight per individual domestic pig. 97
3.7. Statistical summary of the relationship between bone weight and
weight of various categories of soft-tissue for domestic pig. 98
3.8. Descriptive data on dry bone weight per anatomical portion and
total weight per anatomical portion for domestic sheep. 100
3.9. Statistical summary of the relationship between bone weight and
gross weight or biomass of skeletal portions of two domestic sheep. 101
3.10. Relationship between NISP and bone weight of mammalian taxa in
seventeen assemblages. 104
3.11. Results of applying the bone-weight allometry equation to ¬ve
randomly generated collections of domestic sheep bone. 105
3.12. Deer astragalus length and live weight. 110
3.13. Ubiquity and sample size of twenty-eight mammalian taxa in
eighteen sites. 116
3.14. Ubiquity and sample size of mammalian taxa across analytical units
in two sites. 118
3.15. Fictional data illustrating in¬‚uences of NISP and the number of pairs
on the Lincoln“Petersen index. 126
3.16. Abundances of beaver and deer remains at Cathlapotle, and WAE
values and ratios of NISP and WAE values per taxon per assemblage. 135
list of tables xix

3.17. Estimates of individual body size of seventeen white-tailed deer
based on the maximum length of right and left astragali. 139
4.1. Volume excavated and NISP of mammals per annual ¬eld season at
the Meier site. 144
4.2. Annual NISP samples of mammalian genera at the Meier site. 145
4.3. Annual NISP samples of mammalian genera at Cathlapotle. 147
4.4. Mammalian NISP per screen-mesh size class and body-size class for
three sites. 155
4.5. Two sets of faunal samples showing a perfectly nested set of faunas
and a poorly nested set of faunas. 169
5.1. Sample size, taxonomic richness, taxonomic heterogeneity,
taxonomic evenness, and taxonomic dominance of mammalian
genera in eighteen assemblages from eastern Washington State. 181
5.2. NISP and NTAXA for small mammals at Homestead Cave, Utah. 183
5.3. NISP and NTAXA for ungulates at Le Flageolet I, France. 184
5.4. NISP per taxon in two chronologically distinct samples of
eighty-four owl pellets. 188
5.5. Expected values and interpretation of taxonomic abundances in two
temporally distinct assemblages of owl pellets. 188
5.6. Derivation of the Shannon’Wiener index of heterogeneity for the
Meier site. 193
5.7. Total NISP of mammals, NISP of deer, and relative abundance of
deer in eighteen assemblages from eastern Washington State. 199
5.8. Frequencies of bison and nonbison ungulates per time period in
ninety-one assemblages from eastern Washington State. 204
5.9. Frequencies of elk, deer, and medium artiodactyl remains per
stratum at Emeryville Shellmound. 207
5.10. Frequencies of two taxa of small mammal per stratum at Homestead
Cave. 209
6.1. MNE values for six major limb bones of ungulates from the FLK
Zinjanthropus site. 219
6.2. Fictional data showing how the distribution of specimens of two
skeletal elements across different aggregates can in¬‚uence MNE. 223
6.3. NISP and MNE per skeletal part of deer and wapiti at the Meier site. 224
6.4. Frequencies of major skeletal elements in a single mature skeleton of
several common mammalian taxa. 228
6.5. MNE frequencies of left and right skeletal parts of pronghorn from
site 39FA83. 230
list of tables

6.6. Expected MNE frequencies of pronghorn skeletal parts at site 39FA83,
and adjusted residuals and probability values for each. 232
6.7. Frequencies of skeletal elements in a single generic artiodactyl
skeleton. 233
6.8. MNE and MAU frequencies of skeletal parts and portions. 236
6.9. MAU and%MAU frequencies of bison from two sites. 239
6.10. Skeletal-part frequencies for two taxa of artiodactyl. 246
6.11. Expected frequencies of deer and wapiti remains at Meier, adjusted
residuals, and probability values for each. 249
6.12. Ratios of NISP:MNE for four long bones of deer in two sites on the
coast of Oregon State. 252
6.13. African bovid size classes. 255
6.14. NISP and MNE frequencies of skeletal parts of bovid/cervid size class
II remains from Kobeh Cave, Iran. 256
6.15. NISP and MNE frequencies of skeletal parts of saiga antelope from
Prolom II Cave, Ukraine. 257
6.16. Relationship between NISP and MNE in twenty-nine assemblages. 259
6.17. NISP and MNI frequencies of skeletal parts of caprines from
Ngamuriak, Kenya. 260
6.18. Relationship between NISP and MNI per skeletal part or portion in
twenty-two assemblages. 261
7.1. Weathering stages as de¬ned by Behrensmeyer. 267
7.2. Weathering stage data for two collections of mammal remains from
Olduvai Gorge. 268
7.3. Expected frequencies of specimens per weathering stage in two
collections, adjusted residuals, and probability values for each. 269
7.4. Frequencies of cut marks per anatomical area on six experimentally
butchered goat hindlimbs. 288
7.5. Frequencies of arm strokes and cut marks on sixteen limbs of cows
and horses. 290
7.6. Number of cut marks generated and amount of meat removed from
eighteen mammal hindlimbs by butchering. 294
8.1. Statistical summary of relationship between NISP and MNI in
collections of paleontological birds, paleontological mammals,
archaeological birds, and archaeological mammals. 303

Several years ago I had the opportunity to have a relaxed discussion with my doctoral
advisor, Dr. Donald K. Grayson. In the course of that discussion, I asked him if
he would ever revise his then 20-year-old book titled Quantitative Zooarchaeology,
which had been out of print for at least a decade. He said “No” and explained that the
topic had been resolved to his satisfaction such that he could do the kinds of analyses
he wanted to do. A spur-of-the-moment thought prompted me to ask, “What if I
write a revision?” by which I meant not literally a revised edition but instead a new
book that covered some of the same ground but from a 20-years-later perspective.
Don said that he thought that was a ¬ne idea.
After the conversation with Grayson, I began to mentally outline what I would
do in the book. I realized that it would be a good thing for me to write such a
book because, although I thought I understood many of the arguments Grayson had
made regarding the counting of animal remains when I was a graduate student, there
were other arguments made by other investigators subsequent to the publication of
Grayson™s book that I didn™t know (or if I knew of those arguments, I wasn™t sure I
understood them very well). I also knew that the only way for me to learn a topic
well was to write about it because such a task forced me to learn its nuances, its
underpinning assumptions, the interrelations of various aspects of the argument,
and all those things that make an approach or analytical technique work the way that
it does (or not work as it is thought to, as the case may be).
As I mentally outlined the book over the next several months, it occurred to me
that at least one new quantitative unit similar to the traditional ones Grayson had
considered had become a focus of analytical attention over the two decades subse-
quent to the publication of Grayson™s book (MNE, and the related MAU). And an
increasing number of paleozoologists were measuring taxonomic diversity “ a term
that had several different meanings for several different variables as well as being
measured several different ways. What were those measurement techniques and
xxii preface

what were those measured variables? Finally, there were other kinds of phenomena
that zooarchaeologists and paleontologists had begun to regularly tally and analyze.
These phenomena “ butchering marks, carnivore gnawing marks, rodent gnawing
marks, burned bones “ had become analytically important as paleozoologists had
come to realize that to interpret the traditional quantitative measures of taxonomic
abundances, potential biases in those measures caused by differential butchery, car-
nivore attrition, and the like across taxa had to be accounted for. As I indicate in this
volume, there are several ways to tally up carnivore gnawing marks and the like, and
few analysts have explored the fact that each provides a unique result.
Finally, it had become clear to me during the 1990s that many paleozoologists were
unaware of what I took to be two critical things. First, zooarchaeologists seemed
to seldom notice what is published in paleontological journals; at least they sel-
dom referenced that literature. Thus, they were often ignorant of various sugges-
tions made by paleontologists regarding quantitative methods. Paleontologists were
equally unaware of what zooarchaeologists have determined regarding quanti¬ca-
tion of bones and shells and teeth. Therefore, it seemed best to title this volume
Quantitative Paleozoology for the simple reason that were it to be titled “Quantitative
Zooarchaeology,” it likely would not be read by paleontologists. A very interesting
book with the title Quantitative Zoology coauthored by a paleontologist (Simpson et
al. 1960) already exists, so that title could not be used, aside from it being misleading.
Quantitative Paleozoology is a good title for two reasons. The ¬rst reason is that the
subject materials, whether collected by a paleontologist or an archaeologist, do not
have a proximate zoological source (though their source is ultimately zoological) but
rather have a proximate geological source, whether paleontological (without associ-
ated human artifacts) or archaeological (with associated and often causally related
human artifacts). I conceive of all such remains as paleozoological. The second rea-
son Quantitative Paleozoology is a good title is that the volume concerns how to
count or tally, how to quantify zoological materials and their attributes, speci¬cally
those zoological remains recovered from geological contexts. Not all such topics are
discussed here, but many are; for an introduction to many of those that are not, see
Simpson et al. (1960), a still-useful book that was, fortunately, reprinted in 2003.
The second critical thing that many paleozoologists seem to be unaware of is basic
statistical concepts and methods. I was stunned in 2004 to learn that an anonymous
individual who had reviewed a manuscript I submitted for publication did not know
what a “closed array” was and therefore did not understand why my use of this par-
ticular analytical tool could have been in¬‚uencing (some might say biasing, but that
is a particular kind of in¬‚uencing) the statistical results. In the 1960s and early 1970s,
many archaeologists and paleontologists did not have very high levels of statistical
sophistication; I had thought that most of them did have such sophistication (or at
preface xxiii

least knowledge of the basics) in the twenty-¬rst century. The anonymous reviewer™s
comments indicate that at least some of them do not. Therefore, it seemed that any
book on quantitative paleozoology had to include brief discussions of various sta-
tistical and mathematical concepts. In order to not dilute the central focus of the
volume “ quantitative analysis of paleozoological remains “ I have kept discussion
of statistical methods to a minimum, assuming that the serious reader will either
already know what is necessary or will learn it as he or she reads the book. I have,
however, devoted the ¬rst chapter to several critical mathematical concepts as well
as some key paleozoological concepts.
Many of the faunal collections used to illustrate various points in the text were
provided over the years by friends and colleagues who entrusted me with the analysis
of those collections. Many of the things I have learned about quantitative paleozo-
ology are a direct result of their trust. To these individuals, I offer my sincere thanks:
Kenneth M. Ames, David R. Brauner, Jerry R. Galm, Stan Gough, Donald K. Grayson,
David Kirkpatrick, Lynn Larson, Frank C. Leonhardy, Dennis Lewarch, Michael J.
O™Brien, Richard Pettigrew, and Richard Ross. Perhaps more importantly, any clarity
this book brings to the issues covered herein is a result of the collective demand for
clarity by numerous students who sat through countless lectures about the counting
units and methods discussed in this book. A major source of inspiration for the ¬rst
several chapters was provided in 2004 by the Alaska Consortium of Zooarchaeol-
ogists (ACZ). That group invited me to give a daylong workshop on the topics of
quanti¬cation and taphonomy, and that forced me to think through several things
that had previously seemed less than important. I especially thank Diane Hansen
and Becky Saleeby of the ACZ for making that workshop experience memorable.
An early draft of the manuscript was reviewed by Jack Broughton, Corey Hudson,
Alex Miller, and an anonymous individual. Broughton and the anonymous reviewer
ensured that a minimum of both glaring errors in logic and stupid errors in mathe-
matics remain in this version. Broughton and the anonymous reviewer insisted that
I include several recently described analytical techniques, and they identi¬ed where
I overstepped and where I misstepped. These individuals deserve credit for many of
the good things here.
I wrote much of the ¬rst draft of this volume between July 2005 and August 2006.
During that time, I lost my younger brother and both parents. They all had an indirect
hand in this book. My parents taught me to hunt and ¬sh, and all of the things that
accompany those activities. My brother did not discourage me from collecting owl
pellets from his farm equipment shed, or laugh too hard when I collected them; he
even grew to appreciate what could be learned from the mouse bones they contained.
I miss them all, and I dedicate this book to the three of them.
June 2007
Tallying and Counting: Fundamentals

Early in the twentieth century, paleontologist Chester Stock (1929) was, as he put
it, faced with “recording a census” of large mammals from the late Pleistocene as
evidenced by their remains recovered “from the asphalt deposits of Rancho La Brea,”
in Los Angeles, California. Paleontologist Hildegarde Howard (1930) was faced with
a similar challenge with respect to the bird remains from Rancho La Brea. Stock and
Howard could have merely listed the species of mammals and the species of birds,
respectively, that were represented by the faunal remains they had “ they could have
constructed an inventory of taxa “ but they chose to do something more informative
and more analytically powerful. They tallied up how many individuals of each species
were represented by the remains “ they each produced a census. The quantitative
unit they chose became known as the minimum number of individuals, or MNI, a
unit that was quickly (within 25 years) adopted by many paleozoologists. We will
consider this unit in some detail in Chapter 2, but here it is more important to outline
how Stock and Howard de¬ned it and why they decided to provide a census rather
than an inventory of mammals and an inventory of birds.
Stock (1929:282) stated that the tally or “count” of each taxon was “determined
by the number of similar parts of the internal skeleton as for example the skull,
right ramus of mandible, left tibia, right scaphoid. In many cases the total number
of individuals for any single group [read taxon] is probably a minimum estimate.”
Howard (1930:81 “82) indicated that “for each species, the left or the right of the
[skeletal] element occurring in greatest abundance was used to make the count. . . . It
is probable that in many instances the totals present a minimum estimate of the
number of individuals [per taxon] actually represented in the collection.” We will
explore why the procedure Stock and Howard used provides a “minimum” estimate
of abundance in Chapter 2. Stock and Howard each produced a type of pie diagram
to illustrate their respective censuses of mammalian and of avian creatures based on
the bony remains of each (Figure 1.1).
quantitative paleozoology

figure 1.1. Chester Stock™s pie diagram of abundances of ¬ve mammalian orders repre-
sented in faunal remains from Rancho La Brea. Redrawn from Stock (1929).

An inventory of the mammalian taxonomic orders Stock identi¬ed among the
bones and teeth he studied would look like this:

Clearly, the pie diagram in Figure 1.1 reveals more about the structure of the Rancho La
Brea mammalian fauna because it contains not only the same set of taxonomic orders
as the inventory, but it also contains measures of the abundances of animals belonging
to each order. This example illustrates one of the major reasons why paleozoologists
count or tally the animal remains they study. Taxa present in a collection can, on
the one hand, be treated as attributes or as present or absent from a fauna, such
as is given in the inventory above (sometimes referred to as a “species list” if that
taxonomic level is used). On the other hand, abundances of each taxon provide a great
deal more information about the prehistoric fauna. There are times when knowing
only which taxa are present, or knowing only what the frequencies of different taxa
are is all that is wanted or needed analytically. (Two faunas may have the same, or
quite different, frequency distributions of individual organisms across taxa, and the
research question may only require knowing the frequency distributions and not
the taxa.) Knowing both, however, means we know more than when we know just
one or the other. And that is a good reason to count faunal remains and to determine
tallying and counting: fundamentals 3

a census. Counting faunal remains, particularly old or prehistoric remains, and the
variety of attributes they display, whether the remains are from archaeological or
paleontological contexts, is what this book is about.
There is already a book about counting animal remains recovered from archae-
ological and paleontological sites (Grayson 1984), and several other volumes cover
some of the same ground, if in less detail (e.g., Hesse and Wapnish 1985; Klein and
Cruz-Uribe 1984; Reitz and Wing 1999). Noting this, one could legitimately ask why
another book on this topic is necessary. There are several reasons to write a new
book. Much has happened in the ¬eld since Grayson (1984) published his book (and
his book has been out-of-print for several years). Some of what has happened has
been conceptually innovative, such as the de¬nition of new quantitative units meant
to measure newly conceived properties of the paleozoological record. Some of what
has happened has been technically innovative, such as designing new protocols for
tallying animal remains that are thought to provide more accurate re¬‚ections of what
is represented by a collection of remains than tallies based on less technologically
sophisticated methods. And, some of what has happened is misguided or archaic,
such as arguing that if certain biological variables are not mathematically controlled
for, then any count of taxonomic abundances is invalid. It is time (for these reasons)
for a new, up-to-date examination of the quantitative units and counting protocols
paleozoologists use in their studies.
There is yet another reason to produce a new book on quantitative paleozoology.
Today, early in the third millennium, there are more people studying paleozoological
collections than there were 20 years ago. These folks need to be able to communi-
cate clearly and concisely with one another regarding their data and their analyses
because the use of ambiguous terminology thwarts ef¬cient communication and
results in confusion. This point was made more than a decade ago with respect to the
plethora of terms, many unfamiliar to those in the ¬eld, used for quantitative units
in zooarchaeology (Lyman 1994a). Yet, the problem continues today. This problem
had originally been identi¬ed more than 15 years earlier still by Casteel and Grayson
(1977). For whatever reason, terminological ambiguity seems to plague paleozoology
and continues to do so despite it being explicitly identi¬ed twice in the past 30 years.
In my earlier discussion of terminological ambiguity (Lyman 1994a), I did not
advocate a particular terminology, nor am I doing so here. Clearly there are terms
I prefer “ the ones I use in this volume are the ones I learned as a student. What I
am arguing here is that whatever terms or acronyms one uses, these must be clearly
de¬ned at the start so as to avoid misunderstanding. In reading and rereading the
literature on quantitative paleozoology as I prepared this book, I was often dumb-
founded when people used terms such as “bone” and “relative abundance” when it
quantitative paleozoology

was quite clear that they were discussing teeth and absolute abundances, respectively.
Much of the remainder of this chapter is, therefore, devoted to terminology and def-
initions. For quick reference, I have included a glossary of key terms at the end of
this volume.
In this introductory chapter, several basic mathematical and statistical concepts are
de¬ned. This is necessary because these concepts will be used throughout subsequent
chapters and thus the concepts must be understood in order to follow the discussion
in later chapters. Several basic paleozoological concepts are introduced and de¬ned
for the same reason. I begin with these concepts before turning to the mathematical
and statistical concepts.


Throughout this volume the focus is on vertebrates, especially mammals, because
that is the taxonomic group which much of the literature concerns and because it is

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