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to note the absolute frequencies of specimens of each species. If one were to note that
in that collection of ¬fteen specimens, 66.7 percent of the specimens were of rabbits
and 33.3 percent were of turkey, then one would be noting the relative frequency
of each species. Relative frequencies are termed such because they are relative to
one another. A relative frequency is a quantity or estimate that is stated in terms of
another quantity or estimate. The analyst could have different absolute abundances,
say thirty rabbit bones and ¬fteen turkey bones, but rabbit bones would comprise the
relative abundance of 66.7 percent of the collection and turkey bones would comprise
33.3 percent of that collection, the same as when there are ten rabbit bones and ¬ve
turkey bones. Percentages and proportions of a total are relative frequencies. The
term “relative frequencies” is sometimes used in the paleozoological literature to
signify estimates in which a quantity is not stated but rather only that A is greater (or
smaller, or less) than B. In such cases relative frequencies are equivalent to ordinal
scales of measurement. In this volume, the term “relative frequencies” is used in the
more typical sense of percentage or proportional abundances.
Relative frequencies are typically given as percentages of some total set of things,
and the summed relative frequency is always 100 percent (proportions are fractions).
When relative frequencies of kinds of things in a set of things are given as percent-
ages, all of those frequencies must sum to 100 percent rather than 90 percent or 110
percent. Such percentage relative frequencies comprise what is called a closed array
(proportions also form a closed array as they must sum to 1.0).
Another way to think about the difference between absolute and relative frequen-
cies involves comparison of measurements. Let™s say we have two collections of faunal
remains. In collection 1, taxon A is represented by 5 specimens and taxon B is rep-
resented by 10 specimens. In collection 2, taxon A is represented by 50 specimens
and taxon B is represented by 55 specimens. The absolute difference in abundances
of the two taxa in each collection is 5 specimens, but in collection 1, taxon A is only
50 percent as abundant as taxon B whereas in collection 2 taxon A is 90.9 percent as
abundant as taxon B. Or, one could say that in collection 1 the relative abundances
of taxa A and B are 33.3 percent and 66.7 percent, respectively, whereas the relative
abundances of those taxa in collection 2 are 47.6 percent and 52.4 percent, respec-
tively. The difference between absolute and relative frequencies is not a matter of
which is correct and which is not, but rather they are simply two different ways to
measure (describe) the frequencies of things.
Importantly, the absolute frequency of things of kind A in a collection will not
change value if the absolute frequency of kind B in that collection changes, but the
relative frequency of both A and B will change if the absolute frequency of either A
or B changes. This last property is a characteristic “ one could say diagnostic “ of
tallying and counting: fundamentals 15

Table 1.2. Fictional data on the absolute abundances
of two taxa in six chronologically sequent strata

Taxon A Taxon B
Stratum VI 50 (71.4) 20 (28.6)
Stratum V 50 (62.5) 30 (37.5)
Stratum IV 50 (55.6) 40 (44.4)
Stratum III 50 (50.0) 50 (50.0)
Stratum II 50 (45.4) 60 (54.6)
Stratum I 50 (41.7) 70 (58.3)

Relative (percentage) abundances in parentheses.

closed arrays; they must sum to 100 percent. Consider the set of ¬ctional data in
Table 1.2. If we examine these data, we see that Taxon A does not change in abso-
lute abundance over the stratigraphic sequence, but Taxon B does change in abso-
lute abundance. However, relative abundance data suggest that both taxa change in
abundance. This example reveals a ¬nal and critically important aspect of abundance
In paleozoology, absolute abundance data or raw tallies are often given, but when it
comes to interpreting abundance data, it is in terms of relative abundances. Using the
¬ctional data in Table 1.2 as an example, one might read something like the following:

Throughout the stratigraphic sequence (from stratum I as earliest or oldest to stratum
VI as youngest) Taxon A increased in abundance relative to Taxon B, which decreased in
relative abundance. Given that Taxon A prefers habitats that support vegetation adapted
to cool-moist climatic conditions, and Taxon B prefers habitats indicative of warm-dry
climatic conditions, then it seems that over the time span represented by strata I“VI,
the local climate became progressively cooler and moister.

Notice that in the interpretation no mention is made of the absolute abundances
of taxa A and B. Rather, their abundances relative to each other are the focus. The
abundances are not even taken as measures of how many of either taxon was present
on the landscape at the time the strata and faunal remains were deposited. Rather,
the interpretation involves postulating a cause for the shift in relative abundances of
two taxa. One could also postulate that hunting practices or procurement technology
shifted, resulting in the shift in which taxon was taken more frequently. Resolving
these sorts of issues is beyond the scope of this volume, but suf¬ce it to say that
regardless of the interpretive model one calls upon, relative abundances, in the case
of this example relative taxonomic abundances, are interpreted.
quantitative paleozoology


Quantitative data often comprise tallies of different kinds of phenomena. They might
also include a set of measurements of, say, the length of individual specimens. This
book concerns only the former kind of quantitative data “ tallies. It is about how
a paleozoologist might count phenomena (faunal specimens, or attributes thereof)
when one seeks a measure of the magnitude of a particular variable that demands
counts of phenomena (bones, teeth, shells, and fragments thereof, or burned bones,
gnawed bones, or broken bones). How one chooses to tally those phenomena, and
how those tallies are summarized and analyzed statistically, depend in large part on
the research question asked and the target variable that one hopes to measure in
order to answer that question. The choices likely will also depend on the presumed
relationship of the target variable and the chosen measured variable. Discussion of
how one determines the nature of that relationship in particular cases is beyond
the scope of this volume. When necessary to assist discussions in later chapters, a
particular relationship is assumed or identi¬ed.
The terms assemblage or collection denote an aggregate of faunal remains whose
setness has been de¬ned archaeologically (e.g., remains from an excavation unit),
geologically (e.g., remains from a trash pit or a stratum), or analytically (e.g., all
remains of a taxon). Graphs are used whenever possible to exemplify and illustrate
concepts and analytical results, and to display relationships between variables. Statis-
tical analyses are kept relatively simple and are used to evaluate particular properties
of collections. In a few cases, statistical complexities are described in a clearly delin-
eated box of text and may be skipped when reading the main content of a chapter.
Data are often presented in table form so that the reader may replicate the statistical
analyses (and graphs) to ensure understanding. This volume is, however, not meant
to be exhaustive with respect to all of the myriad ways that faunal remains might
be counted, or with respect to how the varied features faunal remains might display
can be counted. Rather, most of the commonly used quantitative units (measured
variables) and their attendant analyses serve as the background against which the
discussion is framed. Target variables are identi¬ed and de¬ned as necessary when
discussing particular quantitative units.
This is not a book about taphonomic, zooarchaeological, or paleontological analy-
ses. There are several excellent titles on each of these topics that are presently available
(e.g., Lyman 1994c; Reitz and Wing 1999; Simpson et al. 1960, respectively). Quantita-
tive Paleozoology is meant as a supplement to those other volumes because it covers in
detail a limited range of topics relevant to various analytical methods and techniques
described in each of those other volumes.
tallying and counting: fundamentals 17


Throughout this volume, extensive use is made of data derived from actual zooarchae-
ological and paleontological collections of vertebrate, usually mammalian, remains.
In several cases, the mammalian remains from a set of modern owl pellets collected
in the 1990s are used to illustrate an analytical procedure or a concept (see Lyman
and Lyman [2003] and Lyman et al. [2001, 2003] for more details on this collection).
In the chapters that follow, many points are illustrated by analyzing faunas from var-
ious places and dating to various time periods. This helps to emphasize that many
properties of the paleozoological record are in at least one sense universal, by which
is meant that those properties are typically found in an average paleo-faunal assem-
blage. By “average” is meant typical and having multiple taxa (usually more than a
half-dozen) and multiple identi¬ed specimens for the total collection (usually more
than, say, 50 specimens). What are rather atypical if not rare or unusual are those
collections that have hundreds if not thousands of specimens, all representing the
same species. The well-known bison (Bison spp.) kill sites of North America do not
seem particularly rare because publications on them are numerous, but in terms of
the faunal record they are rather atypical. An even more unusual paleofauna would
be one consisting of only a couple identi¬ed specimens (say, < 10), each represent-
ing a unique taxon. When necessary, these sorts of relatively unusual collections are
mentioned, but otherwise typical faunas are used to illustrate quantitative concepts
and analyses.
Using the same faunal samples throughout, it will be easy to track different kinds
of interdependence, and how one analytical result in¬‚uences whether or not another
analysis is reasonable or even feasible. And, by the same token, if two faunal samples
from basically the same geographic area and dating to the same time period are
available, then other sorts of analytical insights can be gained. Thus two collections of
mammal remains are used to illustrate signi¬cant points in later chapters. Analyses
of the artifacts and features at each site are ongoing, so some of the background
information is terse and incomplete. The lack of information on particular aspects
of the collections will not make a difference to the points made in this volume.
The collections are zooarchaeological “ they originate in an archaeological context.
These are faunal remains that had associated artifacts; such assemblages are some-
times referred to as archaeofaunas. Both collections consist of mammal remains
recovered from two late-prehistoric sites within 10 km of one another. Both sites are
found in what is locally known as the Portland Basin or the Wapato Valley of north-
western Oregon state and southwestern Washington state. All mammalian remains
from both sites were recovered from one-quarter-inch mesh screens in the ¬eld.
quantitative paleozoology

The Meier site (35CO5) is located downstream (north) of modern Portland, Oregon,
on the ¬‚oodplain of the Columbia River, on the Oregon side. The Meier site com-
prises a single large cedar-plank house that was occupied more or less continuously
between approximately ad 1400 and ad 1800, and associated midden deposits (Ames
1996; Ames et al. 1992). The site was tested in 1973 and 1984. It underwent extensive
excavations every year between 1987 and 1991, inclusively. The 1973 collection was
made by Pettigrew (1981) and studied by Saleeby (1983). The 1984 test was directed
by Ellis (n.d.); recovered faunal remains have not been analyzed. Kenneth Ames of
Portland State University directed the excavations that took place in the late 1980s
and early 1990s. I identi¬ed all mammalian remains collected by Ames during a 1993
research-sponsored leave when I worked with him in Portland.
The other site, Cathlapotle (45CL1), is located northeast of Meier, on the Wash-
ington side of the Columbia River, on a series of levees next to the river. The site
was visited by Meriwether Lewis and William Clark in March of 1806 as they lead
the Corps of Discovery eastward. At the time of their visit the site comprised several
large cedar-plank houses and associated midden deposits (Ames et al. 1999; Ames and
Maschner 1999:110). Radiocarbon dates indicate the main occupation began about
ad 1450. Ceramic trade goods indicate that abandonment of the site occurred about
ad 1834. Auger sampling of the Cathlapotle sediments took place in 1992“1993, and
excavations took place each year from 1993 through 1996. Both the auguring and the
excavations were under the direction of Ames. I identi¬ed all mammalian remains
recovered from this site at the University of Missouri-Columbia campus.
The assemblages of mammalian remains from Meier and Cathlapotle were recov-
ered from similar depositional contexts. At both sites, the deposits variously comprise
exterior (midden and “yard”) deposits and interior deposits (inside of a house). Exte-
rior deposits had very high organic content, lenses of fresh-water mussel shells, and
other indications that they formed as primary or secondary dumps (Ames et al. 1999).
Yard deposits are generally broad, sheet-like deposits that contain intact hearths,
activity areas, pits, evidence of small structures, and so forth. They usually lack the
very high organic content of middens though they can have organic content. Inte-
rior deposits were assigned to walls, benches (deposits below the 2 m-wide sleeping
benches or platforms that ran along the interior side of the house walls), storage pits,
and hearth areas. Faunal remains have not been sorted into these distinct depositional
contexts as yet. Were they to be so assigned, it is likely that assemblages would be
quite small. In later chapters, the in¬‚uences of small sample sizes receive considerable
The houses at Meier and Cathlapotle had extensive sub¬‚oor storage features that,
at Meier at least, formed a cellar almost 2 m deep that extended under the house
tallying and counting: fundamentals 19

Table 1.3. Description of the mammalian faunal record at Meier and at


Meier Precontact Postcontact

Didelphis— “ “ “ “ 10 1
Scapanus 14 4 “ “ 3 2
Sorex “ “ 3 1 1 1
Sylvilagus 16 2 “ “ 1
Lepus “ “ 3 2 40 4
Aplodontia 5 1 61 8 57 8
Tamias 1 1 “ “ “ “
Tamiasciurus 2 1 “ “ “ “
Thomomys 9 5 “ “ “ “
Castor 329 9 111 5 238 7
Peromyscus 35 21 2 1 3 2
Rattus— 1 1 “ “ “ “
Neotoma 1 1 “ “ “ “
Microtus 100 41 10 4 55 22
Ondatra 337 13 56 7 36 4
Erethizon 1 1 “ “ “ “
Canis 90 7 18 3 17 2
Vulpes 2 1 4 1 “ “
Ursus 82 5 45 3 53 4
Procyon 272 20 109 6 84 8
Martes 19 4 1 1 1 1
Mustela 130 17 12 3 9 2
Mephitis 4 2 3 1 “ “
Lutra 45 3 28 3 26 4
Puma 9 1 5 1 5 2
Lynx 22 3 8 1 15 2
Phoca 40 3 26 2 34 2
Ovis “ “ 1 1 1 1
Cervus 832 10 1,091 12 1,793 24
Odocoileus 3,504 56 775 14 1,347 27
Equus— “ “ “ “ 4 1
TOTAL 5,939 “ 2,372 “ 3,834 “

Taxa are historically introduced and not native to the area, hence they are intrusive
to site sediments.
quantitative paleozoology

¬‚oor between the sleeping platforms and the row of hearths in the house™s center. The
Cathlapotle features are less extensive, but are about 2 m wide by 2 m deep. They are
below the sleeping platforms rather than next to them as at Meier. The mammalian
remains from both sites were derived primarily from these storage pits and exterior
Because, with few exceptions, the mammalian genera identi¬ed are monotypic
(include only one species), the basic faunal identi¬cation and quantitative data are
presented by genus (Table 1.3). Stratigraphy at Meier is extremely complex as a
result of multiple episodes of house remodeling and rebuilding; temporally distinct
assemblages could not be distinguished. This assemblage is, therefore, treated as a
whole and not subdivided into subassemblages. The stratigraphy at Cathlapotle, on
the other hand, though also rather complex as a result of the various things that people
did at the site, was suf¬ciently clear that two temporally distinct (sub)assemblages
of faunal remains could be distinguished. Many, but not all of the mammal remains
from Cathlapotle could be sorted into a pre (Euroamerican) contact sample deposited
between ad 1400 and ad 1792, and a postcontact sample deposited between ad 1792
and ad 1835. These two temporally distinct assemblages are referred to in later chapters
simply as the precontact and postcontact assemblages. For most purposes the faunal
remains that could not be assigned to a temporal period are not included in the
analyses presented in later chapters.
The samples of identi¬ed remains from the two sites are not tremendously large by
some standards (Table 1.3). However, based on data compiled by others (especially
Casteel 1977, n.d.), both collections are of reasonable size. That they are not tremen-
dously large is a bene¬t in the sense that this will assist with the detection of possible
in¬‚uences of sample size in later chapters. The three assemblages are described in
Table 1.3. For additional information on the mammal collections not covered in later
chapters, see Lyman (2004a, 2006b, 2006c), Lyman et al. (2002), Lyman and Ames
(2004), and Lyman and Zehr (2003).
Estimating Taxonomic Abundances:

As paleontologists, Chester Stock and Hildegard Howard were interested in the abun-
dance of the mammals that had walked the landscape and birds that had ¬‚own in
the air above the landscape at the time the faunal remains from Rancho La Brea were
deposited (Chapter 1 ). Zooarchaeologists (known as archaeozoologists in Europe),
on the other hand, are typically interested in which taxa provided the most economic
resources and which taxa provided little in the way of economic resources. Thus, as
zooarchaeologist Dexter Perkins (1973:369) noted, “the primary objective of faunal
analysis of material from an archaeological site [or from a paleontological site] is
to establish the relative frequency of each species.” This target variable sought by
paleontologists and zooarchaeologists concerns taxonomic abundances. What are the
frequencies of the taxa in a collection?
In any given collection of paleozoological remains, one might wish to know if car-
nivores are less abundant than herbivores, just as they normally are on the landscape.
Given what he knew about ecological trophic structure “ that herbivores should out-
number carnivores “ imagine Stock™s surprise to learn that the typically observed
food pyramid or ecological trophic structure was upside down. The mammalian
remains from Rancho La Brea represented more carnivores than herbivores ’ for
a reason that many paleontologists thought was a taphonomic reason “ because
scavenging carnivores got “bogged down” or mired in the sticky tar seeping from
the ground and failed to escape. Carnivores were abundant in that tar because they
had died and become entombed there as a result of trying to exploit the carcasses of
herbivores (and perhaps carnivore brethren) that had themselves become mired and
subsequently died there.
The eminently sensible hypothesis that carnivore remains are more abundant than
herbivores for taphonomic reasons (see Spencer et al. [2003] for a recent evaluation of
this hypothesis) concerns the relationship between a target variable and a measured
variable. Stock™s target variable was the frequencies of mammalian taxa comprising
quantitative paleozoology

the animal community on the landscape, but his measured variable was the sample of
bones and teeth from the excavations of the tar pits. Taphonomists have developed an
unwieldy terminology (see the glossary in Lyman 1994c), but several of the terms are
useful here for keeping target variables and measured variables distinct. A biocoenose
is a living community of organisms. Exactly what a community comprises is the
subject of some debate. One de¬nition provided by biologists is this: A community
is comprised of “species that live together in the same place. The member species
can be de¬ned either taxonomically or on the basis of more functional ecological
criteria, such as life form or diet” (Brown and Lomolino 1998:96).
But “most so-called communities are arbitrary and convenient segments of a con-
tinuum of species with overlapping ecological requirements, not involving a high
level of interdependence” (Lawson 1999:7). Thus one commentator notes that a bio-
logical community can be de¬ned one of two ways: As a group of organisms occu-
pying a location, or as a group of organisms with ecological linkages among them
(Southwood 1987). Often the focus is on the former at the expense of the latter; a
community (which may include all organisms or a particular subset of organisms) is
often de¬ned by speci¬c spatial boundaries (Magurran 1988:57). Perhaps not surpris-
ingly, the “nature of boundaries separating adjacent communities is hotly disputed
by community ecologists and paleoecologists” (Hoffman 1979:364). For the sake of
discussion, we assume that a biological community and its boundaries can be de¬ned
on the landscape today.
The taxonomic composition and taxonomic abundances of a biocoenose might
well be the target variable sought by a paleozoologist. However, that biocoenose is
not what a paleozoologist studies. The organisms that comprise a biocoenose must
die before a paleozoologist can study their mortal remains. A thanatocoenose is an
assemblage of dead organisms; it is sometimes referred to as the death assemblage.
Turner (1983) suggested that it be referred to as the “killed population,” but “killed”
implies an active agent of death, such as a predator, disallowing death from other
causes such as old age. Furthermore, the dead organisms may be a “population”
in a statistical sampling sense, but they might not be, depending on the question
asked. Those dead organisms may be a 100 percent sample of some set of dead
organisms (e.g., all of those from a biocoenose, which, after all, must all die), but
they may be less than that, such as when the set of dead organisms represents only
part “ a sample “ of a biocoenose. In this case, the thanatocoenose is not, statistically
speaking, a “population.” It is perhaps best, for this reason alone, to conceive of
a thanatocoenose as a set of dead organisms, usually somehow stratigraphically or
analytically bounded (see the discussion of a faunule later in this chapter).
estimating taxonomic abundances: nisp and mni 23

figure 2.1. Schematic illustration of loss and addition to a set of faunal remains studied
by a paleozoologist.

Given that paleozoologists sample the geological record (i.e., where faunal remains
are deposited as a particular kind of sedimentary particle), they don™t always have a
complete thanatocoenose lying on the lab table. Furthermore, the organisms whose
remains comprise a thanatocoenose may derive from one community (or biocoenose)
or they may derive from more than one community (Shotwell 1955, 1958). A tapho-
coenose is the set of remains of organisms (in our case, faunal remains) found buried
(or perhaps exposed) and spatially (usually stratigraphically) associated. Given that
not all of the remains comprising a taphocoenose will be recovered, and of those that
are recovered not all will be identi¬ed to taxon, what the paleozoologist can identify
comprises what will here be referred to as the identi¬ed assemblage. It is this set of
remains from which measures of taxonomic abundance are derived.
Figure 2.1 is a schematic rendition of the typical differences between a biocoenose
and the identi¬ed assemblage. A biocoenose is a biological community. One or more
biocoenoses is the source of input to a thanatocoenose. The transition from bio-
coenose to thanatocoenose involves accumulation (and deposition) of faunal remains
in a location; accumulation can be active (involve a bone-accumulating agent, such
as a predator that transports prey to a den) or passive (involve deaths of animals
across the landscape, referred to as “background accumulation” [Badgley 1986]).
quantitative paleozoology

The transition from the thanatocoenose to taphocoenose involves both accumu-
lation and dispersal and movement or removal of bones mechanically (such as by
¬‚uvial transport), and also the deterioration or chemical and mechanical breakdown
of skeletal tissue. The transition from the taphocoenose to the identi¬ed assemblage
involves both recovery (usually < 100 percent for any of several reasons) by the pale-
ozoologist and the taxonomic identi¬cation of a subset of the remains comprising
the taphocoenose.
The measured variable of taxonomic abundances originates in the identi¬ed
assemblage; the target variable depends on the question asked (Figure 2.1 ). The
biocoenose was Stock™s target variable. Zooarchaeologists interested in human sub-
sistence and economy often have, as their target variable, a thanatocoenose cre-
ated by human predators. Paleoecologists, whether working as paleontologists or as
zooarchaeologists who are interested in past ecological conditions, have as a target
the biocoenose. Determination of the statistical relationship between an identi¬ed
assemblage and a target variable is a taphonomic concern (Lyman 1994c), but the
paleozoologist should also consider ecological and animal behavior variables as well
as recovery techniques. As the Rancho La Brea materials indicate, animal behavior
can in¬‚uence the accumulation and thus rate of input of animal remains to the

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