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tologists began with rarefaction to identify the general shape of a curve produced by
samples of different sizes and NTAXA (Jamniczky et al. 2003). Those paleontologists
discovered that the sampling to redundancy approach was a valuable tool for assess-
ing sample representativeness. They seem unaware of any of the discussions in the
zooarchaeological literature of their discovery. These paleontologists also do some
impressive computer modeling to try to predict how many additional samples might
be necessary, but this echoes Kintigh™s (1984) method (which they do not reference),
and they tend to caution against its use.
The paleontologists cited in the preceding paragraph made a signi¬cant contribu-
tion to paleontology and introduced an important analytical technique to that disci-
pline. The point here is simple. Read some paleontology if you are a zooarchaeologist;
if you are a paleontologist or paleobiologist, read some zooarchaeology. The cross-
fertilization will be worthwhile.
The means by which a collection of faunal remains is generated “ which sampling
design is used, how large the sample is, how faunal remains are extracted from
sediments “ can and typically does in¬‚uence what is recovered. Speci¬cally, the size
of the sample collected, and the frequencies of many of its attributes, are in¬‚uenced by
what (and how much) is collected. In the next three chapters, several different target
variables are discussed. Throughout, analytical means of detecting and controlling for
sample-size effects are described as quantitative measures of the target variables are
sought. Given that the variables of interest are quantitative, analysts need to be aware
of sample-size effects and to take every precaution to avoid allowing conclusions to be
in¬‚uenced by them. Means to detect such effects and a possible means to control for
them have been described in this chapter. We will return to these analytical techniques
often in Chapters 5, 6, and 7.
Measuring the Taxonomic Structure
and Composition (“Diversity”) of Faunas

One of the most common analytical procedures in paleozoology is to compare faunas
from different time periods, from different geographic locales, or both (e.g., Barnosky
et al. 2005 and references therein). Comparisons may be geared toward answering any
number of questions. Does the taxonomic composition of the compared faunas differ
(and why), and if so, by how much (and why)? Does the number of taxa represented
(NTAXA) differ between faunas (and why), and if so, by how much (and why)? Do
the abundances of taxa vary (and why)? Ignoring the “and why™s,” these and similar
queries are what can be considered proximal questions. The why questions are the
ultimate questions of interest; they constitute a reason(s) to identify and quantify the
faunal remains in the ¬rst place. Was hominid or human dietary change over time
the cause of the change in taxonomic composition, abundance, and so on? Did the
environment (particularly the climate) change such that different ecologies prompted
a change in the taxa present, the number of taxa present, or the abundances of various
taxa? It is beyond the scope of this volume to consider these ultimate why questions
other than as examples. The purpose of this chapter is to explore how quantitative
faunal data can be analytically manipulated in order to produce answers to these
kinds of proximal questions.
Once faunal remains have been identi¬ed as to the taxa they represent, they can be
quanti¬ed or counted any number of ways, many of which are described in Chapters 2
and 3. As indicated in those earlier chapters, NISP tends to be the quantitative unit
of choice for many analyses. NISP is used in this chapter to illustrate how taxonomic
abundance data can be analytically manipulated in order to measure the taxonomic
structure and composition of a collection of paleofaunal remains. MNI and biomass
might also be used to calculate the indices described, but in many cases there are
good reasons to not use them, as argued in earlier chapters.
Use of NISP throughout this chapter is meant to endorse it as the quantitative
unit of choice in such efforts. This does not mean that NISP is without ¬‚aws that
measuring the taxonomic structure and composition 173

might in¬‚uence analytical results. Whether a set of NISP values for an assemblage
suffers from interdependence should be ascertained prior to performing analyses
like those described in this chapter. Methods to do this are described in Chapter 2.
If the NISP values do not seem to be in¬‚uenced by variation in interdependence,
then use NISP values as ordinal scale values. If the NISP values are plagued by
interdependence, then the data are best treated as nominal scale data. As we will see,
even if interdependence does not seem to be a problem, there are other concerns
with using NISP as an estimate of a property of a paleofauna.
The analytical gymnastics involving number of taxa, shared taxa, taxonomic abun-
dances, and the like typically are implicitly aimed at the biocoenose (biological com-
munity) by paleobiologists, whereas zooarchaeologists may seek measures of the
thanatocoenose (killed population) or the biocoenose depending on the research
question. Recall that a biological community is a slippery entity empirically and
conceptually. Allowing that a community can indeed be de¬ned as, say, a naturally
delineated habitat patch (if de¬ned with even greater dif¬culty in the prehistoric
record than in modern ecosystems), ecologists tend to recognize three levels of inclu-
siveness of biological diversity (Whittaker 1972, 1977). Alpha diversity is the diversity
within a single local community; beta diversity is the change in diversity among or
across several communities (recognizably distinct but adjacent habitats); and gamma
diversity is the diversity evident in a set of communities such as is found across a large
area (Loreau 2000) involving more than one kind of habitat. Paleozoologists do not
always ignore these various sorts of diversity (e.g., Sepkoski 1988) when they com-
pare diversity across geographic localities, temporal periods, or both, but sometimes
they do (e.g., Osman and Whitlatch 1978). Of course sometimes they must assume
(or analytically warrant the belief) that the samples they use are each derived from
a single community and are not time and space averaged (e.g., Bush et al. 2004),
though this is not always possible or necessary depending on the question they are
asking (e.g., Jackson and Johnson 2001 ; Sepkoski 1997).
Given its central role in identifying the target variable, diversity is a concept in
need of explicit de¬nition. The title of this chapter is “Measuring the Taxonomic
Structure and Composition (˜Diversity™) of Faunas.” This wording is meant to imply
that diversity signi¬es the structure and composition of a fauna. By structure and
composition is meant such variables as the particular taxa represented in a collec-
tion of faunal remains, the number of taxa represented regardless of which taxa are
represented, the abundances of various taxa, and the like. In the ecological and bio-
logical literature diversity has come to mean any number of these variables (Magurran
1988; Spellerberg and Fedor 2003). In fact, some years ago the term “diversity” sig-
ni¬ed numerous concepts and variables within ecological research, and thus one
quantitative paleozoology

ecologist suggested that it be abandoned because it was too ambiguous (Hurlbert
1971 ).
The term “diversity” was not abandoned, but the lesson here is an important one. Be
aware that the terms analyst A uses may have different meanings than those intended
by analyst B. I follow precedent in zooarchaeology (e.g., Byrd 1997; McCartney and
Glass 1990) and some ecological literature (e.g., Lande 1996), and use the term “diver-
sity” to signify a family of variables used to describe the structure and composition
of faunas and collections of faunal remains. The members of that family of diversity
variables are introduced in the following section. In subsequent sections, quantitative
indices for each variable are discussed. Although it is sometimes obvious that one
fauna differs in one or more ways from another fauna, the indices have been designed
to provide a quantitative measurement of similarities and differences. Many of these
indices provide a continuous measure of similarity or difference, and this facilitates
comparative analyses.


The simplest variable that measures a property of a fauna is the number of identi¬ed
taxa (NTAXA). NTAXA is often referred to in the ecological literature as num-
ber of species or species richness (Gaston 1996), but in fact the number of taxa in
a fauna can be tallied at any taxonomic level so long as only one level is tallied.
Mixing taxonomic levels and summing them to determine NTAXA would produce
results that have unclear meaning, particularly when comparing the structure and
composition of faunas using the variables introduced in this chapter. For exam-
ple, recall that to be taxonomically identi¬able, a bone must retain taxonomically
diagnostic features and if that bone is fragmentary and thus anatomically incom-
plete, then it may not be identi¬able to, say, the species level but only to the genus
level. Thus, differences in richness tallied at multiple taxonomic levels may actually
measure the degree of identi¬ability (and fragmentation) rather than taxonomic
If taxa of different taxonomic levels are summed, then the same taxon may be
counted twice. Consider, for instance, the fact that not all deer bones can be iden-
ti¬ed to species, but some can be so identi¬ed (Jacobson 2003, 2004). In western
North America there are two species of deer “ Odocoileus virginianus and Odocoileus
hemionus. If in a collection of paleozoological remains some remains could be iden-
ti¬ed to one species, other remains could be identi¬ed to the other species, and still
other remains could only be identi¬ed to genus but not species, then to tally all three
measuring the taxonomic structure and composition 175

would be to count one (or perhaps both) species twice “ once at the species level
and once at the genus level (Grayson 1991a). By limiting NTAXA tallies to a single
taxonomic level, the variable being measured is more self evident than were taxa of
varied levels summed, and we have not risked counting the same phenomenon twice.
NTAXA is a tally of the number of taxa identi¬ed; it is a nominal scale measure of
taxonomic abundances (taxa are present or absent). Whether or not NTAXA can be
a ratio scale measure of the number of taxa, or even an ordinal scale measure, is one
of the topics of this chapter.
Stock™s (1929) data for Rancho la Brea indicated an NTAXA of ¬ve mammalian
orders (see Chapter 1 ). The sample of owl pellets mentioned in earlier chapters
(Table 2.9) has a richness of mammalian genera of six (= NTAXA). The Meier site
faunal remains have an NTAXA of twenty-six mammalian genera, and the complete
assemblage from the Cathlapotle site has an NTAXA of twenty-¬ve mammalian
genera (Table 1.3). Over the years, ecologists and biologists have referred to this
variable as taxonomic richness (Gaston 1996; Odum 1971 ; Palmer 1990), taxonomic
variety (Odum 1971 ), taxonomic density (Pianka 1978), and taxonomic diversity
(Brown and Gibson 1983; Colwell et al. 2004; Ricklefs 1979; Spellerberg and Fedor
2003). The term “taxonomic richness” here signi¬es NTAXA. Diversity is used as a
generic term for several variables, including richness. Later in this chapter taxonomic
density is mentioned; just as is implied by the term “density,” this measure is a rate
or ratio (e.g., NTAXA/ NISP).
Paleofaunal samples (or biological communities) may have similar NTAXA values.
Even if they do not have similar NTAXA values, the structure and composition of
the faunas could vary in terms of taxonomic abundances. The several taxa of one
fauna may all have approximately equal abundances, such as in the case of a fauna
with ten taxa and each constitutes 10 percent of the total individuals (or biomass).
The taxa of another fauna may have rather unequal abundances of each of ten taxa,
such as three taxa each representing about 1 percent of the total individuals, another
three taxa each representing about 5 percent of the total individuals, another three
each representing about 10 percent of the total individuals, and the tenth taxon
representing the remaining 50“52 percent of the individuals. In such cases the ¬rst
fauna described is said to be taxonomically even whereas the second fauna described
is taxonomically uneven. Taxonomic evenness, sometimes referred to as taxonomic
equitability (Art 1993; Magurran 1988), is a measure of how individuals are distributed
across categories, in this case, taxa (Smith and Wilson 1996). Faunas are taxonomically
even if each taxon has the same number of individuals (or whatever variable is used to
measure abundances of taxa) as every other taxon, regardless of richness. Faunas are
taxonomically uneven if each taxon has a different number of individuals than every
quantitative paleozoology

figure 5.1. Two ¬ctional faunas with identical taxonomic richness (NTAXA) values but
different taxonomic evenness.

other taxon, regardless of richness. Indices for measuring evenness will be introduced
in this chapter.
Figure 5.1 shows two faunas with the same taxonomic richness: NTAXA = 10.
But those two faunas differ considerably in terms of how individuals are distributed
across taxa, so evenness varies regardless of richness. Can both richness and evenness
be measured simultaneously? Of course. Characterizations of the structure and com-
position of a fauna that measure richness and evenness simultaneously are sometimes
referred to as measures of taxonomic diversity (Magurran 1988; Odum 1971 ; Pianka
1978; Ricklefs 1979; Spellerberg and Fedor 2003) or heterogeneity (references in Peet
1974). Recall that the term “taxonomic diversity” has had (and continues to have)
many meanings. As Peet (1974:285) observed, “diversity has always been de¬ned by
the indices used to measure it.” The term heterogeneity is used in the following to
signify simultaneous measurement of evenness and richness to avoid confusion with
how the term “diversity” is used in this chapter.
A description of heterogeneity that may help conceptualize what the notion means
underscores that the term signi¬es the simultaneous measurement of both evenness
and richness. Pianka (1978:287) used the term diversity the way that heterogeneity
measuring the taxonomic structure and composition 177

figure 5.2. Three ¬ctional faunas (A, B, C) with varying richness values and varying
evenness values.

is used here, and stated that taxonomic heterogeneity “is high when it is dif¬cult
to predict the species of a randomly chosen individual organism and low when an
accurate prediction can be made.” Thus, as NTAXA increases, the predictability of
the taxonomic identity of any single randomly chosen individual decreases; it is easier
to predict which taxon is represented if only two taxa are possible (you have a one out
of two chance, or a 50 percent chance) than it is if ten taxa are possible (you have only
a one out of ten chance, or a 10 percent chance). And, if NTAXA is two, but species
A is represented by ninety-nine individuals and species B is represented by only one
individual, the predictability of the taxonomic identity of any single randomly chosen
individual is high. There is a 99 percent chance a randomly chosen individual will be
taxon A but only a 1 percent chance it will be taxon B. Thus as richness increases, as
evenness increases, or both, heterogeneity increases (because the predictability of the
taxonomic identity of a randomly chosen individual decreases). Figure 5.2 illustrates
three ¬ctional faunas with varying richness values and varying evenness values. Think
about randomly drawing a single individual from any one of these faunas and how
often you could correctly predict the taxonomic identity of that individual.
Taxonomic richness (NTAXA) is directly correlated with heterogeneity (both either
increase, or decrease, together), and taxonomic evenness is also directly correlated
with heterogeneity (both either increase, or decrease, together). In this book the
quantitative paleozoology

term taxonomic heterogeneity means just what Pianka (1978) and others (Peet 1974;
Spellerberg and Fedor 2003) mean when they use the term “ a combined measured of
NTAXA and taxonomic evenness. In later sections of this chapter, several quantitative
measures of heterogeneity are introduced that utilize taxonomic abundance data. But
before those indices are described and exempli¬ed, indices of richness need to be
discussed. As well, indices that measure the degree of similarity of two faunas need to
be described. We start with simple indices of structure and composition, and move
to more (mathematically and conceptually) complex indices.


Two faunas can be compared in terms of several different variables a particular value
of which each fauna displays. These variables are (1) NTAXA or taxonomic richness
(regardless of which taxa are represented), (2) taxonomic composition (the particular
taxa represented), (3) taxonomic heterogeneity, and (4) taxonomic evenness. They
are discussed in the order listed because in that order, complexity (both mathematical
and information content) increases and indices introduced later in this section tend
to rest on indices introduced early.
Taxonomic composition was not mentioned in preceding paragraphs because
richness, heterogeneity, and evenness are, in a sense, taxon free; their values in any
given instance will vary regardless of the taxa present. As paleobiologist Thomas
Olszewski (2004:377) observed, “the number and variety of species in an assemblage,
independent of their identities, provides a means of comparing assemblages from
different times and places. This, in turn, can provide information on changes in
community structure, as opposed to species membership, over ecological as well as
evolutionary timescales” (emphasis added). NTAXA can be the same, say twenty-¬ve,
for any two faunas, but those two faunas may not share any taxa, or they may have
three or ¬fteen or twenty-two taxa in common; NTAXA for both will be twenty-
¬ve regardless of whether taxa are shared by the two faunas. The same applies to
measures of heterogeneity and evenness. Thus one paleoecologist has stated that
“in community analysis, communities are described not by their taxonomic content
but by their levels of diversity” (Andrews 1996:277); I interpret “levels of diversity”
to mean index values of richness, heterogeneity, and/or evenness. A paleozoologist
might wish to know how similar two communities (or assemblages) are in terms of
shared taxa, and thus a discussion of two commonly used measures of taxonomic
similarity is included. First, however, a bit more detail regarding the signi¬cance of
NTAXA is warranted.
measuring the taxonomic structure and composition 179

Taxonomic Richness

Flannery (1965, 1969) used the term broad spectrum to characterize an early (pre-
agricultural) pattern of exploiting numerous kinds of resources and the term special-
ization to label a later, agricultural adaptation in which a small number of resource
types were exploited by individual human groups. Cleland (1966, 1976) used the
terms “diffuse economy” and “focal economy” to label those that exploited a wide
range of resource types and those that used a narrow range of resource types, respec-
tively. Dunnell (1967, 1972) used the terms “extensive” (= diffuse) and “intensive”
(= focal) to signify the same resource-exploitation patterns as Cleland. The move
was on in ecological anthropology to quantify particular instances of dietary breadth
or niche width (Hardesty 1975), and archaeologists kept pace, coining a plethora
of terms along the way. Ecologists used the terms “generalized” and “specialized”
(e.g., Ricklefs 1979), as did some archaeologists (e.g., Quimby 1960), for what is
most fundamentally whether NTAXA is a large value or a small value, respectively.
Determination of which of those taxa, plant or animal, comprising the identi¬ed
assemblage were actually exploited and used by humans is a separate, taphonomic
question (Lyman 1994c) and is beyond the scope of discussion.
Modern interest of biologists and ecologists in NTAXA re¬‚ects growing concerns
over biodiversity, a term with a commonsensical meaning but which tends today to
imply anthropogenically induced disturbances to biota, especially those that result in
a loss of taxonomic variety through extinction (e.g., Pimm and Lawton 1998; Vitousek
et al. 1997). NTAXA is one widely understood aspect of biodiversity because it is a
fundamental measure and does not require the calculation of a derived value to
express it numerically (Gaston 1996). This does not mean that NTAXA values are
not dif¬cult to interpret; indeed they are dif¬cult to interpret (Gaston 1996). It is
nevertheless not unusual to read about how the richness of one fauna compares to
the richness of another. Because the numerical values of NTAXA are whole numbers
and can vary from one into the hundreds for any given faunal collection, it is also
not unusual to read that one fauna has ten more taxa than another, or one fauna
has twice as many taxa as another, or the like. Such statements imply that NTAXA
is a ratio scale measurement. In fact it is likely not a ratio scale measurement in
biology and ecology for many reasons (Gaston 1996; MacKenzie 2005), some of
which are similar to the reasons it is not likely to be a ratio scale measurement in
The value of NTAXA in a particular faunal collection is the easiest mechanically of
the four variables of structure and composition to determine. Simply tally how many
taxa at some predetermined taxonomic level (family, genus, species) are represented
quantitative paleozoology

in a collection; it is a fundamental measure. As noted earlier, the Meier site mam-
mal collection has a taxonomic richness of twenty-six at the genus level, and the
complete Cathlapotle mammal collection has a taxonomic richness of twenty-¬ve
at the genus level. The Meier mammalian fauna is taxonomically richer than the
Cathlapotle mammalian fauna; why the Meier collection is taxonomically richer
than the Cathlapotle collection is another matter. It is easy to eliminate one possible
answer to this particular why question. The Meier collection is smaller ( NISP =
5,939) than the Cathlapotle collection ( NISP = 6,206), so the difference in rich-
ness is likely not a result of sample size; were the Meier collection larger than the
Cathlapotle collection, then the difference in richness might be a function of the fact
that the Meier collection was larger.
NTAXA can vary over space or through time for any number of reasons. The
geographic distributions of species shift daily and seasonally as well as in concert
with long-term (multiple year) climatic shifts. Local colonization and extirpation
occur, and sometimes an individual waif or vagrant wanders into an area simply
by chance. If NTAXA is measured, should it include only resident taxa (ones whose
members breed, reproduce, and remain in the area year round) and ignore seasonal
immigrants (ones that might breed and reproduce in the area but that are present only
part of the year) and vagrant taxa (an individual of which occasionally wanders in to
the area under study and which may stay there until death but does not reproduce
there) (Gaston 1996)? Explicit wording of research questions is the only means to
address this question. But there is also a now well-known problem that is a bit more
dif¬cult to contend with.
Often, taxonomically richer faunas are larger than less taxonomically rich faunas
(e.g., Grayson 1984; Leonard 1989; Sharp 1990). Consider the set of eighteen assem-
blages from eastern Washington used in earlier analyses. Pertinent data are given in
Table 5.1 and graphed in Figure 5.3. As the latter suggests, the two variables, NISP
and NTAXA (of mammalian genera) are closely correlated (r = 0.80, p < 0.0001).
Knowing the total NISP of any of these collections allows close prediction of the
NTAXA in a collection. This is a relationship that has been known for a long time. It
is the species’area relationship, and as indicated in Chapter 4, one way to contend
with the fact that samples of large size often are taxonomically richer than samples of
small size is rarefaction. There are ways other than rarefaction to contend analytically
with sample size effects. Use of rarefaction assumes that a sample size in¬‚uence exists,
but fortunately, we need not simply assume such. We can instead determine empir-
ically if a sample size in¬‚uence exists in any given instance; this involves performing
a statistically assisted search for a signi¬cant relationship between sample size and
richness, such as is exempli¬ed in Figure 5.3. If we ¬nd that such a relationship exists,
measuring the taxonomic structure and composition 181

Table 5.1. Sample size ( NISP), taxonomic richness (S), taxonomic
heterogeneity (H), taxonomic evenness (e), and taxonomic dominance (1/D)
of mammalian genera in eighteen assemblages from eastern Washington State

1 /D
Site NISP S H e
45OK18 31 6 1.449 0.809 3.690
45DO204 48 9 1.965 0.894 6.897
45DO273 84 8 1.234 0.594 2.237
45DO243 157 8 1.241 0.597 2.532
45OK2A 366 10 1.342 0.583 2.933
45DO189 415 15 1.362 0.503 2.427
45DO282 426 11 0.894 0.373 1.647
45DO211 474 15 1.490 0.550 2.688
45DO285 491 15 1.812 0.669 3.937
45DO214 536 17 2.059 0.727 5.556
45DO326 640 16 1.985 0.716 4.608
45DO242 673 13 1.260 0.491 2.564
45OK287 807 10 1.310 0.569 2.890
45OK250 1,077 12 1.129 0.454 2.020
45OK4 1,108 15 1.042 0.385 1.835
45OK2 2,574 18 0.861 0.298 1.590
45OK11 3,549 24 1.728 0.544 3.636
45OK258 4,433 21 0.876 0.288 1.608

we need not stop, throw up our hands in dismay, and curse the day. We have several
analytical options.
Presuming that there are multiple assemblages, one might compare richness
(NTAXA) and sample size ( NISP) per subset of assemblages to determine if some
assemblages display one relationship between the two variables and other assemblages
show another relationship (e.g., Grayson 1998; Grayson and Delpech 1998). Figure 5.4
shows two kinds of relationship between the two variables among 13 assemblages at
one site, Homestead Cave in western Utah State (Grayson 1998, 2000) (Table 5.2). The
oldest three strata (I, II, III) date to a time when climate was moist in what is today a
relatively dry area, and all other strata date to times (after 8300 14 C yr BP) when it was
as dry or drier than today. Ecological theory suggests and empirical data indicate that
as moisture increases (either in abundance or effectiveness), primary productivity
increases and so too does mammalian taxonomic richness; as moisture decreases, so
too does mammalian taxonomic richness (references in Grayson 1998, 2000). More
remains of more taxa were accumulated when it was moist and fewer remains of fewer
figure 5.3. Relationship between genera richness (NTAXA) and sample size (NISP) in

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