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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
richness.
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
176




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
178


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.



I N D I CE S O F S T R U C T U RE A N D S I M I L A R I T Y


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
paleozoology.
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
180


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
eighteen mammalian faunas from eastern Washington State. Data from Table 5.1 .




figure 5.4. Relationships between NISP and NTAXA of small mammals per stratum
(Roman numerals) at Homestead Cave, Utah (after Grayson 1998). Dashed, best-¬t regres-
sion line, r = 0.88, p = 0.3; solid, best-¬t regression line, r = 0.92, p = 0.0001. Faunal material
from strata X and XIII“XVI has not been studied. Data from Table 5.2.
measuring the taxonomic structure and composition 183


Table 5.2. NISP and NTAXA for small
mammals at Homestead Cave, Utah. Data
from Grayson (1998). Faunal remains from
strata X and XIII“XVI were not studied

Stratum NISP NTAXA
XVIII 1047 9
XVII 15,421 17
XII 22,661 14
XI 9,996 14
IX 18,043 16
VIII 8,215 13
VII 11,038 15
VI 18,661 17
V 5,093 13
IV 26,200 19
III 2,774 17
II 7,756 20
I 9,906 19




taxa were accumulated and deposited when it was arid. Despite apparent sample size
effects, the mammal assemblages from Homestead Cave appear just as they should
in terms of the relationship between NTAXA and climate.
Another example of studying the covariation of sample size and taxonomic rich-
ness comes from the Upper Paleolithic rockshelter of Le Flageolet I, France (Grayson
and Delpech 1998). The ungulate remains at this site were largely introduced by
humans, but interestingly, there is yet another pair of relationships between NTAXA
(of ungulates) and NISP (of ungulates) (Table 5.3). There is no patterned rela-
tionship between the associated archaeological culture and which line a particular
assemblage of ungulate remains helps de¬ne (Figure 5.5). The analysts found no clear
indication that the degree of fragmentation was creating the two relationships, and
no indication that the differential transport of skeletal parts by bone accumulators
had created the two relationships (Grayson and Delpech 1998). They concluded that
the difference involved variation in diet breadth, or the width of the niche exploited
by the humans that created the assemblages.
There are other ways to compare taxonomic richness values of assemblages of
different sizes. Recall from Chapter 4, for example, that the original recognition
of the sample-size effect (the species’area relationship) was based on the amount
quantitative paleozoology
184


Table 5.3. NISP and NTAXA for
ungulates at Le Flageolet I, France. Data
from Grayson and Delpech (1998). Strata
with NISP < 30 are not included

Stratum NISP NTAXA
XI 651 6
IX 681 11
VIII 461 9
VII 1,768 10
VI 376 8
V 1,244 7
IV 145 5



of geographic area sampled. Thus, one might compare taxonomic richness with
the amount excavated, either the area or volume excavated. Wolff (1975) showed
long ago that the greater the volume of sediment searched for faunal remains, the
greater the number of taxa found (see Chapter 4). Taxonomic richness increases
as the amount of sediment examined increases because as the amount of sediment
examined increases, NISP increases (more specimens are recovered, so more taxa




figure 5.5. Relationship between NISP and NTAXA per stratum (Roman numerals) at
Le Flageolet I, France (after Grayson and Delpech 1998). Dashed, best-¬t regression line
r = 0.99, p = 0.06; solid, best-¬t regression line, r = 0.98, p = 0.02. Some strata omitted as
sample sizes are too small for inclusion. Cultural associations for each stratum are indicated.
Data from Table 5.3.
measuring the taxonomic structure and composition 185


are identi¬ed). As the amount of sediment examined increases, the amount of area
examined increases, which brings us back to the original species“area relationship
discovered by botanists.
Regardless of the technique used to gain insight to the structure and composition of
a fauna, taxonomic richness is often strongly correlated with sample size. Therefore,
the analyst must be ever on the alert for differences in sample size measured as
NISP as a variable that potentially contributes to differences in NTAXA. The
analyst should also realize that the possible in¬‚uence of sample size on all measures
of taxonomic diversity (structure and composition) might be disputed, such as when
all of a site deposit (all of a single stratum, or all of a site within horizontal and vertical
boundaries) has been excavated. In such cases one might argue that a 100-percent
sample has been collected and that taxonomic richness cannot be considered to be
a function of sample size. This is in some senses true, but it also overlooks two
fundamental issues. First, a very small number of sites (or strata within sites other
than trivial cases such as the ¬ll of a single intrusive pit) have been totally excavated
(meaning that a 100-percent sample has been generated). Second, even if a site is
completely excavated, it is likely to be but a portion of some larger cultural system than
is found in that single site or only a portion of the taphocoenose, thanatocoenose,
or biocoenose. This brings us back to Kintigh™s (1984) fundamental dilemma of
de¬ning the population one wishes to model with available samples. Only when that
population is de¬ned beforehand will we know if we have a 100-percent sample or
not, and even then preservation variation and recovery procedures may result in less
than complete retrieval (Chapter 4).



Taxonomic Composition

Two faunas can have the same NTAXA, but share anywhere from none to all of
the taxa represented. How do we compare faunas in terms of the taxa they hold in
common and those taxa that are unique to one or the other? How do we determine if
two faunas are similar in taxonomic composition, and how do we determine if fauna
A and fauna B are more similar to one another than either is to fauna C? Indices
have been designed to answer these questions and to measure just these features
(see reviews in Cheetham and Hazel 1969; Henderson and Heron 1977; Janson and
Vegelius 1981 ; Raup and Crick 1979). For unclear reasons these indices have seldom
been used by zooarchaeologists (Styles [1981 ] is a noteworthy exception). It could
be a result of benign neglect, or it could be that the in¬‚uences of varying sample
size are a concern. Before considering the latter issue, however, let™s consider some
quantitative paleozoology
186


exemplary indices. These are sometimes referred to as binary coef¬cients, because
they summarize and compare presence“absence (nominal scale) data.
One index is the Jaccard index (J) [originally, “coef¬cient of ¬‚oral community”].
It is calculated as

J = 100C/(A + B ’ C ),

where A is the total number of taxa in fauna A, B is the total number of taxa in
fauna B, and C is the number of taxa common to both A and B. Another index is the
Sorenson index (S), calculated as

S = 100(2C )/(A + B),

where the variables are as de¬ned for the Jaccard index. Given how they are calculated,
the Jaccard index emphasizes differences in two faunas, and the Sorenson index
emphasizes similarities. For example, if A = 6, B = 6, and C = 4, then J = 50whereas S =
66.7. Comparing the Meier site mammalian fauna (A) with the complete Cathlapotle
mammalian fauna (B), A = 26, B = 25, and C = 20. Thus, for these two faunas, J = 64.5
and S = 78.4. Given that the two faunas fall within the same time period, are < 10 km
apart, and occur in virtually identical habitats, it may seem that the indices of faunal
similarity should be considerably higher. This is so because, at least with respect to
statistical precision sampling (as opposed to discovery sampling; see Chapter 4), at
least the Meier site sample seems to be representative because signi¬cant increases
in its size over the last several years of excavation failed to produce any previously
unidenti¬ed taxa (Lyman and Ames 2004).
Why the Meier and Cathlapotle assemblages are not more similar and do not share
more mammalian genera is an ultimate question. It may have to do with variation in
which taxa were accumulated despite similarity of the agents of accumulation; at both
sites humans were the most signi¬cant accumulation agent. Or, it may actually have
to do with a fundamental problem of all such binary coef¬cients (Raup and Crick
1979). That problem can be illustrated with a pair of Venn diagrams (Figure 5.6).
Each of these has been drawn with the Meier and Cathlapotle collections in mind. A
total of thirty-one genera are represented by the two collections. One Venn diagram
suggests each collection is a sample of those thirty-one genera. The other Venn
diagram indicates that each collection is a sample of the total forty mammalian
genera (excluding eight genera of bats) that occur in the area today (Johnson and
Cassidy 1997). Given that neither zooarchaeological collection has signi¬cantly more
than two-thirds of those genera, it is perhaps not surprising that the two do not share
more taxa. Each site collection represents but a sample of the local biotic community.
Another way to make the point of the preceding paragraph is this: Based on earlier
discussions, it should be obvious that sample size (= NISP) will in¬‚uence binary
measuring the taxonomic structure and composition 187




figure 5.6. Two Venn diagrams based on the Meier site and Cathlapotle site collections.
Upper diagram suggests each collection is a sample of the thirty-one genera represented by
the combined collections. Lower diagram indicates that each collection is a sample of the
total forty mammalian genera that occur in the area.


coef¬cients such as the Jaccard and Sorenson indices. This has been known for
decades; the more individuals, the taxonomically richer the sample, so when Paul
Jaccard proposed his index he suggested areas of similar size be sampled, but he
should have suggested similar numbers of individuals be inspected (Williams 1949).
Consider the fact that both the Meier and Cathlapotle collections are samples, and
thus even if remains of all forty mammalian genera known in the area today had
been accumulated and deposited in site deposits, it is likely that remains of rarely
represented taxa would not be recovered. If more of each of those sites had been
excavated, and several thousand more NISP had been recovered from each site, it
is probable that several of those as yet unidenti¬ed genera would occur in those
collections. This would not only represent a shift in the sampling design toward a
discovery model, but it would also increase the magnitude of both the Jaccard index
and the Sorenson index.
Neither the Sorenson index nor the Jaccard index takes advantage of the abundance
of taxa. A simple way to assess the similarity of taxonomic abundances of two faunas
is to calculate a χ 2 statistic (e.g., Broughton et al. 2006; Grayson 1991b; Grayson and
Delpech 1994). To illustrate this, the NISP data for the collection of faunal remains
from eighty-four owl pellets (Table 2.9) is summarized as two chronologically distinct
quantitative paleozoology
188


Table 5.4. NISP per taxon in two chronologically distinct
samples of eighty-four owl pellets

Taxon 1999 sample 2000“2001 sample
Sylvilagus 5 0
Reithrodontomys 0 19
Sorex 40 6
Thomomys 52 16
Microtus 302 403
Peromyscus 1,147 119



samples in Table 5.4. Chronological distinction concerns when the pellets were col-
lected. χ 2 analysis indicates the two samples differ signi¬cantly in terms of taxonomic
abundances (χ 2 = 586.68, p < 0.0001). The two sets of taxonomic abundances are not
correlated (Spearman™s ρ = 0.6, p > 0.2), which also suggests they may have derived
from different populations, but do the abundances of all of the taxa differ signi¬cantly
between the two samples, or the abundances of just a few of the taxa? To answer this
question, adjusted residuals for each cell were calculated (there are six taxa, and 2
years for each, so twelve cells) to determine if any of the observed values were greater,
or less than would be expected were the two temporally distinct samples derived from
different populations. Basically, the adjusted residual provides a way to determine if
the observed and expected values per cell are statistically signi¬cantly different or not
(see Everitt 1977 for discussion of the statistical method). Expected values (compare
with Table 5.4) and interpretations for each cell are given in Table 5.5. Abundances of
four taxa are causing the statistically signi¬cant difference between the two samples;
specimens of Reithrodontomys, Sorex, Microtus, and Peromyscus are not randomly
distributed between the two chronologically distinct samples. Only Sylvilagus and

Table 5.5. Expected values (E) and interpretation (I) of taxonomic abundances in two
temporally distinct assemblages of owl pellets. See Table 5.4 for observed values

Taxon 1999 E 2000’2001 E 1999 I 2000’2001 I
Sylvilagus 3.7 1.3 p > 0.05 p > 0.05
Reithrodontomys 13.9 5.1 p < 0.05, too few p < 0.05, too many
Sorex 33.7 12.3 p < 0.05, too many p < 0.05, too few
Thomomys 49.8 18.2 p > 0.05 p > 0.05
Microtus 516.8 188.2 p < 0.05, too few p < 0.05, too many
Peromyscus 928.0 338.0 p < 0.05, too many p < 0.05, too few
measuring the taxonomic structure and composition 189


Thomomys occur in the two samples in abundances that are not unexpected; abun-
dances of these two taxa suggest the temporally distinct samples were drawn from
the same population.
Some research has suggested that the Sorenson index provides a better estimate
of similarity than Jaccard™s index (Magurran 1988:96). Not surprisingly, ecologists
designed a version of Sorenson™s index to take account of variation in taxonomic
abundances. That index, Sorenson™s quantitative index, is calculated as

Sq = 2 c N /(AN + B N),

where AN is the total frequency of organisms (all taxa summed) in fauna A, BN is
the total frequency of organisms in fauna B, and cN is the sum of the lesser of the
two abundances of taxa shared by the two assemblages. Using the data in Tables 4.2
and 4.3 for Meier and Cathlapotle mammalian genera, AN (Meier) = 6421, BN
(Cathlapotle) = 6,937, and cN = 4,358 (3 Scapanus + 7 Aplodontia + 342 Castor + 5 Peromyscus +
68 Microtus + 106Ondatra + 39Canis + 5 Vulpes + 102 Ursus + 207 Procyon + 2 Martes + 29Mustela +
3 Mephitis + 51 Lutra + 9Felis + 26Lynx + 43 Phoca + 935 Cervus + 2376Odocoileus ). Thus, Sq =
2(4358)/(6421 + 6973) = 8716/13,394 = 0.651, or 65.1. Recall that the (nonquantitative)
Sorenson™s index was 78.4. Thus, regardless of which index of similarity is used, the
faunas seem fairly similar, though less so when the abundances of taxa are included
than when they are ignored.
A simple way to show similarities and differences between two faunas in terms
of shared taxa, unique taxa, and taxonomic abundances, is to generate a bivariate
scatterplot. Figure 5.7 shows relative (percentage) abundances of those taxa from
Meier and Cathlapotle represented by NISP < 200 at both sites. Notice that were the
relative abundances of taxa equivalent at the two sites, the points would fall close to
the diagonal line; the more equal the relative abundances, the closer to the diagonal
the points would fall. Note as well that more of the points fall on the Meier side
of the diagonal. This suggests that those taxa are relatively more abundant at Meier
than they are at Cathlapotle. Such a graph takes advantage of abundance data in a
visual way. Ecologists are working to develop versions of the Jaccard and Sorensen
indices that also take advantage of abundance data (e.g., Chao et al. 2005), but these
are beyond the scope of the discussion here.
That the binary coef¬cients designed to measure taxonomic similarities of faunal
collections have been largely ignored by zooarchaeologists is likely a good thing. Those
coef¬cients are heavily in¬‚uenced by the sample sizes (= NISP) of the compared
collections because taxonomic richness is signi¬cantly in¬‚uenced by sample size
(Chao et al. 2005). Again, one might use rarefaction in an effort to control sample-
size effects, and that is what some paleozoologists have done (e.g., Barnosky et al. 2005;
quantitative paleozoology
190




figure 5.7. Bivariate scatterplot of relative (percentage) abundances of mammalian genera
at the Meier site and Cathlapotle. Only genera for which NISP < 200 are plotted. Diagonal
line is shown for reference.



Byrd 1997). This could be a good thing, but it is perhaps unwise for the simple reason
that as was noted more than 20 years ago, the rarefaction procedure was designed
to be used with quantitative units that are statistically independent of one another
(Grayson 1984:152). Those units are also ratio scale values. NISP tallies comprise
units that are probably statistically interdependent and that are also typically at best
ordinal scale values. Given these facts, should one choose to perform a rarefaction
analysis using NISP values, the results should be interpreted in at most ordinal scale
terms. An example will make this clear.
A rarefaction curve based on the eighteen assemblages listed in Table 5.1 con-
structed using Holland™s (2005) Analytical Rarefaction is shown in Figure 5.8 and
suggests that, given a total NTAXA of twenty-eight for the area represented by those
eighteen collections, none of the collections contains all twenty-eight taxa, most
collections contain very few taxa, but none contain too few for their size, and four
(45DO214, 45DO326, 45DO211, 45DO285) of the eighteen collections seem to con-
tain more taxa than they should given their size ( NISP). The rarefaction curve
measuring the taxonomic structure and composition 191




figure 5.8. Rarefaction analysis of eighteen assemblages of mammal remains from eastern
Washington State using Holland™s (2005) Analytical Rarefaction. Data from Table 5.1 .



thus reveals something we didn™t know before because it presents the data in a
unique, interpolated way. If I were analyzing these collections, I would try to deter-
mine why four of the collections were unexpectedly taxonomically rich; perhaps they
are temporally unique, functionally/behaviorally unique, or located in a particular
microenvironment.
Were one to perform a rarefaction analysis like that shown in Figure 5.8, one should
¬rst determine if those assemblages are nested. Recall from Chapter 4 that in a series
of perfectly nested faunas, successively smaller faunas will have fewer of the taxa
represented in those faunas that are successively larger, and larger faunas will have
all those taxa represented in smaller faunas plus additional taxa. The interpretive
assumption is that nested faunas all derive from the same parent population. There
are ways to test the degree of nestedness of faunas. That has been done with the faunas
in Figure 5.8; consider Figure 4.12, which shows that the nestedness “temperature”
for this set of eighteen faunas is 18.23 —¦ , meaning the faunas are relatively strongly
nested. The rarefaction analysis in Figure 5.8 thus seems reasonable, if one is willing
to allow an unknown degree of skeletal specimen interdependence and, thus, allow
a bit of statistical sloppiness.
quantitative paleozoology
192


Taxonomic Heterogeneity

Several indices have been developed to measure taxonomic heterogeneity. Paleozool-
ogists have tended to use only two of these, although there are several different ones
that are occasionally mentioned (e.g., Andrews 1996). By far the most popular one
among zooarchaeologists is the Shannon’Wiener index, sometimes referred to as
the Shannon index. It generally varies between 1.5 and 3.5 (Magurran 1988:35); larger
values signify greater heterogeneity. The Shannon index is calculated as:

H =’ Pi (ln Pi ),

where Pi is the proportion (P) of taxon i in the assemblage. The proportion (some-
times referred to as “importance”) of each taxon in the collection is multiplied by
the natural log of that proportion. Because proportions are < 1, transforming those
values to natural logs results in a negative sign. Values of the products of the multi-
plications are summed, and then converted from a negative value to a positive value
by the negative or ““” sign in front of the summation ( ) sign.
Let™s say we want to determine the taxonomic heterogeneity (at the genus level)
of the total Meier site mammal collection (Table 4.2). The data and mathematical
steps for calculating the value of the Shannon’Wiener index are summarized in
Table 5.6. NTAXA for this collection is 26. The heterogeneity index is 1.556, suggesting
the total Meier site mammal collection is somewhat heterogeneous. For comparative
purposes, consider the fact that the Shannon’Wiener heterogeneity index for the
total Cathlapotle collection, without distinction of the Precontact and Postcontact
assemblages (Table 4.3), has a value of 1.487, indicating that the heterogeneity of the
Cathlapotle collection is a bit less than that of the Meier collection. One contributing
factor here is that the Meier collection, with twenty-six taxa, is taxonomically richer
than the Cathlapotle collection, which contains remains of only twenty-four taxa.
Does a difference in the evenness of the two assemblages also contribute to the dif-
ference in heterogeneity? To answer that question requires calculation of an evenness
index for each collection.
Because heterogeneity is a function of taxonomic richness and evenness, it is
possible that heterogeneity will also be a function of sample size (e.g., Grayson 1981b).
Thus, if one wishes to measure heterogeneity and compare that variable across several
different samples, it is advisable to determine if there is any relationship between the
measures of heterogeneity and NISP for a set of samples. Once again, consider
the eighteen assemblages from eastern Washington State (Table 5.1 ). The relationship
between sample size per site and heterogeneity per site is, in the case of these eighteen
measuring the taxonomic structure and composition 193


Table 5.6. Derivation of the Shannon’Wiener index of heterogeneity for the
Meier site (original data from Table 4.2). Logs are natural logarithms

Taxon NISP Proportion (p) Log of p p(log p) Running sum
’5.878 ’0.016 ’0.016
Scapanus 18 0.00280
’5.878 ’0.016 ’0.032
Sylvilagus 18 0.00280
’6.822 ’0.007436 ’0.039
Aplodontia 7 0.00109
’8.740 ’0.001398 ’0.041
Tamias 1 0.00016
’8.079 ’0.002504 ’0.043
Tamiasciurus 2 0.00031
’6.571 ’0.009199 ’0.053
Thomomys 9 0.00140
’2.933 ’0.156 ’0.209
Castor 342 0.05326
’5.212 ’0.028 ’0.237
Peromyscus 35 0.00545
’8.740 ’0.001398 ’0.238
Rattus 1 0.00016
’8.740 ’0.001398 ’0.239
Neotoma 1 0.00016
’4.162 ’0.065 ’0.304
Microtus 100 0.01557
’2.843 ’0.166 ’0.470
Ondatra 374 0.05825
’8.740 ’0.001398 ’0.472
Erethizon 1 0.00016
’4.058 ’0.070 ’0.542
Canis 111 0.01729
’7.156 ’0.00582 ’0.547
Vulpes 5 0.00078
’4.142 ’0.066 ’0.613
Ursus 102 0.01589
’3.108 ’0.139 ’0.752
Procyon 287 0.04470
’5.773 ’0.018 ’0.770
Martes 20 0.00311
’3.869 ’0.081 ’0.851
Mustela 134 0.02087
’7.386 ’0.004579 ’0.856
Mephitis 4 0.00062
’4.836 ’0.038 ’0.894
Lutra 51 0.00794
’6.571 ’0.009199 ’0.903
Puma 9 0.00140
’5.333 ’0.026 ’0.929
Lynx 31 0.00483
’5.006 ’0.034 ’0.963
Phoca 43 0.00670
’1.927 ’0.281 ’1.244
Cervus 935 0.14562
’0.530 ’0.312 ’1.556
Odocoileus 3,780 0.58869
= ’ = 1.556
6,421 1.0 “ “



assemblages, not statistically signi¬cant, suggesting that variation in heterogeneity
is not being driven by variation in sample size (Figure 5.9). Given the insigni¬cant
correlation between sample size and heterogeneity, we might feel safe in comparing
heterogeneities across these eighteen assemblages were it not for the fact that sample
size and richness are strongly correlated among them (Figure 5.3), and the fact that as
richness increases so too does heterogeneity. Only in those instances in which there
is no such correlation (between sample size and richness and between sample size
and heterogeneity) might one make statements about variation between assemblages
quantitative paleozoology
194




figure 5.9. The relationship between taxonomic heterogeneity (H) and sample size (NISP)
in eighteen assemblages of mammal remains from eastern Washington State. Best-¬t regres-
sion line is insigni¬cant (r = “0.30, p > 0.2). Data from Table 5.1 .

and taxonomic heterogeneity. Otherwise, variation in heterogeneity may be a result
of variation in sample size across the compared collections.
Notice that I said “might” and “may” with respect to the possible in¬‚uence of
sample size on heterogeneity. Heterogeneity is a summary measure of the relative
(proportional) abundances of taxa. There is, therefore, a potential problem with the
analysis attending Figure 5.9. Speci¬cally, the problem concerns the fact that relative
abundances are involved. That problem can be circumvented by using a statistical test
other than a form of correlation analysis. That test will be introduced after evenness
is discussed.



Taxonomic Evenness

How are individuals distributed across taxa? Are all taxa represented by about the
same number of individuals (an even fauna), or do some taxa contain many individ-
uals whereas other taxa contain very few individuals (an uneven fauna)? To answer
such questions beyond comparing histograms showing the distribution of individ-
uals across taxa in each fauna (the histograms may not be visually distinguishable;
measuring the taxonomic structure and composition 195




figure 5.10. Frequency distribution of NISP values across six mammalian genera in a
collection of owl pellets. Data from Table 2.9.



Figure 5.2), an index of evenness can be calculated. One index that is regularly used to
measure evenness quantitatively requires the Shannon’Wiener heterogeneity index,
which is divided by the log of NTAXA or richness (Magurran 1988). Thus, evenness
is calculated as:

e = H/ lnS,

where H is the Shannon’Wiener heterogeneity index and S is taxonomic richness.
The lower the value of e, known as the Shannon index of evenness (Magurran 1988),
the less even the assemblage. The Shannon index, e, is constrained to fall between 0
and 1, with a value of 1 indicating an even fauna or that all taxa are equally abundant
(Magurran 1988).
Consider the assemblage of mammals represented in the previously mentioned
owl pellet collection and described in Table 2.8. NTAXA (S) is 6, using the NISP
values for this collection the Shannon’Wiener heterogeneity index (H) is 0.922, and
the Shannon index of evenness (e) is (0.922/1.792 =) 0.515. Inspection of Figure 5.10,
which shows the frequency distribution of NISP across the taxa, suggests that indeed,
this fauna is not very even, just as its calculated e value suggests.
Recall the question posed above after the Shannon’Wiener heterogeneity indices
for the Meier collection and for the Cathlapotle collection were calculated “ the Meier
collection was more heterogeneous in part because it was taxonomically richer than
the Cathlapotle collection, but did a difference in the evenness of the two faunas also
quantitative paleozoology
196


contribute to that difference in heterogeneity? For Meier, e = 1.556/3.258 (where 3.258
is the natural log of 26), so e = 0.4776; for Cathlapotle, e = 1.487/3.178 (where 3.178
is the natural log of 24), so e = 0.4679. The evenness index e varies between 0 and 1 ;
if e = 1, then all taxa are equally abundant (specimens are equably distributed across
taxa). So, the Meier collection seems to be slightly more even than the Cathlapotle
collection “ identi¬ed specimens are a bit more equably distributed across the twenty-
six taxa of the Meier collection than identi¬ed specimens are distributed across
the twenty-four taxa of the Cathlapotle collection. Thus, not only does the greater
richness of the Meier collection contribute to greater heterogeneity, so too does the
greater evenness of the Meier collection contribute to its heterogeneity being greater
than that evident in the Cathlapotle collection.
As with richness and heterogeneity, there are cases when taxonomic evenness
seems to be driven by sample size, though there are also cases where there is no such
relationship (e.g., Grayson and Delpech 1998; Grayson et al. 2001 ; Nagaoka 2001 ,
2002). Until a few years ago, to determine whether or not evenness was driven by
sample size, one measured the strength of the relationship between the two variables.
Consider the eighteen assemblages of mammal remains from eastern Washington
State (Table 5.1 ). Sample size and evenness values among these eighteen assemblages
are strongly correlated (Figure 5.11 ); about 53 percent of the variation in evenness is
explained by variation in NISP (r = 0.73, p < 0.002). On the basis of that correlation,
the paleozoologist would have previously concluded that it would be ill-advised to
suggest variation in evenness across these assemblages was due to some ecological,
environmental, or human behavioral variable rather than simple difference in sample
size. There is now a better way to search for sample size effects on measures of relative
abundance that will be described shortly. First, another measure of evenness needs
to be introduced.
Another index of evenness occasionally used by zooarchaeologists is the reciprocal
of Simpson™s index (Grayson and Delpech 2002; James 1990; Jones 2004; Schmitt and
Lupo 1995; Wolverton 2005). If one assumes that the population is in¬nitely large,
the index is calculated as

1/ pi2 ,

where pi is the proportional abundance of taxon i in the total collection (Magurran
1988:39). However, because the population of organisms in a community, and the
sample of remains in a deposit, are ¬nite, it is appropriate to calculate Simpson™s
index as:

ni [ni ’ 1 ]/N[N ’ 1 ],
measuring the taxonomic structure and composition 197




figure 5.11. Relationship between taxonomic evenness (e) and sample size (NISP) in
eighteen assemblages of mammal remains from eastern Washington State. Best-¬t regression
line is signi¬cant (r = “0.73, p = 0.0005). Data from Table 5.1 .


where ni is the number of specimens of the ith taxon, and N is the total number
of specimens of all taxa (Magurran 1988). The more evenly distributed individuals
(or specimens) are across taxa, the larger the value of this index. Simpson™s index is
known as D because it is more sensitive to the dominance of an assemblage by a single
taxon than is e and D is also less sensitive to taxonomic richness (Magurran 1988).
The reciprocal or inverse of Simpson™s index is used by ecologists and paleozoologists
because the lower the value of the reciprocal, the more the assemblage is dominated
by a single taxon, or the less evenly individuals are distributed across all taxa in the
assemblage. Thus, as 1 /D decreases, the more an assemblage is dominated by a single
taxon. The reciprocal of Simpson™s index for the owl pellet assemblage (Table 2.9) is
1.314, suggesting that the assemblage is fairly strongly dominated by a single taxon (in
this case, Peromyscus), just as we would conclude by simple inspection of Figure 5.10.
The inverse of Simpson™s index of dominance, or 1 /D, for each of the eighteen
assemblages of mammalian genera from eastern Washington State is given in Table 5.1 .
Those index values are only weakly correlated with the NISP per sample size (r =
’0.43, 0.1 > p > 0.05), as might be surmised from the wide scatter of points around
quantitative paleozoology
198




figure 5.12. Relationship between sample size and the reciprocal of Simpson™s dominance
index (1 /D) in eighteen assemblages of mammal remains from eastern Washington State.
Best-¬t regression line is weakly signi¬cant (r = “0.43, 0.1 > p > 0.05). Data from Table 5.1 .


the simple best-¬t regression line (Figure 5.12). Thus, one would likely be tempted to
conclude that taxonomic evenness or dominance in these eighteen assemblages does
not seem to be signi¬cantly in¬‚uenced by sample size and thus one could discuss
differences in evenness or dominance in terms of ecological variation in site settings
or variation among the taphonomic agents that accumulated the remains or the
like. But again, a correlation has been sought between sample size ( NISP) per
assemblage and a measure of relative abundance (proportions). It is now time to
discuss that issue.



Discussion

Simple regression analysis such as is illustrated in Figure 5.9 is a reasonable way to
search for sample size effects if absolute measures of sample size are used, such as when
one seeks to determine if there is a relationship between NTAXA and NISP. What
measuring the taxonomic structure and composition 199


Table 5.7. Total NISP of mammals, NISP of deer
(Odocoileus spp.), and relative (%) abundance of deer in
eighteen assemblages from eastern Washington State

Site NISP Deer NISP % Deer
45OK18 31 0 0
45DO204 48 5 10.4
45DO273 84 6 7.1
45DO243 157 34 21.7
45OK2A 366 87 23.8
45DO189 415 251 51.8
45DO282 426 4 0.9
45DO211 474 45 9.5
45DO285 491 33 6.7
45DO214 536 184 34.3
45DO326 640 120 18.8
45DO242 673 368 54.7
45OK287 807 252 31.2
45OK250 1,077 738 68.5
45OK4 1,108 803 72.5
45OK2 2,574 2,021 78.5
45OK11 3,549 1,668 47.0
45OK258 4,433 3,458 78.0



about those cases when relative abundances (percentages or proportions) of one or
more taxa are of interest? Perhaps the paleozoologist wishes to know if the percentages
of a taxon in a series of assemblages increase or decrease in a patterned manner (over
time if the assemblages are chronologically distinct, or over space if the assemblages
are arrayed over an expanse of geographic space). Consider the relative abundance of
deer in the eighteen assemblages from eastern Washington State (Table 5.7). The per-
centage of each assemblage™s NISP representing deer is strongly correlated with
the NISP per assemblage (Spearman™s ρ = 0.763, p = 0.0002), suggesting there
may be a sample-size effect driving the trend. Grayson (1984:126“127) suggested an
empirical way to contend with cases when one ¬nds a correlation between the rel-
ative abundance of one or more taxa and NISP across multiple samples: “Remove
assemblages in order of increasing sample size until the correlation between sam-
ple size and relative abundance is no longer signi¬cant.” Doing so with the eigh-
teen eastern Washington State assemblages results in elimination of the ten smallest
quantitative paleozoology
200


assemblages “ those with NISP < 600. When those ten assemblages are eliminated,
the correlation between the relative abundance of deer and total assemblage size is
no longer signi¬cant (ρ = 0.667, p = 0.08).
There is a way to evaluate whether relative abundances are in¬‚uenced by sample size
without eliminating assemblages. And it is more statistically sensitive to detecting true
sample size effects than the correlation technique when percentages or proportions
are used as measures of abundance. Cannon (2000, 2001 ) pointed out that correlating
(spatial or temporal) trends in relative abundances of taxa with sample size ( NISP)
is statistically not the best way to search for sample size effects. This is so because
relative abundances do not register whether sample sizes are ¬ve or ¬ve thousand.
Statistically, noting the difference between an absolute tally of ¬ve and an absolute
tally of ¬ve thousand is quite different than saying each comprises 5 percent of the
total collection (100 and 100,000, respectively). Small samples make ruling out sample
size effects dif¬cult; their effect on correlations may simply be due to sampling error
rather than any accurate re¬‚ection of abundance. Rare phenomena are particularly
dif¬cult to inventory “ they will be absent from collections “ unless the samples are
large. If the abundances of several rare taxa are not quite equal in the target population,
but samples are small, the true relative abundances of those rare taxa likely will not
be accurately re¬‚ected by small samples (Grayson 1978a, 1979, 1984). A correlation
between the relative abundance of a taxon and NISP across multiple assemblages
may be driven by small samples simply because of sampling error inherent in those
assemblages.
Using simulated samples drawn from ¬ctional but known populations, Cannon
(2001 ) showed that absolutely small samples of populations that have trends in the
relative abundance of a taxon often display no trends, and also that absolutely small
samples of populations that have no trends in the relative abundance of a taxon
often display trends. Thus, using the regression approach to search for sample size
effects (as with how the data in Table 5.7 were examined) may lead to commission
of a Type I error (rejecting a true null hypothesis that there is no true trend in
relative abundances when in fact there is no trend) or commission of a Type II
error (accepting a false null hypothesis that there is no true trend in abundances
when in fact there is a trend). In both cases, the null hypothesis is that no trend
is present, but sampling error has produced samples that are not representative of
the population. Furthermore, the presence of a signi¬cant correlation coef¬cient is
interpreted as indicating that sample size is the source of the correlation, and the
absence of a signi¬cant correlation coef¬cient is interpreted as indicating that sample
size is not the source of the correlation. As Cannon (2001 :185) astutely observed, the
measuring the taxonomic structure and composition 201


¬rst interpretation at best rests on an incomplete understanding of the relationship
between relative abundances and sample size; the second interpretation presumes
sample sizes are suf¬ciently large to warrant con¬dence but in fact may be too small.
Cannon (2000, 2001 ) suggested that rather than regression analysis or calculation
of a correlation coef¬cient, a different statistical test be used to ascertain if sample
size effects plague an analysis of relative abundances. Cochran™s test of linear trends
is a form of χ 2 analysis that tests for trends among multiple rank-ordered samples
(Zar 1996:562“565). As Cannon (2000:332) notes, Cochran™s test is constructed such
that “signi¬cant trends will not be found when samples are so small that random
error cannot be ruled out at a speci¬ed con¬dence level as the cause of differences
in relative abundance between samples.” Cochran™s linear test seeks trends (either
across space or over time) in relative abundance in such a way as to more directly
take absolute sample size into account than correlation-based analyses. One ¬rst
calculates a standard χ 2 statistic, and then determines how much of that statistic is
the result of a linear trend; if the latter is suf¬ciently (statistically signi¬cant) large,
then one concludes that there is indeed a linear trend in the data independent of
sample size.
Let us return yet again to the eighteen assemblages from eastern Washington State
and the relative abundance of deer remains to determine if there is a linear trend
in the relative abundance of deer or not (Table 5.7). The overall χ 2 statistic is large
and signi¬cant (χ 2 = 4196.6, p < 0.0001), suggesting there is a signi¬cant association
between sample size and frequency of deer remains. The χ 2 statistic for a linear
trend is also signi¬cant (χ 2 = 2239.3, p < 0.0001), suggesting there is signi¬cant
trend in the abundance of deer remains across the eighteen assemblages regardless
of the sizes of those assemblages. Figure 5.13 suggests that there is indeed a trend in
relative abundance of deer across the eighteen assemblages (r = 0.79, p < 0.001). The
problem is that Figure 5.13 gives no indication of possible sample size in¬‚uences on
those relative abundances. Cochran™s test for linear trends does just that, though due
to its relatively recent introduction to paleozoology (Cannon 2000, 2001 ), it has as
yet seldom been used (e.g., Cannon 2003; Nagaoka 2005a; Wolverton 2005).
There are several other, nonstatistical points to keep in mind regarding whether or
not sample size in¬‚uences seem to exist. One is that taxonomic richness, heterogene-
ity, and evenness (regardless of the exact index calculated) were designed for extant
ecological communities (e.g., Jones 2004), and they were designed to use tallies of
individual (statistically independent) organisms as the quantitative units (Grayson
1984). Because it is likely that NISP values are not statistically independent tallies per
taxon, cautious interpretation of paleozoological values for richness, heterogeneity,
quantitative paleozoology
202




figure 5.13. Percentage abundance of deer in eighteen assemblages from eastern Wash-
ington State.



and evenness should be foremost in one™s mind. Do not be misled into thinking
about these variables as if they are ratio scale variables; chances are good that they
are not, and chances are fair that they may not even be ordinal scale variables. If it can
be shown that taxonomic abundance data based on NISP are ordinal scale variables
(see Chapter 2 for description of a method), then it can be argued that the index
values are also ordinal scale values.
Another point made by Nagaoka (2001 , 2002) about evenness extends to hetero-
geneity. She noted that evenness does not take into account the position of taxa in
a rank ordered (based on abundance) set of taxa. Using her example, taxon A may
comprise 80 percent and taxon B 20 percent of assemblage I, but taxon B comprises
20 percent and taxon B 80 percent of assemblage II. Evenness and heterogeneity
indices will not register these obvious differences, so inspection of how much each
taxon is contributing may be required if something other than simply an index of
faunal structure (is the fauna even or uneven, heterogeneous or homogeneous) is
desired. Jones (2004) adds that evenness will be in¬‚uenced by NTAXA (as will hetero-
geneity). The important point therefore is that evenness and heterogeneity cannot
be considered independently of richness or of each other. One might choose to focus
analysis on one variable, but the other variables (with the possible exception of rich-
ness) will likely require examination in order to correctly interpret the target variable.
measuring the taxonomic structure and composition 203




figure 5.14. Abundance of bison remains relative to abundance of all ungulate remains
over the past 10,500 (C14) years in eastern Washington State.




T RE N D S I N T A XO N O M I C A B U N D A N CE S


For nearly as long as paleozoologists have measured taxonomic abundances evident
in the collections of remains they study, they have also tracked those abundances
through time and across space. Sometimes that tracking has involved tables of num-
bers, each column representing a taxon, each row a stratum if the analyst was inter-
ested in temporal variation in abundances. If the analyst was interested in variation
in taxonomic abundances across space, each row could be a geographically distinct
collection locality whereas each column was a distinct taxon. Tables of numbers pre-
sented data, but if more than a few rows and columns were included, such tables are
dif¬cult to interpret visually. A reasonable alternative, then, was to construct a graph
displaying taxonomic abundances across time or space, although raw data might not
be included.
Both tables of numbers and graphs of taxonomic abundances are still constructed
by paleozoologists because they are useful analytical techniques. The graph in Fig-
ure 5.14 is based on data in Table 5.8 (from Lyman 2004b). The graph shows the relative
abundance of bison (Bison spp.) remains in eastern Washington State more or less
by 500-year bins since the terminal Pleistocene; several bins are lumped to simplify
the graph. The graph is signi¬cant for several reasons. First, it shows the abundance
of bison remains relative to the abundance of remains of all other ungulates in the
paleozoological record. There is no correlation between the relative abundance of
quantitative paleozoology
204


Table 5.8. Frequencies (NISP) of bison and nonbison ungulates per time
period in ninety-one assemblages from eastern Washington State

Time period (yr BP) Bison (Bison sp.) Nonbison ungulates Total
100“500 4 4,196 4,200
501 “1,000 107 3,838 3,945
1,001 “1,500 131 1,512 1,643
1,501 “2,000 73 1,182 1,255
2,001 “2,500 375 218 593
2,501 “3,000 4 3,851 3,855
3,001 “3,500 5 1,639 1,644
3,501 “4,000 1 414 415
4,001 “5,000 1 776 777
5,001 “6,000 10 2,111 2,121
6,001 “8,000 0 405 405
8,001 “10,500 186 102 288




bison and the number of assemblages per period (p > 0.5); there is no correlation
between the total ungulate NISP and bison NISP per temporal period (p > 0.5). The
abundance of bison remains does not seem to be a function of sampling intensity
or sample size. χ 2 analysis indicates there are signi¬cant differences in the relative
abundances of bison remains in the samples (χ 2 = 8291.5, p < 0.0001); the test for lin-
ear trends indicates there is a trend in the abundance of bison remains (χ 2 trend =
109.55, p < 0.0001). The data indicate an increase in bison over time. Grass was
least abundant in the geographic area of concern between 8,000 and 4,000 14 C
years ago, consistent with the few remains of bison; bison eat mostly grass. Bison
likely immigrated from Montana and Wyoming through southern Idaho, 2,500 years
ago or later, when ¬re frequencies increased (based on the amount of charcoal
deposited in lake sediments) and made the immigration route more hospitable
(Lyman 2004b). The graph in Figure 5.14 shows the history of the frequency of
bison remains in eastern Washington clearly. Similar graphs have been around in
paleozoology for several decades (e.g., Ziegler 1973; Stiner et al. 2000). The graph in
Figure 5.14 plots only the relative abundance of bison remains; most other graphs
plot multiple taxa simultaneously and thus such graphs can sometimes be dif¬cult to
interpret.
Another way to graph taxonomic abundances that has seen some recent popularity
is of more deductive derivation. Popularized in the early 1990s, a group of paleozo-
ologists, many of whom work in the western United States, calculated indices of
measuring the taxonomic structure and composition 205


taxonomic abundance and plotted those index values against (usually) time or (less
often) space. The seminal work was Bayham™s (1979) plotting of the ratio of abun-
dances of large to small animals. His reasoning in doing so was that large animals
(grouped by taxon) were more ef¬ciently exploited (cost less in terms of energy
expended relative to energy earned) than were small animals given tenets of foraging
theory (see Stephens and Krebs [1986] for a theoretical statement). Bayham™s notion
and his method were re¬ned by Broughton (1994a, 1994b, 1999; see also James 1990)
in a series of studies on mammalian, piscean, and avian faunas from California, and
were subsequently used by a number of others working in both the New World (e.g.,
Butler 2000; Dean 2001 ; Lyman 2003a, 2003b, 2004d) and the Old World (e.g., Butler
2001 ; Grayson and Delpech 1998; Nagaoka 2001 , 2002; Stiner et al. 1999).
The sort of graph referred to is exempli¬ed in Figure 5.15. This is a simple bivariate
scatterplot of the abundance of North American elk (or wapiti, Cervus elaphus)
remains relative to the abundance of all ungulate remains in eighty-six assemblages
of mammalian remains from sites in eastern Washington State. In an earlier analysis,
I found that the absolute abundance of elk remains is not correlated with the total
ungulate sample size ( NISP) per assemblage (r = 0.16, p = 0.14) (Lyman 2004d);
removing the three largest collections (NISP > 1800), the correlation becomes weak
but signi¬cant (r = 0.33, p < 0.005). The relative abundance of elk per assemblage is
not correlated with assemblage age (r = 0.006, p > 0.9), and the slope of the simple
best-¬t regression line is not signi¬cantly different from zero. On this basis I suggested
that there is no evidence here that the abundance of elk relative to the abundance of
all ungulates changed over the 10,000 years represented (Lyman 2004d).
Since the earlier analysis, the χ 2 test for linear trends has been introduced to pale-
ozoology. That test suggests there is indeed a trend in the relative abundance of elk
remains over time (χ 2 trend = 112.96, p < 0.0001). The scatterplot in Figure 5.15
gives no indication of whether the trend is for elk remains to increase or decrease
over time. Thus one advantage of the sort of graph shown in Figure 5.15 is exempli-
¬ed by the included simple best-¬t regression line, which hints at a decrease in elk
abundance over time (despite it having a slope statistically indistinguishable from
no slope). Remember, however, that taxonomic abundance data are often at best
only ordinal scale data, and seldom are they ratio scale data. Therefore, the regres-
sion line in Figure 5.15 should not be interpreted literally as indicative of ratio scale
relative abundances of elk. Instead, that line assists with the identi¬cation of a trend
in (in this case) elk relative abundances. Consider another example, one that displays
a graphically visible trend.
The Emeryville Shellmound site on the shore of San Francisco Bay in Califor-
nia produced a large fauna from strati¬ed deposits. Paleozoologist Jack Broughton
quantitative paleozoology
206




figure 5.15. Bivariate scatterplot of elk abundances relative to the sum of all ungulate
remains in eighty-six assemblages from eastern Washington State. The simple best-¬t regres-
sion line is shown to assist with identifying trends in elk relative abundance.


(1999) analyzed those faunal remains and found a number of trends in taxonomic
abundances. One of the more interesting ones concerns the abundance of remains
of North American elk relative to the abundance of deer (Odocoileus sp.) remains.
To monitor change in the abundance of elk over time, Broughton calculated an
“elk’deer index” for each assemblage in each stratum (several strata produced more
than one assemblage). The index was calculated as elk NISP/ (elk NISP + deer
NISP + medium artiodactyl NISP), where it is very likely that all medium artiodactyl
remains are from deer. The data and index value for each assemblage are given in
Table 5.9. As shown in Figure 5.16, plotting the index value, which is effectively the
proportion of cervid remains that represent elk, against the stratum from which it
derives suggests that elk became less available to human occupants of the Emeryville
Shellmound site over time (stratum 1 is youngest, stratum 10 is oldest). That it is
indeed the case that elk availability decreased over time relative to deer is con¬rmed
by the simple best-¬t regression line through the point scatter (r = 0.62, p = 0.008).
The χ 2 test for trends also suggests that there is a trend in the relative abundance
of elk remains (χ 2 trend = 638.8, p < 0.0001), but does not indicate the direction of
change in abundance.
Changes in taxonomic abundances can be monitored more directly than with
the indices of relative elk abundances presented in Figure 5.16 as proportions of
some larger group of taxa. Table 5.10 lists the abundances of remains of two taxa of
measuring the taxonomic structure and composition 207


Table 5.9. Frequencies (NISP) of elk, deer, and
medium artiodactyl remains per stratum at Emeryville
Shellmound. Data from Broughton (1999)

Medium Elk-Deer
Stratum Elk Deer Artiodactyl Index
1 0 100 122 0.0
1 0 35 58 0.0
2 8 758 958 0.005
3 17 294 365 0.025
3 1 8 12 0.048
4 81 72 76 0.354
5 40 52 56 0.270
6 11 20 18 0.224
7 12 10 13 0.343
7 184 94 76 0.520
8 75 46 56 0.424
8 116 87 83 0.406
9 23 79 51 0.150
9 68 67 62 0.345
10 50 95 94 0.209
10 59 122 103 0.208
10 63 105 88 0.246



mammals recovered from the strati¬ed deposits of Homestead Cave in Utah State
(Grayson 2000). The deposits span the terminal Pleistocene and entire Holocene.
Based on pollen and plant macrofossil records, local climate shifted from cool and
moist relative to today, to more or less modern climate by about 8,000 years ago.
The two taxa were chosen from the several dozen represented in the site to illustrate
trends in abundance here; Neotoma cinerea prefers cool, moist conditions relative to
Dipodomys sp., which prefers warmer and drier conditions. The absolute abundance
of Neotoma cinerea is not correlated with the stratum total NISP (ρ = 0.13, p > 0.6);
the absolute abundance of Dipodomys sp. is correlated with the stratum total NISP
(ρ = 0.82, p = 0.0003), but given the exceptionally large abundances of remains in
all strata, I doubt that sample size is a problem.
Given the climatic preferences of the two taxa, and the environmental history
coincident with deposition of the strata in Homestead Cave, Neotoma cinerea should
decrease in abundance and Dipodomys sp. should increase. That is in fact precisely
quantitative paleozoology
208




figure 5.16. Bivariate scatterplot of elk“deer index against stratum at Emeryville Shell“
mound. The simple best-¬t regression line is shown to assist with identifying trends in elk
relative abundance. Data from Table 5.9.




what the relative abundances of remains of each taxon do. On the one hand, Neotoma
cinerea remains decrease in relative abundance during the terminal Pleistocene and
earliest Holocene (strata I, II, III) and virtually disappear after that (Figure 5.17; χ 2
trend = 13,034, p < 0.0001). Remains of Dipodomys sp., on the other hand, increase
rapidly during the terminal Pleistocene and earliest Holocene, and after about 8,000
BP (after the deposition of stratum VI), they comprise more than half the total NISP
per stratum (Figure 5.17; χ 2 trend = 25,457, p < 0.0001).
Two methods for examining trends in taxonomic abundances over time have been
described. One involves calculating an index of a taxon™s abundance within a lim-
ited set of taxa. The index can be expressed as a proportion or a percentage. The
other method involves calculating the proportion or percentage of a taxon™s abun-
dance within the entire assemblage. Broughton (1999) was interested in determining
whether elk availability was decreased by human predation and were replaced by deer
(Figure 5.16). Grayson (2000) was interested in the contribution of particular taxa
measuring the taxonomic structure and composition 209


Table 5.10. Frequencies (NISP) of two taxa of small mammal per stratum at
Homestead Cave. Remains from strata X, XIII, XIV, XV were not analyzed. Data
from Grayson (2000)

Neotoma Percent of Dipodomys Percent of Stratum
Stratum cinerea Total NISP sp. Total NISP Total NISP
I 2,577 25.1 360 3.5 10,275
II 1,508 19.2 1,329 16.9 7,855
III 306 10.6 1,056 36.6 2,884
IV 242 0.9 13,712 51.5 26,615
V 1 0.02 2,965 58.0 5,109
VI 5 0.02 15,173 62.4 24,330
VII 4 0.03 9,868 71.0 13,905
VIII 5 0.06 5,742 69.3 8,289
IX 1 0.005 15,477 70.1 22,088
XI 0 0 6,820 67.6 10,096
XII 0 0 16,753 73.3 22,860
XVI 0 0 4,371 69.4 6,296
XVII 9 0.06 10,418 67.0 15,548
XVIII 0 0 720 68.8 1,047



to the entire mammalian fauna. The choice of method was guided by the research
question being asked.



CO N C L U S I O N


There are many reasons to compare the taxonomic abundances displayed by dif-
ferent collections. Simplistically, these can be reduced to two general categories of
questions “ those concerning paleoenvironmental conditions (was it hot or cool,
dry or moist?), and those concerning human or hominid adaptations (what did
they eat, and how much)? Those categories concern ultimate questions; they are
answered with detailed contextual, associational, and taphonomic analysis of tax-
onomic abundances. The concern of this chapter has been to describe ways that
taxonomic abundance data might be analyzed and studied, to answer more proximal
questions, questions closer to the quantitative data themselves. Toward that end,
diversity was de¬ned as a generic term for variation in taxonomic richness, even-
ness, and/or heterogeneity. Indices for each of the latter variables were described and
quantitative paleozoology
210




figure 5.17. Relative abundances of Neotoma cinerea and Dipodomys spp. at Homestead
Cave. Data from Table 5.10.



exempli¬ed. Two methods of monitoring trends in taxonomic abundances over time
were discussed. No doubt, there are other methods and indices that might be used.
Ecologists are regularly inventing new measures of taxonomic structure and compo-
sition, and re¬ning old ones. Paleozoologists should, and often do, pay attention to
those developments and adopt new indices and quantitative methods developed by
ecologists. In so doing, paleozoologists potentially adopt a family of problems the
identi¬cation of which is a good way to conclude this chapter.
Earlier the biological concept of community was de¬ned, and it was noted that
biological communities are sometimes dif¬cult to identify; the identi¬cation problem
is exacerbated when one seeks to identify a paleocommunity on the basis of the fossil
record (e.g., Bennington and Bambach 1996). This fact was explicitly dealt with more
than 50 years ago by paleozoologist J. Arnold Shotwell (1955, 1958) when he attempted
to use quantitative measures of skeletal completeness to distinguish taxa comprising
the proximal paleocommunity from taxa comprising distal (distant) communities.
Taphonomists and those with a quantitative bent were quick to point out some of the
analytical dif¬culties with what Shotwell proposed (Grayson 1978b and references
measuring the taxonomic structure and composition 211


therein). With the bene¬t of another couple decades of re¬‚ection, there is yet another
problem that attends Shotwell™s method, a problem that potentially plagues any and
all of the indices and measures of taxonomic abundances discussed in this chapter.
That problem is what is known as “time averaging.”
The temporal resolution available in the paleozoological record is seldom of the
¬ne scale, intrageneration resolution that is provided to zoologists. The temporal
acuity of the paleozoological record is such that, very often, any stratigraphically
bounded sample is a palimpsest or time-averaged collection representing multiple
generations, multiple seasons, multiple years, and typically multiple decades or even
centuries or millennia (Peterson 1977; Schindel 1980). This means that concepts such
as taxonomic richness, evenness, and heterogeneity, which derive from extant com-
munities, may never be of the same temporal resolution in the paleozoological record
as they are in the modern or extant zoological record (but see Olszewski and Kidwell
2007). Ecological time is seldom the same as paleozoological time (see also Grayson
and Delpech 1998). One result of recognition of this potential problem has been a
series of “¬delity studies,” introduced in Chapter 2 and de¬ned as “the quantitative
faithfulness of the [fossil] record of morphs, age classes, species richness, species
abundance, trophic structure, etc. to the original biological signals” (Behrensmeyer
et al. 2000:120). Many of these studies originate in taphonomic concerns regarding the
preservation of animal remains or the rate of input of those remains. Fewer concern
the difference between ecological time and paleontological time either studied empir-
ically or focusing on key quantitative concepts such as richness and evenness (see
Broughton and Grayson [1993], Lyman [2003b], and Olszewski and Kidwell [2007]
for exceptions). The critical point to contemplate is the relationship between the
property (richness, relative abundance, etc.) of a paleofauna that has been measured
and the temporal resolution of that value. Does it encompass a decade, a century,
more? And how might that in¬‚uence interpretations? An example will highlight the
signi¬cance of these questions.
If the elk abundance data for the eighty-six individual collections in Figure 5.15
are lumped into 500-year bins (1 “500 BP, 501 “1000 BP, etc.), and the elk index
recalculated using only elk and deer remains (bison, pronghorn, bighorn excluded),
the result is rather different than that shown in Figure 5.15. The resulting graph and
best-¬t regression line suggest there is a signi¬cant relationship between age and
the relative abundance of elk (r = 0.489, p = 0.064) (Figure 5.18). The slope of the
line suggests elk availability decreased over time. The χ 2 test for trends con¬rms
the trend in the relative abundance of elk remains (χ 2 trend = 9.67, p = 0.002;
including all ungulates, χ 2 trend = 42.5, p < 0.0001). Something not apparent in the
statistics is that elk seem least abundant between about 7,500 and 4,000 BP, precisely
quantitative paleozoology
212




figure 5.18. Bivariate scatterplot of elk abundances relative to the sum of all ungulate
remains in eighty-six assemblages from eastern Washington State summed by age for con-
secutive 500-year bins. The simple best-¬t regression line is shown to assist with identifying
trends in elk relative abundance. Compare with Figure 5.15. Note that there are no data for
the 6,001 “6,500, 7,001 “7,500, and 7,501 “8,000 bins.

when climate was least conducive to elk reproduction (Lyman 2004a, 2004d, and
references therein). Whatever the case, comparison of Figures 5.15 and 5.18 make it
clear that time averaging can in¬‚uence analytical results, as can the taxa included in
the measure of relative abundance.
Do not let the preceding mislead you. Time averaging may not always be a bad
thing. It has been suggested, for example, that either time averaged samples formed
by natural processes, or those formed by analytical lumping of assemblages may
serve to ¬lter out “noise” in a paleofaunal signal (Olszewski 1999; see also Muir and
Driver 2002). Whether time averaging is a good thing or a bad thing will depend
on the research question being asked and the attendant target variable that must be
measured or estimated in order to answer the research question. Similarly, lumping
assemblages from different spatial locations may also result in an averaging or muting
measuring the taxonomic structure and composition 213


of the paleofaunal signal (Lyman 2003b). Thus, one must be explicit about the spa-
tiotemporal coordinates (and their boundaries) pertinent to the research question
being asked. Either that, or we rewrite the ecological variables we seek to measure in
paleozoological spatiotemporal units. To reiterate, the research questions of interest
should dictate the temporal resolution necessary for a clear answer.
6
Skeletal Completeness, Frequencies
of Skeletal Parts, and Fragmentation

The minimum number of individuals (MNI) is typically de¬ned as something like
the most frequently occurring skeletal part (Table 2.4). Variation in how that def-
inition can be operationalized are differences in size, age, sex, or recovery context
(aggregation) considered renders MNI as a derived measure. But on a general, in
some ways less discriminating scale, how the basic de¬nition of MNI is operation-
alized is simply this: Given all the remains of a taxon in a collection (how the spa-
tiotemporal boundaries of that collection are de¬ned need not concern us initially),
redundant skeletal parts are each tallied as a single MNI. Redundant skeletal parts
means that specimens overlap anatomically. Two left femora of deer overlap anatom-
ically and are redundant with one another, just as are two upper right second molars,
three right distal humeri, and four left innominates. In the order listed, the MNI
values are 2, 2, 3, and 4. To reiterate, redundant that is, anatomically overlapping
skeletal parts each represent a unique individual or a tally of one MNI.
How MNI is operationalized on a general scale by redundant skeletal parts forces
us to recognize a previously unmentioned quantitative unit. That unit was not really
distinctively named until 1982, but it had played an important role in paleozoology
for decades prior to that time. Today that quantitative unit is known as the minimum
number of elements, or MNE. This unit not only is, in fact, the basis of MNI, it is also
the basis of another important quantitative unit that has at least two different names
(MAU,%survivorship), and it is, ¬nally, somewhat of a misnomer. The purposes of
this chapter are to make all of these points clear and to illustrate if and how MNE
might be analytically useful.
Another purpose of this chapter is to review the means to analytically determine,
and interpret, other quantitative variables that paleozoologists sometimes measure.
One concerns which parts or portions of the represented skeletons are present; are
those parts represented in abundances that reveal something of the taphonomic his-
tory of the collection, such as accumulation or preservation? Another concerns the
skeletal completeness, skeletal parts, and fragmentation 215


degree of skeletal completeness; how complete, on average, is each of the multiple
skeletons represented? The ¬nal variable that has been studied using MNE concerns
bone fragmentation. Techniques for quantifying the degree of fragmentation evi-
dent in a collection of faunal remains are reviewed, and pertinent concepts de¬ned.
Tallying the frequencies of skeletal parts, measuring skeletal completeness, and mea-
suring the degree of fragmentation all rest in one way or another on tallies of MNEi,
where i is a particular skeletal element, part, or portion. An historical overview of
MNE sets the stage for subsequent discussions of how it and its related quantitative
units have been and can be used. The overview provides the requisite background
to consideration of how skeletal completeness is measured and how fragmentation
is quanti¬ed.



H I S T O R Y O F T H E M N E Q U A N T I T A T IVE U N I T


When Chester Stock tallied up abundances of mammalian taxa represented by the
Rancho La Brea remains (Chapter 1 ), he determined the minimum number of indi-
viduals. To determine MNI, he tallied redundant or anatomically overlapping skeletal
parts; that is, he determined the MNE of each unique skeletal part whether ¬rst cervi-
cal vertebrae, left mandibles, right humeri, or left tibiae and used the largest number
as his MNI. All subsequent paleozoologists who have derived an MNI from a collec-
tion have ¬rst determined the MNE for at least the most common skeletal parts if
not all skeletal parts of a taxon, and then used the greatest MNE value as the MNI
value for that taxon. As put some years ago, MNE is the minimum number of skeletal
portions necessary to account for the specimens representing that portion (Lyman
1994c:102). How and why did explicit recognition of MNE emerge?
Traditionally, paleozoologists such as Chester Stock sought measures of taxonomic
abundances. Thus, MNI, biomass, NISP, and the like were designed to measure
those abundances. But with increases in our knowledge of how the paleozoological
record formed, taphonomic concerns came to the fore. Was, perhaps, taxon A more
abundant than taxon B in a collection because taxon A was more abundant on the
landscape than taxon B was at the time the remains of each were accumulated and
deposited? Or, did the agent or process of bone accumulation simply collect more
of taxon A than of taxon B? Or, did the agent or process of bone preservation (or
destruction) result in bones of taxon A being more frequently preserved than those of
taxon B? These were taphonomic questions that concerned skeletal-part abundances
and, thus, depending on their answers, could signi¬cantly in¬‚uence how taxonomic
abundance data were interpreted.
quantitative paleozoology
216

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