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do so would limit archaeological applications” (Reitz et al. 1987:311). What is meant
here is that sexual variation, ontogenetic variation, and seasonal variation can not
quantitative paleozoology
108


always be determined from archaeological remains, so to construct allometry formu-
lae that account for these sorts of variation is unnecessary. It is, of course, precisely
such variation that reduces mathematically elegant solutions, whether Guthrie™s and
White™s simplistic average live weight, or Uerpmann™s bone weight conversion, or
allometric formulae, to producing at best ordinal scale results.
One variant of skeletal mass allometry is Needs-Howarth™s (1995:95) suggestion
that “once the soft-tissue biomass weight has been estimated, its caloric content can
be calculated.” She used skeletal mass allometry to estimate soft-tissue biomass, and
then used U.S. Department of Agriculture standards to estimate calories per gram
of edible tissue. She correctly noted that “edible tissue” likely varied cross-culturally,
that individual variation in animal condition was masked by the procedure, and
that the caloric results comprised “a relative [ordinal scale], indirect [derived], and
probably distorted quanti¬cation of what the inhabitants of the site actually ate”
(Needs-Howarth 1995:99). These comments suggest that the probability of distor-
tion is > 0.99, and the degree of distortion may render the results nominal scale. Yet
Needs-Howarth (1995:97) echoes those advocating skeletal mass allometry when she
argues that soft tissue biomass estimates, “insofar as these are accurate for archae-
ological material, provide a more biologically justi¬able estimate of potential food
intake represented by excavated bone, than do NISP or MNI.” Although true (largely
because NISP and MNI are not meant to estimate “food intake”), the critical ques-
tion concerns the accuracy of the soft-tissue biomass estimates, whether or not those
estimates are converted to calories.



B O N E S I ZE A N D A N I M A L S I ZE A L L O M E T R Y


There is another technique for measuring biomass of taxa that is also based on allom-
etry. This technique uses one or more linear measurements of bone size to estimate
individual body size or biomass (e.g., Casteel 1974; Noodle 1973; Witt 1960). In at least
one instance it was explicitly proposed as an alternative to White™s (1953a) procedure
for estimating meat weight (Emerson 1978, 1983). What is sometimes referred to
as linear allometry also received some consideration by those who examined bone-
weight allometry (Reitz and Cordier 1983; Reitz and Wing 1999; Reitz et al. 1987).
The latter quickly dispensed with the bone size allometry option because it did not
include all (weighable) bone and thus deleted some potentially informative data.
Furthermore, it was noted that if the measured skeletal element or part was not also
the most common element and thus was not used to de¬ne MNI, then any measure of
biomass based on bone size would necessarily be an underestimate because a number
estimating taxonomic abundances: other methods 109


of specimens less than the MNI would provide the data. As well, the allometry for-
mulae were based on, typically, one linear dimension yet were meant to estimate live
weight of a complete animal. Bone weight advocates noted that such a procedure
assumed an animal was eaten completely, from nose to tail, yet bone weight did not
require that assumption. Finally, bone weight advocates implied that linear dimen-
sion allometry demanded species-level identi¬cation and thus could not incorporate
into the analysis many specimens, yet bone weight allometry could incorporate those
specimens identi¬ed only to taxonomic class or order. Nevertheless, linear allometry
has seen some use in zooarchaeology. Before reviewing that use, consider how linear
allometry is used in paleontology.
Vertebrate paleontologists have long used linear allometry to estimate the size of
prehistoric animals (references in Damuth and MacFadden 1990). They are thus well
aware of problems such as those identi¬ed by the advocates of skeletal mass allome-
try. Paleontological interest in body size is a direct result of the relationships between
body size and functional anatomy, physiology, and metabolism, as well as the pale-
oecological implications of body mass inherent in, for example, Bergmann™s rule
(Blackburn et al. 1999). Thus, solving or circumventing problems of linear allome-
try methods have in the past 10“20 years become quite important in paleontology
(e.g., Anyonge 1993; Anyonge and Roman 2006; Egi 2001 ; Mendoza et al. 2006;
Reynolds 2002; Smith 2002; Wroe et al. 2003). Some of the problems with skeletal
mass allometry are avoided by using multiple linear dimensions of multiple skeletal
elements to estimate the sizes of bodies. Thus, femur length may suggest one body
size but the breadth of the proximal humerus suggests another body size, which
encounters head on the problem of possible skeletal element interdependence. Inter-
dependence is, of course, not a problem if only one skeleton is involved. But the
use of multiple dimensions and multiple elements avoids the problem of measured
bones being fewer than the MNI; it also avoids the equivalence of 10 kilograms of
phalanges giving the same amount of biomass as 10 kilograms of femora. And, mea-
suring multiple bones, particularly if multiple dimensions of each kind of skeletal
element are measured, provides more than a single data point (such as bone weight
does) from which to estimate body mass.
Regression equations are built from known comparative skeletons and the inde-
pendent variable (a dimension of bone size) is plugged in and the equation solved to
determine a value of the dependent variable (body mass). A paleontologist may or
may not attempt to estimate the total biomass represented by the bone collection, and
does not often use the derived estimates of body size to estimate taxonomic abun-
dances in the form of biomass. Because those analytical steps are seldom taken, the
number of inferential layers, one built atop another, and the number of attendant
quantitative paleozoology
110


Table 3.12. Deer astragalus length (millimeters) and live weight
(kilograms). Data from Emerson (1978)

Astragalus Astragalus
length Weight length Weight
26.0 7.53 41.0 61.37
27.0 7.53 41.0 86.86
27.0 7.53 41.0 64.18
28.0 16.06 41.0 64.18
28.0 10.39 41.0 69.85
30.0 10.39 41.5 67.04
32.0 24.54 41.5 64.18
33.0 27.35 41.5 55.70
33.0 24.54 41.5 64.18
33.0 10.39 42.0 67.04
34.0 30.21 42.0 67.04
34.0 35.88 42.0 61.37
34.0 33.02 42.0 64.18
34.0 35.88 42.5 64.18
35.0 33.02 42.5 64.18
35.0 16.06 42.5 67.04
36.0 55.70 42.5 64.18
38.0 55.70 42.5 64.18
38.0 58.51 42.5 64.18
38.5 55.70 42.5 58.51
38.5 52.84 42.5 75.52
39.0 69.85 43.0 64.18
39.0 75.52 43.0 84.00
39.0 52.84 43.0 69.85
39.0 58.51 43.0 67.04
39.0 58.51 43.0 64.18
39.0 69.85 43.5 78.33
39.5 58.51 44.0 81.19
40.0 64.18 44.0 75.52
40.0 67.04 44.5 72.67
40.0 58.51 44.5 81.19
40.0 67.04 45.0 84.00
40.5 64.18 45.0 72.67
41.0 67.04 45.0 81.19
41.0 58.51 45.0 72.67
41.0 64.18
estimating taxonomic abundances: other methods 111


assumptions, are fewer than they are when a zooarchaeologist seeks to determine
weights of useable meat from biomass estimates. Of course, the analytical goal and
thus the target variable(s) of the paleontologist are different than those of a zooar-
chaeologist. The paleontological target variable often concerns something other than
taxonomic abundances, such as the average body mass of adult members of a taxon
to gain insight to physiology or metabolism or the like. One begins with one or more
measurements of a bone (or several bones) and then estimates body mass based on
bone size. An example will make the analytical protocol clear.
Based on a sample of seventy-one white-tailed deer (Odocoileus virginianus),
Emerson (1978) argued that the length of the astragalus would provide fairly accurate
estimates of the live weight of individual deer. He weighed ¬eld-dressed carcasses,
converted those weights to live weights using a “commonly accepted regression equa-
tion” developed by wildlife biologists (Emerson 1978:36), measured the length of an
astragalus from each carcass, and then a regressed astragalus length against (esti-
mated) live weight. His data are presented in Table 3.12, and a bivariate scatterplot of
those data and the statistical results of his analysis are given in Figure 3.6. I converted
Emerson™s weights, which were given in pounds, to kilograms, and I reversed the axes
in Figure 3.6 from what Emerson (1978:42; 1983:66) originally illustrated because in
an archaeological setting the length of the astragalus would be the independent vari-
able and carcass weight would be the dependent variable. Emerson suggested that
the regression equation he derived from the data could be used to predict the live
weight of individual deer represented in an archaeological collection of astragali. The
equation I derived from those data (Y = “104.96 + 4.11 X; where Y is the live weight
or biomass in kilograms, and X is the length of the astragalus in millimeters) could
also be used in this fashion, with certain caveats.
Later workers were explicit about the fact that using linear allometry to mea-
sure biomass provided at best ordinal scale data, even when sex and age could be
controlled (Purdue 1983, 1987). Purdue (1987:10) was particularly insightful when
he observed that an estimate of biomass provided by linear allometry “should be
viewed as an index that smooths multiple compounding factors and is useful only
in an ordinal sense.” Purdue (1987) derived several measurements of biomass from
multiple skeletal elements and calculated an average biomass per individual animal,
further smoothing his results. Some researchers argue that proximal limb elements
of mammals, such as the humerus and femur, should be used rather than distal
limb elements such as the radius-ulna, tibia, and metapodials because proximal limb
elements produce higher coef¬cients of determination describing the relationship
between a linear dimension of a bone and body weight (McMahon 1975; Noodle
quantitative paleozoology
112




figure 3.6. Relationship between lateral length (millimeters) of white-tailed deer astragali
and body weight (kilograms). 95 percent con¬dence interval indicated by dashed lines. Some
points represent multiple specimens. Data from Table 3.12.



1973; Reitz and Honerkamp 1983). This may be so, but we need only worry about
it if we desire ratio scale results, and such results are impossible to attain with any
biomass (or usable meat) measurement technique.
Before we leave the subject of bone size, a ¬nal point needs to be made. As with
the skeleton™s weight being closely related to the body™s biomass, many (but not all)
linear dimensions of skeletal elements are also correlated with body size (Orchard
2005, and references therein). Paleozoologists can exploit that relationship in one
of two ways. One is to match bones (are a left and a right specimen members of
a bilateral pair or not) based on the principle that unique skeletal elements from
the same individual will predict essentially the same body size (Nichol and Creak
1979); those prehistoric specimens that suggest they are from the same size animal
could be matched or inferred to be from the same animal. This exploits bone size
to control for skeletal element interdependence and allows anatomical re¬tting. In
a similar sort of analysis, different skeletal elements that represent a unique body
size could each be inferred to represent a unique individual, thereby increasing the
total number of individuals to a value likely to be greater than a standard MNI
estimating taxonomic abundances: other methods 113


(Orchard 2005). However, one dif¬culty here is determining when a difference in
body size (indicated by difference in bone size) also represents a different individual.
Furthermore, aggregation will in¬‚uence tallies of individuals because it is likely that
bilateral pairs and nonmatching specimens will only be sought within each aggregate.
Because of these dif¬culties, results derived using these procedures will be at best
ordinal scale measures of taxonomic abundances.
Paleozoologists can also use the relationship of bone size to body size to mon-
itor clines (character gradients) over time and space. And they can do so without
converting bone size to an estimate of body size or body mass (e.g., Butler and Dela-
corte 2004; Lyman 2004b; Lyman and O™Brien 2005; Purdue 1980, 1986). Even then,
however, it would likely be imprudent to suggest that a shift represented, say, a 5
percent decrease in size because that decrease is best considered ordinal scale. If the
shift were based on averages, much variation would be smoothed. Use of skeletal ele-
ment size would not provide quantitative information like measures of taxonomic
abundances or of biomass. But, as with many quantitative measures discussed thus
far, the research question (or problem) one asks dictates a particular target variable,
and whether or not we can design a measured variable that correlates strongly with
that target variable is the challenge. Biomass, usable meat, and consumed meat are
similar sorts of measures, sometimes derived from a collection of faunal remains
with very similar techniques. Given that they are based on the identi¬ed assemblage
(Figure 2.1 ), how do they relate to a target variable?
More than 35 years ago, paleozoologist John Guilday (1970) determined the MNI
represented by a sample of remains recovered from the site of an historic fort. His-
torical documents indicated that the fort had been occupied continuously for about
2,364 days by anywhere from 8 to 4,000 men. The faunal remains represented approx-
imately 1,815 kilograms of meat. Guilday (1970) noted that at a standard ¬eld ration
of about a half kilogram of meat per man per day, the site could have been occu-
pied by 4,000 men for one day, or by only two men the entire time it was in fact
occupied. He concluded that calculations of meat weight were “patently ridicu-
lous.” There is an important lesson here. Given that archaeologists usually excavate
only part of a site and thus collect but a sample of the faunal remains in the site
deposits, why would anyone want to try to calculate meat amounts? A partial answer
seems to be that many believe meat amounts provide ordinal scale estimates of
which taxa provided the most food and which provided the least. Whether those
amounts are in fact ordinal scale is usually assumed rather than tested. To perform
a test, examine the magnitude of difference between taxon speci¬c amounts (e.g.,
Figures 3.4“3.5).
quantitative paleozoology
114


UBIQUITY


What is termed a “ubiquity index” has long been used in paleoethnobotany (Popper
1988). Ubiquity concerns the frequency of (depositional) contexts in which a taxon
occurs and thus it is measured in several ways. In the simplest way, the absolute
frequency of distinct archaeological features in a particular archaeological context
that contains a taxon is tallied, and the total is a measure of the ubiquity of that taxon
in the archaeological context under consideration (e.g., Purdue et al. 1989; Stahl 2000).
A variant of this procedure is to determine the percentage of assemblages (whether of
sites, components, strata, or features) that contain remains of a taxon (e.g., Lubinski
2000). The other major way to measure ubiquity is to construct a bivariate scatterplot
with the number of archaeological contexts containing remains of a taxon on one axis
and the NISP of the taxon on the other axis (Styles 1981:43). Styles (1981:44) cautions
that the bivariate scatterplot “is not a direct measure of taxon importance” because
it in part measures human behaviors as well as natural taphonomic processes. The
bivariate scatterplot also allows visual assessment of intrataxonomic variation in
ubiquity and simultaneous assessment of the in¬‚uence of sample size on ubiquity. If
some taxa are more ubiquitous than others with similar sample sizes, it is reasonable
to conclude that some taphonomic agent or process accumulated and deposited, or
dispersed remains of one taxon differently than another. Identi¬cation of the agent
or process is a taphonomic issue (Lyman 1994c).
The ubiquity index can be calculated in other ways. These tend to be derivative
of the ¬rst technique. Consider the taxonomic abundance (NISP) data from the
collection of eighty-four owl pellets in Table 2.8. Note that Sylvilagus is represented
in two pellets, Reithrodontomys is represented in four pellets, Sorex in seven pellets,
Thomomys in eleven pellets, Microtus in forty-nine pellets, and Peromyscus in sixty
pellets. If ubiquity of a taxon is measured as the total number of pellets in which a
taxon occurs, then the relationship between NISP and ubiquity of a taxon is very
strong and signi¬cant (Figure 3.7; r = 0.997, p < 0.0001). That shouldn™t be surprising.
On the one hand, a taxon can occur in no more pellets (or any other context) than its
NISP, so, for example, Sylvilagus can occur in only ¬ve pellets because it has an NISP
of ¬ve, and Reithrodontomys can occur in no more than nineteen pellets because
it has an NISP of nineteen. In other words, the number of contexts (Ncontexts) in
which a taxon occurs or ubiquity ¤ NISP. A taxon with NISP > Ncontexts, on the
other hand, can occur in as many as Ncontexts; it is not limited in its ubiquity.
The most obvious other way to measure ubiquity is to tally up the number of sites
in a region that contain remains of a taxon (e.g., Butler and Campbell 2004). Or,
tally up the number of collections or temporally distinct assemblages within a single
estimating taxonomic abundances: other methods 115




figure 3.7. Relationship between NISP and ubiquity (number of pellets in which a taxon
occurs) of six genera in a collection of eighty-four owl pellets. See Table 2.8.


site in which a taxon occurs. However, any such tally, regardless of the spatial or
temporal scale at which ubiquity is measured, may well re¬‚ect sample size. Consider
the data for eighteen sites in eastern Washington State. Fourteen of these sites were
used in analyses discussed in Chapter 2; four additional sites are included here to
increase the number of assemblages examined. The taxa (all mammals) represented
are unimportant to this exercise. What is important is that all eighteen collections are
from a single stretch of river about 45 km long. There are minor habitat differences
among the sites, and some age variation but all date to the last 7,000 years. All sites
have the same probability of producing the same taxa. Thus, all taxa should be equally
ubiquitous across these sites if every site was sampled in a manner equivalent to every
other site (all else being equal, such as accumulation, preservation, and recovery). The
only difference in sampling across the sites was the volume of sediment excavated, and
thus, not surprisingly, the total NISP per site varies. The last leads to the prediction
that taxa with many NISP will tend to be more ubiquitous than taxa with few NISP.
Do the data meet this prediction?
Both NISP and ubiquity data for the twenty-eight taxa represented are presented
in Table 3.13. NISP values per taxon have been summed across all 18 sites, and range
quantitative paleozoology
116


Table 3.13. Ubiquity and sample size of twenty-eight mammalian taxa in
eighteen sites. NISP is the total NISP per taxon for all sites summed.
Ubiquity is the number of sites in which remains of a taxon occur

Taxon NISP Ubiquity Taxon NISP Ubiquity
1 37 8 15 106 15
2 77 3 16 6 1
3 176 15 17 9 2
4 35 9 18 14 2
5 793 17 19 10 2
6 95 13 20 9 5
7 14 6 21 63 7
8 23 4 22 10 3
9 1,022 18 23 7 3
10 140 16 24 273 11
11 75 10 25 24 2
12 29 8 26 107 11
13 2,706 18 27 10,062 17
14 4 3 28 1,953 14


from a low of 4 to a high of 10,062 per taxon. Ubiquity ranges from one to eighteen.
The relationship between log NISP per taxon and log ubiquity per taxon is statistically
signi¬cant (r = 0.802, p < 0.0001). The relationship between the two is described by the
equation Y = 0.192X0.34 and is shown in Figure 3.8. Across these eighteen assemblages
ubiquity is strongly related to sample size measured as NISP. This means that if more
of each site with low NISP values had been excavated, it is likely that they would have
eventually produced not only more NISP but also more of the taxa documented in
nearby sites that they currently lack. Thus, to say that in the area and time range
sampled by these eighteen collections, some taxa were relatively ubiquitous (for
whatever reason) whereas other taxa were not very widespread and had low ubiquity
might be correct, but it might also be incorrect in the sense that ubiquity is a function
of sample size measured as NISP. Taxa that do not occur in many collections may be
nonubiquitous because an insuf¬cient amount of excavation has been done at some
sites and thus few of the remains of these less ubiquitous taxa were recovered.
But one might argue that taxa represented by a total NISP < 18 could not possibly
have a ubiquity of eighteen. The ubiquity of a taxon can be no greater than that
taxon™s NISP across all recovery contexts, and that mechanical truism may be
in¬‚uencing statistical results. If we omit all taxa in Table 3.13 with NISP < 18, the
correlation between log NISP and log Ubiquity for the remaining nineteen taxa is a bit
estimating taxonomic abundances: other methods 117




figure 3.8. Relationship between NISP and ubiquity of twenty-eight taxa in eighteen sites.
Data from Table 3.13.


weaker than when all twenty-eight taxa are included, but that correlation coef¬cient
is still signi¬cant (r = 0.67, p = 0.002). Thus it would be unwise to argue that more
ubiquitous taxa were “more important” than those that are less ubiquitous. In this
set of eighteen collections we cannot discount the possibility that ubiquitous taxa are
ubiquitous because excavations produced many specimens of each; nonubiquitous
taxa are not ubiquitous because relatively few specimens of each were recovered.
Those rarely represented taxa may not be very ubiquitous because they are rare on the
landscape, or they were rarely accumulated, or their remains were rarely preserved, or
rarely recovered. How to determine which of these possibilities holds in any given case
demands taphonomic analysis. Such analysis is oftentimes dif¬cult when remains are
few in number, which is of course the case when taxa are not ubiquitous.
In the case described in the preceding paragraph ubiquity was measured across
multiple sites, but ubiquity can also be measured across analytical units or strata or
features within a single site. In these cases, too, any measure of ubiquity is prone to be
larger with larger sample sizes (greater NISP values). This can be shown using two
of the multicomponent collections in the eighteen-site sample. Data for these two
collections are given in Table 3.14. In both sites the ubiquity of taxa is strongly related to
sample size. Site 45DO189 has seven analytical units and ¬fteen total mammalian taxa
(Lyman 1988). Ubiquity is signi¬cantly correlated with NISP (r = 0.662, p = 0.007).
Site 45OK2 has four analytical units and eighteen total mammalian taxa (Livingston
quantitative paleozoology
118


Table 3.14. Ubiquity and sample size of mammalian taxa across analytical units in
two sites.

45OK2: Ubiquity 45DO189: Ubiquity
(Nmax = 4) (Nmax = 7)
taxon NISP taxon NISP
1 6 2 1 1 1
2 7 3 2 6 4
3 6 2 3 86 6
4 27 3 4 14 5
5 9 2 5 1 1
6 2 1 6 13 3
7 1 1 7 4 3
8 110 4 8 10 2
9 14 4 9 6 4
10 272 4 10 1 1
11 7 3 11 1 1
12 6 1 12 2 2
13 2 2 13 251 7
14 1 1 14 5 2
15 16 4 15 14 6
16 7 4
17 2,021 4
18 51 3

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