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the relationship between the bone weight of a single individual pig and the weight
of muscle tissue of that individual, and the relationship between the bone weight of
a single individual and the total soft-tissue weight of an individual (muscle + fat +
hide) because he was unsure how completely the soft tissues of a pig might be used by
prehistoric consumers. He found that the relationships between both variable pairs
varied with the ontogenetic age of the pig; the ratio of bone weight to soft-tissue
weight increased as ontogenetic age increased.
I used the same data (Table 3.6) and expanded Casteel™s analysis to include another
variable pair “ the relationship of an individual™s bone weight and that individual™s
muscle + fat tissue weight. I replicated Casteel™s results for the two variable pairs he
examined, although my statistics are slightly different than his, likely as a result of my
use of a different computer program (although the negative sign for the calculated Y
intercept is not included in the published version of Casteel™s analysis). The statistical
relationships between bone weight per individual animal and the weight of various
categories of soft tissue are summarized in Table 3.7 and illustrated in Figure 3.2. The
relationship between bone weight and muscle weight, between bone weight and soft-
tissue weight, and between bone weight and soft tissue, regardless of the soft tissues
included, are all curvilinear. The relationship is described by the power-function
formula Y = aXb , where X is the bone weight per individual, Y is the soft-tissue
(however de¬ned) or complete carcass weight, a is the Y intercept, b is the slope of
the best-¬t regression line, and a and b are empirically determined. Regardless of
how soft tissue is de¬ned for the domestic pig data, the coef¬cient of determination
(r2 ) is greater than 0.99; more than 99 percent of the variation in soft-tissue weight
is accounted for by variation in bone weight (Table 3.7).
quantitative paleozoology
98


Table 3.7. Statistical summary of the relationship between bone weight (X)
and weight of various categories of soft-tissue (Y) for domestic pig (based on
data in Table 3.6)

Soft tissue Regression equation r p
Y = ’0.38(X)1.25
Musclea 0.999 < 0.0001
Y = ’0.47(X)1.35
Muscle + fata 0.997 < 0.0001
Y = ’0.66(X)1.39
Muscle + fat + hide 0.996 < 0.0001

a
also determined by Casteel (1978).


Table 3.7 and Figure 3.2 highlight the fact that the weight of the skeleton in an
individual is tightly related to the weight of the soft tissue of that individual. But the
relationship between the two variables is not constant; it is not linear. Thus were one
to develop a means to estimate biomass or usable meat from the weight of bone,
a single conversion factor would not provide accurate results. To produce accurate
results, one should empirically derive an equation in the form of a power function




figure 3.2. Relationship between bone weight per individual and soft-tissue weight in
domestic pig. The curves are best-¬t, second-order polynomials. Data from McMeekan
(1940); see Tables 3.6 and 3.7.
estimating taxonomic abundances: other methods 99


to account for the curvilinear (allometric) relationship between bone weight and
soft-tissue weight. But even with such an equation, various dif¬culties remain. For
example, what conversion value should be used to transform a measure of biomass
into a measure of usable meat, the actual variable zooarchaeologists who advocate
the weight method want to measure (e.g., Barrett 1993)? A different formula for
each taxon would control for intertaxonomic variation. What about intrataxonomic
variation? And there are several other slippery issues as well.
Many commentators have pointed out that preservational (diagenetic or post-
burial) conditions will alter the weight of bones, and thus the relationship between
archaeological bone weight and soft-tissue weight will be altered (Barrett 1993; Lyman
1979; Wing and Brown 1979). Casteel (1978) noted that empirically deriving an equa-
tion that describes the relationship between meat weight and bone weight of an
individual presumes that a collection of bones from a site represents a single (per-
haps impossibly) large individual. This is another way of saying that the amount
of meat associated with phalanges of an individual is not the same as the amount
associated with the scapulae or the femora of an individual. Jackson (1989:604) put
it this way: the weight method treats “all bone fragments of a given weight as if they
supported a similar amount of tissue regardless of the element from which they orig-
inated. . . . [The] formulae treat bone weight as if it came from a single individual.”
If a sample consists of more than a few specimens, it is likely that those specimens
represent more than one individual. Thus Chaplin (1971 ) recommended that a con-
version value be determined for each bone in the skeleton or for each portion of a
skeleton. Is that possible?
Chaplin™s concern, as well as the concern of many others who have commented on
the problem, is that the skeletal mass allometry equations used by zooarchaeologists
do not account for the fact that a single skeleton of deer may weigh the same as,
say, ¬fty deer metacarpals. But formulae such as those for domestic pigs (Table 3.7)
presume that one has weighed one or more skeletons, not piles of metacarpals, or
collections of selected skeletal elements from various individuals. Data on weights of
carcass portions and bones published by Binford (1978) show that Chaplin™s suggested
solution does not resolve all of the problems with the weight method. Binford™s data
are for two domestic sheep (Ovis aries); they are for a 6-month-old lamb and a 90-
month-old female (Table 3.8). The relationship between bone weight and gross weight
for each carcass portion for each individual is graphed in Figure 3.3. The statistical
relationships between the two sets of data are summarized in Table 3.9. The graph
(Figure 3.3) indicates that the relationship is steeper in the older sheep (slope = 1.063)
than in the younger individual (slope = 0.826); Casteel™s (1978) data for the pig might
prompt us to make similar predictions. The ratio of bone weight to biomass is greater
quantitative paleozoology
100


Table 3.8. Descriptive data on dry bone weight per anatomical portion and total
(soft-tissue + bone) weight per anatomical portion for domestic sheep. All weights are
grams. Weights for limbs are for one side only. Data from Binford (1978:16)

6 month old, 90 month old,
dry bone 6 month old, dry bone 90 month old,
Skeletal portion weight total weight weight total weight
Skull 152.40 317.52 294.82 938.05
Mandible 92.02 408.24 167.60 1,193.87
Atlas-axis 53.08 272.16 87.90 408.24
Cervical 73.40 725.76 137.40 1,088.64
Thoracic 91.60 637.27 288.58 1,758.20
Lumbar 69.68 315.29 205.35 871.29
Pelvis-sacrum 122.34 1,140.08 319.80 1,623.55
Ribs 121.90 1,360.80 373.04 1,995.84
Sternum 18.47 907.29 52.75 1,859.76
Scapula 29.50 556.80 75.10 844.76
Humerus 56.50 385.47 95.10 584.86
Radius-ulna 45.30 214.15 88.50 324.90
Metacarpal 32.10 86.81 51.50 135.08
Phalanges (front) 16.20 71.04 38.40 106.41
Femur 73.17 985.75 121.00 1,474.20
Tibia & tarsals 56.96 282.69 114.00 498.96
Metatarsal 51.50 140.61 59.49 149.69
Phalanges (rear) 16.20 55.65 38.40 99.79



in older than in younger individuals, apparently even across the skeleton. The point
scatters also suggest that the relationship between bone weight and gross weight is
not very tight regardless of the age of an individual; the coef¬cient of determination
(r 2 ) is < 0.6 for both. If these data are representative of the relationship between
bone weight and biomass, they are also representative of the relationship between
bone weight and weight of soft tissue. They suggest that intrataxonomic variation,
or individual variation in the relationship of the two variables, may be dif¬cult to
account for in any single formula for a taxon.
Consider how the variation shown in Figure 3.1 relates to that shown in Figure 3.3.
We are seeing a re¬‚ection of some of the same (individual or intrataxonomic) sources
of variation in both. It is precisely for this reason that Barrett (1993), the strongest
recent advocate of perfecting and using the weight method, must conclude that the
method at best produces ordinal scale data on biomass and usable meat, and may not
estimating taxonomic abundances: other methods 101


Table 3.9. Statistical summary of the relationship between bone weight (X)
and gross weight or biomass (Y) of skeletal portions of two domestic sheep
(based on data in Table 3.8)

r2
Sheep age Regression equation r p
Y = 1.109X0.826
6 months 0.593 0.350 0.0095
Y = 0.6X1.063
90 months 0.759 0.576 0.0003



even produce that scale of resolution. Barrett (1993:11) does not use these words, but
instead indicates that the method is perhaps best used to estimate “a range of meat
yield estimates for groups of excavated bone” and suggests that “meat yield estimates
can be graphed [with] error bars to reveal broad patterns in the archaeological
assemblage.” Thus he presents an exemplary range of meat yield values as follows:
mammals “ 345.31 to 441.5 kilograms; ¬sh “ 82.26 to 140.46 kilograms; and birds “
0.58 to 1.07 kilograms. Such data are clearly ordinal scale. In this case the ranges do
not overlap, but the discussion in Chapter 2 implies that biomass and usable meat




figure 3.3. Relationship between bone weight per skeletal portion and gross weight per
skeletal portion in 6-month-old domestic sheep and a 90-month-old domestic sheep. Simple
best-¬t regression lines are shown for reference. Data from Table 3.8.
quantitative paleozoology
102


or meat yield may not be even ordinal scale data. And based on discussions in this
chapter and in Chapter 2, it is likely that ranges of biomass per taxon may overlap,
making them nominal scale data.



Bone Weight

Can we use the weight of skeletal tissue as a fundamental measure of taxonomic
abundance? Uerpmann (1973) suggested using the weight method to derive meat
weight, then using a conversion factor to change meat weight to numbers of indi-
viduals. A procedure that is mathematically the reverse of that proposed by White
(1953a) is required to perform Uerpmann™s second conversion, and thus is subject to
all of the problems that attend White™s analytical protocol. And, the ¬rst conversion
must contend with all the problems with the weight method presented thus far. In
light of these facts, it is no surprise that no one has actually done what Uerpmann
suggested. What some individuals have done, however, is to use bone weight as a fun-
damental measure of taxonomic abundances (McClure 2004; Tuma 2004). That is,
bone weight per taxon is recorded and then interpreted as is, without being converted
to biomass or to usable meat. Does this procedure solve or circumvent problems that
attend NISP and MNI as measures of taxonomic abundances? It is easy to show that
bone weight per taxon has problems of its own.
First, as Barrett (1993:3) points out, this “method is attractively simple but it
requires an assumption that the bone weight to body weight ratios for different
[taxa] are virtually identical.” Bone weight might indicate which taxon represents
the most biomass (regardless of how much soft tissue is involved) but only if the ratio
of bone weight to body weight is the same across all taxa. But we know that different
taxa have different ratios (as do different individuals within each taxon). Thus, to use
a simple example, if one taxon™s average (to account for individual variation) ratio is
5 percent and another taxon™s average ratio is 10 percent, then 10 kilograms of bone
of each represent 200 kilograms of biomass for the ¬rst taxon and 100 kilograms of
biomass for the second taxon. Bone weight indicates that the two taxa are equally
abundant, but their biomass indicates that they are not.
Does bone weight provide information about taxonomic abundances in general
that is not provided by, say, NISP? An immediate objection that this could not
possibly be the case might involve noting that a bison (Bison bison) or a domestic
cow (Bos taurus) has more or less the same number of skeletal elements as a squirrel
(Spermophilus sp. or Sciurus sp.) or a mouse (Microtus sp. or Mus sp.), but the bones
that comprise the skeleton of the former two taxa are much larger than the bones
estimating taxonomic abundances: other methods 103


of the skeletons of the latter two taxa. A femur of a cow will weigh considerably
more than the femur of a mouse. And given the relationship between bone weight
and biomass or weight of soft tissue, a mouse femur cannot represent the same
biomass or the same amount of soft tissue as a cow femur. These observations do
not comprise a reason to reject the possibility that bone weight might duplicate the
taxonomic abundance data provided by NISP. Are NISP and bone weight related in
such a manner as to be redundant measures of taxonomic abundances?
To answer the question just posed, I determined the correlation between bone
weight and NISP of mammal remains in seventeen collections from North America,
South America, and the Near East (Table 3.10). These collections represent seven to
twenty-two taxa; some collections date to the historic period, others are prehistoric
in age. They were chosen because I had access to published reports describing them.
NISP and bone weight are signi¬cantly correlated (p ¤ 0.05) in fourteen of the
seventeen collections. In so far as these seventeen collections are representative of
all such data sets, they suggest that, with respect to variation in abundances of at
least mammalian taxa, bone weight is often redundant with NISP as a measure of
taxonomic abundance. It is beyond my scope here to explore in detail why these two
variables are often correlated.
A vocal advocate of using bone weight allometry as a measure of taxonomic abun-
dance has been Elizabeth Reitz (and colleagues) at the University of Georgia. Using
curated modern skeletons with associated live weight data, Reitz developed sev-
eral formulae of the power function form that allow one to convert archaeological
bone weight of general taxonomic categories such as mammals, birds, turtles, and
several categories of ¬sh into biomass (Reitz and Cordier 1983; Reitz et al. 1987).
These formulae were repeated and used many times during the 1980s and early 1990s
(various references in Table 3.10), and were repeated yet again in a zooarchaeology
text book (Reitz and Wing 1999) and in articles published in the third millennium
(Reitz 2003). That a plethora of intrataxonomic and intertaxonomic variations were
smoothed away by the use of a single formula in the general taxonomic category
went largely unremarked.
When advocated, the allometric formulae were characterized as “based on samples
drawn from known biological populations; the archaeological data [to which they
were applied] are considered samples of archaeological populations rather than of
individuals. This is the case even when original live weight is estimated for individu-
als” (Reitz et al. 1987:307). The key problem was also recognized: “Use of archaeolog-
ical bone weight as the independent value merely predicts the amount of body mass
that amount of bone could support as if the bone represented the skeletal mass of
a real animal” (Reitz and Cordier 1983:247). If a deer skeleton weighs 25 kilograms,
quantitative paleozoology
104


Table 3.10. Relationship between NISP and bone weight of mammalian taxa
in seventeen assemblages

N of
Assemblage taxa r p Reference
< 0.0001
Winslow 10 0.929 Landon (1996)
= 0.0065
Spencer“Pierce 10 0.791 Landon (1996)
= 0.0027
Paddy™s 7 0.927 Landon (1996)
= 0.0035
Feature F 8 0.884 Tuma (2004)
= 0.0004
Feature E 9 0.920 Tuma (2004)
< 0.0001
Three sites 11 0.963 McClure (2004)
< 0.0001
Hirbet“Ez Zeraqon 10 0.942 Dechert (1995)
< 0.0001
Tell Abu Sarbut 20 0.922 van Es (1995)
< 0.0001
Carthago 11 0.903 Weinstock (1995)
= 0.108
New Halos 7 0.659 Prummel (2003)
= 0.008
Washington, AR 7 0.884 Stewart-Abernathy
and Ruff (1989)
< 0.0001
SE Coast 14 0.896 Reitz and Honerkamp
(1983)
= 0.0058
Paloma 8 0.863 Reitz (1988)
< 0.0001
NW Company 10 0.966 Ewen (1986)
< 0.0001
Pirincay 22 0.767 Miller and Gill (1990)
= 0.0514
Mose 14 0.530 Reitz (1994)
= 0.08
Iroquois 8 0.651 Scott (2003)



then 25 kilograms of phalanges will suggest a biomass equivalent of one deer. Because
the bone-weight allometric equation is founded on individual animals, it produces
results that are not ratio scale measures of biomass when applied to archaeological
collections consisting of a few bones from each of several skeletons, and they may
not be ordinal scale.
Using the data in Table 3.8 ¬ve “collections” of 10 skeletal portions each were gen-
erated by randomly drawing individual skeletal portions and random assignment of
each portion to either the 6-month-old sheep or the 90-month-old sheep of Binford
(1978). Using the data in Table 3.8, the total bone weight and the gross weight of
each was summed for each of the ¬ve collections. Beginning with one collection,
another collection was successively added until ¬ve collections had been generated.
This produced ¬ve collections of different sizes (number of skeletal portions varied).
Finally, the general bone weight allometry formula for mammals generated by Reitz
estimating taxonomic abundances: other methods 105


Table 3.11. Results of applying the bone-weight allometry equation (Y = 1.12X0.9 ) of
Reitz and Cordier (1983) to ¬ve collections of domestic sheep bone randomly
generated from Table 3.8. All weights are grams

N of skeletal Allometry Actual biomass
Collection Bone weight portions biomass (from Table 3.8) Difference
1 837.07 10 5,623.4 6,169.8 546.4
2 2,103.93 20 12,882.5 14,454.8 1,572.3
3 3,279.75 30 19,054.6 22,560.8 3,506.2
4 4,008.04 40 22,908.7 27,357.9 4,449.2
5 4,810.76 50 26,915.3 31,938.8 5,023.5



and Cordier (1983) was used to estimate biomass for each of the ¬ve collections. That
formula is: Y = 1.12X 0.9 where Y is biomass, X is bone weight, 1.12 is the Y intercept,
and 0.9 is the slope. (Another way to present this equation that makes it mathemat-
ically easier to calculate by hand is: log Y = 1.12 + 0.9X.) Results of applying this
formula to the randomly generated collections of sheep bone are shown in Table 3.11
where it is clear that the bone-weight allometry formula consistently underestimates
biomass as measured by summing individual skeletal portions, and it does so with
increasing magnitude as bone weight increases. This occurs because the bone weight
allometry equation does not allow for intrataxonomic variation, nor does it account
for the fact that the equation is built as if archaeological bone weight concerns com-
plete skeletons, not various bones representing incomplete skeletons. And if that is
not enough to worry about, aggregation will in¬‚uence the results of applying the
bone-weight allometry equations because different aggregates will distribute bones
and thus bone weight differently across collections.
Biomass data determined by the skeletal mass allometry method are likely at best
ordinal scale for many reasons. What has not previously been noted is that the
taxonomic distribution of biomass data for faunal collections tends to look much
like that distribution for NISP and MNI data (Figures 2.13“2.16). The distributions
for two faunas described by Quitmyer and Reitz (2006) are shown in Figure 3.4. To
generate these ¬gures only data for vertebrate taxa (mammals, ¬sh, birds, reptiles)
identi¬ed to at least the genus level were used. The taxa represented by low biomass
values tend to tie or differ minimally in value whereas taxa represented by high
biomass values tend to differ in value by considerable amounts. As with NISP and
MNI data (see Chapter 2), taxa with low biomass amounts are likely not even ordinal
scale but instead nominal scale. Taxa with high biomass amounts may well be ordinal
quantitative paleozoology
106




figure 3.4. Frequency distributions of biomass per taxon in two sites (Cathead Creek and
Devil™s Walking Stick) in Florida State. Data from Quitmyer and Reitz (2006).




scale. Lest one think this distribution is a function of the multiple taxonomic groups
included in Figure 3.4, Figure 3.5 shows a similar distribution for the biomass of
mammals only in a collection described by Carder et al. (2004).
The most serious problems with bone weight allometry, then, are two. First,
the method smoothes intrataxonomic and intertaxonomic variations. As Needs-
Howarth (1995:94) correctly observed, “like average meat weight computations [of
Guthrie and White], this method cannot take into consideration differences in
[individual] condition.” Second, the bone weight allometry method is based on the
weight of complete individual skeletons, yet is applied to commingled not-necessarily
random accumulations of bones from multiple skeletons. Both of these problems are
estimating taxonomic abundances: other methods 107




100




figure 3.5. Frequency distributions of biomass per mammalian taxon in a site in Georgia
State. Data from Carder et al. (2004).




dealt with in a subtle way by the method™s advocates. Biomass amounts estimated
using the allometry formulae are said to be “hypothetical amounts” (Reitz and
Cordier 1983:247), to be “approximate” measures of abundance (Reitz and Cordier
1983:248), or to be “estimates” (Reitz et al. 1987:307). These are other ways to say that
biomass estimates are, at best, ordinal scale.
The argument that bone weight allometry formulae should be used because they
provide abundance data in a “morphological nutritional format” (Reitz and Cordier
1983:248) is weak. The bone weight allometry formulae provide at best ordinal scale
data on taxonomic abundance that may be redundant with taxonomic abundance
measures based on NISP. At least, that seems to be the case with the class Mammalia. It
may not be the case when bone weights for other classes of vertebrates or invertebrates
are added to the mix. But it is likely that allometry formulae for birds, ¬nny ¬sh,
shell¬sh, reptiles, amphibians, and other categories of animals will be subject to the
same kinds of problems as are described in Tables 3.8 and 3.11 .
Advocates of the weight method seem to be aware of the fact that bone weight
allometry, although based on biological and physiological principles, and although
mathematically elegant, produces at best ordinal scale data. They indicate that
“It seems unwise to generate allometric equations for each sex or for various
[ontogenetic, seasonal] weight conditions, even if a data base could be acquired; to
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



1984). Here, ubiquity is also signi¬cantly correlated with NISP (r = 0.709, p = 0.001).
The relationship of sample size and ubiquity across analytical units at 45DO189
is illustrated in Figure 3.9; that relationship as it is manifest at 45OK2 is shown in
Figure 3.10. Again, some taxa may indeed be more ubiquitous than others in the sense
of being found associated with more spatiotemporal analytical units. But it is dif¬cult
to make this argument on empirical grounds because the available data suggest that
had more of each analytical unit with low NISP values been excavated, NISP would
have been larger, more taxa would have been found in those units, and the ubiquity
of rarely represented taxa (those with low NISP values) would have increased.
Dean (2005a:416“417) cited an ethnobotany text as indicating that ubiquity mea-
sures minimize in¬‚uences of “random variations [in] NISP counts” when seeking
to measure taxonomic abundances, and those measures also allow comparisons of
assemblages from different habitats, assemblages collected using different recovery
procedures, and assemblages subject to varied preservation. To be sure, sampling
different habitats will in¬‚uence NISP, as will differential preservation and recovery.
But in so far as ubiquity is a function of NISP “ and the examples given above suggest
estimating taxonomic abundances: other methods 119




figure 3.9. Relationship between NISP and ubiquity of ¬fteen taxa in seven analytical
units in site 45DO189. Data from Table 3.14.


that ubiquity will often be a function of NISP “ differential sampling intensity, dif-
ferential preservation, and differential recovery will also in¬‚uence ubiquity because
they in¬‚uence NISP (see also Kadane 1988).
The preceding is not to say that ubiquity measures are valueless. These could be
quite useful if the in¬‚uences of sample size could be controlled. If, say, the NISP values
of several taxa are very similar (say within 5 percent of each other), and one taxon
has a high ubiquity value and another has a low value, then it would be reasonable
to suspect that some mechanism or agent of accumulation had dispersed widely the
remains of the former taxon and perhaps that same mechanism or agent (or another
one) had concentrated (or failed to disperse) the remains of the latter taxon. Given
this possibility, it is dif¬cult to understand why ubiquity has not been measured more
frequently.



M A TCH I N G A N D P A I R I N G


Recall the de¬nitions of MNI provided by Stock, Howard, Adams, and the ornithol-
ogists interested in raptor diets (and see Table 2.4). White (1953a:397) de¬ned MNI
quantitative paleozoology
120




figure 3.10. Relationship between NISP and ubiquity of eighteen taxa in four analytical
units in site 45OK2. Data from Table 3.14.


this way: The “number of individuals represented by the excavation sample [is deter-
mined as follows.] Separate the most abundant element of the species found . . . into
right and left components and use the greater number as the unit of calculation”
(see also White 1953b:61). White went on to note that this procedure would produce
a “slight error on the conservative side because, without the expenditure of a great
deal of time with small returns, we cannot be sure all of the lefts match all of the
rights” (1953a:397).
What White was getting at with the idea of “matching” is this. Recall that when
faced with three left and two right scapulae of a taxon, the number of individuals is
a minimum because at least three individuals had to contribute these bones. Perhaps
as many as ¬ve individuals contributed the scapulae, but unless we can show that
the two rights do not “match” or bilaterally pair with any of the three left scapulae,
then we must conclude that the two rights are from two of the three individuals
represented by the lefts. How do we make a determination of whether any of the
lefts match any of the rights? Usually bilaterally paired bones are compared, when
these are elements with left and right members, such as scapulae, humeri, tibiae, and
so on. Skulls are not paired bones, but mandibles are; vertebrae are not, but ribs
estimating taxonomic abundances: other methods 121


are, although ribs are seldom matched because they tend to not be taxonomically
diagnostic beyond the family level (if that).
To determine if two potentially paired bones indeed “match” or are bilaterally
paired, they must be compared under the assumption of bilateral symmetry. The
two members of the possible pair (obviously from the same species) are compared in
terms of their size, their ontogenetic (growth) development, the sex of the individual
represented, and the like (Chaplin 1971 :70). Because vertebrates, such as mammals
and birds, are more-or-less bilaterally symmetrical, the left bone should closely match
the right bone in terms of all characteristics if they are from the same individual.
White thought that matching would gain little, but provided little data to this effect.
It is legitimate to ask, then: What does identifying bilaterally paired bones gain in
terms of measures of taxonomic abundance? In fact, can bilateral pairs be accurately
identi¬ed? To answer these questions, the basics of the matching procedure and how
it in¬‚uences measures of taxonomic abundance are reviewed ¬rst. Then a study of
how accurate identi¬cations of bilateral mates might be is presented.



More Pairs Means Fewer Individuals

In his seminal example, Chaplin (1971 :71 “75) described a ¬ctional example of how
identifying pairs would provide a different number of individuals than a Whitean
MNI. He did not reference White, but Chaplin (1971 :70) did note that a Whitean
MNI “ one de¬ned by the most common skeletal element or part “ would constitute
a “not necessarily very satisfactory estimate of the true minimum.” If one had, say,
eleven distal left humeri and ¬ve proximal right humeri, and none of these specimens
overlapped anatomically, then the Whitean MNI would be eleven but Chaplin™s point
was that there might actually be twelve, thirteen, fourteen, ¬fteen, or even sixteen
individuals represented if some of the proximal right specimens were not from the
same animals as the left distal specimens. Thus he focused on identifying those
specimens without matches; matches would not increase the MNI, but bones without
matches would increase that number because they would be added to the number
of pairs or matches. Thus, more pairs mean fewer individuals and fewer pairs mean
more individuals. Left specimens without a mate and right specimens without a
mate are added to the number of pairs as independent representatives of individual
organisms. The more pairs of left and right elements, the fewer independent left and
right elements added to the total. White™s method of determining MNI assumes all
lefts pair up with a right element, and all rights pair up with a left element. Chaplin
was unwilling to make this assumption.
quantitative paleozoology
122


Chaplin™s (1971 ) example of how matching in¬‚uences measures of taxonomic
abundance involved domestic sheep (Ovis aries) tibiae. He used ¬ctional data, but
those data illustrate the issues involved nicely. The NISP of left specimens was thirteen;
some specimens were anatomically complete left tibiae, some represented various
portions of left tibiae. The (minimum) number of skeletal elements represented
(based on age, sex, size) was ten, which also represented the MNI for left tibiae. The
NISP of right tibia specimens in Chaplin™s example was seventeen; these represented
¬fteen elements and ¬fteen MNI. Based on age (epiphyseal fusion) and size (see
below), Chaplin identi¬ed bilateral pairs of left and right tibiae. He derived a formula
for calculating what he called the “grand minimum total” or GMT of individuals.
This formula is:

GMT = (C t /2) + D t ,

where C t is the total number of skeletal elements (not specimens) making up bilater-
ally matched pairs and D t is the total number of elements (not specimens) without
bilateral mates. In his example, Chaplin identi¬ed eight pairs comprising sixteen
elements (eight lefts and eight rights), and had two unmatched lefts and seven
unmatched rights. Thus, C t = 16, Dt = 9, and GMT = (16/2) + 9 = 8 + 9 = 17
individuals. Thus, in this example, the Whitean “most common element” MNI was
¬fteen (based on right tibiae), but matching bilateral elements indicated that because
some elements lacked their bilateral mate and represented independent organisms,
a more accurate (but still a minimum) tally of individuals was seventeen.
A Whitean “most common element” MNI assumes that each left humerus, say, has
a bilateral mate among the right humeri, so only the lefts, or only the rights, but not
both lefts and rights contribute to the MNI tally (see Table 2.5). Chaplin™s GMT can
produce larger tallies of individuals because both left humeri and right humeri can
contribute to the tally. Matching establishes that some left humeri are independent
(come from a different individual organism) of all right humeri, and some right
humeri are independent of all left humeri. Therefore, two “most common elements” “
left and right humeri “ are identi¬ed rather than either left or right humeri only.
Calculating GMT for a collection will give a larger number of individuals the fewer
the identi¬ed pairs. In Chaplin™s example, if we reduce the number of pairs to 7
(C t = 14), that increases D t to 11, so GMT = (14/2) + 11 = 7 + 11 = 18, simply
because we have added one more independent element (another left, or right, tibia
in this example) to the tally. This might make GMT attractive, but do not be fooled
by larger numbers. To be sure, GMT can produce larger numbers of individuals than
the Whitean “most common element” MNI. But does that gain us anything with
respect to measuring taxonomic abundances?
estimating taxonomic abundances: other methods 123


First, the absence of pairs means that MNI = NISP. GMT provides measures of
taxonomic abundance between NISP and Whitean MNI values. In Chaplin™s example,
NISP = 30, GMT = 17, and (Whitean) MNI = 15. Given this, and arguments about
the statistical relationship between MNI and NISP, GMT will be a function of NISP.
Taxonomic abundances based on GMT will also at best be ordinal scale. Think of
GMT as simply a different way to aggregate faunal remains to derive MNI values.
GMT values will depend heavily on aggregation, just as MNI does. This is so because
it is unlikely that one would seek to identify bilateral pairs (or a lack thereof) among
assemblages of tibiae from different strata deposited at different times (unless one
was interested in postdepositional disturbance processes that resulted in inter-strata
movement of specimens). Rather one would choose to seek a bilateral pair among
skeletal elements that potentially derive from the same animal. Thus, how one de¬nes
aggregates plagues GMT just as it does MNI.
Another problem with determination of GMT concerns identifying bilateral pairs.
Because this problem af¬‚icts all measures of taxonomic abundance that use bilateral
pairs in the calculation, it is addressed later in this chapter. The bottom line to
Chaplin™s GMT should be clear. Although GMT tries to make quantitative use of
independent left and right skeletal elements, it is plagued by many of the same
dif¬culties as Whitean MNI values. That it produces data with no more quantitative
resolution or validity than NISP with respect to measures of taxonomic abundances
should cause one to pause before calculating GMT, if it is calculated at all.



The Lincoln“Petersen Index

Chaplin™s (1971 ) GMT is not the only quantitative procedure meant to measure
taxonomic abundances that uses bilateral pair data (e.g., Krantz 1968; Lie 1980, 1983;
Wild and Nichol 1983a, 1983b; Winder 1991 ). A couple of these other techniques
have undergone critical evaluation (Allen and Guy 1984; Bokonyi 1970; Casteel 1977;
During 1986; Fieller and Turner 1982; Gautier 1984; Horton 1984), and are seldom used
these days. They are not considered further. But there is one method that requires
comment because it has several supporters, it has been suggested at least twice by
independent workers (Allen and Guy 1984; Fieller and Turner 1982), and it might
well be suggested yet again given that versions of it are used by wildlife biologists
today (e.g., Amstrup et al. 2006; Hopkins and Kennedy 2004; Slade and Blair 2000).
More importantly, biological anthropologists have recently suggested it is useful for
estimating the number of individual humans in commingled assemblages of remains
(Adams and Konigsberg 2004).
quantitative paleozoology
124


The most frequently advocated method of using identi¬ed bilateral pairs in the
service of measuring taxonomic abundances is analogous to (and in fact derived
from) a procedure used by wildlife biologists to estimate taxonomic abundances.
In wildlife biology, it is known as “capture“recapture analysis,” where a sample of
animals is captured, tallied, and each captured individual (n1 ) is marked (m1 ) and
released (Nichols [1992] provides a good introduction). Then a second sample of
animals (n2 ) is captured. The number of previously marked (m1 ) individuals that
are recaptured (m2 ) and the number of unmarked (new) individuals (n2 ) in the
second sample are tallied. These values “ n1 , n2 , m1 , m2 “ are used to estimate the size
of the population from which the two samples were drawn. The quantitative measure
is usually referred to as the Petersen index, and less often as the Lincoln index (Fieller
and Turner 1982; Turner 1980, 1983); it is here referred to as the Lincoln“Petersen
index. Several paleozoologists ¬nd this index to be superior to Whitean MNI values
and also superior to Chaplin™s GMT values (e.g., Allen and Guy 1984; Fieller and
Turner 1982; Turner 1980, 1983; Turner and Fieller 1985; Winder 1991 ).
In the Lincoln“Petersen index, n1 = m1 . After release of the marked individuals
comprising the ¬rst sample, the proportion (P) of marked individuals in the popu-
lation can be symbolized as n1 /Y = P or m1 /Y = P, where Y is the population size.
What we of course do not know but seek to estimate is Y. So, we convert m1 /Y =
P ¬rst to m1 = PY (multiply both sides of the equals sign by Y), then convert the latter
to m1 /P = Y (divide both sides of the equals sign by P). The Lincoln“Petersen index
assumes that the proportion of marked individuals in the second sample effectively
estimates the proportion of marked individuals in the population, or P = (m2 /n2 ).
Substituting (m2 /n2 ) for P into Y = m1 /P, the result is

Y = m1 /(m2 /n2 ).

Because division by a fraction is equivalent to multiplying by the reciprocal of that
fraction,

Y = m1 n2 /m2 .

And because m1 = n1 , the preceding equation can be rewritten as

Y = n1 n2 /m2 .

Either of the last two formulae provides an estimate of the size of the population
from which the individuals comprising the two samples (n1 and n2 ) were drawn. The
reasoning is illustrated in Figure 3.11 .
Zooarchaeologists who advocate use of the Lincoln“Petersen index for estimating
taxonomic abundances observe that bilaterally paired skeletal elements, such as left
estimating taxonomic abundances: other methods 125




figure 3.11. A model of how the Lincoln“Petersen index is calculated. Square on the left is
the population (twenty individuals) divided into four subpopulations (a“d). Square on the
right illustrates the captured and marked ¬rst sample (n1 or m1 ; shaded), and the second
sample (n2 ; cross-hatched) comprising some marked individuals from the ¬rst sample (cell
b = m2 ) and individuals captured for the ¬rst time (cell d).


and right femora, can be used as follows. The lefts can be considered one sample (say,
n1 ), and the rights can be considered the other sample (say, n2 ). Identifying bilateral
pairs of left and right elements is analogous to ¬nding a marked individual in the
second sample. If left elements are treated as the ¬rst sample, L = n1 ; if right elements
are treated as the second sample, R = n2 ; and if the number of paired bones is treated
as the number of marked recaptures, m2 = number of bilateral pairs, then we can
substitute these symbols into the Lincoln“Petersen index to estimate the number
of individuals in the population from which the bones came. The formula can be
written as

LPind = L R/m2 ,

where LPind is the estimated number of individuals given by the Lincoln“Petersen
index, L is the number of left elements, R is the number of right elements, and m2
is the number of bilateral pairs. In wildlife biology, by convention, if no pairs are
found, LPind is estimated as LPind = (n1 + 1)(n2 + 1). And by convention, LPind is
rounded up to the nearest whole number.
LPind provides an estimate of taxonomic abundance that is greater than MNI and
GMT. The calculated value of LPind for a taxon in any given assemblage depends on
the NISP for that taxon and also on the number of bilateral pairs of skeletal elements
of that taxon regardless of NISP. In the ¬ctional data in Table 3.15, for the sake of
simplicity, each specimen is an anatomically complete skeletal element. As NISP
(= L + R) per row increases in Table 3.15, if the number of pairs (m2 ) remains
quantitative paleozoology
126


Table 3.15. Fictional data illustrating in¬‚uences of NISP and
the number of pairs on the Lincoln“Petersen index (LPind )

NISP Left (n1 ) Right (n2 ) Pairs (m2 ) LPind
20 10 10 2 50
20 10 10 3 34
20 10 10 4 25
20 10 10 5 20
20 10 10 6 17
20 10 10 7 15
20 10 10 8 13
40 20 20 3 134
60 30 30 3 300
80 40 40 3 533
100 50 50 3 834



stable, then the associated LPind increases. As NISP increases from 20, to 40, to 60,
to 80, to 100, if m2 = 3, then LPind increases from 34, to, 134, to 300, to 533, to 834,
respectively. And, if the NISP per row remains stable but m2 increases, then LPind
decreases. Consider those rows in which NISP = 20. As m2 increases from 2 to
8 by increments of 1, LPind decreases from 50, to 34, to 25, to 20, to 17, to 15, to 13.
Increase in NISP causes the estimated number of individuals to increase (all else [m2 ]
equal); increase in the number of pairs causes the estimated number of individuals
to decrease (all else [NISP] equal) until all bones are paired in which case m2 = LPind .
Fieller and Turner (1982) identify several properties of LPind that they argue are
bene¬cial to estimates of taxonomic abundance. One is that con¬dence intervals
can be calculated for any value; as they put it, “it is possible to specify a range of
plausible values for the total population size that are ˜reasonably™ consistent with the
observed proportion of tagged animals” or paired bones (Fieller and Turner 1982:53).
Calculation of both LPind and its associated con¬dence interval for a taxon rests on
several assumptions that, if violated, can cause the estimate to be far off the mark.
For example, the capture“recapture-based Lincoln“Petersen index assumes that in
the time between the release of marked individuals (n1 = m1 ) and the collection
of the second sample (n2 ), the marked individuals will be randomly mixed into the
population. That is, it is assumed that the probability of drawing a marked individual
in n2 will not be in¬‚uenced by the fact that that marked individual was also a part
of the ¬rst sample or n1 . Despite more than 25 years of detailed ethnoarchaeological
studies of faunal remains, only a small bit of that research has focused on the spatial
estimating taxonomic abundances: other methods 127


distribution of those remains (e.g., Bartram et al. 1991 ), and only a small fraction of
that research has focused on matching (e.g., Waguespack 2002). We do not yet know
that the requisite assumption is valid, but the limited available data suggest that it
will not always be. Faunal remains are seldom randomly distributed.
Some suggest the bene¬t of LPind is that it “accounts for random data loss” (Adams
and Konigsberg 2004:140). In taphonomic terms, whether or not a left humerus, say, is
accumulated or preserved should not in¬‚uence the accumulation and preservation of
its bilateral (right) mate. Fieller and Turner (1982) argue that calculation of multiple
LPind values and their respective con¬dence intervals based on different skeletal
elements “ humeri, radii, femora, and so on “ should produce similar estimates of a
taxon™s abundance if the assumptions requisite to its calculation are not violated. The
only thing these similar values indicate is that the included paired skeletal elements
have spatial distributions and preservation potentials suf¬ciently similar that each
provides a similar LPind value. Whether left and right femora are randomly distributed
relative to each other and also relative to both left and right humeri is a separate
question. This distinction is con¬rmed by Fieller and Turner™s (1982:55) suggestion
that dissimilarity in LPind values for different elements reveals something about
“differential deposition [that is] of considerable interest.” Do not confuse deposition
in site sediments with deposition in the area excavated. We do not need to calculate
LPind values to determine that the parts of skeletons are differentially represented,
whether due to varied deposition or preservation. Does LPind provide something not
provided by other measures of taxonomic abundances?
Fieller and Turner (1982:54) argue that LPind is the only quantitative unit that
provides an “estimation of the original killed population size.” According to Fieller
and Turner (1982:51), MNI (of either the Whitean most common element type, or
Chaplin™s GMT type) provides a “simple count” of the number of individuals nec-
essary to account for the bones on the lab table. They argue that LPind , in contrast,
provides an estimate of the original killed population because it takes into account
“missing material” and thus it is a “conventional statistical estimate” (Fieller and
Turner 1982:51). Ringrose (1993:129) agrees that the Lincoln“Peterson index provides
estimates of taxonomic abundances within the “death assemblage.” And Adams and
Konigsberg (2004:138) seem to agree but say the method “estimates the original num-
ber of individuals represented by the osteological assemblage” (emphasis in original).
But consider whether the population of twenty individuals shown in Figure 3.11 com-
prises the biocoenose, the thanatocoenose, or the taphocoenose. Recall Figure 2.1 ,
where the differences between a biocoenose (living population on the landscape),
a thanatocoenose (population of dead individuals, or killed population), a tapho-
coenose (what is accumulated, deposited, and preserved in a site), and an identi¬ed
quantitative paleozoology
128


assemblage (what was recovered, identi¬ed, and reported) are shown graphically.
Fieller and Turner (1982) argue that the thanatocoenose from which the identi¬ed
assemblage is derived is the target variable. They suggest that if MNI or GMT is used
the measured variable constitutes the identi¬ed assemblage and if LPind is used then
the estimated variable is the thanatocoenose.
In response to Fieller and Turner™s (1982; see also Turner 1983) arguments regard-
ing measured and target variables, and their attendant advocacy of the Lincoln“
Petersen index, Grayson (1984:88) pointed out that “an unmatched bone whose part-
ner has simply not been collected has a very different meaning from an unmatched
bone whose partner has disappeared.” Winder (1991 :126) implied the “very differ-
ent meaning” was insigni¬cant because both the failure to recover a bone and the
lack of preservation of a bone merely concerned “classical sampling theory.” But,
Turner (1983:319) himself contradicts this when he points out that “if 100 animals
were killed, 60 whole carcasses removed from the site and only a random sample
of the bones from the remaining 40 animals deposited, then estimates based on the
excavated sample can only refer to the 40 individuals which in this case constitute the
killed population.” How can this situation be mathematically different from a case
in which 100 animals are deposited in a site but bones of only forty animals preserve
and are sampled? How can Turner™s example, or the immediately preceding one, be
mathematically different from a case in which 100 animals are deposited, but bones
of only forty are sampled?
There are no mathematical differences between the three possibilities. This is so
because if the drawn sample consists of sixty bones (thirty-¬ve lefts, twenty-¬ve
rights) drawn randomly from forty (out of 100) animals with skeletons compris-
ing only one bilateral pair, and there are twenty pairs, the LPind = 44 regardless of
anything else. Certainly those forty-four individuals originated in the biocoenose,
passed through the thanatocoenose ¬lter, then through the taphocoenose ¬lter, and
¬nally through the ¬lters of recovery, analysis, identi¬cation, and pair matching.
Which of those “populations” do those forty-four individuals estimate the size of?
That is the key question. Perhaps we do not need an answer for one simple reason.
As Fieller and Turner (1982:57) correctly emphasize, “fundamental to the [Lincoln“
Petersen] method is the ability to determine the precise number of matches in the
assemblage of skeletal parts considered. Omission of true matches in¬‚ates the esti-
mate [and] inclusion of false matches has the opposite effect” (see Table 3.15). This,
then, comprises another requisite assumption “ that analysts can accurately identify
bilateral pairs. It is dif¬cult to determine if this assumption is warranted because few
published tests of it exist. It is necessary, then, to consider the validity with which
bilateral pairs might be identi¬ed. If they cannot be consistently validly identi¬ed,
estimating taxonomic abundances: other methods 129


then any use of the Lincoln“Petersen index (or any other use of what are thought to
be bilaterally paired skeletal elements) is likely invalid.



Identifying Bilateral Pairs

Krantz (1968:287) noted early on that “in experienced hands there should be little
doubt as to which mandibles [or any other bilaterally paired elements] pair off and
which do not.” Twenty years later, Todd (1987:180) provided a detailed statement on
the procedure for identifying bilateral pairs:

Initial estimates of possible anatomical re¬ts can be based on metric attributes of the
elements. In the case of bilateral re¬ts, potential candidates for pairs can be further
examined visually. Familiarity with elements from individual carcasses allows for the
recognition of attributes that are individually distinctive and bilaterally uniform. The
patterns of muscle attachment shape and prominence, synovial fovea shape and depth,
and the proportions of components of articular surfaces within paired elements in the
[animal] carcass create an individually distinctive “¬nger print” for element mates.
Bilateral mates are usually mirror images of each other in these attributes.

Two problems accompany anatomical matching. First, matching takes a consid-
erable amount of time (Adams and Konigsberg 2004; White 1953a); more time is
required as the size of the collection (and thus the number of possible pairs) increases.
The other problem is more serious. The analyst can determine the sex of the individ-
ual represented by paired bones in a mammal skeleton from a very limited number
of skeletal elements (innominates, frontals of some antler-bearing ungulates), unless
the taxon under consideration is sexually dimorphic. Exacerbating the dif¬culty of
matching is the fact that the degree to which paired bones (and teeth) display the
same ontogenetic stage simultaneously is unclear. Thus for illustrative purposes the
focus here is bone size. This criterion is used by virtually all who have identi¬ed
bilaterally paired bones (e.g., Allen and Guy 1984; Chase and Hagaman 1987; Enloe
2003a, 2003b; Enloe and David 1992; Fieller and Turner 1982; Morlan 1983; Nichol and
Creak 1979; Todd 1987; Todd and Frison 1992; Turner 1983; Wild and Nichol 1983b).
Chaplin (1971 :74) provides an early example of a matching procedure based on
bone size. He indicates that left and right distal tibiae of sheep (Ovis aries) can be
identi¬ed as bilateral pairs from the same individual if they are identical in “maximum
width,” or if they are within ¤ 0.3 mm of each other in maximum width, but lefts
and rights are not pairs if their maximum widths differ by ≥ 0.4 mm. How he
established the 0.3 vs. 0.4 mm maximum width is not speci¬ed, but it introduces the
quantitative paleozoology
130


matching problem. Identifying bilaterally paired bones in paleozoological collections
rests on the assumption that left and right skeletal elements from the same organism
will be symmetrical. Bones (and teeth) are, however, typically asymmetrical to some
degree. Indeed, temporally ¬‚uctuating asymmetry has in the past two or three decades
become a very important research topic in biology (e.g., Gangestad and Thornhill
1998; Palmer 1986, 1994, 1996; Palmer and Strobeck 1986; Pankakoski 1985). To identify
bilateral pairs among a commingled set of left and right elements from multiple
individuals of a taxon demands that we answer the question “How symmetrical is
symmetrical enough to conclude a left and right humerus (for example) are from the
same individual” (Lyman 2006a)? Answering that question involves determining a
“tolerance” or the maximum allowable asymmetry between bilaterally paired bones
(Nichol and Creak 1979). Determination of the tolerance rests on study of known
pairs.
Adams and Konigsberg (2004) performed a “test for the accuracy of pair-matching”
by choosing skeletons of ¬fteen humans recovered from an early historic burial
ground associated with an archaeological village. Based on morphological indica-
tors such as “robusticity, muscle markings, epiphyseal shape, bilateral expression of
periosteal reaction, and general symmetry” (Adams and Konigsberg 2004:145), they
successfully identi¬ed all pairs of femora, all pairs of tibiae, and all but one pair of
humeri. But they also suggested that the error rate might increase were the sample
size to increase because large samples would obscure between-individual variation
(Adams and Konigsberg 2004:146). As sample size increases (as the number of indi-
viduals increases), the degree of discontinuity between individuals will decrease such
that one individual will, in a sense, blend into another individual. This will occur
with either morphological traits or metric (size) traits.
The bivariate scatterplot in Figure 3.12 shows two measurements of paired distal
humeri from forty-eight museum skeletons of deer. Both white-tailed deer (O. vir-
ginianus, N = 17 pairs) and mule deer (O. hemionus, N = 30 pairs) are included;
the forty-eighth pair of distal humeri is from a hybrid of the two species. Both
species are represented in many paleozoological collections in western North America
(Livingston 1987; Lyman 2006b) and their remains can occasionally be distinguished
based on morphological criteria (Jacobson 2003, 2004); the two species cannot be
distinguished on the basis of the size of the distal humerus. The two measurements
taken on the distal humeri were the anterior breadth of the distal trochlea (DBt) and
the minimum (antero-posterior) diameter of the (latero-medial) center of the distal
trochlea (MNd). Use of two measurements rather than one should make any effort to
identify bilateral mates more accurate because specimens must be symmetrical in
two dimensions rather than one.
estimating taxonomic abundances: other methods 131




figure 3.12. Latero-medial width of the distal condyle and minimum antero-posterior
diameter of the middle groove of the distal condyle of forty-eight pairs of left and right
distal humeri of Odocoileus virginianus and Odocoileus hemionus. Try to determine which
left element is the bilateral match of which right element.



Conceive the difference between the left and right DBt as de¬ning the length of
one side of the right angle of a right triangle (= a in Figure 3.13), and the absolute
difference between the left and right MNd as de¬ning the length of the other side
of the right angle of the right triangle (= b in Figure 3.13). Then, the Pythagorean
theorem (a2 + b2 = c2 ) can be used to ¬nd how asymmetrical the distal humeri are in
terms of the two measurements. If the left and right distal humeri were perfectly sym-
metrical, then the hypotenuse (c-value) of the right triangle would be zero because
a = 0 and b = 0. None of the distal humeri pairs include specimens that are perfectly
symmetrical; the hypotenuse length or c-value of the triangle de¬ned by the left
and right specimens of each pair > 0.0. There is no statistically signi¬cant difference
between the c-values displayed by pairs of distal humeri of the two deer species
(O. virginianus, 0.753 ± 0.81 ; O. hemionus, 0.467 ± 0.282; Student™s t = 1.771 ;
p > 0.08), so the mean of all forty-seven, plus the hybrid (forty-eighth specimen),
was determined; the average c-value = 0.561 ± 0.541. A tolerance level one might
adopt is a c-value ¤ 0.561 ; any set of one left and one right distal humerus of deer the
DBt and MNd measurements of which de¬ned a c-value ¤ 0.561 would be identi¬ed
as a bilateral pair.
quantitative paleozoology
132




figure 3.13. A model of how two dimensions of a bone can be used to determine degree
of (a)symmetry between bilaterally paired left and right elements. Upper, the Pythagorean
theorem describing how the lengths of the three sides of a right triangle are related; lower, a
model of how two measurements of a skeletal part considered together de¬ne a right triangle.
The length of the hypotenuse (c-value in the text) is a measure of how (a)symmetrical two
specimens are; specimens L and R are more symmetrical than specimens l and r.


Were you to try to identify bilateral pairs of one left distal humerus and one
right distal humerus using the tolerance level just identi¬ed, you might get some
of the pairs correct. But you likely could not match them all because of the chosen
tolerance level (some pairs would have c-values > 0.561), and of those that you did
match, some would likely represent incorrectly identi¬ed pairs. With respect to the
latter, consider Figure 3.12 again. Assuming we did not know which lefts went with
which rights in this ¬gure, use of the c-value of 0.561 to identify pairs in this data
set is dif¬cult if not impossible because of the large number of specimens. Earlier
analysts seem to have recognized this problem, although their wording was inexplicit
(e.g., Uerpmann 1973:311). Later commentators were more explicit. Nichol and Wild
(1984:36“37) noted that “it is much harder to identify the extra unmatchable elements
in a collection of bones from a larger number of animals of a species than it is in a
smaller collection. For example, if there are 100 lefts and 100 rights of a bone, it will
be rather dif¬cult to produce an estimate of MNI much greater than 100, whether
estimating taxonomic abundances: other methods 133


100 or 200 animals are represented, while it may be very easy to see that a single left
and a single right come from different individuals.”
The blizzard of points in Figure 3.12 comprising both left and right specimens com-
prises the problem. Within the center of the distribution it is effectively impossible to
determine which lefts go with which rights, and in a paleozoological sample approxi-
mating this size it would be impossible to identify true pairs and to ¬nd truly unpaired
specimens. Only at the peripheries of this point scatter do we ¬nd individual left ele-
ments without multiple possible right mates and individual right elements without
multiple possible left mates. Exacerbating the problem are the facts that populations
of deer killed and deposited in many sites (= thanatocoenose) likely represent sev-
eral dozen individuals, yet archaeologists generally collect only a sample of those
remains “ perhaps as little as 10 percent or even less “ the Whitean MNI of the
population (= thanatocoenose) might be 6“10. This is in part why the Lincoln“
Petersen index seems so attractive “ the manner in which it is calculated explicitly
acknowledges that the materials at hand are a sample of a population (though which
population in Figure 2.1 is unclear). But Figure 3.12 indicates that even were one to
use the tolerance level or c-value of 0.561 for distal humeri based on the model in
Figure 3.13, it is likely that false pairs would be identi¬ed. A more conservative c-value,
such as, say, 0.25, would overlook many true pairs and still result in the identi¬cation
of some false pairs.
Perhaps bilateral pairs could be identi¬ed using morphological criteria such as the
size and rugosity of muscle scars and other traits, but deciding which left elements to
compare with which right elements likely would begin with similarly sized specimens.
Similarly, it might be possible to identify bilateral pairs in samples of fewer than a
dozen lefts and fewer than a dozen rights, but if these specimens comprise but a
sample of the population (and it is likely they will for one or both of two reasons “
only part of the population was recovered because of sampling and recovery, or only
part of the population was recovered because of differential preservation), then who
is to say that the population would not approximate that in Figure 3.12 (see Lyman
2006a for a real example).
In light of this discussion of distal humeri and a similar analysis of deer astragali
discussed elsewhere (Lyman 2006a), the assumption that analysts can accurately
identify bilateral pairs required of quantitative units, such as the Lincoln“Petersen,
index is unwarranted. And there is yet another seldom acknowledged dif¬culty with
quantitative methods aimed at measuring or estimating taxonomic abundances that
require information on the number of bilateral pairs in the assemblage.
The Lincoln“Petersen index is dependent on aggregation. Pairs would not be
sought among a set of left skeletal elements from a stratum deposited about
3,000 years ago and a set of right elements recovered from a stratum deposited
quantitative paleozoology
134


about 2,000 years ago (unless perhaps one sought to measure postdepositional dis-
turbance). This underscores in yet another way the potentially signi¬cant in¬‚uence
of aggregation on derived quantitative measures and estimates. Even if we have a sin-
gle stratum, and we are comfortable with the procedure we use to identify bilateral
pairs, have we gained any resolution with respect to taxonomic abundances? The
data in Table 3.15 suggest it is unlikely that we have.


CO R RE C T I N G F O R V A R I O U S T H I N G S


When Shotwell (1955, 1958) discussed how he estimated taxonomic abundances, he
noted that not only do individuals of different taxa have different numbers of skeletal
elements per individual, individuals of different taxa also have different numbers
of taxonomically identi¬able skeletal elements. (For sake of simplicity, ignore the
potentiality that skeletal elements might be broken and thus constitute specimens
rather than skeletal elements.) Thus he advocated determination of the corrected
number of skeletal elements per taxon, or “the number that would be expected
if all species contributed the same number (the standard number of elements) of
recognizable elements” (Shotwell 1955:331). To calculate the corrected number of
skeletal elements (CNSE), he used the equation:

CNSE = [E (SNE)]/ENE,

where E is the number of elements identi¬ed in a collection, SNE is the standard
number of elements per individual that the analyst can identify, and ENE is the
estimated number of elements that the paleozoologist can identify in one complete
skeleton of the taxon under consideration. SNE is, according to Shotwell (1955), an
arbitrary number chosen so as to reduce the amount of corrective math.
It was argued in Chapter 2 that corrections for variation in the frequency of iden-
ti¬able elements per taxon were unnecessary for several reasons. Nevertheless, such
weighting of skeletal frequencies has been suggested by more than one paleozo-
ologist (e.g., Gilinsky and Bennington 1994; Plug and Badenhorst 2006; Plug and
Sampson 1996). Holtzman (1979), for example, suggests calculation of what he terms
the “weighted abundance of elements” or WAE. This value is calculated as

WAE = NE j /NEi j ,

where NE j is the frequency of skeletal elements of taxon j identi¬ed in an assemblage,
and NEi j is the frequency of skeletal elements of individual i of taxon j that can be
identi¬ed. Because WAE uses the number of skeletal elements rather than the number
of specimens, Holtzman (1979:80) argued that it “is less susceptible to biases arising
estimating taxonomic abundances: other methods 135


Table 3.16. Abundances of beaver and deer remains at
Cathlapotle, and WAE values and ratios of NISP and WAE
values per taxon per assemblage

NISP WAE Ratio, beaver: deer
Beaver, precontact 111 1.247 NISP, precontact
= 0.143
Beaver, postcontact 238 2.674 NISP, postcontact
= 0.177
Deer, precontact 775 14.091 WAE, precontact
= 0.088
Deer, postcontact 1,347 24.491 WAE, postcontact
= 0.109



from variation in degree of fragmentation or number of [identi¬able] elements per
individual,” although he also acknowledged that it worked well only if differential
preservation across taxa was not a problem. The methods used for determining the
number of skeletal elements represented by a collection of anatomically incomplete
specimens (an assemblage of broken bones) are considered in Chapter 4. It suf¬ces
here to note that Holtzman™s WAE can be described as the number of skeletal elements
identi¬ed per taxon, adjusted to account for the number of elements in one com-
plete skeleton that can be identi¬ed by the paleozoologist. An example will illustrate
Shotwell™s and Holtzman™s concerns.
Although the frequencies of deer remains and of beaver remains from Cathlapotle
are NISP (Table 1.3), let us treat them as if they are frequencies of anatomically
complete skeletal elements. Frequencies of the two taxa are given in Table 3.16. If

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