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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

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