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represented from more than one [recovery provenience].” He said this with spe-
ci¬c reference to his “MNI-II” values. But he only revealed the problem; he did not
explore its implications. This problem and its implications were later documented
at length by Grayson (1973, 1979, 1984). This problem is, in short, known as the
aggregation problem, where an aggregate is an assemblage or collection of faunal
remains the boundaries of which are chosen by the analyst, whether those bound-
aries correspond to stratigraphic boundaries or arbitrarily and arti¬cially bounded
excavation/collection units.
Grayson (1973) termed what Adams called “Minimums I” values the minimum
distinction method, and termed what Adams called “Minimums II” values the maxi-
mum distinction method. The former involves determination of MNI for the complete
assemblage considered as one aggregate; the latter involves determination of MNI
independently for each assemblage, each from a distinct recovery provenience speci-
¬ed by the analyst. The minimum distinction method is so-called because it produces
the lowest or smallest MNI values for a complete collection. The maximum distinc-
tion method is so-called because it produces the greatest or largest MNI values for
a collection (MNI values for all assemblages from unique recovery proveniences
are summed); it produces more than the minimum distinction method because it
considers a large number of (small) aggregates (or [sub]assemblages of remains).
The minimum distinction method considers only one large aggregate “ all remains
treated as a single collection. Adams did not care for either the minimum distinc-
tion method or the maximum distinction method because, despite the differences
in their results, both produced minimum numbers of individuals. Furthermore, the
maximum distinction method “ determining MNI based on individual recovery
proveniences “ required that one assume specimens in one provenience unit were
independent of all specimens in other provenience units, and Adams did not want
to make that assumption. It is ¬tting that we hereafter refer to this potential problem
of interaggregate interdependence of skeletal specimens as Adams™s dilemma.
That the aggregation problem is widespread is easy to show. Recall the collection
of remains of six genera of prey in eighty-four owl pellets; the NISP“MNI data pairs
for this collection are plotted in Figure 2.8. That ¬gure is based on the minimum
distinction method because all remains were lumped together to form one aggre-
gate. This means that only one skeletal element per taxon contributes to the MNI,
regardless of how many pellets contain remains of a taxon. What happens to the MNI
values for the taxa represented in the sample of eighty-four pellets when one shifts
from the minimum to the maximum distinction method is shown in Table 2.8. The
NISP values stay the same regardless of how MNI is determined “ whether the maxi-
mum or minimum distinction method is used. The MNI is greater in ¬ve of six taxa
estimating taxonomic abundances: nisp and mni 59


Table 2.10. Differences in site total MNI between the MNI minimum distinction results and
the MNI maximum distinction results

Richness Mean
N of (N of N taxa increase
Site assemblages NISP genera) MNImin MNImax increase per genus
45OK2A 4 366 10 30 39 4 of 10 0.9
45DO211 4 474 15 108 117 4 of 15 0.6
45DO285 4 491 15 66 102 12 of 15 2.4
45DO214 4 536 17 67 108 11 of 17 2.4
45DO326 4 640 16 53 81 14 of 16 1.75
45DO242 4 673 13 38 52 7 of 13 1.1
45OK250 3 1,077 12 62 79 8 of 12 1.4
45OK4 3 1,108 15 65 82 7 of 15 1.1
45OK2 4 2,574 18 66 105 13 of 18 2.2
45OK11 2 3,549 24 202 231 14 of 24 0.6
45OK258 2 4,433 21 117 139 10 of 21 1.0


when the maximum distinction method is used relative to the minimum distinction
method (Table 2.8). The ratio of Peromyscus to Microtus “ the subject of published
interpretations of this collection (Lyman et al. 2001, 2003) “ shifts from 1.81 :1 for
the minimum distinction MNI, to 1.86:1 for the maximum distinction MNI, to 1.80
for NISP. In this case, the differences are small, and statistically insigni¬cant; the
chi-square value is 0.41 if Sylvilagus is omitted so that the assemblage™s data pairs
meet the requirements of the test (p > 0.5). Even given the small differences in ratios
of Peromyscus to Microtus, the critical question is: Which ratio is correct? There is no
clear or obvious answer.
The aggregation problem is pernicious. Of the fourteen archaeological assemblages
summarized in Table 2.7, eleven have multiple components or temporally distinct
(sub)assemblages; the other three consist of only one assemblage. For purposes of
generating the regression equations in Table 2.7, I used the minimum distinction
MNI values for all fourteen sites. What happens to the MNI values for the eleven
sites with multiple (sub)assemblages if the maximum distinction method is used
and MNI is derived for each taxon in each (sub)assemblage independently? First, the
total MNI for each of the eleven sites increases when one shifts from MNImin(imum
distinction) to MNImax(imum distinction) (Table 2.10). Why? Because more kinds
of most common elements are speci¬ed in the latter than in the former.
Second, the total MNI for each site increases between nine and forty-one when
one shifts from MNImin to MNImax; the average increase is 23.7 individuals per
quantitative paleozoology
60



Number of Taxa




Amount of Increase in MNI
figure 2.9. Amount by which a taxon™s MNI increases if the minimum distinction MNI
is changed to the maximum distinction MNI in eleven assemblages (see Table 2.10 for other
data on these assemblages).


site (Table 2.10). This is not a lot in terms of absolute abundance, but think of it
this way: In site 45OK2A, MNImin is thirty and MNImax is thirty-nine; that is a
30 percent increase. In the sample of eleven sites, the site total MNImax increases
over MNImin from 8 percent (45DO211) to as much as 61 percent (45DO214); the
average increase is a bit more than 35 percent. The third thing to note regarding
the shift from MNImin to MNImax is that four to fourteen taxa per site increase in
abundance. Not all taxa increase, and any given taxon does not increase consistently
in all sites. Ratios of taxonomic abundances shift around rather unpredictably as a
result. Note, for example, that the amount by which any taxon™s MNI increases is one
to sixteen (Figure 2.9). Consider, for example, how the ratio of deer (Odocoileus spp.)
to gopher (Thomomys sp.) changes across all eleven sites when one uses MNImin
compared to when one uses MNImax (Figure 2.10). If the MNI of both taxa changed
consistently (say, all increase by 10 percent) when shifting from the minimum to the
maximum distinction method, the ratios would not change and all points would fall
on the diagonal in Figure 2.10. Instead, the eleven collections fall various distances
from that line, meaning that the ratios change more in some sites than in others; the
changes in most abundant skeletal parts are not patterned. There is marked variation
in which skeletal part de¬nes the MNI for either or both deer and gophers across the
(sub)assemblages.
estimating taxonomic abundances: nisp and mni 61



MNImax Ratio




MNImin Ratio
figure 2.10. Change in the ratio of deer (Odocoileus spp.) to gopher (Thomomys sp.)
abundances in eleven assemblages when MNImax is used instead of MNImin. If the ratios
did not change, all points should fall on the diagonal line rather than above and to the left,
or below and to the right of that line.

The most abundant skeletal part for each of the thirteen mammalian genera at
Cathlapotle (Table 1.3) that have more than 1 MNI in each of the two temporally
distinct (sub)assemblages are listed in Table 2.11 . Only three taxa (of a possible
thirteen) have more than one most abundant part (e.g., Castor in the postcontact
assemblage), indicating rather skeletally uneven representation of individual car-
casses. More importantly, it is virtually impossible to predict which part of a genus
will be most abundant in one (sub)assemblage based on which part of that genus is
most abundant in the other (sub)assemblage, particularly when left and right-side
designations are considered (Table 2.11 ). If the side designation is not considered,
then only four genera (Aplodontia, Castor, Microtus, Ondatra) out of thirteen are
represented by the same skeletal part in both (sub)assemblages. That two of these
four particular genera are the ones represented by the same skeletal part regardless
of side is, in this case, easy to explain. Only skulls and mandibles of Microtus were
identi¬ed among the mammal remains at Cathlapotle; postcranial remains of this
genus were not identi¬ed and this markedly increases the probability that the
same skeletal part (regardless of side) will be identi¬ed in both components. The
quantitative paleozoology
62


Table 2.11. The most abundant skeletal part representing thirteen mammalian
genera in two (sub)assemblages at Cathlapotle. When more than one skeletal
part represented the same MNI, all skeletal parts are listed. R, right; L, left

Taxon Precontact assemblage Postcontact assemblage
Lepus R proximal tibia R mandible
Aplodontia L mandible R mandible
Castor L femur R mandible, R femur
Microtus L mandible R mandible
Ondatra L mandible R mandible
Canis R P4 L dP4
Ursus L m2 R ulna
Procyon R proximal radius L m1
Mustela R mandible R distal humerus
Lutra R proximal radius R mandible, R distal humerus
Phoca L distal humerus R temporal
Cervus L astragalus L naviculo cuboid
Odocoileus R calcaneum R m3, R astragalus


mandible of Aplodontia is the most frequent skeletal part in both (sub)assemblages
because it was selectively retained by site occupants as a wood-working tool “ a
chisel or engraver (Lyman and Zehr 2003). It is unclear why the same skeletal part
provides the MNImax of Castor and Ondatra in both subassemblages, but those
parts are particularly robust and thus relatively immune to taphonomic attritional
processes.
The most frequent skeletal parts in Table 2.11 are from all parts of the skeleton “
the head (upper and lower teeth, mandibles), the forelimb, and the hindlimb. It is
likely, given what we know about taphonomy at this time, that this is the pattern that
will emerge in most cases. Because taphonomic processes in¬‚uencing the survival
and distribution of faunal remains are not perfectly correlated with remains that are
(or those that are not) taxonomically identi¬able (Lyman 1994c), it is unlikely that
we will ¬nd cases in which the MNImin and MNImax values for a given collection
will be perfectly correlated at a ratio scale. They might be correlated at an ordinal
scale, but it is quite likely even then that the correlation coef¬cient will be less than
1.0. Shifts in taxonomic abundances will likely not be uniform across all taxa when
one shifts from MNImin to MNImax.
Different aggregates of faunal materials making up a total collection will not only
produce different MNI values, but they will do so differentially across taxa. Let™s
say we have one taxon represented in a collection from a site, and that this taxon
is represented by twenty-¬ve left and thirty right distal humeri, the most common
estimating taxonomic abundances: nisp and mni 63


Table 2.12. Fictional data showing how the distribution of most abundant
skeletal elements of one taxon can in¬‚uence MNI across different
aggregates. If stratigraphic boundaries are ignored, a minimum of thirty
individuals is represented by thirty right humeri. Using stratigraphic
boundaries to de¬ne aggregates, the total MNI is forty-seven because the
most abundant element is left humeri in stratum 1, but the most
abundant element in strata 2 and 3 is left humeri

Left humeri Right humeri MNI per stratum
Stratum 1 22 5 22
Stratum 2 3 17 17
Stratum 3 0 8 8
MNI 25 30 47


skeletal part. Obviously, we have a MNImin of thirty (assuming that we ¬nd matches
in terms of age, sex, and size for all possible pairs of elements; i.e., the twenty-¬ve
left specimens all have matching right specimens). But there are also three strata (or
horizontally distinct recovery contexts, if you prefer) comprising the site, and the
humeri are distributed across those strata as indicated in Table 2.12. When we sum
the MNImax values in Table 2.12, we have a site total of MNI = 47. Why? Because
whereas with MNImin we had only one most common skeletal part in the form of
the right distal humeri ( = 30), we now have in Stratum 1 the left humerus as the
most common part whereas in Strata 2 and 3 the right humerus is the most common
part. The change from one kind of most common skeletal part to two kinds resulted
in an increase of 17 MNI (57 percent).
As a ¬nal example, let™s say we have two taxa. Taxon 1 is represented by the
remains of 7 individuals (= MNImin); those remains consist of 7 R humeri, 6 L
humeri, 6 R femora, and 5 L femora ( NISP = 24). Taxon 2 is represented by the
remains of 14 individuals (= MNImin); those remains consist of 14 R humeri, 7 L
humeri, 6 R femora, and 10 L femora ( NISP = 37). If we de¬ne faunal assemblages
stratigraphically, and there are three strata in the site, we may ¬nd the stratigraphic
distribution of skeletal parts indicated in Table 2.13. In that table the MNI for taxon
1 shifts from MNImin = 7 to MNImax = 10, and the MNI for taxon 2 does not shift
but rather both MNImin = 14 and MNImax = 14. The change in taxon 1 is the result
of changes in the number of most abundant skeletal parts de¬ned for this taxon as the
aggregates change. Most disconcerting is the fact that the ratio of taxon 1 to taxon 2
changes from 7:14 (or 1:2) to 12:14 (or 1:1.2) with a simple change in aggregates. Again,
these changes result from speci¬cation of different most common skeletal parts with
each different set of aggregates.
quantitative paleozoology
64


Table 2.13. Fictional data showing how the distribution of skeletal elements of
two taxa across different aggregates can in¬‚uence MNI. If stratigraphic
boundaries are ignored, there are only seven individuals (R humeri) of taxon 1,
and fourteen individuals (R humeri) of taxon 2. Aggregates de¬ned by
stratigraphic boundaries produce twelve individuals of taxon 1 and fourteen
individuals of taxon 2

Taxon 1 Taxon 2
Stratum 1 6 R humeri, 2 L humeri, 3 R femora, 4 R humeri, 1 L humerus, 4 L
3 L femora (MNImax = 6) femur (MNImax = 4)
Stratum 2 1 R humerus, 4 L humerus, 1 R 4 R humeri, 1 L humeri, 3 R
femora, 1 L femur (MNImax = 4) femora, 1 L femur
(MNImax = 4)
Stratum 3 1 L femur, 2 R femora 6 R humeri, 5 L humeri, 4 R
(MNImax = 2) femora, 4 L femora
(MNImax = 6)



Changes like those documented above are likely to occur more often than not. This
renders MNI a very unstable measurement unit. Of course, changes in aggregation
may not cause MNI values to ¬‚uctuate if the distribution of most abundant skeletal
parts is the same for each taxon. Consider, for example, the two-taxon ¬ctional data
given in the earlier example, but this time with similar distributions of most abundant
elements across the three strata, as shown in Table 2.14. The most abundant element
of both taxa (R humerus) has a similar distribution across all three strata and displays
its greatest frequency in Stratum 1. The ratio of taxon 1 to taxon 2 is 1 :2 in all three
strata by the MNImax method. The ratio of 1:2 is given by the MNImin method as
well.
Studying the distribution of most abundant elements per taxon across different
aggregates may reveal much about site formation and taphonomic history, as Grayson
(1979, 1984) noted years ago. I am, however, unaware of any such studies in the
literature. This is surprising given interest in site structure (e.g., O™Connell 1987).
Perhaps the lack of such studies is an instance of benign neglect. Whatever the case,
consideration of how aggregation in¬‚uences MNI deserves more study than it has
received because of the insight it will provide to MNI as a measure of taxonomic
abundance and also because of the insights it may grant to site structure. In such
studies, an aggregate of any kind might be de¬ned “ by a site as a whole, by a stratum,
by an archaeological feature (each pit, house ¬‚oor, hearth, etc.), by an arbitrary
excavation unit (say, 2 m — 2 m — 10 cm thick), or some combination thereof.
estimating taxonomic abundances: nisp and mni 65


Table 2.14. Fictional data showing that identical distributions of most common
skeletal elements of two taxa across different aggregates will not in¬‚uence MNI.
Note that the NISP per skeletal element is the same as in Table 2.13. Note also
that the four distinct skeletal elements have similar frequency distributions
across the three strata, and that the ratio of taxon 1 to taxon 2 is 1:2 in each of
the three strata, and that MNI values determined while ignoring stratigraphic
boundaries also produce a ratio of 1:2

Taxon 1 Taxon 2
Stratum 1 5 R humeri, 4 L humeri, 4 R 10 R humeri, 5 L humerus, 4 R
femora, 3 L femora femur, 8 L femur
(MNImax = 5) (MNImax = 10)
Stratum 2 1 R humerus, 1 L humerus, 1 R 2 R humeri, 1 L humeri, 1 R
femora, 1 L femur femora, 1 L femur
(MNImax = 1) (MNImax = 2)
Stratum 3 1 R humerus, 1 L humerus, 1 R 2 R humeri, 1 L humeri, 1 R
femur, 1 L femora femora, 1 L femora
(MNImax = 1) (MNImax = 2)



A ¬nal point to consider involves Uerpmann™s (1973:311) observation that the “dif-
ference between number of ¬nds [NISP] and ˜minimum number of individuals™
increases as the size of the sample increases” (Uerpmann 1973:311). The difference
between NISP per taxon and MNI per taxon will increase as NISP increases (Fig-
ure 2.4). Because larger sample sizes allow greater differences between values, differ-
ences between MNImin and MNImax will be greatest in large samples and smallest in
small samples. Thus, large sample sizes, which are desired for statistical reasons (large
samples tend to be more representative than small samples of the population from
which they are drawn, and they tend to increase the statistical power of a test), tend to
be the ones in which MNI ¬‚uctuates the most as different aggregates are de¬ned. As
Grayson (1979:210) noted, “This is not the usual behavior of a unit of measurement.”
Restating problem seven, MNI measures not only taxonomic abundances but
aggregation methods as well (Grayson 1984). This can be shown graphically and
statistically by considering the relationship between NISP and MNI as modeled in
Figure 2.4, but with log-transformed data such that the relationship is linear. The
slope of the simple best-¬t regression line describing the relationship between NISP
data and taxonomically corresponding MNI data should be less steep when more
agglomerative (larger aggregates) methods are used to calculate MNI (MNImin)
than when less agglomerative (smaller aggregates) methods are used to calculate
quantitative paleozoology
66




figure 2.11. Relationships between NISP and MNImin, and NISP and MNImax at site
45DO214.


MNI (MNImax). This is so because MNImin involves few most common elements
so it is dif¬cult to ¬nd and thus add a new most common element. MNImax involves
many most common elements so it is easy (relatively speaking) to ¬nd and thus
add a new most common element. Consider site 45DO214 among the collections
from eastern Washington State mentioned previously (Table 2.7). The slope of the
simple best-¬t regression line describing the relationship between NISP and MNImin
is 0.44 (Table 2.7); the slope of the simple best-¬t regression line describing the
relationship between NISP and MNImax is 0.57. Both sets of data points and both
best-¬t regression lines are included in Figure 2.11 , which shows that the slope for
MNImin is less steep than that for MNImax.
The example of 45DO214 indicates that MNI not only measures taxonomic abun-
dances but it also measures aggregation. But we do not want measures of two variables
to obscure each other, particularly when one may approximate the target variable
and the other has nothing whatsoever to do with the target variable. Is there, perhaps,
a logical way to de¬ne aggregates such that the measures of taxonomic abundances
provided by MNI can be treated as if the aggregates do not signi¬cantly in¬‚uence
those abundances?
estimating taxonomic abundances: nisp and mni 67


De¬ning Aggregates

Recall that an assemblage of faunal remains is the set of remains from a horizon-
tally and vertically bounded space, usually a geological space such as a stratum or a
part thereof. Following Grayson (1984), the term aggregate is used as a synonym for
assemblage, and the term aggregation for the process of de¬ning the spatial bound-
aries of a faunal assemblage. Despite Grayson™s (1973) recognition of the aggregation
problem more than 30 years ago, few analysts other than Grayson (1979, 1984) have
subsequently explored its implications with their own data. Thus it is not unusual to
¬nd paleozoologists still calculating MNI values without considering the aggregation
problem (e.g., Trapani et al. 2006). The aggregation problem is not even mentioned
in one textbook on zooarchaeology (Rackham 1994).
Payne (1972) suggests that aggregates of faunal remains should be de¬ned on
the basis of the homogeneity of taxa and their frequencies. Ignore for the moment
the question of how similar is similar enough for two assemblages to be considered
homogeneous (Payne did not address this question), and consider the following three
things. First, this procedure assumes that natural faunal aggregates exist and we have
but to discover them. But whether natural discoverable faunal aggregates exist or
not is unclear. Furthermore, what kinds of faunal aggregates are to be searched for “
those representing a depositional event, a human-behavior, a death event, or . . .
what? Perhaps the research question being asked would help specify the appropriate
aggregate, but other problems attend their de¬nition. The second thing to consider,
then, is that Payne™s protocol precludes the study of stasis because one aggregates,
say, stratigraphically sequent, similar (homogeneous) assemblages. Finally, Payne™s
procedure comprises a circular process: Change in the fauna would be identi¬ed based
on how the aggregates were de¬ned “ the property of differences or nonhomogeneity
interpreted as change “ because aggregates are de¬ned on the basis of similarity and
homogeneity. Based on these three observations, we might use nonfaunal criteria to
de¬ne aggregates.
Ringrose (1993:128) argues that “not all levels of aggregation are likely to be sensible,
so that the problem [of the in¬‚uence of aggregation on MNI] is perhaps less than it
might seem at ¬rst. If it is not possible for specimens from the same individual to be
present in two locations [that is, to be tallied in two distinct aggregates], then it is
nonsensical to calculate the MNI at a level of aggregation where these two locations
are taken together, since specimens will be, implicitly, counted as being possibly
from the same individual when in fact they cannot be.” Implementing this protocol
of de¬ning aggregates demands a great deal of knowledge regarding the taphonomic
history of the materials under study. Some of it might be found by re¬tting studies
quantitative paleozoology
68


(e.g., Rapson and Todd 1992; Todd and Stanford 1992). However, this is again using
faunal data to de¬ne aggregates and thus imparts a degree of circularity to those
de¬nitions. It also can introduce the problem of matching potentially paired (left
and right) skeletal parts (e.g., Todd and Frison 1992).
Some zooarchaeologists indicate that one should de¬ne faunal aggregates based
on “cultural units rather than arbitrary ones related to excavation logistics” (Reitz
and Wing 1999:198). This is all well and good, but does this mean that two pits con-
taining bones and originating in the same stratum (dating to the same time period
and apparently representing the same cultural context given stratigraphic contem-
poraneity) should be considered separately or together? Archaeologist James Ford
(1962) argued long ago that archaeological “cultural units” such as cultures, phases,
periods, and the like were often de¬ned on the basis of stratigraphically bounded
aggregates of artifacts, but that it was unclear why there should be any necessary rela-
tionship between sediment deposition boundaries and boundaries between cultures.
I agree (Lyman and O™Brien 1999). So what are we to do?
Let us begin by glancing at the solution that paleontologists have used. Fagerstrom
(1964:1198), a paleontologist interested in past biological communities, suggested that
a fossil assemblage representing a community was “any group of fossils from a suitably
restricted stratigraphic interval and geographic locality.” What is suitable is not clear,
though it is hinted at in other paleontological concepts. In vertebrate paleontology, a
faunule is an assemblage of associated animal remains from one or several contiguous
strata, dominated by members of one biological community (Tedford 1970:677). And,
a local fauna is a set of remains from one locality or several closely spaced localities
which are stratigraphically equivalent or nearly so, thus it is a set of taxa close in
(geological) time and (geographic) space (Tedford 1970:678). Identifying prehistoric
faunal communities “ or faunules “ was what Shotwell (1955, 1958) was concerned
about, and he emphasized the taphonomic problems with doing so when one used
an aggregate of fossils the boundaries of which were set by excavation strategies and
stratigraphy.
The preceding brief discussion hints at two things. First, paleontologists often
seek, like Chester Stock and Hildegard Howard did, to determine the census of a
paleocommunity, or a biocoenose. That is their target variable, and they acknowledge
the geological mode of occurrence of the faunal materials that they study, and they
use stratigraphic boundaries and extent of exposures to collect a sample of those
materials. The second thing hinted at is an extremely critical detail. Reitz and Wing
(1999:197) mention it when they state that the aggregates of faunal remains de¬ned
“may depend on the research problem.” Any aggregates de¬ned must depend on the
research problem, as well as whatever taphonomic and site-formational information
is available. Thus, on the one hand, human behaviorally signi¬cant assemblages of
estimating taxonomic abundances: nisp and mni 69


remains, such as those in cache pits or in trash middens or on house ¬‚oors are likely
to be important to questions about human interactions with fauna. On the other
hand, questions regarding paleoecology are likely to be phrased in such a manner
as to require temporally and spatially distinct assemblages of remains, perhaps but
not necessarily representing one “biological community” but certainly providing
insights to the nature of biocoenoses. Temporally distinct assemblages but perhaps
not human behaviorally signi¬cant ones would be of interest to paleoecologists.
Valensi (2000:358) noted that aggregation based on excavation levels “gave an over-
estimation of MNI [as a result of specimen] interdependence [across] some levels.”
Interdependence was recognized by re¬tting specimens of both lithic and bone spec-
imens that came from different depositional units. Valensi used archaeostratigraphic
units as the basis for de¬ning aggregates, and found re¬tting specimens that came
from different units. Her analysis suggests a protocol for de¬ning aggregates. Re¬ts of
lithic specimens would provide nonfaunal criteria for de¬ning faunal aggregates. The
paleozoologist could adopt a rule, such as only when re¬ts across aggregates are min-
imal, whereas re¬ts within aggregates are maximized, have appropriate aggregates
for determining MNI been de¬ned. However, not only is the time cost incredibly
high if the assemblage is large “ do the faunal re¬ts, using the same rule, de¬ne the
same aggregates as the lithics (or ceramics)?
Research questions about taphonomic histories likely will require an estimate of
a taphocoenose, those about hunter or predator selectivity will require not only an
estimate of a thanatocoenose but also the biocoenose from which it derived. Explicit
statement of the research problem and research questions should help the paleo-
zoologist de¬ne aggregates that are pertinent. Of course, any available taphonomic
information such as obvious re¬ts should also be consulted to help set geological
spatial boundaries around the aggregate(s). This does not mean that one will auto-
matically have aggregates that do not share specimens from the same individual, but
perhaps those will be so rare as to not signi¬cantly bias any statistical results.


DISCUSSION


Thus far the problems with NISP as a quantitative unit giving valid measures of
taxonomic abundances (even in a taphocoenose, let alone in a thanatocoenose or
biocoenose) have been considered and it has been argued that all but one of those
problems “ that of possible specimen interdependence “ can be fairly easily resolved
analytically. (Some analysts still fail to realize how easily many of the problems with
NISP can be resolved analytically [e.g., O™Connor 2001 ].) Problems with MNI as
a quantitative unit giving valid measures of taxonomic abundances have also been
quantitative paleozoology
70


identi¬ed and discussed, and it has been shown that many of those are also readily
dealt with analytically. The problem that remains with MNI is aggregation. As implied
above, there is no magic algorithm for solving the aggregation problem because each
aggregate speci¬ed by the analyst may, or may not, have a set of faunal remains all
of which are indeed independent of all other faunal remains in all other aggregates.
Earlier I referred to the latter as Adams™s dilemma. It is aptly referred to as a dilemma
because if, say, stratigraphically bounded aggregates are chosen as the assemblages
to be analyzed, one must assume that the faunal remains in each are independent of
all other faunal remains in other aggregates. But, of course, they might not be.
A chosen sampling design may indicate where to excavate and which screen-
mesh size to use, but the faunal specimens recovered are a result of the taphonomic
history of the assemblage “ which bones and teeth were accumulated, deposited, and
still exist, and where they are located, both horizontally and vertically. The existing
remains of a single individual may be in one or more horizontal loci, in one or more
vertical loci (or strata), or both. (No two specimens can, of course, occupy exactly the
same horizontal and vertical position. By same location, I mean a spatially limited,
horizontally and vertically bounded unit.) Even attempting to match and pair all
skeletal specimens from all excavated recovery proveniences, we will likely never
know what the correct aggregates of faunal remains should be. By correct is meant
those that are not only relevant to our research questions, but also ones de¬ned such
that specimens from a single carcass are not distributed across two or more aggregates.
Given that we cannot know this, we either assume Adams™s dilemma does not exist,
or, we do something other than determine MNI values.
There is, in fact, a relatively simple solution to Adams™s dilemma. The solution
rests on the fact that quite often, virtually the same information regarding taxo-
nomic abundances in an assemblage is found in NISP as is found in MNI. This
statistical relationship has been known for some time (Casteel 1977, n.d.; Grayson
1978a, 1979). In short, MNI is redundant with NISP, where “redundant” means that
the two quantitative units produce the same information. The “same information”
can mean identical, or simply statistically indistinguishable. To show that MNI and
NISP provide the same information in both of these senses, consider the owl pellet
data mentioned before. Recall that the sample comprises eighty-four pellets, that the
relationship between NISP and MNImin is linear (Figure 2.8), and that the relation-
ship is strong (r = 0.989, p < 0.0002). For this sample, 97.8 percent of the variation in
MNI values is explained by variation in NISP values. Clearly, MNI is redundant with
NISP. And, the same applies to the fourteen samples of mammal remains from east-
ern Washington State (Table 2.7). For these assemblages, the relationship between
NISP and MNImin is typically strong (r > 0.75 for 13 of the 14) and signi¬cant
(p < 0.01 for all). For thirteen of these fourteen assemblages, NISP accounts for
estimating taxonomic abundances: nisp and mni 71


more than 51 percent of the variation in MNI. MNI provides information about
taxonomic abundances that is redundant with that provided by NISP (Figure 2.4).
But so what? Constructing an answer to this question requires a consideration of the
scale of measurement represented by NISP and by MNI.



W H I CH S C A L E O F M E A S U RE M E N T ?


Some years ago, Grayson (1984:94“96) noted several critical things. First, he noted that
converting from one ratio scale to another ratio scale based on different measurement
units will not alter the value of a ratio of measurements. This is so because both
ratio scales have natural zero points and their respective units of measurement stay
constant in each. Thus, the ratio of the weight of two items will not alter if ¬rst
measured in pounds and then in kilograms. If the two items are 50 pounds and
75 pounds, the ratio of their weights is 1:1.5; the two items weigh 22.68 kilograms
and 34.02 kilograms, respectively, for a ratio of 1:1.5. As noted earlier in this chapter,
aggregation has the unsavory characteristic of altering MNI tallies, thereby causing
ratios of taxa to change as the manner in which faunal remains are aggregated changes.
The second thing Grayson (1984) noted was that MNI values are not ratio scale
values precisely because they are minimum numbers (Table 2.4). The actual number
of animals represented (by the identi¬ed assemblage) could be as great as the NISP,
although it likely will fall somewhere between the MNI and the NISP given the
probability (> 0.0) of some interdependence of specimens. Thus it cannot be argued
that a taxon represented by an MNI of ten is half as abundant as a taxon represented
by an MNI of twenty, nor can it be argued that if two taxa each have MNI values
of ¬fteen they are equally abundant. Figure 2.12 plots ratios of the abundances of
each pair of taxa based on NISP, MNImin, and MNImax measures of the four least
common taxa in the collection of eighty-four owl pellets (Table 2.9). The ratios vary
by greater or lesser amounts across the three quantitative measures. In particular,
note the variation in ratios between the MNImin and MNImax values. There is no
way to determine which set of ratios most closely measures the actual abundances
of taxa. Clearly, it is ill-advised to treat MNI values as ratio scale because there are
many reasons why they likely are not.
Unfortunately, it is unlikely that NISP values are ratio scale. As Grayson (1984)
noted, if MNI provides minimum tallies, NISP provides maximum tallies. Given that
we do not know the nature (extent) of interdependence of the specimens comprising
the NISP for any given taxon in any given collection, and given that intertaxonomic
variation in such interdependence will differentially in¬‚uence how closely NISP
tracks a taxon™s actual abundance, it is unlikely that ratios of taxa based on NISP values
quantitative paleozoology
72


Table 2.15. Ratios of abundances of pairs of taxa in eighty-four
owl pellets. Original data from Table 2.8. Taxon 1, Sylvilagus;
taxon 2, Reithrodontomys; taxon 3, Sorex; taxon 4, Thomomys

Taxon pair NISP MNImin MNImax
1 “2 0.26 0.20 0.40
1 “3 0.11 0.20 0.29
1 “4 0.07 0.12 0.17
2“3 0.41 1.00 0.71
2“4 0.28 0.62 0.42
3“4 0.68 0.62 0.58

are in fact ratio scale. There is no way to know which set of ratios of abundances of
taxa in the owl pellet fauna (Table 2.15), if any, most accurately re¬‚ects the actual ratio
scale abundances of the taxa. As Grayson (1984:96) noted, because “we know nothing
of the nature of the frequency distribution [of taxonomic abundances] that begins
with MNI and ends at NISP for a set of taxa,” knowledge of ratio scale abundances
of taxa is precluded.
If MNI and NISP do not provide ratio scale taxonomic abundance data, do they
perhaps provide ordinal scale abundance data? Again, Grayson (1984:96“99) provided
Ratio




Taxa Pair
figure 2.12. Ratios of abundances of four least common taxa in a collection of eighty-four
owl pellets based on NISP, MNImax, and MNImin. Taxon 1, Sylvilagus; 2, Reithrodontomys;
3, Sorex; 4, Thomomys. Data from Table 2.8.
estimating taxonomic abundances: nisp and mni 73




figure 2.13. Frequency distributions of NISP and MNI taxonomic abundances in the
Cathlapotle fauna. Data from Table 1.3.



a clear answer. The rank order abundances of taxa are often quite similar across NISP
and MNI; if the two sets of values are signi¬cantly correlated on an ordinal scale, then
the included taxonomic abundances are ordinal scale. Why NISP and MNI should
often be correlated comprises the critical insight as to why we can conclude they are
ordinal scale. In most multitaxa faunas, a few taxa are represented by many individu-
als and specimens, and many taxa are represented by few individuals and specimens.
As taxonomic abundances increase (whether NISP or MNI), the magnitude of the
differences between abundances of adjacent taxa increases. Such frequency distribu-
tions increase the probability that taxonomic abundances are ordinal scale because
there is less chance that variation in aggregation (MNI) or specimen interdependence
(NISP) will alter rank order abundances.
Summing the precontact and postcontact assemblages, eighteen taxa in the Cath-
lapotle fauna (Table 1.3) are represented by seven or fewer individuals whereas only
seven taxa are represented by more than ten individuals (Figure 2.13). Similarly, 20
taxa are represented by 100 or fewer specimens whereas only 5 taxa are represented by
quantitative paleozoology
74




figure 2.14. Frequency distributions of NISP and MNI taxonomic abundances in the
45OK258 fauna in eastern Washington State.




more than 100 specimens. One of the mammalian faunas from eastern Washington
State that has been used in other analyses “ site 45OK258 “ has similar frequency
distributions (Figure 2.14). Grayson (1979, 1984) presented numerous other faunas
with right skewed distributions of taxonomic abundances. Lest one think this sort of
frequency distribution is a function of the faunas we examined, two more examples
may convince the skeptic. A right skewed frequency distribution is found in the two
summed late prehistoric assemblages of mammal remains from the western Canadian
Arctic described by Morrison (1979) (Figure 2.15). And such a frequency distribu-
tion is also found among historic era mammalian faunas described by Landon (1996)
(Figure 2.16).
It matters little why many faunas display a right skewed frequency distribution
of taxonomic abundances [Box 2.2]. The important point is, as Grayson (1984:99)
put it, the “degree of rank order stability will be closely related to the degree of
estimating taxonomic abundances: nisp and mni 75




figure 2.15. Frequency distributions of NISP and MNI taxonomic abundances in two
lumped late-prehistoric mammal assemblages from the western Canadian Arctic. Data from
Morrison (1997).



separation of the taxa involved in terms of their MNI- or NISP-based sample sizes.”
The greater the separation between the abundance of taxon A and the abundance
of taxon B, the less likely changes in aggregation “ if abundances are MNI values “
or specimen interdependence “ if abundances are NISP values “ will alter the rank
order abundances of those taxa. The rank order abundances of rarely represented
taxa, because their abundances are not widely separated, likely will shift with changes
in aggregation and specimen interdependence. As Grayson (1984:98) suggests, “it is
questionable whether [rarely represented taxa] should be treated in anything other
than a nominal, presence/absence sense.”
quantitative paleozoology
76




figure 2.16. Frequency distributions of NISP and MNI taxonomic abundances in four
lumped historic era mammalian faunas. Data from Landon (1996).




Box 2.2

This sort of frequency distribution is known as right skewed “ the tail is to the
right. Such a frequency distribution may result from the accumulation agent
focusing on one or a few taxa “ the frequently represented ones “ and the rarely
represented taxa are background or idiosyncratic accumulations. Alternatively,
recovery may create the frequency distribution. This would be suggested by rare
remains of small animals and frequent remains of large animals (see Chapter 4).
Finally, perhaps the frequency distribution represents what is on the landscape
if accumulation, preservation, and recovery were all random with respect to the
biocoenose.
estimating taxonomic abundances: nisp and mni 77


One can determine if taxonomic abundances are ordinal scale “ that their rank
order of abundance does not alter with counting method “ by calculating the rank
order correlation between taxonomic abundances produced by the most agglom-
erative approach to quanti¬cation (MNImin) with the most divisive approach to
quanti¬cation (NISP). In most cases, there will be a limited number of ways to
aggregate faunal remains (e.g., by site, by stratum, by excavation unit, from most to
least agglomerative). If the rank orders of abundances indicated by the most and by
the least agglomerative methods are signi¬cantly correlated, then the effects of aggre-
gation, of specimen interdependence, or both are such that they do not in¬‚uence the
ordinal scale abundances of taxa (Grayson 1984:106). Analysis and statistical manip-
ulation of the rank ordered abundances is appropriate. Grayson (1979:216, 1984:98)
cautioned, however, that aggregation will tend to most strongly in¬‚uence the rank
ordered MNI abundances of rarely represented taxa precisely because they are rare
and thus there are minimal to no gaps between their absolute abundances (MNI
of one vs. two, say). Changes in aggregation will cause shifts in taxonomic absolute
abundances and thus changes in rank ordered abundances, especially increasing or
decreasing the number of tied ranks (because there are few ranks of rare taxa, say
one’three or four, yet typically a half dozen or more taxa in those ranks). A similar
argument applies to NISP and interdependence. Rarely represented taxa are more
likely to shift rank orders of abundance than abundant taxa if interdependence could
be validly determined because the abundances of rare taxa will not be separated by
large gaps in abundance, whereas abundant taxa are likely to be separated by large
differences in abundance.
If the rank order abundances ¬‚uctuate across different tallying methods such that
NISP and MNImin are not correlated, then one must conclude that the data are at
best nominal scale. Taxa must be treated not as quantitative variables, but as qualita-
tive variables or attributes of a collection; taxa must be treated simply as present in or
absent from the collection under study. The analyst could initiate a detailed tapho-
nomic study in an effort to determine if such things as intertaxonomic variation in
fragmentation are in¬‚uencing analytical results. Alternatively, a qualitative interpre-
tation of the taxa present would be reasonable, such as saying that the prehistoric
occupants of the archaeological site that produced the faunal remains ate various taxa,
but not delving into whether more of taxon A or more of taxon B was eaten. Given that
the greatest changes in rank ordered abundances will be in rarely represented taxa, it
is the rare taxa that likely should be treated as nominal scale. How rare is “rare” in any
given assemblage is an empirical issue. The paleozoologist could initiate an explo-
ration of how rare is rare by generating a graph like those in Figures 2.13“2.16, paying
attention to which taxa fall to the left and have no gaps between their abundances.
quantitative paleozoology
78


If NISP and MNI both might produce ordinal scale data on taxonomic abundances,
which should be used? I have argued that the de¬nition of aggregates is a serious prob-
lem given minimal logical consideration by most paleozoologists, yet the aggregates
de¬ned will typically have an in¬‚uence of greater or lesser magnitude on MNI values.
I have also pointed out that MNI is a derived measure and as such MNI values will be
in¬‚uenced by the attributes the analyst chooses to assess specimen interdependence,
such as size, ontogenetic age, and sex. One who prefers MNI might ¬nd the prob-
lems of aggregation and derivation to be minor ones relative to those associated with
NISP, but NISP is additive regardless of aggregation; MNI is not. NISP is in¬‚uenced
by specimen interdependence but MNI is not (at least, not as much, remembering
Adams™s dilemma). Acknowledging the combination of dif¬culties attending each
quantitative unit, which should be used? Given that NISP is redundant with MNI,
the answer seems obvious. Use NISP to determine taxonomic abundances.



RE S O L U T I O N


MNI is at best an ordinal-scale measurement unit. NISP is likely to provide an ordinal-
scale measure of taxonomic abundances at best. MNI underestimates the true abun-
dance of some taxa, overestimates others, and accurately estimates the abundances
of still others. NISP is likely to do the same, although the taxa the abundances of
which are overestimated may not be the same as those that are overestimated by MNI,
and so on. And, if MNI provides minimum values and as a result cannot provide
mathematically valid ratios, then because NISP provides maximum values it cannot
provide mathematically valid ratios either. Finally, recall the tight statistical relation-
ships found between the NISP and the MNI (usually MNImin) evident in many
assemblages (Tables 2.6 and 2.7; plus assemblages described by Bobrowsky [1982],
Casteel [1977, n.d.], Hesse [1982], Grayson [1979, 1981b], and Klein and Cruz-Uribe
[1984]). That relationship suggests that if MNI is at best an ordinal-scale measure
of taxonomic abundances, so, too, is NISP. The argument can be made in reverse
order; if NISP is ordinal scale and is correlated with MNI, then MNI is also ordinal
scale.
Do not be confused by the argument that NISP is at best an ordinal-scale measure
of taxonomic abundances. Figures 2.5“2.8 and 2.11 , and Tables 2.6 and 2.7 all treat
NISP data as if they are ratio scale, but note that no ratio scale interpretations of
those data have been offered. Were the owl pellet data in Table 2.9 and Figure 2.8 to
be interpreted in ratio scale terms, one might say that Reithrodontomys was nearly
estimating taxonomic abundances: nisp and mni 79


four times as abundant as Sylvilagus based on NISP, or ¬ve times as abundant based
on MNImin. NISP and MNI data for the six genera in the eighty-four owl pellets
are presented in ratio scale terms, but are interpreted in ordinal-scale terms (Lyman
and Lyman 2003). This is not an unusual analytical protocol. It is, for example,
typical of how palynologists operate; they present ratio scale data on abundances
of plant taxa in a pollen diagram and interpret those data in ordinal scale terms
(Moore et al. 1991). The reasons for this protocol are similar to those in paleozoology.
There is, for example, intertaxonomic variation in the rate of pollen production,
intertaxonomic variation in the accumulation rate (and transport distance) of pollen,
and the like. Palynologists realize that counting pollen grains will produce ratio
scale counts but that those counts are best interpreted in ordinal scale terms. With
respect to paleozoological data, MNI and NISP are both typically at best ordinal scale
measures of taxonomic abundance, and they are correlated, often rather strongly.
The information on taxonomic abundances provided by MNI is also often provided
by NISP.
NISP is a fundamental measurement whereas MNI is a derived measurement.
The only analyst-related source of variation in NISP involves identi¬cation skills.
That source of variation is joined by other analyst-related sources when MNI is
calculated. How pairs of left and right elements are sought by an analyst can vary.
Does the analyst doing the matching consider only size, only shape, only ontogenetic
age? Are the specimens matched visually as when all left femora are laid out on the
lab table and compared with all right femora, or are verbal descriptions compared?
And there is always the potential for interobserver variation even if precisely the
same methods of matching are used. Finally, it is unclear if two analysts will de¬ne
precisely the same aggregates even if they have the same research question. Despite
such issues, paleozoologists continue to try to design valid ways to derive MNI values
(e.g., Avery 2002; Vasileiadou et al. 2007).
In light of the discussion to this point, one conclusion seems inescapable: Why
bother with MNI when NISP is more fundamental, less derived, and the two provide
redundant information? True, NISP seems to have more problems than MNI, but
many of the problems with NISP are easily dealt with analytically or concern inter-
dependence. Fragmentation, for example, increases NISP to some degree; rather
than tally one skeletal element in an assemblage with broken skeletal elements, two
or more pieces (specimens) of the same element are tallied. The same applies to
intertaxonomic variation in differential transport of skeletal parts and portions,
intertaxonomic variation in numbers of identi¬able elements, and the like. Such
criticisms of NISP not only reduce to concerns about specimen interdependence,
quantitative paleozoology
80


they seem to originate speci¬cally from the perspective that an individual organism
is the proper counting unit, regardless of anything else. Recall that MNI seems to
be commonsensical to calculate and that it has a basis in empirical reality because
of the individuality of every organism. But empirical veri¬ability of individuals is a
weak warrant to use individuals as the quantitative unit in paleozoology, especially
when it is recognized that bones and teeth are also empirically veri¬able biological
units. And, just because much of biology focuses on individual organisms or mul-
tiples thereof, should paleozoology adopt that focal unit? The answer to that ques-
tion depends on the research problem under investigation and the attendant target
variable(s).
If one adopts the argument that NISP should be the preferred unit with which
to measure taxonomic abundances, then there remains the potential problem of
specimen interdependence that plagues NISP. As Grayson (1979, 1984) has argued,
that problem is rather easily dealt with also. He noted that the “effect of interdepen-
dence upon specimen counts is much the same as that of aggregation on minimum
numbers: both have the potential of differentially altering measured taxonomic abun-
dances” (Grayson 1979:222). Grayson argued that aggregation will not differentially
alter MNI if, and this is a critical if, most abundant specimens are identically dis-
tributed across aggregation units (Table 2.14 and associated discussion). Similarly,
Grayson (1979:223) noted that the interdependence of specimens should not signif-
icantly in¬‚uence NISP as a measure of taxonomic abundances if, and again this is
a critical if, “all specimens are independent of one another,” or “interdependence
is randomly distributed across taxa.” The former is unlikely, and there is no well
established method for determining whether or not specimens are independent of
one another, or even if they are truly interdependent. How do we determine if inter-
dependence is randomly distributed across taxa?
MNI is a function of NISP; if we know the NISPi values for an assemblage we
can typically rather closely predict what the MNIi values for that assemblage will be.
And note that although MNI measures both taxonomic abundances and aggregation
method, it does provide what are likely to be independent values, especially if we
determine MNImin in order to avoid Adams™s dilemma that skeletal parts in different
aggregates may not be independent. Finally, note that NISP values are likely to be
interdependent to some degree. Putting these observations together, it seems logical
to conclude that if MNImin and NISP are correlated, then we can assume that
interdependence of identi¬ed specimens is randomly distributed across taxa because
MNImin is not in¬‚uenced by interdependence. In conjunction with the fact that MNI
is redundant with NISP, there is little reason to use MNI as a measure of taxonomic
estimating taxonomic abundances: nisp and mni 81


abundances. NISP will work nicely as a unit with which to measure taxonomic
abundances at an ordinal scale.



CO N C L U S I O N


NISP is to be preferred over MNI as the quantitative unit used to measure taxonomic
abundances. Throughout much of this chapter, the target variable has been referred to
as taxonomic abundances, with only occasional reference to whether those abundances
pertained to a biocoenose, thanatocoenose, taphocoenose, or identi¬ed assemblage.
It should be clear, however, that what is measured by either MNI or NISP concerns
the set of materials lying on the lab table. The taxonomic abundances are most
directly related to the identi¬ed assemblage, less directly to the taphocoenose, even
less directly to the thanatocoenose, and least directly to the biocoenose from which
the remains derived in the ¬rst place. It is in part for this reason that at least one
alternative method “ that of matching paired bones discussed in Chapter 3 “ was
proposed. A more direct measure of the thanatocoenose was desired, but whether or
not such is actually attained is debatable.
Aggregate de¬nition must depend on the research question being asked. That
question should explicitly state the target variable(s), and it should be identi¬ed as
the identi¬ed assemblage, the taphocoenose, the thanatocoenose, or the biocoenose.
Grayson (1979, 1984) seldom mentioned which of these potential target variables was
of interest, though his substantive analyses at the time suggest he sought a measure
of taxonomic abundances within the biocoenose. Grayson was particularly worried
about the statistical and mathematical properties and relationships of NISP and
MNI. This concern is re¬‚ected by his focus on the effects of aggregation and of
interdependence. But many other analysts also failed to make explicit which one (or
more) of the potential target variables was of interest. It is in part for this reason “
the lack of an explicitly speci¬ed target variable “ that many paleozoologists, espe-
cially zooarchaeologists, have argued for decades about how to determine taxonomic
abundances. There is not nearly as extensive a literature on this topic in paleontol-
ogy, which is not to say that there are not titles on this topic in the paleontological
literature (e.g., Badgley 1986; Gilinsky and Bennington 1994; Holtzman 1979). The
reason that there is not as extensive a literature in paleontology as there is in zooar-
chaeology is because the former generally has one and only one target variable, and
it is the same regardless of researcher. That target is the biocoenose. Zooarchaeolo-
gists, on the other hand, often have rather different target variables depending on the
quantitative paleozoology
82


questions they are asking. What did people eat versus what was available to exploit, for
example.
Explicitly specifying the exact target variable will go a long way toward clarifying
an appropriate (valid) quantitative unit. It is exactly such speci¬cation that prompted
some researchers to develop and use methods of measuring taxonomic abundances
other than NISP and MNI. We turn to those alternative units in Chapter 3, and then
in Chapter 4 we return to NISP and MNI to explore how they have been and can be
used to measure properties of prehistoric faunas.
3
Estimating Taxonomic Abundances:
Other Methods

In Chapter 2, the two methods of measuring taxonomic abundances “ NISP and
MNI “ most commonly used in paleozoology were discussed. In this chapter other
methods that have been used to quantify taxonomic abundances or what is sometimes
loosely referred to as taxonomic importance are described. In so doing, perhaps
methods that work better than NISP and MNI in some situations can be identi¬ed.
And, we can explore how and why some of these methods are less accurate, valid, or
reliable than NISP, MNI, or each other, and whether or not they should be used at
all. This last point is critical because virtually all of the alternative methods discussed
here have occasionally been advocated as better than NISP or MNI as measures of
taxonomic abundances within a biocoenose. Because most of them were proposed
20 or more years ago, it seems appropriate to evaluate them in light of the new
knowledge that has been gained over the past two decades.
The problems that attend NISP and MNI suggest that counting units different than
MNI and NISP should be designed and used. And the literature contains arguments
that counting units other than NISP and MNI should be used to determine taxonomic
abundances. Clason (1972:141), for example, argues that MNI should be termed
the “estimated minimum number of individuals,” and he uses the word estimated
“intentionally because a real calculation of the minimum number of individuals is
not possible.” He does not explain what he means, but given his other remarks it
seems that he is concerned that MNI produces a minimum minimum. This is so
because matching of bilaterally paired bones (left and right humeri, for example)
will be less than perfect (some matches will not be identi¬ed, other matches will be
incorrect), the true minimum number of individuals (MNI) (given that we cannot
match each humerus with each tibia, each femur with each m3, etc.) represented by
a collection will never be known. Of course that is true, but it also is fatalistic. Perfect
data are seldom available in many scienti¬c disciplines. Its absence from paleozoology
is hardly a reason to not try to learn the limitations (analytical and interpretive) of
quantitative paleozoology
84


the data that are available. For example, do NISP values provide accurate ordinal
scale measures of taxonomic abundances in a thanatocoenose or biocoenose? If so,
then MNI values are unnecessary.
Another reason that alternative quantitative methods and units have been pro-
posed as replacements for NISP and MNI is that the alternatives occasionally are
designed to answer a different question than “Is taxon A more abundant than taxon
B, and if so, by how much?” As I emphasized at the end of Chapter 2, explicitly
de¬ning the target variable that we are trying to measure should help us evaluate old
measures and design better new ones. That is, in some cases, exactly what those who
proposed the alternative measures discussed below had in mind. In the following,
several of those alternative measurement units are reviewed. The ¬rst is one that is
frequently advocated by zooarchaeologists and a related measure occasionally used
by paleontologists “ meat weight and biomass, respectively “ that often rests on a
calculation of MNI. The second is a quantitative method “ ubiquity “ that has sel-
dom been used in paleozoology. Advocates of the third method “ calculation of the
Lincoln’Petersen index “ argue that it provides a more accurate estimate of taxo-
nomic abundances within the thanatocoenose or biocoenose than do either NISP
or standard Whitean MNI values. Brief discussion of several other suggestions that
have been made with respect to estimating the most probable number of individuals
represented in a collection concludes the chapter.



B I O M A S S A N D M E A T WE I G H T


Paleontologists sometimes measure biomass, de¬ned by biologists as the total
amount of all biological tissue in a speci¬ed area or of a speci¬ed population. Pale-
ontologists generally modify this de¬nition to mean the total amount of biological
tissue represented by taxa represented in the collection of animal remains they are
studying (e.g., Damuth 1982; Guthrie 1968; Scott 1982; Staff et al. 1985). Zooarchaeol-
ogists (and sometimes ornithologists) also sometimes measure the amount of “meat”
(or perhaps more accurately, the amount of consumable soft tissue) represented in a
faunal collection (White 1953a). The amount of meat is some fraction of the biomass
represented by an assemblage because not all tissue making up biomass is consum-
able. There are several methods that have been designed to measure biomass and
several other ones designed to measure meat weight. Meat weight is usually a deriva-
tive of biomass, so we begin with biomass. It tends to be the less derived of the two
given the methods used to calculate it.
estimating taxonomic abundances: other methods 85


Measuring Biomass

In an early use of biomass, paleontologist R. D. Guthrie (1968:351) multiplied the
“approximate annual average [live weight] of all age classes” of each species repre-
sented by their percentage frequency in each of four assemblages. He used genetically
closely related modern taxa as an analog for the weight of individuals among the
extinct prehistoric taxa represented in the assemblages. He used “annual” averages
because of the marked seasonal changes in body weight among the mammalian taxa
he was studying (e.g., Guthrie 1982, 1984a, 1984b). The average weight of all age
classes accounted for the fact that youngsters of all taxa (plants and animals) weigh
less than adults. Guthrie was particularly interested in the mammalian biomass that
could be supported by what has subsequently been referred to as the “mammoth
steppe” habitats of the late Pleistocene Arctic, so MNI was not the best measure of
taxonomic abundances given the nuances of the question he was asking. Guthrie
apparently used the equivalent of MNImin as the value for taxonomic frequencies
in each assemblage, and multiplied that amount by the annual average live weight
of all age classes to obtain his measures of biomass. Given that his research question
concerned ¬‚oral habitats, in his analysis he retained a distinction between grazers
(indicative of grassland) and nongrazers.
Guthrie™s analysis is instructive for the simple reason that he was explicitly aware
of several of the most signi¬cant variables that had to be dealt with were he to
measure the prehistoric biomass of mammals. These include seasonal variations in
body weight and ontogenetic (development or age) variation in body weight. The
deer (Odocoileus sp.) and wapiti (Cervus sp.) remains from Cathlapotle illustrate
the problems attending these variables. The MNI values, average live weights, and
estimated biomass for each taxon in each assemblage are given in Table 3.1 . The
average annual live weight of all ages and both sexes reported by White (1953a) was
used to estimate the biomass of the two taxa. The MNI abundances indicate deer
outnumber wapiti slightly in both assemblages; the ratio of deer to wapiti based on
MNI is 1 :0.86 in the precontact assemblage and 1 :0.89 in the postcontact assemblage.
But as White (1953a, 1953b) likely would have predicted, given differences in body
size, the biomass of wapiti “ the larger of the two ungulates “ is greater than that of
deer in both assemblages; the ratio of deer to wapiti biomass is 1 :3.4 in the precontact
assemblage and 1 :3.6 in the postcontact assemblage. Given that deer tend to browse
a bit more than wapiti, and wapiti graze a bit more than deer, one might be tempted
to conclude there was more grassland than shrubland or forest in the area. The
biomass measures also suggest wapiti tissue is more abundant than deer tissue (in
quantitative paleozoology
86


Table 3.1. Biomass of deer and wapiti at Cathlapotle

Average live Precontact Precontact Postcontact Postcontact
weight (kg) MNI biomass MNI biomass
Wapiti 350 12 4,200 24 8,400
Deer 87 14 1,218 27 2,349




these collections), which contradicts the measure of taxonomic abundance provided
by MNI.
Biomass estimates of the sort represented in Table 3.1 are not without problems.
Most obviously, the biomass of deer and the biomass of wapiti are likely to not be
ratio scale measures given that they are based on MNI, which is a measure that is
likely to be, at best, only ordinal scale. Furthermore, if a method like that represented
in Table 3.1 is used to calculate biomass, then the in¬‚uence on the result of MNImin
versus MNImax can be substantial. Aggregation with respect to calculating MNI
plagues this kind of biomass measurement. And, there are other problems as well.



Problems with Measuring Biomass (based on MNI)

A variable that Guthrie did not worry about was whether his assemblages of faunal
remains were coarse-grained palimpsests or ¬ne-grained snapshots. He noted that
each of the four assemblages he studied had been collected from deposits that repre-
sented “a relatively short duration” of time and that this “narrow unit of time permits
the [paleoecologist] to consider these fossil assemblages as remnants of a community
which occupied the immediate area where they were recovered” (Guthrie 1968:347).
Exactly how much time was represented by the accumulation and deposition of each
assemblage was unclear. That several hundreds or perhaps even thousands of years
are represented by the assemblages would not be an unreasonable guess. Whatever
the case, the point here is that paleozoological estimates of biomass are not measures
of “standing crop” or the amount of biomass at one point in time (Krantz 1977).
Biologists measure biomass at, effectively, one point in time; it may take them a
month or two to actually measure it, but relatively speaking their measurements are
¬ne grained. A paleozoologist, however he turns a collection of bones into a measure
of biomass, is not measuring the same variable in terms of time that a biologist
is. The paleozoologist is measuring that variable in terms of paleoecological time.
Any collection of faunal remains with several taxa and several individuals of each
estimating taxonomic abundances: other methods 87


is likely to have been accumulated and deposited over some period of time greater
than a year or even a decade. At present, we lack the taphonomic knowledge and
paleochronometers that would allow us to determine the temporal duration over
which a collection of faunal remains was accumulated and deposited. Such “time-
averaged” collections may not always be a bad thing (e.g., Kowalewski et al. 1998;
Lyman 2003b), but whether they are or not will depend on the temporal resolution
required by one™s research question.
Another variable that Guthrie did not consider was individual variation; Guthrie
used an average weight. All members of a taxon, even though they might be the same
sex, the same age, the same health status, and are raised in the same habitat, will
not weigh exactly the same as each other all of the time. Add in sex differences, age
differences, health differences, minor habitat variation, and the range of individual
variation increases accordingly. Figure 3.1 is redrawn from Brown (1961 ), a biologist
who weighed live black-tailed deer (Odocoileus hemionus columbianus) in western
Washington State. The ¬gure shows a couple things relevant to measuring the biomass
of deer, even assuming that we can derive MNI accurately. First, the two lines are
each based on a single individual (one male, one female); minimums and maximums
reported by Brown (1961 ) for other individuals for a limited number of months
are also plotted in Figure 3.1 . The potential magnitude of individual variation is
remarkable.
Second, males are consistently larger than females, except perhaps at birth. Using
MNI without distinguishing males and females masks sexual variation. The third
thing to note in Figure 3.1 is the growth of deer over the ¬rst 2“3 years of life. They
increase in size (and the biomass of individual deer increases) as they grow. Use of an
average adult live weight as a multiplier ignores ontogenetic variation. Fourth, note
the variation in weight by season in adult deer (≥ 3 years of age). This is a particularly
pernicious problem in temperate latitudes where seasonal variation in forage causes
many animal species to gain weight in the spring, summer, and early fall, and lose
weight in the late fall and winter (Guthrie 1984a).
But, you might suggest, we can control for ontogenetic age at death and season
of death of the organism based on tooth eruption and wear, and we can control for
sexual dimorphism by determining the sex of the individual represented by various
animal remains. Certainly we can determine the age at death and the season of
death of at least some deer and some wapiti represented in a collection based on
tooth eruption and wear. In many instances with the deer and wapiti remains from
Meier and from Cathlapotle, however, estimates of ontogenetic age were coarse “
each estimate of age at death included a range of ±several months “ particularly
for individuals older than about 4 years. Regardless of the age estimation process,
quantitative paleozoology
88




figure 3.1. Ontogenetic, seasonal, and sexual variation in live weight of one male and one
female Columbian black-tailed deer. Points are for one individual, vertical lines through
points indicate observed range across multiple individuals. Modi¬ed from Brown (1961 ).



in no case were multiple lower teeth “ the skeletal elements used to determine the
age of deer and wapiti “ the most common element and thus in no case did teeth
provide both ontogenetic data and the MNI (Table 2.11 ). There is no way, then, to
determine how many 6-month-old deer and wapiti, how many 12-month-old deer
and wapiti, how many 18-month-old deer and wapiti, and so on, are represented
without inadvertently omitting some of the forty-one deer (MNImax) and thirty-six
wapiti (MNImax) represented (Table 3.1 ). Examine Figure 3.1 again and consider
how such data might be used paleozoologically. Were the same kind of data available
for wapiti, a pair of curves not unlike those in Figure 3.1 would likely be produced.



Solving Some Problems in Biomass Measurement

Signi¬cant problems with Guthrie™s protocol involve his use of an average adult live
weight and simple MNI measures (no accounting for age, sex, or size variation) of
estimating taxonomic abundances: other methods 89


taxonomic abundance. More recently, paleobiologists who have estimated prehistoric
biomass have distinguished taxa with high abundance in the fossil record from those
with low abundance, and also distinguished taxa that included mostly large individ-
uals from those that included mostly small individuals (Bambach 1993). A relatively
abundant taxon made up of large individuals represents more biomass than a rela-
tively rare taxon made up of small individuals. This analytical procedure solves many
problems because it avoids measurement error. It does so by sacri¬cing resolution;
taxonomic abundances are ordinal scale estimates as are estimates of modal body size
of individuals in a population of a taxon. Biomass estimates based on these variables
cannot be better than ordinal scale. Other forms of corrections have been proposed
in the context of estimating meat weight, the measurement we turn to next.



Measuring Meat Weight

White™s (1953a) seminal procedure for measuring the amount of meat or consumable
tissue represented by a collection of archaeological faunal remains was similar to
Guthrie™s for estimating biomass, plus one additional analytical step. First, determine
the MNI (per taxon). Second, multiply the MNI (for a taxon) by the amount of
meat one average individual (of the taxon) would provide. Third, an additional step
(actually performed second in order according to White), involves multiplying the
total live weight per average individual by the proportion of that weight thought to
be edible. The mathematical equivalent would be to calculate the biomass of each
taxon as Guthrie (1968) did, and then multiply that value by the proportion thought
to be edible (White 1953a). In this case, for example, the biomass of deer and that of
wapiti at Cathlapotle would, according to White (1953a), each be multiplied by 0.5 to
obtain the amount of edible tissue each taxon provided. White provided “pounds of
usable meat” for nearly three dozen species of mammals and more than two dozen
species of birds.
White™s procedure shares features with Guthrie™s. For example, the biomass of
a single individual (what he called “average live weight”) that he used to derive
usable meat amounts is an average of both sexes and all age classes, except for several
sexually dimorphic species. Smith (1975) suggested that because many animal taxa
are sexually dimorphic, such as deer and wapiti (but not considered as such by White),
the analyst should establish the sex ratio in a collection and add that to the procedure
for estimation of biomass. If some individuals were males and some were females,
then step 2 of White™s protocol had to be performed twice for a taxon, once for each
sex. For example, in the postcontact assemblage at Cathlapotle, the sex ratio of wapiti
quantitative paleozoology
90


Table 3.2. Meat weight for deer and wapiti at Cathlapotle, postcontact
assemblage

Average live Postcontact Postcontact Percent Meat
weight (kg) MNI biomass edible weight
Wapiti male 400 10 4,000 50 2,000
Wapiti female 300 14 4,200 50 2,100
Deer male 100 8 800 50 400
Deer female 70 19 1,330 50 665


is three males to four females, and the sex ratio for deer is three males to seven females
(both based on anatomical features of the innominate). If those sex ratios are used to
estimate the number of males and females among the total MNI, and then biomass
and meat weight are recalculated using the estimated number of males and the
estimated number of females (based on the observed sex ratio), the calculated values
are different than when sexual dimorphism is not considered (Table 3.2). The ratio
of deer to wapiti biomass increases from 1 :3.6 without sexual dimorphism included
to 1 :3.8 when it is included. Because White™s conversion factor to derive meat weight
is 50 percent for both taxa and both sexes, the deer to wapiti meat weight ratio is also
1 :3.8. We have gained resolution as to taxonomic abundances only if MNI values are
ratio scale values and only if the estimated sex ratio is accurate. The latter may not
be given that the total number of specimens that could be sexed is much less than
twenty-four for wapiti and much less than twenty-seven for deer.
Smith (1975) also suggested that the analyst should determine the age structure or
demography of each taxon represented by the collection. This could be done using
species speci¬c schedules of mandibular tooth eruption and wear. The proportion
of the total MNI represented by each age class in the collection is then be added into
the conversion of MNI into biomass. Estimating the number of individual deer and
wapiti in each of several age categories at Cathlapotle is not possible. To get a feel
for what is involved here, consider yet again Figure 3.1 , and think about the fact that
similar data, although not as ¬ne-grained, exist for wapiti (Hudson et al. 2002).
Problems that attend White™s (1953a) measurement protocol include the fact that
the values for converting the biomass of one individual into mass of edible tissue are
debatable (Stewart and Stahl 1977). White (1953a:397) derived his conversion values
from (1) the gross morphology of the taxon (heavy-bodied, short-legged taxa vs. light-
bodied, long-legged); (2) the percentage of live weight that professional butchers and
meat packers estimated was usable meat; and (3) the presumed level of ef¬ciency
of primitive butchers. He thought his percentages would “give reasonably accurate
estimating taxonomic abundances: other methods 91


Table 3.3. Comparison of White™s (1953a) conversion values (percentage
of live weight) to derive usable meat with Stewart and Stahl™s (1977)
conversion values (percentages of live weight) to derive usable meat

Taxon White Stewart and Stahl
58“74a
Mole (Condylura cristata) 70
Rabbit (Oryctolagus cuniculus) 50 40.7
Chipmunk (Tamias striatus) 70 39.7
Squirrel (Sciurus carolinensis) 70 26.0
Beaver (Castor canadensis) 70 32.2
Muskrat (Ondatra zibethicus) 70 51.9
Dog (Canis familiaris) 50 80.8
Black bear (Ursus americanus) 70 64.8
Fisher (Martes pennanti) 70 64.8
Lynx (Lynx sp.) 50 42.5
Seal (Phoca hispida) 70 30
57 b
Deer (Odocoileus sp.) 50

a
based on two individuals.
b
from Smith (1975).

results” and that any error would be “relatively constant,” likely believing that errors
were randomly distributed within and between taxa. Smith (1975) suggested that
White™s conversion factor for deer of 50 percent was too low and opted for 57 percent.
Stewart and Stahl (1977:267) measured the body weight of a dozen carcasses of various
taxa, then weighed the “edible tissues and organs,” and calculated the latter as a
percentage of the former. Overall, their values for the percentage of edible tissue of a
carcass differ from White™s (Table 3.3). Stewart and Stahl indicated that their data did
not conclusively provide a set of conversion values that gave more accurate measures
of edible tissue than White™s. They hoped such an alternative set of conversion values
could be developed, but no other set of conversion values has been proposed. Recent
researchers have used White™s (1953a) original values (e.g., Stiner 2005).
The problem identi¬ed by Stewart and Stahl (1977) may be greater than they
imagined. It is likely that no set of conversion values that are consistently ordinal scale
values, let alone ratio scale values, can be developed. Based on modern butchering
practices of ri¬‚e-equipped hunters, data have been compiled on the amount of tissue
that might be consumed. The percentage of live weight that comprises usable tissue
of male and female wapiti of different ages varies considerably (Table 3.4). Were one
to develop a set of conversion values such as Stewart and Stahl (1977) proposed, that
set would need to include not just a conversion value for every species, it would need
quantitative paleozoology
92


Table 3.4. Variation by age and sex of wapiti butchered
weight (eviscerated, skinned, lower legs removed) as a
percentage of live weight. From Hudson et al. (2002:250)

Age Male Female
2 years 45 48
2 to 4 years 44 46
≥ 5 years 42 51


multiple conversion values for each species. A different conversion value would be
necessary for each age class of each sex (Table 3.4). Figure 3.1 makes it clear that
numerous conversion values are required for each taxon if one hopes to have ratio
scale measures of usable meat. And this is not the only signi¬cant methodological
hurdle to perfecting White™s protocol.
Table 3.5 demonstrates that depending on how a carcass was butchered, and what
the butcher thought was edible, the conversion values may vary considerably. For a
mature male wapiti with a live weight of 350 kilograms, the proportion of live weight
that comprises usable tissue varies more than 40 percent over several different stages
of butchering. Not only that, whatever conversion value is used, that value assumes
complete consumption “ from nose through tail, as one anonymous commentator
put it “ of the carcass. As Binford (1978) demonstrated in an ethnoarchaeological
context and Lyman (1979) argued from the perspective of historic zooarchaeological
data, such an assumption is unwarranted (see also Schulz and Gust 1983). A single
deer femur in an archaeological site does not necessarily represent the meat of an
entire animal, regardless of the conversion value one uses to transform that bone
specimen into amount of usable meat (or biomass). Lyman (1979) suggested deter-
mining the minimum number of butchering units, say, hindquarters of a species
of mammal, and applying a conversion value to that quantitative unit. This sim-
ply shifts the problem of deriving a minimum number of carcasses “ the standard
MNI “ to deriving a minimum number of each of several distinct butchering units
(assuming such can be identi¬ed archaeologically), and it retains the problem of
developing conversion values for multiple age“sex categories that may not be visible
paleozoologically. The same problems attend similar suggestions by Schulz and Gust
(1983) who used historical documents to estimate the rank order economic value of
different butchering units (see also Huelsbeck 1989; Lyman 1987b).
Along these lines, Betts (2000:30) suggested that in an historic archaeological con-
text the zooarchaeologist would do well to base estimates of meat amounts “on
consumer units with a known relationship to the [faunal] material being analyzed.”
He suggested that rather than calculate meat weight per taxon based on the MNI
estimating taxonomic abundances: other methods 93


Table 3.5. Weight of a 350-kilogram male wapiti in various
stages of butchering. From Hudson et al. (2002:250)

Weight of Proportion of
Butchering stage carcass live weight
Live weight 350 1.0
Bled weight 340 0.97
Eviscerated 228 0.65
Hide and lower legs 189 0.54
removed



per taxon, the analyst should determine the frequency of consumer units per taxon.
Consumer units might be standard quarters, wholesale units, or retail-like units of
an animal, or something else. This procedure merely relocates the problem from
converting an MNI value to meat weight to converting a (minimum?) number of
consumer units to meat weight. Betts (2000) uses a conversion procedure not unlike
White™s (1953a), complete with all its attendant problems and weaknesses. Thus Betts
(2000:30) correctly emphasizes that his suggested procedure “merely provides esti-
mates of the actual meat contributions indicated by the remains.” Those contribution
amounts are at best ordinal scale.
We are left with a grim picture of measurements of meat weight using protocols
such as Guthrie™s and White™s. Are there better techniques for measuring taxonomic
abundances based on biomass or meat weight or both? Indeed, there are other ones,
though these too have some serious weaknesses that make them rather tenuous.



The Weight Method (Skeletal Mass Allometry)

A variable that one might measure is the weight of skeletal material per taxon.
This quantitative unit was suggested by several zooarchaeologists in the 1960s and
1970s as one that could be used to measure either biomass or edible meat (Reed
1963; Uerpmann 1973; Ziegler 1973). Despite signi¬cant criticisms (Casteel 1978;
Chaplin 1971 ; Jackson 1989; Lyman 1979), zooarchaeologists the world over continue
to measure and interpret the weight of osseous material (e.g., Dechert 1995; van Es
1995; Jackson and Scott 2002; Landon 1996; McClure 2004; Prummel 2003; Tuma
2004; Weinstock 1995). One zooarchaeologist has provided a detailed review of the
nuances of this method, and argues that it should be studied further and perfected
because of its value (Barrett 1993). It is worthwhile, then, to consider this quantitative
variable in some detail.
quantitative paleozoology
94


First, the bone weight or, simply, weight method is based on the biological property
of allometry. Allometry concerns the relationship of the size of one property of a
body to the size of another. The size of a particular organ to the size of another in a
body, the size of the head relative to the rest of the body, or the size of a limb relative
to the size of the body are all allometric relationships. Allometry concerns the study
of such relationships and if and how those relationships change during the ontogeny
of an organism. The weight method developed by zooarchaeologists cashes in on
the allometric relationship between bone weight and the total body weight of an
organism. As biologists have noted, “animal skeletons scale allometrically with body
mass, so that skeletons of large animals are proportionately more massive than those
of small animals” (Prange et al. 1979:103). The ratio of bone weight to live weight
per individual is greater for large individuals (whether of the same or different taxa)
than that ratio is for small individuals (Needs-Howarth 1995). The presumption is
that if the statistical nature of the relationship between these two variables can be
determined, then that relationship can be used to convert bone weight observed in
an archaeological collection into biomass or usable meat weight.
As summarized by Casteel (1978), many of the original analytical protocols for
using the weight method involved two steps once the specimens comprising a collec-
tion of faunal remains had been identi¬ed to taxon. First, weigh all remains of each
taxon separately. Then, convert the bone weight of each taxon to either a measure
of biomass or of usable meat weight. As might be expected given the comments on
White™s (1953a) conversion values presented earlier, the conversion values proposed
by those advocating the weight method varied considerably from author to author.
Cook and Treganza (1950:245), for example, estimated that dry bone represented
about 6 percent of the original live weight of a mammal and of a bird. Adopting
this estimate, the weight of dry bone would be converted to biomass by multiplying
that weight by 16.67 (Casteel 1978). In contrast, Reed (1963) estimated that dry bone
weight comprised about 7.5 percent of the original live weight of a mammal. Were
one to adopt this estimate, the weight of dry bone would be converted to biomass by
multiplying that weight by 13.33 (Casteel 1978). As Casteel (1978) pointed out, empir-
ical studies (as opposed to Cook and Treganza™s and Reed™s estimates) suggested that
anywhere from about 8.5 to 13 percent of the body weight of mammals constituted
bone weight. Ignoring the slippery issue of choosing which percentage to use, once
you have biomass per taxon, you may want to convert that to usable meat, which
introduces problems like those associated with White™s (1953a) analytical protocol.
Shortly after the weight method began to see some use, Chaplin (1971 :68) noted that
anyone using it had to assume that the relationship between bone weight and biomass
(or usable meat weight, whichever was sought) was constant. This was so because
estimating taxonomic abundances: other methods 95


the conversion value chosen was a constant; it did not vary. Thus, if 5 kilograms of
bone represented 60 kilograms of biomass, then 10 kilograms of bone represented
120 kilograms of biomass, 15 kilograms of bone represented 180 kilograms of biomass,
and so on. In Chaplin™s eyes, such an assumption was not warranted. Furthermore,
in some ways anticipating later criticisms of White™s (1953a) MNI-based method,
Chaplin (1971 ) noted that there was some controversy over which conversion value
to use given individual variation within a taxon as well as the fact that an individual™s
weight would vary over time (recall Figure 3.1 ). Chaplin (1971 :68, 69) concluded
that the “relationship of bone weight and body weight is not an exact one” and he
recommended “the meat/bone ratio must be established for each bone, at different
ages of the animal and for each sex.” The meat’bone ratio constitutes recognition
that people might not have consumed an entire carcass, that 5 kilograms of phalanges
do not represent the same amount of biomass and usable meat as do 5 kilograms
of femora of the same taxon, and that 5 kilograms of humeri from 6-month-old
females do not represent the same amount of biomass as do 5 kilograms of tibiae
from 36-month-old males of the same taxon.
Those who have used bone weight as a measure of taxonomic abundance over the
last 15“20 years usually give reasons as to why it is a measure that should be used.
They also often state that it is a better measure of taxonomic abundance than either
NISP or MNI. Those arguments can be summarized as follows:

1 Measures of bone weight allow the summation or merger of abundance data into
more general taxonomic categories such as a taxonomic family or “large
mammal.”
2 Measures of bone weight are not in¬‚uenced by fragmentation.
3 Measures of bone weight circumvent interanalyst variation in identi¬cation skills
that bias measures of taxonomic abundance.
4 Because of the statistical relationship between bone weight and body weight,
bone weight provides proxy measures of usable meat and of the importance or
contribution of a taxon to diet.

This list may seem impressive if not overly long. Critical scrutiny of the arguments
indicates, however, that each is a justi¬cation to not use other measures of taxonomic
abundance (particularly NISP and MNI) rather than a warrant to use bone weight.
This is so because all four statements are easily shown to be variously false, of minimal
signi¬cance, or to apply to bone weight as well as to other measures of taxonomic
abundance.
The ¬rst reason given to use bone weight is certainly true because one can sum the
weights of specimens identi¬ed as, say, deer with the weight of specimens identi¬ed
quantitative paleozoology
96


as deer size. The signi¬cance of the ¬rst statement resides, however, in the unspoken
underpinning assumption that were one to use NISP or MNI to quantify taxonomic
abundances, one would not determine the MNI for categories like a taxonomic family
or large mammal or deer size. That is false; these same categories have been used by
paleozoologists. A well-known example is the ¬ve size categories of African bovid
that zooarchaeologists use because of dif¬culties with identifying the genus or species
of bovid represented by bones and teeth (Brain 1981 ; Bunn and Kroll 1986).
The second reason given to use bone weight is also true, but it ignores the fact
that increasingly intensive fragmentation makes identi¬cation progressively more
dif¬cult. A fragment of medium- or small-size mammal long bone diaphysis might
be confused with a similar fragment from a large- to medium-size bird, for exam-
ple (Driver 1992). Thus fragmentation can in¬‚uence which bones are weighed “
those that are identi¬able are weighed, and intensively fragmented specimens will be
unidenti¬able. The second reason also relates to the ¬rst in the sense that fragments
that cannot be identi¬ed to species but that can be identi¬ed to, say, taxonomic family
can indeed be weighed (just as they can be tallied for the NISP of a taxonomic fam-
ily), but at the cost of losing ¬ne-scale taxonomic resolution (just as when fragments
identi¬able to genus or species are included in NISP tallies of a taxonomic family).
The third reason given to measure bone weight identi¬es a real problem regard-
less of whether one quanti¬es taxonomic abundances with NISP, MNI, or bone
weight (Gobalet 2001; Lyman 2005a). Specimens that are not identi¬ed “ regardless
of whether the categories of identi¬cation are species, genera, families, large, medium,
and small mammal, or whatever “ are simply not tallied nor are they weighed. There-
fore, this reason, like the preceding two, is not a valid warrant to measure bone weight.
The fourth reason contends with the fact that neither an NISP of one mouse and
of one elephant, nor an MNI of one mouse and of one elephant provides an accurate
measure of the contribution of those two taxa to diet. But the fourth reason is not
a good warrant to use bone weight to get at usable meat weight. The problem was
originally identi¬ed by Chaplin (1971 ). If one converts bone weight to biomass or
weight of usable meat, one must assume the relationship between the two variables is
constant and linear. That is, one assumes a single conversion value such as 7.5 percent
of an (average?) individual™s total weight represents the weight of the skeleton, and
the remainder is soft tissue. Chaplin (1971 ) argued that the relationship is in fact
not constant, and Casteel (1978) showed that the relationship is neither constant nor
linear.
Casteel (1978) used previously published data (McMeekan 1940) on the relation-
ship between bone weight and biomass of a domestic pig (Sus scrofa) to show that
the relationship between the two variables is curvilinear. Casteel (1978) examined
estimating taxonomic abundances: other methods 97


Table 3.6. Descriptive data on animal age (weeks), bone weight per individual,
and soft-tissue weight per individual domestic pig. All weights are grams. From
McMeekan (1940)

Bone Muscle Muscle + fat Muscle + fat +
Age weight weight weight hide weight
Birth 242.7 388 439 545
4 767 1,901 2,885 3,240
8 1,730 4,182 6,156 6,990
16 3,962 12,669 19,796 21,534
20 5,214 17,718 30,904 33,198
24 6,438 23,015 43,904 46,979
28 7,396 31,647 66,160 69,602

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