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reduces identi¬ability by disassociating if not destroying the distinctive landmarks
used to tell that bone A is a rabbit tibia whereas bone B is a duck humerus (Lyman
2005a; Marshall and Pilgram 1993). Problem 5 concerns intertaxonomic differences
in preservation and may be related to problem 4 given that fragmentation in¬‚uences
preservation by effectively destroying bones through the process of rendering them
unidenti¬able. If preservational processes vary intertaxonomically, then NISP values
will be differentially in¬‚uenced across taxa. The magnitude of the fragmentation
problem can be evaluated analytically (see Chapter 6). Fragmentation and preserva-
tion are taphonomic processes and may well render NISP data nominal scale with
respect to taxonomic abundances.
Problem 6 is a serious concern to many zooarchaeologists because it is true that
NISP is a poor measure of diet because the meat from the bones of one elephant
will feed more people than the meat from the bones of one mouse. Furthermore,
ethnoarchaeological data suggest that we cannot assume that each individual animal
carcass was consumed entirely (e.g., Binford 1978; Gifford-Gonzalez 1989; Lyman
1979). But if we are concerned with dietary issues, we have in fact changed the
target variable from a measure of taxonomic abundances “ are there more elephants
represented in the collection, or more mice “ to one concerning how much of each
taxon was eaten. Because we are asking a different question, a quantitative unit or
measured variable different than one that simply tallies taxonomic abundances would
seem to be required (see Chapter 3).
Problem 7 is that NISP does not include inherent rules for dealing with articulated
elements, and while rules have been suggested (e.g., Clason 1972), these are not
agreed upon by all paleozoologists or used consistently. A common example concerns
estimating taxonomic abundances: nisp and mni 35


what to do with a mandible or maxilla that contains teeth. The mandible (dentary)
is a discrete anatomical organ, as is each tooth. In ungulates that means a single
mandible (say, the left side) containing all teeth will have 4 incisforms (3 incisors
and a canine that has evolved into the form of an incisor), 3 deciduous premolars, 3
permanent premolars, and 3 molars. It is rare to ¬nd mandibles with all 6 premolars
(the deciduous ones nearly worn to nothing and about to fall out of the mandible; the
permanent ones still forming and without developed roots but beginning to erupt).
So, ignoring that possibility for the moment, when a mandible with all teeth is found,
do we tally an NISP of 1, or do we tally an NISP of 11 (mandible + 4 incisiforms + 3
premolars + 3 molars)? How do we tally an articulated hind limb of an artiodactyl;
as 1, or as 15 (femur + patella + tibia + distal ¬bula [lateral malleolus] + calcaneus +
astragalus + naviculo cuboid + 4th tarsal + metatarsal + 6 phalanges [not to mention
sesamoids])?
The paleozoologist should be consistent in applying across all taxa the tallying
method chosen, and also be explicit about which method is used “ tally articulated
specimens as 1, or tally each distinct anatomical element, articulated or not, as 1. Per-
haps the most important aspect of dealing with this problem is granting ¬‚exibility to
meet the needs of analysis and the nature of the collection. Each mandible, for exam-
ple, can be tallied as 1 regardless of whether it includes teeth or not (noting which
teeth if any are present for purposes other than estimating taxonomic abundances,
although ontogenetic age differences indicated by the teeth may play a role in esti-
mating abundances [see the discussion of MNI]). But which skeletal elements were
articulated when found and which were isolated or not articulated with other spec-
imens is seldom noted by excavators. Thus, the paleozoologist may be forced to
tally each specimen individually as 1, noting when one specimen “articulates” with
another if they come from the same excavation unit, which is not necessarily the
same as saying that it was “articulated” when it was found.
Noting that the problems listed thus far may vary not only intertaxonomically, but
intrataxonomically within and between strata (problem 8) sounds hopelessly fatalis-
tic. However, it is largely an analytical matter to determine if indeed this taphonomic
problem applies in any given case. Even if it does, it may not preclude statistical
comparisons of assemblages of faunal remains. Before arguments and examples of
why this is so are presented, we consider what is likely the most serious problem with
NISP. As a preface, note that most of the problems with NISP discussed so far are
not fatal to it as a measure of taxonomic abundance. Most of these problems were
identi¬ed and subsequently reiterated time and time again not as reasons to abandon
NISP and design a new quantitative unit but rather were presented as warrants to
use MNI (Grayson 1979, 1984). A prime example of this is problem 6. That problem “
that NISP doesn™t give a good estimate of the amount of meat provided “ is like
quantitative paleozoology
36


Table 2.3. The differential exaggeration of sample
sizes by NISP

Taxon A Taxon B Taxon C
NISP 1 10 10
MNI 1 1 10



saying that because a tape measure doesn™t measure color, the tape measure is ¬‚awed.
Of course, the tape measure was not designed to measure color, or weight, or mate-
rial type; rather, it was designed to provide measures of linear distance. Because a
measurement unit doesn™t measure a particular variable is no reason to discard that
unit completely. No one has demonstrated that NISP doesn™t provide valid and accu-
rate measures of taxonomic abundances in a taphocoenose, in a thanatocoenose, or
in a biocoenose. Indeed, virtually all of the problems with NISP do not universally
invalidate it as a unit with which to measure taxonomic abundances.
None of the preceding is meant to imply that NISP is a valid measure of taxonomic
abundances in a taphocoenose, in a thanatocoenose, or in a biocoenose. It might be a
valid measure of taxonomic abundances, but that remains to be determined. Before
discussing how to make that determination, the most serious problem with NISP
must be identi¬ed. This problem must be considered at length precisely because it is
so worrisome.


A Problem We ShouldWorry About

That NISP may differentially exaggerate sample sizes across taxa (problem 9) is
evident in the example in Table 2.3. This table illustrates that if one has an NISP of 1,
then at least 1 individual (MNI) is represented; if NISP = 2, then MNI = 1 or 2; if
NISP = 3, then MNI = 1, 2, or 3; and so on. Thus, were we to compare the abundances
of taxa A, B, and C in Table 2.3, taxon B would be over-represented by NISP relative
to taxa A and C. This is so because for taxa A and C, each individual (MNI) is
represented by one specimen, so each specimen contributes an MNI of 1. But for
taxon B, each individual is represented by an NISP of 10, so each specimen in effect
contributes one-tenth of an individual MNI.
Problem 10 is that NISP is an ordinal-scale measure of abundance so some powerful
statistical analyses and inferences are precluded. We can often say that taxon A is more
abundant than taxon B, but we do not know by how much with respect to a target
variable consisting of the thanatocoenose or the biocoenose. This is so even when we
estimating taxonomic abundances: nisp and mni 37


can control for variation in fragmentation, variation in the number of identi¬able
elements per individual of different taxa, and all those other problems that af¬‚ict
NISP. Notice that I said we can “often” say that one taxon is more abundant than
another; I did not say that we can “always” say this. We return to this point later in
this chapter.
The potential overrepresentation of some taxa by NISP is in fact a super¬cial
concern, but it is intimately related to the deeper, more serious concern expressed in
problem 11 “ NISP suffers from the fact that skeletal specimens may be interdependent
(Grayson 1979, 1984). The specimens of a taxon in a collection, or various subsets
of those specimens, may be from the same individual animal (or each subset from a
different individual). This precludes various statistical analyses and tests of taxonomic
abundance data tallied as NISP that demand independent data, that is, each tally of
“1 ” is independent of every other one. Some analysts have argued that specimen
interdependence is not a serious problem. Gautier (1984), for example, based on
estimates of preservation rates at various sites, notes the probability that an animal
would be represented by a single specimen, by two specimens (the product of two
independent probabilities represented by two specimens), by three specimens (the
product of three independent probabilities), and so on. He ¬nds that the probabilities
for NISP > 1 for any given individual are quite low, so Gautier (1984:240) concludes
“the degree of interdependence (i.e., the fact that an animal is represented by several
bones and hence counted several times) is much less than many analysts fear.”
Gautier™s (1984) estimates of preservation rates are based on a compilation of many
estimates “ the estimated duration of occupation of the site in years, the estimated
size of the human population that occupied the site, the estimated number of animals
necessary to provide suf¬cient food for the human occupants, the estimated degree
of preservation of faunal remains, the estimated fraction of the site excavated, and the
estimated rate of identi¬cation of faunal remains. As these estimates are added up,
one in¬‚uencing another, the ¬nal estimate of whether two specimens derive from the
same animal is likely quite wide of the mark. The estimate is like a radiocarbon age of
1,000 years with an associated standard deviation of 900 years. Furthermore, Gautier™s
estimates must assume that the taphonomic history of each specimen is independent
of the taphonomic history of every other specimen, even when two specimens derive
from the same individual animal. We know that that is false (Lyman 1994c), else we
would never ¬nd articulated bones.
So, presuming that there is some degree of interdependence of specimens tallied
for NISP values, what is the paleozoologist to do? One option is to accept Gautier™s
arguments, and as Perkins (1973:367) suggests, “in the absence of archaeological
evidence to the contrary we must assume that each [specimen] came from a different
quantitative paleozoology
38


individual.” This allows statistical manipulation of NISP data as if each tally of 1 for
each taxon was indeed independent of every other tally of 1 for that taxon. But it
is also likely that skeletal elements of individual animals were not accumulated and
deposited completely independently of each other (Ringrose 1993). They were, after
all, articulated and held together during the life of the organism. Actualistic work
indicates that although complete skeletons may not accumulate as such, portions of
skeletons comprising multiple elements are very often accumulated by both human
and nonhuman taphonomic agents (e.g., Binford 1978, 1981; Blumenschine 1986;
Dom´nguez-Rodrigo 1999a; Haynes 1988; Lyman 1989, 1994c). This brings us back to
±
the question at the beginning of this paragraph: Given that there is some unknown
(and largely unknowable) degree of interdependence in NISP values, what is the
paleozoologist to do?
One thing we might do is assume that interdependence is randomly distributed
across all taxa and all assemblages (Grayson 1979). Assuming this does not, of course,
make it so. But if we could show that interdependence was distributed across taxa and
assemblages in such a way as to not signi¬cantly in¬‚uence measures of taxonomic
abundances, then we would have an empirical warrant for using NISP to measure
those abundances. So, the question shifts from: “Given the likelihood that there is
some interdependence, what are we to do?” to “How are we to show that the nature
and degree of interdependence does not signi¬cantly in¬‚uence NISP measures of
taxonomic abundance?” The answer to the new question must come after we consider
the other quantitative unit that is regularly used to measure taxonomic abundances.



(MNI)
T H E M I N I M U M N U M B E R O F I N D IV I D U A L S


Given the many dif¬culties with using NISP to measure taxonomic abundances, it is
not surprising that Stock (1929) and Howard (1930) estimated abundances of mam-
mals and birds at Rancho La Brea (Chapter 1 ) using a measure other than NISP.
The measure they used is the minimum number of individuals (MNI). Prior to the
middle 1990s, a plethora of acronyms were used for this quantitative unit (Lyman
1994a). As with NISP, MNI usually (but not always) is given for each identi¬ed taxon,
so the acronym is more completely given as MNIi, where i again signi¬es each dis-
tinct taxon and, again, is seldom shown but is instead understood. Recall that Stock
and Howard both de¬ned MNI as the most commonly occurring skeletal element
of a taxon in an assemblage. Thus, if an assemblage consists of three left and two
right scapulae of a species of mammal, then there must be at least (a minimum
of) three individuals of that species represented by the ¬ve specimens because each
estimating taxonomic abundances: nisp and mni 39


individual mammal has only one left and one right scapula. The number of indi-
viduals is a minimum because there may actually be ¬ve individuals represented by
the ¬ve scapulae, but it presently is dif¬cult to determine in each and every case
which left scapula goes with which right scapula (come from the same individ-
ual), nor can we always determine when potentially paired elements do not come
from the same individual. Thus, the actual number of individuals (ANI) represented
by the identi¬ed assemblage of a taxon is dif¬cult to determine, except perhaps in
those rare cases when the taxon is represented by more or less complete articulated
skeletons.
MNI is an attractive quantitative unit because it solves many of the problems that
attend NISP. In particular, it solves the critical problem of specimen interdependence
given how MNI is usually de¬ned “ the most commonly occurring kind of skeletal
specimen of a taxon in a collection. This is indeed how many (but certainly not all)
analysts de¬ne the term (Table 2.4). If the most commonly occurring kind of skeletal
specimen of taxon A is distal left tibiae, then tally up distal left tibiae; the total equals
the MNI of taxon A. If the most commonly occurring kind of skeletal specimen of
taxon B is the right m3, then tally those up and the total gives the MNI for taxon
B. No single individual of any known mammalian taxon possesses more than one
distal left tibia or more than one right m3, so each one of those kinds of specimens
in a collection must represent a unique individual that was alive in the past. An easy
way to conceptualize MNI is this: If two skeletal specimens overlap anatomically,
then they must be from distinct, independent individual organisms because they
are redundant with one another (Lyman 1994b). If the two specimens ¬t together
in a manner like two conjoining pieces of a jigsaw puzzle, then they are from the
same individual and are interdependent. But if the two specimens do not overlap
anatomically and they do not ¬t together like two pieces of a jigsaw puzzle, then they
may be from the same individual unless they are clearly of different size, ontogenetic
(developmental) age, or sex. If they are of the same size, age, and sex, but do not
overlap or conjoin, then they may or may not be from the same individual. That is a
sticky point to which we will return in force in Chapter 3.
MNI seems to have originated in paleontology with individuals such as Stock
(1929) and Howard (1930). It has been suggested that MNI was introduced to
(zoo)archaeologists in 1953 by Theodore White (Grayson 1979), a paleontologist who
worked with zooarchaeological collections, and this could well be correct. However,
an archaeologist working a few years prior to White used MNI as a measure of
taxonomic abundances.
In his unpublished Master™s thesis, William Adams (1949:23“24) estimated the
“approximate number of animals represented by the sample” of bones and teeth he
quantitative paleozoology
40


Table 2.4. Some published de¬nitions of MNI

1. “the number of similar parts of the internal skeleton as for example the
skull, right ramus of mandible, left tibia, right scaphoid” (Stock 1929:282).
2. “for each species, the left or the right of the [skeletal] element occurring in
greatest abundance” (Howard 1930:81 “82).
3. “the bone with the highest total will indicate the minimum number”
(Adams 1949:24).
4. “separate the most abundant element of the species into right and left
components and use the greater number as the unit of calculation” (White
1953a:397).
5. “the [skeletal] element present most frequently” (Shotwell 1955:330); “that
number of individuals which are necessary to account for all of the skeletal
elements (specimens) of a particular species found in a site” (Shotwell
1958:272).
6. the number of lefts and of rights of each element, those matching in terms
of age and size tallied as from the same individual, those not matched tallied
separately as from different individuals (Chaplin 1971).
7. “equal to the greatest number of identical bones per taxon” (Mollhagen et
al. 1972:785).
8. “a count of the most frequent diagnostic skeletal part” (Perkins 1973:368).
9. “the most frequently occurring bone” (Uerpmann 1973:311).
10. “the number that is suf¬cient to account for all the bones assigned to the
species; the most abundant body part” (Klein 1980:227).
11. “the least number of carcasses that could have produced the recovered
remains . . . determined by taking the raw count of the most commonly
retrieved bone element that occurs only once in the skeleton” (Gilbert and
Singer 1982:31 “32).
12. “may be based upon counts of the most abundant element present from one
side of the body or on counts determined by joint consideration of skeletal
parts represented; the size, age, and wear-state of specimens” (Badgley
1986:329).
13. “essentially the sample frequency of the most abundant skeletal part” (Plug
and Plug 1990:54).
14. “the smallest number of individual animals needed to account for the
specimens of a taxon found in a location” (Ringrose 1993:126).
15. “the most frequently occurring element” (Rackham 1994:39).
16. “the higher of the left- and right-side counts (if appropriate “ obviously not
if the most abundant element is an unpaired bone such as the atlas) is taken
as the smallest number of individual animals which could account for the
sample” (O™Connor 2000:59).
estimating taxonomic abundances: nisp and mni 41


had studied. He chose “certain bones as readily identi¬able, easily distinguished with
regard to right or left position in the body and not commonly used for artifacts,”
and tallied up the occurrences of each for two taxa in each of ¬ve distinct recovery
proveniences (p. 24). He noted that “since any one animal can possess only one of each
of these bones, then the bone with the highest total will indicate the minimum number
of mammals represented by the bone sample from that [recovery provenience]”
(p. 24). Adams summed the MNI values indicated by each assemblage of bones from
a unique recovery provenience and noted that in so doing, he had to assume “that parts
of one individual are not represented from more than one [recovery provenience]”
(p. 24); he assumed that skeletal remains in one provenience were independent of
those in all others. Despite these signi¬cant insights, Adams (1949:24) abandoned
MNI values because they provided only “minimum numbers,” and he believed that
assigning a “maximum number would be a matter of guesswork.” Adams desired
a quantitative unit that provided ratio’scale taxonomic abundances. Adams did
not reference Stock or any other paleontologist who had previously used MNI as a
quantitative unit. Circumstantial evidence therefore suggests that Adams invented
(if you will) MNI independently of its invention in paleontology. But because he did
not publish his discussion, few zooarchaeologists seem to have been aware of the
MNI quantitative unit prior to White™s work. At least few of them used MNI prior
to the late 1950s, by which time it had been used in clever ways by Theodore White,
who published his results in archaeological venues.
Unlike Adams, White (1953a, 1953b) did not seek to estimate taxonomic abun-
dances when he introduced MNI to zooarchaeologists. Rather, he sought to estimate
the amount of meat provided by each taxon; that was his target variable. He (1953a:397)
noted that “four deer [Odocoileus sp.]” were needed to provide as much meat as “one
bison [Bison bison] cow,” and NISP would not reveal how much meat was provided
by each of these taxa. Being a paleontologist who likely was familiar with, and used to
seeing MNI values reported in the paleontological literature (e.g., Howard 1930; Stock
1929), White was aware of a quantitative unit (MNI) that could be easily converted
to meat weight. White may have believed that there was no other reason that animal
remains would be of interest to archaeologists, other than to reveal some aspects of
human behavior. Diet “ what folks ate “ was an obvious human behavior re¬‚ected
by animal remains.
Methods, including White™s, to estimate meat weight (and the related variable,
biomass) are discussed in Chapter 3. The important point here is that MNI was
introduced to zooarchaeologists not as a replacement for NISP as a measure of
taxonomic abundances. Rather, MNI was introduced to zooarchaeology in order to
measure something else, speci¬cally the amount of meat represented by a collection
quantitative paleozoology
42


of faunal remains. From a historical perspective, this is interesting for the simple
reason that MNI was used in yet another discipline originally to estimate taxonomic
abundances. The measurement of biomass and meat weight was introduced in that
discipline as a replacement for MNI as a measure of diet, that is, for virtually the
same reason MNI was introduced in zooarchaeology.
One of the things that ornithologists are interested in is the diet of birds. Raptors
(hawks and eagles) and owls hunt, among other animals, small mammals “ various
insectivores, rodents, and leporids “ and, depending on the taxon of the bird, swallow
partial or complete carcasses of their prey. After 12“24 hours or so, a “pellet” of hair,
bones, and teeth is regurgitated (the common terms in the ornithological literature
are “egested” or “cast”). Depending on the bird, the bones and teeth are often in
very good condition (not broken or excessively corroded from digestive acids) and
retain many taxonomically diagnostic features (Andrews 1990). Because pellets are
deposited beneath roosts (resting areas) and nests, a collection of pellets from such
a location can reveal much about the diet of the bird.
Studies of such pellets and the faunal remains they contain have a deep history
in ornithology (e.g., Errington 1930; Fisher 1896; Marti 1987; Pearson and Pearson
1947). Because ornithologists study the remains of prey in those pellets in order to
answer some of the same questions that paleozoologists do (Which taxon is most
abundant and which is least abundant on the landscape? Which taxon provided the
most sustenance to the predator? [e.g., Andrews 1990; Mayhew 1977]), ornithologists
have grappled with some of the same issues that paleozoologists have, especially with
respect to how to quantify the remains of vertebrate prey. Ornithologists quickly
¬gured out that NISP might not give a valid indication of which prey taxon was the
most frequently consumed, so they did one of two things. They either tallied only
skulls, or they determined the MNI based on whether the skull, left mandible, or right
mandible was the most common skeletal element in a collection. They used both of
these approaches as early as the 1940s (references in Lyman et al. 2003), describing
how they counted taxonomic abundances. The earliest formal de¬nition of MNI by
an ornithologist of which I am aware is Mollhagen et al.™s (1972:785): the “minimum
number of animals [is] equal to the greatest number of identical bones per taxon.” No
ornithologist who uses MNI, references Stock or any other paleontologist who used
MNI, suggesting yet another independent invention of MNI. Near universal adoption
of MNI as the quantitative unit of choice of ornithologists lead quickly to recognition
that an MNI of ¬ve for each of two taxa did not give an accurate measure of diet
when individuals of those two taxa were of rather different size. Thus, ornithologists
determined the live weights of average adult individuals of common prey species and
estimating taxonomic abundances: nisp and mni 43


used those data to determine the composition of a bird™s diet (Steenhof 1983), much
as White (1953a, 1953b) had done 30 years earlier.
Given that three separate disciplines have used MNI, and all of them (granting
Adams™s ¬‚irtation with it) seem to have independently invented it, one might think
that MNI is a well-understood unit of measurement. It is commonsensical to cal-
culate, and it has a basis in the empirically veri¬able reality of the individuality
and physical discreteness and boundedness of every organism. But MNI is not a
well-understood quantitative unit. It has a number of problems, just like NISP. And
also just like NISP, several of the problems with MNI are trivial or easily dealt with
analytically, but one of them is rather serious.



Strengths(?) of MNI

Klein (1980:227) stated that unlike NISP, MNI is not affected by differential fragmen-
tation, and suggested that this was a reason to seriously consider using MNI values as
measures of taxonomic abundance, particularly when comparing assemblages with
different degrees of fragmentation. He was concerned that a taxon, the remains of
which had not been broken, would be underrepresented by NISP relative to a taxon the
remains of which had been broken, all else being equal. Although Klein is correct that
fragmentation will increase NISP, he is only partially correct because in reality frag-
mentation can in¬‚uence MNI in two ways. First, fragmentation of moderate intensity,
say, breaking each element into two more or less equal size pieces, will not in¬‚uence
MNI because specimens will retain anatomically and taxonomically diagnostic fea-
tures (Lyman 1994b). Second, as the intensity of fragmentation increases, meaning
that as fragments get smaller and represent less of the skeletal element from which
they originate, the more dif¬cult it will be to identify those fragments as to skeletal
element represented and to taxon. This is so because progressively smaller fragments
are successively less likely to retain anatomically and taxonomically diagnostic fea-
tures (Lyman and O™Brien 1987). Thus fragmentation ¬rst increases NISP (but not
MNI), but then as fragmentation intensi¬es, NISP decreases and so too does MNI.
The relationship between fragmentation and NISP, and that between fragmen-
tation and MNI, was spelled out by Marshall and Pilgrim (1993) with respect to
measuring the frequencies of individual skeletal parts. Because MNI is based on the
most frequent skeletal part, Marshall and Pilgrim™s ¬ndings are equally applicable
to both NISP and MNI. Fragmentation in¬‚uences MNI, although in a manner dif-
ferent than it does NISP. Breaking a skeletal element into pieces will ¬rst increase,
quantitative paleozoology
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