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assemblages could not be distinguished. This assemblage is, therefore, treated as a
whole and not subdivided into subassemblages. The stratigraphy at Cathlapotle, on
the other hand, though also rather complex as a result of the various things that people
did at the site, was suf¬ciently clear that two temporally distinct (sub)assemblages
of faunal remains could be distinguished. Many, but not all of the mammal remains
from Cathlapotle could be sorted into a pre (Euroamerican) contact sample deposited
between ad 1400 and ad 1792, and a postcontact sample deposited between ad 1792
and ad 1835. These two temporally distinct assemblages are referred to in later chapters
simply as the precontact and postcontact assemblages. For most purposes the faunal
remains that could not be assigned to a temporal period are not included in the
analyses presented in later chapters.
The samples of identi¬ed remains from the two sites are not tremendously large by
some standards (Table 1.3). However, based on data compiled by others (especially
Casteel 1977, n.d.), both collections are of reasonable size. That they are not tremen-
dously large is a bene¬t in the sense that this will assist with the detection of possible
in¬‚uences of sample size in later chapters. The three assemblages are described in
Table 1.3. For additional information on the mammal collections not covered in later
chapters, see Lyman (2004a, 2006b, 2006c), Lyman et al. (2002), Lyman and Ames
(2004), and Lyman and Zehr (2003).
2
Estimating Taxonomic Abundances:
NISP and MNI

As paleontologists, Chester Stock and Hildegard Howard were interested in the abun-
dance of the mammals that had walked the landscape and birds that had ¬‚own in
the air above the landscape at the time the faunal remains from Rancho La Brea were
deposited (Chapter 1 ). Zooarchaeologists (known as archaeozoologists in Europe),
on the other hand, are typically interested in which taxa provided the most economic
resources and which taxa provided little in the way of economic resources. Thus, as
zooarchaeologist Dexter Perkins (1973:369) noted, “the primary objective of faunal
analysis of material from an archaeological site [or from a paleontological site] is
to establish the relative frequency of each species.” This target variable sought by
paleontologists and zooarchaeologists concerns taxonomic abundances. What are the
frequencies of the taxa in a collection?
In any given collection of paleozoological remains, one might wish to know if car-
nivores are less abundant than herbivores, just as they normally are on the landscape.
Given what he knew about ecological trophic structure “ that herbivores should out-
number carnivores “ imagine Stock™s surprise to learn that the typically observed
food pyramid or ecological trophic structure was upside down. The mammalian
remains from Rancho La Brea represented more carnivores than herbivores ’ for
a reason that many paleontologists thought was a taphonomic reason “ because
scavenging carnivores got “bogged down” or mired in the sticky tar seeping from
the ground and failed to escape. Carnivores were abundant in that tar because they
had died and become entombed there as a result of trying to exploit the carcasses of
herbivores (and perhaps carnivore brethren) that had themselves become mired and
subsequently died there.
The eminently sensible hypothesis that carnivore remains are more abundant than
herbivores for taphonomic reasons (see Spencer et al. [2003] for a recent evaluation of
this hypothesis) concerns the relationship between a target variable and a measured
variable. Stock™s target variable was the frequencies of mammalian taxa comprising
quantitative paleozoology
22


the animal community on the landscape, but his measured variable was the sample of
bones and teeth from the excavations of the tar pits. Taphonomists have developed an
unwieldy terminology (see the glossary in Lyman 1994c), but several of the terms are
useful here for keeping target variables and measured variables distinct. A biocoenose
is a living community of organisms. Exactly what a community comprises is the
subject of some debate. One de¬nition provided by biologists is this: A community
is comprised of “species that live together in the same place. The member species
can be de¬ned either taxonomically or on the basis of more functional ecological
criteria, such as life form or diet” (Brown and Lomolino 1998:96).
But “most so-called communities are arbitrary and convenient segments of a con-
tinuum of species with overlapping ecological requirements, not involving a high
level of interdependence” (Lawson 1999:7). Thus one commentator notes that a bio-
logical community can be de¬ned one of two ways: As a group of organisms occu-
pying a location, or as a group of organisms with ecological linkages among them
(Southwood 1987). Often the focus is on the former at the expense of the latter; a
community (which may include all organisms or a particular subset of organisms) is
often de¬ned by speci¬c spatial boundaries (Magurran 1988:57). Perhaps not surpris-
ingly, the “nature of boundaries separating adjacent communities is hotly disputed
by community ecologists and paleoecologists” (Hoffman 1979:364). For the sake of
discussion, we assume that a biological community and its boundaries can be de¬ned
on the landscape today.
The taxonomic composition and taxonomic abundances of a biocoenose might
well be the target variable sought by a paleozoologist. However, that biocoenose is
not what a paleozoologist studies. The organisms that comprise a biocoenose must
die before a paleozoologist can study their mortal remains. A thanatocoenose is an
assemblage of dead organisms; it is sometimes referred to as the death assemblage.
Turner (1983) suggested that it be referred to as the “killed population,” but “killed”
implies an active agent of death, such as a predator, disallowing death from other
causes such as old age. Furthermore, the dead organisms may be a “population”
in a statistical sampling sense, but they might not be, depending on the question
asked. Those dead organisms may be a 100 percent sample of some set of dead
organisms (e.g., all of those from a biocoenose, which, after all, must all die), but
they may be less than that, such as when the set of dead organisms represents only
part “ a sample “ of a biocoenose. In this case, the thanatocoenose is not, statistically
speaking, a “population.” It is perhaps best, for this reason alone, to conceive of
a thanatocoenose as a set of dead organisms, usually somehow stratigraphically or
analytically bounded (see the discussion of a faunule later in this chapter).
estimating taxonomic abundances: nisp and mni 23




figure 2.1. Schematic illustration of loss and addition to a set of faunal remains studied
by a paleozoologist.


Given that paleozoologists sample the geological record (i.e., where faunal remains
are deposited as a particular kind of sedimentary particle), they don™t always have a
complete thanatocoenose lying on the lab table. Furthermore, the organisms whose
remains comprise a thanatocoenose may derive from one community (or biocoenose)
or they may derive from more than one community (Shotwell 1955, 1958). A tapho-
coenose is the set of remains of organisms (in our case, faunal remains) found buried
(or perhaps exposed) and spatially (usually stratigraphically) associated. Given that
not all of the remains comprising a taphocoenose will be recovered, and of those that
are recovered not all will be identi¬ed to taxon, what the paleozoologist can identify
comprises what will here be referred to as the identi¬ed assemblage. It is this set of
remains from which measures of taxonomic abundance are derived.
Figure 2.1 is a schematic rendition of the typical differences between a biocoenose
and the identi¬ed assemblage. A biocoenose is a biological community. One or more
biocoenoses is the source of input to a thanatocoenose. The transition from bio-
coenose to thanatocoenose involves accumulation (and deposition) of faunal remains
in a location; accumulation can be active (involve a bone-accumulating agent, such
as a predator that transports prey to a den) or passive (involve deaths of animals
across the landscape, referred to as “background accumulation” [Badgley 1986]).
quantitative paleozoology
24


The transition from the thanatocoenose to taphocoenose involves both accumu-
lation and dispersal and movement or removal of bones mechanically (such as by
¬‚uvial transport), and also the deterioration or chemical and mechanical breakdown
of skeletal tissue. The transition from the taphocoenose to the identi¬ed assemblage
involves both recovery (usually < 100 percent for any of several reasons) by the pale-
ozoologist and the taxonomic identi¬cation of a subset of the remains comprising
the taphocoenose.
The measured variable of taxonomic abundances originates in the identi¬ed
assemblage; the target variable depends on the question asked (Figure 2.1 ). The
biocoenose was Stock™s target variable. Zooarchaeologists interested in human sub-
sistence and economy often have, as their target variable, a thanatocoenose cre-
ated by human predators. Paleoecologists, whether working as paleontologists or as
zooarchaeologists who are interested in past ecological conditions, have as a target
the biocoenose. Determination of the statistical relationship between an identi¬ed
assemblage and a target variable is a taphonomic concern (Lyman 1994c), but the
paleozoologist should also consider ecological and animal behavior variables as well
as recovery techniques. As the Rancho La Brea materials indicate, animal behavior
can in¬‚uence the accumulation and thus rate of input of animal remains to the
geological record.
Not all taxonomic abundances at Rancho La Brea can be attributed to historical
contingencies of how and why the faunal remains present were originally accumu-
lated. Did, perhaps, local habitats support more artiodactyls than perissodactyls, or
as with the carnivores at Rancho La Brea, did a particular bone-accumulation agent
bring more even-toed herbivores than odd-toed herbivores to the tar pits? Whatever
the case, we measure taxonomic abundances in the identi¬ed assemblage and use
those values as proxy measures or estimates of a thanatocoenose or a biocoenose. It
is the task of taphonomic analyses to ascertain how good (or how biased) an esti-
mate of a particular target variable the measured variable might be. Paleozoologists
have, over the past 20 years or so become very concerned over how good an estimate
of a biocoenose an identi¬ed assemblage might provide (e.g., Gilbert and Singer
1982; Ringrose 1993; Turner 1983). This concern has resulted in research known as
¬delity studies, or assessment of “the quantitative faithfulness of the [fossil] record
of morphs, age classes, species richness, species abundance, trophic structure, etc. to
the original biological signals” (Behrensmeyer et al. 2000:120).
Comparisons of faunal remains with organisms making up a biological community
from which the remains derive suggest that ¬delity can range from quite high to rather
low with respect to the variables of interest, and not all variables display equivalent
¬delity in any given set of remains (Hadly 1999; Kidwell 2001, 2002; Kowalewski et al.
estimating taxonomic abundances: nisp and mni 25


2003; Lyman and Lyman 2003). If there is no taphonomic reason for artiodactyl
remains to outnumber perissodactyl remains at Rancho La Brea, for example, then
an ecological explanation “ there were more artiodactyls than perissodactyls on
the landscape to be accumulated because climatic conditions created habitats more
favorable to artiodactyls “ is likely.
The distinction between measured taxonomic abundances and target taxonomic
abundances will be important throughout the remainder of this chapter, so keep it in
mind. Turner (1983) suggests that often one must assume that the relative taxonomic
abundances evident in an identi¬ed assemblage are a statistically accurate re¬‚ection
of those abundances in a taphocoenose, a thanatocoenose, and a biocoenose. This
is true, but it is also incomplete in the sense that we can do more than assume
accurate re¬‚ections; we can often test the general accuracy of the re¬‚ection with
data independent of the identi¬ed assemblage at hand. The fauna represented by the
identi¬ed assemblage should align ecologically with, say, ¬‚oral (pollen, phytoliths,
plant macrofossils) data. If it does not, then either the identi¬ed faunal assemblage is
not an accurate re¬‚ection of the biocoenose, or the plant record is not. Similarly, an
identi¬ed faunal assemblage at a nearby site (assuming similar ages) should align with
the assemblage under consideration; two taphonomically independent assemblages
should have statistically indistinguishable taxonomic abundances (and the more
taphonomically independent samples that indicate the same biocoenose, the more
accurate the conclusion). If they do not, one or both of the assemblages may not be a
good re¬‚ection or estimate of taxonomic abundances within the local biocoenose
(Grayson 1981a; Lundelius 1964).
Regardless of whether one is interested in the taphonomic history of a collec-
tion of faunal remains (how and why those remains were differentially accumulated,
deposited, preserved [and some would say recovered]), in the biogeographical impli-
cations of the taxa represented by those remains (why are these taxa here but not other
taxa), in the paleoecological implications of the represented taxa (do the represented
species signify warm or cool climates, or moist or dry habitats), or in the subsistence
and foraging behaviors of the accumulation organism (human if an archaeologi-
cal site, a carnivore if a den), taxonomic abundances are typically part of the data
scrutinized for answers to the research question. As Grayson (1979:200) noted, “It is
virtually impossible to ¬nd any faunal analysis that does not present one or more
measures of taxonomic abundance. [This variable] is a basic one.” The critical tac-
tical decision concerns choosing a method to measure the abundances of the taxa
represented in a collection. It is easy to show that this is no simple matter.
When Stock tallied up the remains from Rancho La Brea (Figure 1.1 ), it is likely
that he re¬‚ected on the fact that proboscideans have more bones in one skeleton
quantitative paleozoology
26


than do perissodactyls. The former have ¬ve digits at the end of each limb whereas
various perissodactyls, late Pleistocene equids in particular, have only one digit at
the end of each limb. Thus, simply tallying up how many bones (and teeth) each
taxon contributed to a collection could potentially produce inaccurate estimates of
the abundances of the various taxa represented. If each skeleton of taxon A produces
75 identi¬able bones, and each skeleton of taxon B produces 90 identi¬able bones,
then if 5 individuals of each were mired at Rancho La Brea, one would have 5 skulls
of each taxon but 375 bones (number of identi¬ed specimens, or NISP) of taxon A
and 450 bones (= NISP) of taxon B.
Ignoring for the moment potential differences in the number of teeth various taxa
may have, simple tallies of the skeletal specimens of taxa A and B could produce mis-
leading insights to which one of the two was more abundant on the landscape. Note
that NISP is the measured variable whereas taxonomic abundances in the biocoenose
is the target variable. Recognizing the differences between these two variables is crit-
ical to understanding whether a measure is valid or not. Is the target variable, for
example, the frequency of each taxon recovered from the site (identi¬ed assemblage),
the frequency of each taxon preserved in the site sediments (taphocoenose), the fre-
quency of each taxon accumulated and deposited in the site (taphocoenose, thana-
tocoenose), or the frequency of each taxon available on the landscape (biocoenose)?
This question underscores the simple fact that accumulation, deposition, preser-
vation, recovery, and identi¬cation of faunal remains can all weaken in unpre-
dictable ways the statistical relationship between the measured variable and the target
variable.
If a measure of taxonomic abundances is desired, then what sort of quantitative
unit should be used? Obviously, we want a unit that allows us to estimate taxo-
nomic abundances in a sample of bones, teeth, and shell lying on the lab table.
That is, we want a unit that measures taxonomic abundances within the identi¬ed
assemblage; how closely those abundances match up with taxonomic abundances in
the thanatocoenose or biocoenose from which the identi¬ed assemblage derives is a
separate question that requires detailed taphonomic analyses and other sorts of data.
We cannot presume that taxonomic abundances are the same across the identi¬ed,
taphocoenose, thanatocoenose, and biocoenose assemblages. But as noted above,
we can sometimes perform empirical tests to determine if this is so or not. In this
chapter the two fundamental quantitative units originally designed to measure tax-
onomic abundances are discussed. These quantitative units are known as NISP and
MNI; they are considered in turn. Biomass and meat weight and other quantitative
methods used to measure taxonomic abundances are discussed in Chapter 3.
estimating taxonomic abundances: nisp and mni 27


(NISP)
THE NUMBER OF IDENTIF IED SPECIMENS


The most fundamental unit by which faunal remains are tallied is the number of
identi¬ed specimens, or NISP. It is just what it sounds like “ the number of skeletal
elements (bones and teeth) and fragments thereof “ all specimens “ identi¬ed as to
the taxon they represent. A related measure sometimes mentioned is the number of
specimens (NSP) comprising a collection or assemblage. The NSP includes bones,
teeth, and fragments thereof some of which have been identi¬ed to taxon, plus
those specimens that have not or cannot be identi¬ed to taxon. Typically, “identi¬ed
to taxon” means identi¬ed as to the skeletal element and to the taxonomic order,
family, genus, or species represented by the specimen. Most taxonomically diagnostic
anatomical features are also diagnostic of skeletal element (is it a humerus or a
tibia?). Many paleozoologists do not tally nondescript pieces of bone that are from
the taxonomic class Mammalia if those pieces cannot be assigned to taxonomic
order, family, genus, or species. This is so because taxonomic identi¬cations such
as “mammal long bone fragment” generally, but not always, are of little analytical
utility. But don™t misunderstand. The research problem or question one is grappling
with should, if carefully phrased, indicate whether or not an otherwise nondescript
piece of “mammal long bone” is worthy of tallying or not. For the remainder of this
book, “identi¬ed” means that a specimen has been minimally identi¬ed as to skeletal
element and to at least taxonomic family (if not genus or species), unless otherwise
noted. As Stock™s (1929) example summarized in Chapter 1 makes clear, much may
be learned from taxonomic order-level identi¬cations.
Virtually all paleozoological collections consist of some NSP of which a fraction
makes up the NISP. NISP is the number of identi¬ed (to skeletal element and at
least taxonomic family) specimens determined for each taxon for each assemblage.
When one says NISP, what is meant is NISPi where i signi¬es a particular taxon.
This is analogous to statistical symbolism because the i is seldom shown; rather, it
is understood. Thus, one has an NISP of 10 for deer (Odocoileus sp.) and an NISP
of 5 for rabbits (Sylvilagus sp.). In some cases the symbolism may be more complex,
such as NISPij, where i is for the taxon as before, and j is for a particular skeletal
element or part, such as a humerus or distal tibia. Again, the ij is not shown but is
understood. It is likely for these reasons of implied symbolism that it is unusual to
see the plural form of NISP, such as NISPs; in my experience (which may not be
representative), it is more common to read “NISP values” when more than one taxon
or skeletal element is intended, as when an NISP value is given for each of multiple
taxa.
quantitative paleozoology
28


Advantages of NISP

The acronym NISP and its meanings, both implied (ij) and explicit (number of
identi¬ed specimens), should be clear. Its operationalization may also seem to be
clear and straightforward. For any pile of faunal remains, identify every specimen that
you can (to skeletal element and taxon), and then tally up how many specimens you
identi¬ed per taxon (and perhaps also noting how many specimens represent each
kind of skeletal element, depending on your research question). NISP is an observed
measure because it is a direct tally, and so it is not subject to some of the problems
that derived measures such as MNI are. In part because NISP is an observed or
fundamental measure, it has advantages over other units used to measure taxonomic
abundances. First, NISP can be tallied as identi¬cations are done. That is, NISP is
additive or cumulative; the analyst does not have to recalculate NISP every time a
new bag of faunal remains is opened and new specimens identi¬ed. This property
makes NISP a fundamental measure. Every identi¬ed specimen represents a tally of
“1.” Add up all the tallies of “1 ” for each taxon to derive the total NISP per taxon or
NISPi.
NISP is, however, not free of problems. One long recognized (Clason 1972;
Lawrence 1973) but seldom mentioned problem in¬‚uences both NISP and MNI. Dif-
ferent analysts may identify different specimens in a pile of faunal remains (Gobalet
2001). The sets of specimens that any two analysts identify will be quite similar “
all complete teeth and complete limb bones are likely to be identi¬ed, assuming
both analysts have access to similar comparative collections “ but they may not be
identical, which means interanalyst comparability is imperfect. Whether a particular
specimen is identi¬able or not depends on the anatomical landmarks available on
that specimen (Lyman 2005a), and experience and training will in¬‚uence what an
individual analyst will identify because that experience and training dictates which
landmarks the paleozoologist has learned are useful.
Interobserver difference in what is identi¬ed can be a serious source of variation in
NISP tallies. Because it concerns what is identi¬ed, interobserver difference applies
to any conceivable measure of taxonomic abundance. As with other kinds of interob-
server difference, it is not just dif¬cult to control. It is impossible to control (unless
every paleozoologist studies every collection) and it is likely for this reason that few
paleozoologists have mentioned it. It is mentioned here for sake of completeness
and because it may be an important consideration when one analyst compares his
or her tallies with someone else™s for a different collection. Because it cannot be con-
trolled, it is not considered further. But there are other potential problems with NISP.
One might think that interobserver variation in how to tally what is identi¬ed for
estimating taxonomic abundances: nisp and mni 29


purposes of producing an NISP value will not vary from investigator to investigator
because each identi¬ed specimen represents a tally of 1. But, does it? Answering this
question brings us to some of the weaknesses internal to NISP, weaknesses identi¬ed
and described by many researchers.



Problems with NISP

When Stock (1929) presented his census of Rancho La Brea mammals, he tallied the
minimum number of individual(s) animals “ what are now called MNI values “
rather than NISP. It is likely he did so because he recognized that members of the
Carnivora have different numbers of ¬rst (or proximal) phalanges per individual
(usually 4 or 5 per limb) than do the Perissodactyla (Pleistocene horses have one) or
the Artiodactyla (usually two). NISP tallies of ¬rst phalanges for a single dog would
be 16 (ignoring the vestigial ¬rst + second phalanx of the ¬rst digit of each foot), for
a single horse the NISP of ¬rst phalanges would be 4, and for a cervid the NISP of
¬rst phalanges would be 8.
Many problems with using NISP to measure taxonomic abundances have been
described over the years by numerous authors (e.g., B¨ k¨ nyi 1970; Breitburg
oo
1991; Chaplin 1971; Gautier 1984; Grayson 1973, 1979; Higham 1968; Hudson 1990;
O™Connor 2001, 2003; Payne 1972; Perkins 1973; Ringrose 1993; Shotwell 1955; Uerp-
mann 1973). Long lists of the possible weaknesses and potential problems with using
NISP as a measure of taxonomic abundances are given by Grayson (1979, 1984). The
following is based on his lists, and is supplemented with concerns expressed by pale-
ontologists (e.g., Shotwell 1955, 1958; Van Valen 1964; Vermeij and Herbert 2004):

1 NISP varies intertaxonomically because different taxa have different
frequencies of bones and teeth (the number of elements that are identi¬able
varies intertaxonomically);
2 NISP will vary with variation in fertility (number of offspring per reproductive
event) and fecundity (number of reproductive events per unit of time);
3 NISP is affected by differential recovery or collection (large specimens [of
large organisms] will be preferentially recovered relative to small specimens
[generally of small organisms]);
4 NISP is affected by butchering patterns (different taxa are differentially
butchered, one result of which is intertaxonomic differential accumulation of
skeletal parts, and another of which is intertaxonomic differential
fragmentation of skeletal elements);
quantitative paleozoology
30


5 NISP is affected by differential preservation (similar to problem 4;
taphonomic in¬‚uences may vary intertaxonomically);
6 NISP is a poor measure of diet (the bones of one elephant provide more meat
than the bones of one mouse);
7 NISP does not contend with articulated elements (is each tooth in a mandible
tallied as an individual specimen, plus the mandible itself tallied?);
8 the problems identi¬ed may vary between strata within a site, between distinct
sites, or both, rendering statistical comparison of site or stratum speci¬c
assemblages invalid;
9 NISP may differentially exaggerate sample sizes across taxa;
10 NISP may be an ordinal scale measure and if so some powerful statistical
analyses are precluded as are some kinds of inferences;
11 NISP suffers from the potential interdependence of skeletal remains.



Problems, Schmoblems

The list of problems analysts have identi¬ed as plaguing NISP values may seem
disconcerting. Indeed, the length of the list may give one cause to wonder why anyone
would measure taxonomic abundances using NISP in the ¬rst place. Do not, however,
let such wonder convince you that NISP values are worthless. Some problems overlap
with one another in terms of their effects or in terms of how they might be dealt
with analytically. And notice that the list comprises a set of “possible weaknesses and
potential problems.” Several of the problems are easily dealt with analytically.
Problem 1 can be controlled in several ways, such as only counting elements held
in identical frequencies by the taxa under study (e.g., Plug and Sampson 1996).
Do not tally phalanges of artiodactyls and perissodactyls when comparing their
abundances; tally only scapulae, humeri, femora, and other elements that occur in
identical frequencies in individuals of both taxa. In short, do not include tallies of
elements that vary in frequency intertaxonomically. Or, weight NISP by dividing it
by the number of identi¬able elements per single complete skeleton in each taxon.
So, if, say, horses always have 100 elements per complete skeleton and bison always
have 85 elements per skeleton, then weight observed abundances of NISP for horses
and for bison accordingly. This solution was suggested more than 50 years ago by
paleontologist J. Arnold Shotwell (1955, 1958). It is, however, not without problems,
such as requiring the assumption that complete skeletons (rather than a limb or
two) were accumulated and deposited in the collection location. The assumption
comprises a taphonomic problem, and might be addressed by consideration of which
estimating taxonomic abundances: nisp and mni 31


skeletal elements are present. What about variation in rates of input of skeletal parts
to the geological record?
We don™t need to worry about correcting for differences in number of skeletal
elements per taxon because, to retain the example, late-Pleistocene horses always
have the same number of skeletal elements in each of their skeletons as every other
late-Pleistocene horse, and late-Pleistocene bison have the same number of skeletal
elements in each of their skeletons. Thus, we know that if the NISP of bison increases
relative to the NISP of horses (the measured variables), then perhaps the abundance
of bison (on the landscape, or in the identi¬ed assemblage) increased relative to the
abundance of horses (the target variables). Bison NISP did not increase relative to
horse NISP because bison evolved to have more bones or horses evolved to have
fewer bones over the time represented. The same argument applies to variables that
in¬‚uence the rate of input of skeletal parts to the faunal record. Shotwell (1955,
1958) was concerned that different taxa input bones to the paleozoological record
at different rates. A few years later Van Valen (1964) spelled out his concern that
different taxa have different longevities; taxa with short individual life spans input
more skeletal parts to the faunal record than taxa with long individual life spans, all
else being equal (same number of skeletal parts per taxon, same population size on
the landscape).
Problem 2 was recently stated by Vermeij and Herbert (2004), who worried that
intertaxonomic variation in fertility and fecundity in¬‚uenced the rate of skeletal
part input. They noted that “short-lived (often small-bodied) species will be greatly
over represented in a fossil sample relative to species with long generation times,
long individual life spans, slow rates of turnover, and large body size” (Vermeij and
Herbert 2004:2). If taxon A has an individual average life span of 10 years whereas
taxon B has an individual average life span of 1 year, then taxon B will be represented
by ten times the number of individuals as taxon A (all else being equal). Vermeij
and Herbert (2004:3) were concerned that measures of “predator-prey ratios and
prey availability” would be artifacts of variation in life span. Their primary solution
to problem 2 requires data on average life spans, in some cases derivable from the
growth increments evident in the hard parts of organisms. In the absence of the
requisite ontogenetic data, a secondary solution they suggest is to restrict sampling
“to organisms of comparable generation time,” though this solution also seems to
require taxon-speci¬c ontogenetic information.
The ¬rst solution is, in fact, identical in reasoning to the one suggested by Shotwell
(1955, 1958) for the problem of mammalian taxa with different numbers of (identi-
¬able) skeletal elements per individual. They are “identical” because both Shotwell
and Vermeij and Herbert were concerned about biological factors that in¬‚uence the
quantitative paleozoology
32


Table 2.1. Fictional data on abundances (NISP) of three taxa in
¬ve strata

Stratum Taxon A Taxon B Taxon C Total
50 (77)—
V 10 (15) 5 (8) 65
IV 40 (67) 10 (16.5) 10 (16.5) 60
III 30 (55) 10 (18) 15 (27) 55
II 20 (40) 10 (20) 20 (40) 50
I 10 (22) 10 (22) 25 (56) 45


Relative (percentage) abundances of each taxon given in parentheses.

rate at which skeletal remains are created and input to the paleozoological record.
Taxa with many skeletal elements per individual and taxa with high fecundity both
have higher rates of input than taxa with few skeletal elements per individual and
taxa with low fecundity, respectively. When faced with the former problem, Shotwell
suggested that the analyst should determine a “corrected number of specimens” per
taxon, a value calculated by dividing each taxon™s NISP by the number of identi¬able
elements in one skeleton of that taxon. If an individual skeleton of taxon A poten-
tially contributes 10 (identi¬able) elements and taxon B 5 elements, then divide the
observed NISP for A by 10 and the observed NISP for B by 5 in order to compare
the abundances of the two taxa. A similar procedure for invertebrates is described
by Kowalewski et al. (2003). The procedures norm all taxon-speci¬c NISP values to
a common scale “ the number of identi¬able skeletal elements per individual per
taxon. In light of Vermeij and Herbert™s concern, a paleozoologist could norm all
taxonomic abundances to a single life span, based on the duration of all life spans
measured in the same unit, say, a year.
The concerns of Shotwell, Van Valen, and Vermeij and Herbert are all easily dis-
pensed with. Table 2.1 lists ¬ctional NISP values for three taxa in ¬ve strata. Because
we know that taxon A has 10 skeletal elements per individual, taxon B has 1 skeletal
element per individual, and taxon C has 5 skeletal elements per individual, we choose
to weight their abundances accordingly. The results of that weighting are shown in
Table 2.2. For ease of conceptualizing what has happened, consult Figure 2.2. Note
that over the ¬ve strata, whether the NISP values are the raw tallies or the weighted
tallies corrected for differences in number of skeletal elements per taxon, taxon A
increases from stratum I to stratum V whereas taxon C decreases over that same span.
Weighting does not change the results, at least with respect to increases and decreases
in the relative abundances of taxa A and C. But, you might counter, in the unweighted
data taxon B is often not very abundant at all, and it too gradually decreases from
stratum I to stratum V. In the weighted data, however, taxon B is more abundant than
estimating taxonomic abundances: nisp and mni 33


Table 2.2. Data in Table 2.1 adjusted as if each individual of taxon A had
ten skeletal elements per individual, taxon B had one skeletal element
per individual, and taxon C had ¬ve skeletal elements per individual

Stratum Taxon A Taxon B Taxon C Total
5 (31.5)—
V 10 (62.5) 1 (6.25) 16
IV 4 (25) 10 (62.5) 2 (12.5) 16
III 3 (18.75) 10 (62.5) 3 (18.75) 16
II 2 (12.5) 10 (62.5) 4 (25) 16
I 1 (6.25) 10 (62.5) 5 (31.25) 16


Relative (percentage) abundance in parentheses.


A and C combined, and taxon B doesn™t change in relative abundance over the strati-
graphic sequence. That is a good point “ it suggests the data are ordinal scale “ and
we will return to it. First, however, we need to consider other problems with NISP.
Problem 3 concerns collection bias. Correction factors might be designed to
account for the fact that small bones and teeth and shells tend to come from small
organisms, and these tend to escape visual detection and to fall through coarse-
meshed hardware cloth meant to allow the passage of sediment but not faunal




figure 2.2. Taxonomic relative abundances across ¬ve strata. Data from Tables 2.1
(unweighted) and 2.2 (weighted).
quantitative paleozoology
34


remains. The design of correction values has also been a long-standing interest among
zooarchaeologists (e.g., Payne 1972; Thomas 1969), but again, there are problems with
these values. For example, if one uses correction values, one must assume that the
samples used to derive those values are on average representative of all situations “
within any given excavation unit, within any given stratum of a site, and within any
given site “ where small remains may fall through screens (see Chapter 4). As long as
recovery methods do not differ between strata, such as using 1 /4-inch mesh hardware
cloth for every other stratum and using 1 /8-inch mesh hardware cloth for the other
strata, remains of mice will be as consistently recovered in all recovery contexts as
are remains of rabbits and deer.
The preceding does not allow for differential fragmentation across taxa, the issue
raised by problem 4. If rabbit bones are quite fragmented and small, they may fall
through screens much more readily than unfractured remains of mice (Cannon
1999). Large bones may be more likely to be fractured by humans or carnivores
because they contain more nutrients (marrow) than small bones. Fragmentation
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
44


and then decrease NISP as fragmentation intensity increases and specimens become
unidenti¬able; moderate breakage will not in¬‚uence MNI, but intensive fragmenta-
tion will result in a decrease in MNI as progressively more specimens fail to retain
suf¬cient anatomical landmarks to allow identi¬cation.
Klein (1980) is correct that MNI will not be in¬‚uenced by fragmentation, whereas
NISP will be, but only in the limited case of assemblages with little fragmentation.
Both NISP and MNI values will be in¬‚uenced by intensive fragmentation. We do
not know, however, the degree of fragmentation intensity at which fragmentation
begins to decrease identi¬ability and to reduce values of both NISP and MNI (Lyman
1994b). The dif¬culty of establishing this degree of fragmentation is exacerbated by
the fact that small fragments are unidenti¬able to skeletal element.
MNI overcomes such problems as intertaxonomic variation in the number of
identi¬able elements per individual. But as I noted, in regard to this problem as it
pertains to NISP, it is easy to analytically correct for intertaxonomic variation in the
number of identi¬able skeletal elements per individual. Either normalize all NISP by
dividing those values by a value that accounts for variation in identi¬able elements
per skeleton, or delete from tallies those taxonomically unique elements (such as
upper incisors in equids when comparing their abundance to bovids, who don™t
have upper incisors).
The most important advantage of MNI is that it overcomes possible specimen
interdependence because of how MNI is de¬ned (Table 2.4). As Ringrose (1993:127)
noted, the “basic principle of the MNI is to avoid ˜counting the same animal twice.™”
If MNI is derived according to the de¬nitions in Table 2.4, there is no way for
two or more specimens in one assemblage to be from the same individual. This is
illustrated in Table 2.5. Notice in that table of ¬ctional data that there is a minimum
of seven individuals (= MNI). Notice also that all postcranial elements have been
assigned to an individual already represented by a skull and both mandibles. The
left scapulae do not represent, so far as we can tell in light of modern methods, an
eighth individual, a ninth individual, and so on, nor do the right scapulae, the left
humeri, and so on. Here, NISP = 71, but obviously if we tally NISP, we count the
¬rst individual ¬fteen times (= NISP for that individual), the second individual is
counted fourteen times, and so on. Of course, the right radius assigned to individual
number ¬ve may actually go with individual number four, or with individual number
eight, but we cannot determine that. Thus, the number of individuals represented
by the seventy-one specimens listed in Table 2.5 is a minimum of seven individuals,
but the specimens might represent more.
MNI would seem to avoid the interdependence problem within an assemblage
such as shown in Table 2.5. But note the emphasized phrase “ within an assemblage.
estimating taxonomic abundances: nisp and mni 45


Table 2.5. A ¬ctional sample of seventy-one skeletal
elements representing a minimum of seven individuals (I)

I.1 I.2 I.3 I.4 I.5 I.6 I.7
+—
Skull + + + + + +
L mandible + + + + + + +
R mandible + + + + + + +
L scapula + + + + + +
R scapula + + + + + +
L humerus + + + + + +
R humerus + + + + +
L radius + + + + +
R radius + + + + +
L innominate + + + +
R innominate + + + +
L femur + + +
R femur + + +
L tibia + +
R tibia +
NISP 15 14 13 11 9 6 3


+ denotes a skeletal element is represented.


What about between assemblages? What if the left femur of an individual is in one
assemblage and the matching right femur is in another assemblage? Were we to tally
each as part of an MNI calculation in the two assemblages, we would have counted
that single individual twice. This introduces the most serious problem with MNI “
aggregation “ and there are other, less serious but signi¬cant problems as well.



Problems with MNI

As with NISP, analysts have identi¬ed what they take to be serious problems with
MNI (e.g., Casteel n.d.; Fieller and Turner 1982; Gilbert et al. 1981; Grayson 1973,
1979, 1984; Klein 1980; Klein and Cruz-Uribe 1984; Plug and Plug 1990; Ringrose
1993; Turner 1983, 1984; Turner and Fieller 1985). These include:

1 MNI is dif¬cult to calculate because it is not simply additive;
2 MNI can be derived using different methods, thereby reducing comparability;
3 MNI values do not accurately re¬‚ect the thanatocoenose or the biocoenose;
quantitative paleozoology
46


4 MNI values exaggerate the importance of rarely represented taxa, or taxa
represented by low NISP values;
5 MNI values are minimums and thus ratios of taxonomic abundances cannot be
calculated;
6 MNI is a function of sample size or NISP, such that as NISP increases, so too
does MNI; and
7 different aggregates of specimens comprising a total collection will produce
different MNI values.

The ¬rst problem “ MNI is dif¬cult to determine “ is not worth considering. No one
has ever said research of any kind was, or should be, easy. But related to this problem
is the fact that MNI is not additive like NISP is. Rather, every time a new bag of faunal
remains is opened and specimens identi¬ed, one has to rederive the MNI (assuming
it was derived before). This is so because the most common skeletal part per taxon
may change with the addition of another bag of bones. This problem, too, is trivial
given that research often involves calculation and recalculation, again and again, as
new data are collected or as new insights are gained and adjustments are made to a
data set.
That different researchers use different methods to derive MNI values (the second
problem) is evidenced by variations in the de¬nitions of MNI in Table 2.4. This
problem is akin to the one that different analysts will produce different NISP values
for the same collection of remains given their varied expertise at identi¬cation.
There is no real way to control this problem, so the methods used to derive MNI
values should be stated explicitly. Were remains matched by size? By age? By recovery
context? All of these or other variables? Potential and varied use of these criteria make
MNI a derived measure.
Some have argued that to not attempt to match potentially paired remains such as
left femora with right femora “ to determine if they originated in the same individual “
results in a misleading MNI value (Fieller and Turner 1982). White (1953a:397) thought
that matching would require “the expenditure of a great deal of effort with small
return [to] be sure all of the lefts match all of the rights.” That is, he believed that
checking every possible bilateral pair of bones for matches (based on the notion of
bilateral symmetry “ that a left element is a mirror image of its right element mate),
and assuming that each of those matches derived from the same individual “ would
result in a relatively small increase in the MNI value, and thus not much in the way of
alteration of taxonomic abundances. Whether or not White was correct with respect
to the magnitude of change in MNI values when matching is undertaken is unclear,
but likely is assemblage speci¬c for many reasons (Lyman 2006a). Some argue that
estimating taxonomic abundances: nisp and mni 47


the difference would be considerable whereas others seem to think it would not be
if “a great deal of effort” were expended, whatever the result, it will be a function of
the identi¬ed assemblage at hand and the procedures used to analytically manipulate
the bilateral pair data rather than the act of matching and identifying bilateral pairs
itself (compare Fieller and Turner [1982] with Horton [1984]).
The third problem, too, can be said to characterize both NISP and MNI. NISP
is a count of identi¬able specimens in the assemblage rather than a measure of
the thanatocoenose or the biocoenose. Similarly, given its de¬nition, MNI is the
minimum number of animals necessary to produce the identi¬ed specimens com-
prising the identi¬ed assemblage. Both quantitative units describe the assemblage
using two rather different variables. Whether either NISP or MNI more accurately
re¬‚ects the thanatocoenose or the biocoenose cannot be assumed given the contin-
gent and particularistic nature of the taphonomic history of the assemblage (e.g.,
Gilbert and Singer 1982; Ringrose 1993; Turner 1983). But, as I noted with respect
to NISP, there are ways to test if the identi¬ed assemblage rendered as a set of MNI
values accurately re¬‚ects the biocoenose. Are the taxonomic abundances indicated by
MNI values what would be expected given independent evidence of environmental
conditions? Do MNI abundances match those from contemporaneous nearby faunal
assemblages that experienced independent taphonomic histories? If the answers to
these questions are all “yes,” then it would be reasonable to suppose that the tax-
onomic abundances in the collection under study are fairly accurate re¬‚ections of
those abundances in the thanatocoenose as well as the biocoenose.
The fourth problem can be appreciated by recalling Table 2.3. There, taxon A is
rarely represented (NISP = 1) whereas taxon B is frequently represented (NISP =
10), but both taxa have an MNI of 1. MNI exaggerates the representation of taxon A
relative to taxon B™s representation. Although this observation is true, it is merely the
converse of the related problem with NISP. Thus one might argue that MNI and NISP
are equally ¬‚awed in this respect. If you are uncomfortable with that, you could note
that taxon A in Table 2.3 is represented by one tibia, and tally only tibiae identi¬ed
as taxon B when comparing abundances of these two taxa. It is likely that such a
procedure would decrease the disparity in representation of the two taxa, but it also
demands the assumption that the other specimens of taxon B are interdependent with
that taxon™s tibiae, an assumption that would likely be dif¬cult to warrant empirically
or theoretically. (Some specimens may be interdependent, but it seems improbable
that all would be interdependent.)
Plug and Plug (1990) identi¬ed the ¬fth problem: MNI values are minimums and
thus ratios of MNI values cannot be validly calculated (see also Gilbert et al. 1981).
They note that if the MNI of taxon A is 10 and the MNI of taxon B is 20, we cannot
quantitative paleozoology
48


use simple arithmetic to calculate the A:B ratio because, with respect to the true
number of individuals, it is very likely that A ≥ 10 and B ≥ 20. Thus any ratio A:B
cannot be validly calculated. MNI values are not ratio scale. Instead, they are perhaps
ordinal scale. Thus we can say, in Plug and Plug™s case of A:B, that it is likely that
A < B, but we cannot say by how much given that both A and B are minimum
values, and we don™t know their true values. A similar argument can be made with
respect to NISP values. They are maximum estimates of taxonomic abundances, so
a ratio of NISP values for two taxa, although easily calculated, may not actually be
a ratio scale measure of taxonomic abundances. That MNI values are minimums
is clear from how they are derived (Table 2.4). Paleozoologists have known these
things since the MNI quantitative unit was introduced (e.g., Adams 1949). What is
perhaps less well-known is that recent simulations indicate that MNI often provides
values considerably lower than the actual number of individuals (ANI) present in a
collection (Rogers 2000a). To illustrate this, look at Table 2.5 one more time. Here,
the MNI is seven; the NISP is seventy-one. If each skeletal element is independent
of every other element (each comes from a different organism), then the ANI is
seventy-one, an order of magnitude greater than the MNI value.
The fact that MNI increases as NISP increases (problem 6) has been recognized for
some time in zooarchaeology (Casteel 1977, n.d.; Ducos 1968; Grayson 1978a). Some
have argued that this statistical relationship warrants use of NISP rather than MNI to
measure taxonomic abundances; the reason is that the same information regarding
taxonomic abundances is contained in both quantitative units, so there is no reason
to determine MNI. Others have noted that although this statistical relationship does
indeed exist between the two measures, the precise nature of the relationship depends
on the particular set of remains involved (e.g., Bobrowsky 1982; Grayson 1984; Hesse
1982; Klein and Cruz-Uribe 1984). Some researchers use the last observation “ that the
relationship between NISP and MNI is statistically particularistic “ to argue that one
cannot predict MNI from NISP in a new sample based on the statistical relationship
of the two in previously studied samples, so perhaps MNI should be determined
(Klein and Cruz-Uribe 1984). This is a clever insight, and it is correct, but it does
not mean we must determine MNI values when seeking measures of taxonomic
abundance. We need not determine MNI because of the relationship between the
NISP for a taxon in an assemblage and its attendant MNI.
It is commonsensical that as the NISP of a taxon increases so too should the MNI for
that taxon. This is so because every individual skeleton comprises a limited number
of elements (or what might become identi¬able specimens comprising the paleozo-
ological record). Adding randomly chosen skeletal elements selected from, say, 100
skeletons of an identi¬ed assemblage, the ¬rst element will contribute one individual.
estimating taxonomic abundances: nisp and mni 49




figure 2.3. The theoretical limits of the relationship between NISP and MNI. Modi¬ed
from Grayson (1978a). Line A indicates that every new specimen does not contribute a new
individual. Line B indicates that every new specimen contributes a new individual.



That is, NISP = 1 = MNI. The second element will contribute another NISP
( NISP = 2), but that element might, or might not, contribute another individual
( MNI = 1 or 2). The third element will contribute yet another NISP ( NISP = 3),
and it might contribute another individual or it might not ( MNI = 1, 2, or 3). And
so on until the probability of adding a bone or tooth of an already represented skele-
ton is greater than the probability of adding a bone of an unrepresented skeleton,
at which point the rate of increase in MNI will slow relative to the rate of increase
of NISP. As Grayson (1978a) noted, there are two limits to the possible relation-
ship between NISP and MNI. Either every new skeletal element derives from the
same individual and thus every NISP > 1 contributes nothing to the MNI tally, or
every new skeletal element derives from a different, unique individual and thus every
NISP ≥ 1 contributes another MNI. These relationships express the limits of all
possible relationships between NISP and MNI (Figure 2.3).
The individual limits to the relationship between NISP and MNI (Figure 2.3) are
unlikely to be found in the real world. Unless one is dealing with, say, the moderately
fragmented skeleton of a single individual animal (NISP is several hundred), it is
likely that NISP will increase more rapidly than MNI. In fact, unless one is dealing
with an assemblage of remains of a single taxon that has but one identi¬able skeletal
element (such as the unbroken shells of a gastropod), it is likely that new NISP
will often be added without adding any MNI. The general relationship between
NISP and MNI is described by the line in Figure 2.4. It is relatively easy to show
that this is indeed the relationship that is found in case after case. The relationship
quantitative paleozoology
50




figure 2.4. The theoretically expected relationship between NISP and MNI. Modi¬ed
from Casteel (1977). As NISP increases, it takes progressively more specimens to add new
individuals.


is curvilinear because, given a ¬nite NISP and a ¬nite MNI, specimens from an
individual already represented are progressively more likely to be added as the sample
size ( NISP) increases. Whatever the kind of skeletal part that is the most frequent
or most common and thus de¬nes MNI, that kind of part will become progressively
more dif¬cult to ¬nd (Grayson 1984).
Ducos (1968) found that this curvilinear relationship could be made linear (and
thus perhaps more easily understood when graphed) if both the NISP data and the
MNI data were log transformed (see Box for additional discussion). As Grayson
(1984:52) later noted, untransformed NISP data and untransformed MNI data may
sometimes be related in a linear fashion, but they often are not. The means to tell if
they are not involves examination (either visual or statistical) of the residuals (the
distance above and below the regression line of the plotted points and the pattern of
the distribution of those points). Typically, log transformation reduces the dispersal
of points to a statistically insigni¬cant level. The slope of the best-¬t regression line
summarizes the rate of change in MNI relative to the rate of change in NISP and
is described by a single number representing a power function (or exponent); the
larger the number, the steeper the slope.
Casteel (1977) found the relationship modeled in Figure 2.4 in a series of assem-
blages of zooarchaeological and paleontological materials representing numerous
taxa. His data originally were comprised of 610 paired NISP“MNI values. (A paired
NISP“MNI value is the NISP value and the MNI value for a taxon in an assemblage
of remains.) Casteel subsequently expanded his data set (Casteel n.d.) to include 3,440
estimating taxonomic abundances: nisp and mni 51



BOX 2.1

It is often easier to grasp intuitively a linear relationship between two variables
than a curvilinear one. In many cases log transformation of NISP and MNI data
causes what is otherwise a curvilinear relationship to become linear. The typical
form of a linear relationship can be expressed by the equation Y = a + bX, where
X is the independent variable (in this case, NISP), Y is the dependent variable
(in this case, MNI), a is the Y intercept (where the line describing the linear rela-
tionship intersects the Y axis), and b is the slope of the line (where the slope of
the line describing the linear relationship represents how fast Y changes relative
to change in X). The simple best-¬t regression line in a graph showing the rela-
tionship between log transformed NISP data and log transformed MNI data is
described by the formula Y = aXb , where the variables Y, a, X, and b are as de¬ned
above. This formula describes what is referred to as a power curve; if b is positive
the curve extends upward from the lower left to the upper right of the graph; if b
is negative the curve extends downward from the upper left to the lower right. If
we transform both sides of Y = aXb to logarithms, then we have log Y = log a +
b log X, linear relationship between log Y and log X. In this volume, I present the
relationship between log X or log NISP, and log Y or log MNI, in the form Y = aXb ,
or what is simply a different form of the linear relationship. The Y intercept should
be zero, given that a zero value for NISP must produce a zero value for MNI, but
practice has been to allow the empirical data to identify a Y intercept; I follow
this practice here noting that should the empirically determined Y intercept dif-
fer considerably from zero, the data used should be inspected to determine why.
Variables a and b are constants determined empirically for each data set.


paired NISP“MNI values. (The manuscript in which Casteel used this larger data set
was never published. It was written in 1977, and afterwards cited occasionally by his
colleagues [e.g., Bobrowsky 1982; Grayson 1979]. I obtained a copy of the manuscript
from Grayson in the late 1970s.) In both cases, Casteel found a statistically signi¬cant
relationship between NISP and MNI like that shown in Figure 2.4. Bobrowsky (1982)
found the same relationship between paired NISP“MNI values using much smaller
data sets. Both Casteel (1977, n.d.) and Bobrowsky (1982) graphed the relationship
using untransformed data; Grayson (1984) and Hesse (1982) used log-transformed
data in their graphs of the relationship. Grayson (1984) summarized many cases
that had been reported by others, and reported several new cases to show that the
relationship was essentially ubiquitous. Klein and Cruz-Uribe (1984) found the same
quantitative paleozoology
52




figure 2.5. Relationship between NISP and MNI data pairs for mammal remains from
the Meier site (data in Table 1.3). See Table 2.6 for statistical summaries.



relationship between NISP and MNI using data sets different from those used by
Casteel, Bobrowsky, Grayson, and Hesse.
The large collection from Meier ( NISP = 5939) shows the relationship between
NISP and MNI nicely (Figure 2.5). The NISP“MNI data pairs are strongly correlated
(Pearson™s r = 0.8734, p < 0.0001). The slope of the best-¬t regression line (= 0.487) is
similar to that reported by others for other data sets; Casteel (1977) reported a slope
of 0.52, for example, and Grayson (1984) reported six others that ranged from 0.40 to
0.64. The precontact assemblage from Cathlapotle (Table 1.3) also shows the nature of
the relationship between NISP“MNI data pairs (Figure 2.6), as does the postcontact
assemblage from that site (Figure 2.7). In all three cases, the correlation coef¬cient is
strong (r > 0.87) and signi¬cant (p < 0.0001). The statistical relationships between
the two variables in each of these three assemblages are summarized in Table 2.6.
The relationship between NISP and MNI shown in Figures 2.5, 2.6, and 2.7 is not
unique to the Portland Basin. Recall that Casteel, Grayson, Hesse, Bobrowsky, and
Klein and Cruz-Uribe found exactly the same relationship between the two variables
in collections from all over the world and representing many time periods and taxa.
estimating taxonomic abundances: nisp and mni 53


Table 2.6. Statistical summary of the relationship between NISP and MNI for
mammal assemblages from Meier (Figure 2.5) and Cathlapotle (Figures 2.6 and 2.7)
(see Table 1.3 for data).

N of
Site Regression equation r p NISP taxa
MNI = ’0.06(NISP)0.487 <0.0001
Meier 0.873 5,939 26
MNI = ’0.098(NISP)0.42 <0.0001
Cathlapotle, precontact 0.916 2,372 21
MNI = ’0.0557(NISP)0.44 <0.0001
Cathlapotle, postcontact 0.901 3,834 24



Together, these cases suggest that the relationship is nearly ubiquitous. Table 2.7 sum-
marizes the statistical relationship between NISP and MNI in fourteen assemblages
of mammal remains from fourteen sites in eastern Washington State. I, along with
two fellow graduate students at the time, identi¬ed the taxa in these collections in
the late 1970s. All fourteen collections display the same kind of relationship between
NISP and MNI as is evident for Meier and Cathlapotle.




figure 2.6. Relationship between NISP and MNI data pairs for the precontact mammal
remains from the Cathlapotle site (data in Table 1.3). See Table 2.6 for statistical summaries.
quantitative paleozoology
54




figure 2.7. Relationship between NISP and MNI data pairs for the postcontact mammal
remains from the Cathlapotle site (data in Table 1.3). See Table 2.6 for statistical summaries.


That NISP“MNI data pairs are often tightly related (the correlation coef¬cient is
large) even in nonarchaeological contexts is also easy to show. Consider a sample of
eighty-four pellets likely cast by a barn owl (Tyto alba) in eastern Washington State.
NISP and MNI values for the total assemblage of prey remains in the eighty-four
pellets (Table 2.8) are arrayed in a bivariate scatterplot in Figure 2.8. The relationship
between the values of the two is linear and strong (r = 0.989, p = 0.0002), as it is
among the archaeological samples discussed previously; the regression equation is:
MNI = “1.57(NISP)0.935 . The same relationship holds for paleontological collections
as well, as Grayson (1978a) showed some years ago.
The fact that NISP and MNI are often strongly correlated could be used to argue
that we should use MNI as the quantitative unit for measures of taxonomic abun-
dance because of the potential for the interdependence of specimens in NISP tallies.
Indeed, Hudson (1990) argued on the basis of ethnoarchaeological data, and Bre-
itburg (1991) on the basis of historic-era zooarchaeological data supplemented by
written documents, that MNI provides more accurate measures of taxonomic abun-
dances than NISP. That MNI would indeed sometimes be a more accurate measure of
taxonomic abundances than NISP is to be expected given everything we know about
the two quantitative units and the in¬‚uences of taphonomic processes and recovery
estimating taxonomic abundances: nisp and mni 55


Table 2.7. Statistical summary of the relationship between NISP and MNI for
mammal assemblages from fourteen archaeological sites in eastern Washington State

Site Regression equation r p NISP N of taxa
MNI = ’0.114(NISP)0.58
45DO273 0.816 0.0136 84 8
MNI = 0.01 (NISP)0.36
45OK2A 0.849 0.0019 366 10
MNI = ’0.178(NISP)0.628
45DO282 0.875 0.0004 426 11
MNI = ’0.12(NISP)0.64 < 0.0001
45DO211 0.847 474 15
MNI = ’0.19(NISP)0.51
45DO285 0.721 0.0024 491 15
MNI = ’0.07(NISP)0.44
45DO214 0.765 0.0003 536 17
MNI = 0.02(NISP)0.3
45DO326 0.56 0.0242 640 16
MNI = ’0.093(NISP)0.4 < 0.0001
45DO242 0.89 673 13
MNI = ’0.04(NISP)0.21
45OK287 0.786 0.007 807 10
MNI = ’0.019(NISP)0.41
45OK250 0.776 0.003 1,077 12
MNI = ’0.072(NISP)0.48 < 0.0001
45OK4 0.881 1,108 15
MNI = ’0.158(NISP)0.4
45OK2 0.769 0.0002 2,574 18
MNI = ’0.124(NISP)0.5 < 0.0001
45OK11 0.849 3,549 24
MNI = ’0.094(NISP)0.47 < 0.0001
45OK258 0.863 4,433 21


and identi¬cation skills. What we don™t know, and can™t really know most of the time,
is whether MNI is a more accurate measure of taxonomic abundances than NISP for
any given assemblage of paleozoological remains. Hudson (1990) and Breitburg (1991)
knew that MNI provided more accurate measures of the thanatocoenosis because
they knew the original taxonomic abundances of the death assemblage. We don™t

Table 2.8. Maximum distinction (each pellet considered independently) and
minimum distinction (all pellets considered together) MNI values for six genera
of mammals in a sample of eighty-four owl pellets. The right femur is the most
abundant element for Microtus, and the left femur is the most abundant
element for Peromyscus in the minimum distinction column

Minimum Maximum
Taxon NISP distinction MNI distinction MNI
Sylvilagus 5 1 2
Reithrodontomys 19 5 5
Sorex 46 5 7
Thomomys 68 8 12
Microtus 705 104 118
Peromyscus 1,266 188 220
2,109 310 364
quantitative paleozoology
56




figure 2.8. Relationship between NISP and MNI data pairs for remains of six mammalian
genera in eighty-four owl pellets. The regression equation is MNI = “0.389(NISP)0.149 , and
the correlation coef¬cient of the simple best-¬t regression line is signi¬cant (r = 0.999, p <
0.0001). Data from Table 2.8.



know what the thanatocoenosis is in paleozoological contexts; it might be our target
variable.
That the relationship between NISP and MNI is particularistic and its precise
nature is dependent on the samples used is true. But the truth of that claim is
not a necessary basis for rejecting NISP in favor of MNI. This is so for several
reasons. First, as I noted earlier, NISP often contains virtually the same information
regarding taxonomic abundances as does MNI. Second, there are fewer analytical
steps in tallying NISP than in deriving MNI, so there are fewer layers (to borrow a
metaphor) in the house of cards upon which NISP rests than in the house of cards
upon which MNI rests. Do not misinterpret this second point; the simplest method
is not being advocated as the best just because it is simpler or easier or contains fewer
analytical steps. Rather, because NISP contains fewer steps and, more importantly,
fewer assumptions than MNI regarding taphonomy, recovery, identi¬cation skills,
and the like, perhaps NISP should be preferred. Finally, there is still problem seven,
which concerns how to aggregate faunal remains in order to produce MNI values.
No such problem exists with NISP, re¬‚ecting the fact that NISP is simply additive
and that MNI is not additive. It is time, then, to turn to what is likely the most serious
problem with MNI.
estimating taxonomic abundances: nisp and mni 57


Table 2.9. Adams™s (1949) data for calculating MNI values based on Odocoileus sp.
remains. MNI-I is equivalent to the MNI minimum distinction (one aggregate,
MNI = 118); MNI-II is equivalent to the MNI maximum distinction (¬ve aggregates,
MNI = 120)

Recovery Distal right Distal left Distal right Distal left
provenience humerus humerus femur femur MNI-II
A 38 42 10 11 42
B 5 12 1 1 12
C 30 42 10 10 42
D 11 9 3 5 11
E 9 13 2 7 13
MNI-I 93 118 26 34



Aggregation

Although MNI solves the problem of interdependence of specimens inherent to
NISP, MNI has its own signi¬cant problem. That problem is readily introduced by
considering the data that Adams (1949) presented when he determined the MNI
of deer (Odocoileus virginianus) per recovery provenience unit in the collection he
studied (Table 2.9). Adams distinguished what he referred to as “Minimums I”
and “Minimums II,” the individual column totals and the individual row totals,
respectively. I have substituted MNI for “Minimums” in Table 2.9 because MNI is
indeed what Adams meant. Notice that were one to ignore recovery provenience,
and just tally up the most frequently occurring skeletal part, distal left humeri would
be most abundant among the four skeletal parts, so the site-wide MNI “ or Adams™s
“MNI-I” “ is 118. But if the analyst were to tally up the most frequently occurring
skeletal part per unique recovery provenience, then distal left humeri would be the
most abundant skeletal part in four of the ¬ve recovery proveniences, but right distal
humeri would be the most abundant skeletal part in the ¬fth recovery provenience.
Thus the total MNI for the values summed over the ¬ve recovery proveniences “
Adams™s “MNI-II” “ is 120. Grayson (1984) later presented an example from a single
site in which differences between MNImni and MNImax values varied across nearly
two dozen taxa from 0 to 250 percent (the latter, MNImin = 15 and MNImax = 38).
It makes little difference whether Adams™s ¬ve distinct recovery proveniences are
horizontally distinct (like units in an excavation grid), vertically distinct (as with
strata), or both (as with grid units per stratum). His data illustrate the most sig-
ni¬cant problem that attends MNI. This problem was revealed by Adams (1949:24)
when he commented that one must assume “that parts of one individual are not
quantitative paleozoology
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