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


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



RE S O L U T I O N


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


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


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


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



CO N C L U S I O N


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


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

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


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



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


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


Measuring Biomass

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


Table 3.1. Biomass of deer and wapiti at Cathlapotle

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




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



Problems with Measuring Biomass (based on MNI)

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


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

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