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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

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