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1 38.78 54.426 38.36 52.700 1.726
2 40.38 61.002 40.08 59.769 1.233
3 43.10 72.181 42.86 71.195 0.986
4 39.90 59.029 40.00 59.440 0.411
5 36.84 46.452 36.74 46.041 0.411
6 43.74 74.811 43.32 73.085 1.726
7 38.94 55.083 38.88 54.837 0.246
8 42.76 70.784 42.44 69.468 1.316
9 38.94 55.083 38.38 52.782 2.301
10 43.74 74.811 43.46 73.661 1.150
11 42.86 71.195 42.94 71.523 0.328
12 41.72 66.509 41.36 65.030 1.479
13 41.80 66.838 41.92 67.331 0.493
14 37.44 48.918 37.54 49.329 0.411
15 39.70 58.207 39.82 58.700 0.493
16 40.88 63.057 40.72 62.399 0.658
17 40.52 61.577 40.38 61.002 0.575

wise to not do so (Lyman 2006a). All of the problems that attend identifying bilateral
pairs also plague Orchard™s (2005) method.


None of the quantitative units and methods occasionally used to estimate or measure
taxonomic abundances reviewed in this chapter have been widely adopted or seen
more than sporadic use. When Grayson (1984) wrote his synopsis of quantitative
zooarchaeology, he focused on NISP and MNI because they were at the time the
most widely used units. His discussions of other methods such as the Lincoln“
Petersen index were terse. I have attempted here to empirically support, or refute
claims regarding these other methods. Thus, we ¬nd that biomass and meat weight
quantitative paleozoology

estimates compound many weaknesses of MNI because of requisite assumptions
regarding average live weights and edible tissue amounts. Ubiquity as a measure
of the “importance” of a taxon is strongly in¬‚uenced by sample size measured as
NISP; it provides information on taxonomic abundance that is virtually identical
to information provided by NISP. Ubiquity might measure some as yet unknown
(taphonomic?) variable if two taxa with statistically indistinguishable sample sizes
have different ubiquities, but what that variable might be is unclear.
Numerous quantitative methods have been proposed as improvements to MNI.
Virtually all involve investing what Theodore White thought would be a great deal of
time determining which left elements pair up bilaterally with which right elements.
The validity of estimates of taxonomic abundance provided by those methods rests
on the validity of pair identi¬cation. The pair identi¬cation procedure rests on the
notion of bilateral symmetry but no organism is perfectly bilaterally symmetrical,
so one must decide how symmetrical is symmetrical enough. Even if that decision
can be made, in large samples (of more than, say, two dozen specimens) potential
bilateral mates for any specimen are multiple. This highlights the fact that false pairs
are likely to be identi¬ed even in small samples of lefts and rights.
Other methods discussed in this chapter concern efforts to correct for intertaxo-
nomic variation in (i) number of identi¬able elements per individual, (ii) transport or
accumulation, and (iii) fragmentation. These variables can be analytically accounted
for in NISP (see Chapter 2). Where are we left, then, with respect to measuring tax-
onomic abundances? As alluded to in the preceding chapter, I agree with Grayson
(1979, 1984) and the numerous paleobiologists who use NISP to measure taxonomic
abundances. It is cumulative or simply additive, meaning it is primary data or an
observed measure; and it serves as the basis for many derived measures (and hence
is correlated with many of them). I use it virtually exclusively in subsequent chapters
when issues of taxonomic abundance are under study. When I do not, I explain why;
generally I use quantitative units other than NISP when the target variable is not
taxonomic abundances.
Sampling, Recovery, and Sample Size

It is commonsensical to note that what is recovered “ the amount recovered of
each kind, and the number of kinds “ will in¬‚uence quantitative analyses (Cannon
1999). As we have seen in earlier chapters, sample size in¬‚uences many measures and
estimates of taxonomic abundances. The size of a sample of faunal remains measured
as the number of specimens recovered is in turn in¬‚uenced by the sampling design
chosen (how much is excavated) and the recovery techniques (passing sediment
through ¬ne- or coarse-mesh sieves) used to implement that sampling design. This
chapter focuses on how one generates a collection of faunal remains (sampling and
recovery), properties of the resultant sample, and ways to examine the in¬‚uences of
sample size on selected target variables.
Paleozoologists have long worried about how methods of recovery might pro-
duce collections that are not representative of a target variable (e.g., Hibbard 1949;
Kuehne 1971 ; McKenna 1962; Payne 1972; Thomas 1969). Exacerbating this worry
is the fact that paleozoologists collect samples of faunal remains from geological
contexts (Krumbein 1965; Ward 1984). This is true on at least two levels. First, pale-
ozoologists never (or at least very seldom) collect all of the faunal remains from
a deposit, paleontological location, or archaeological site. Second, the target vari-
able usually resides in an entity other than the “identi¬ed assemblage” (Figure 2.1 ).
If the target variable is the taphocoenose (either that which is preserved or that
which was deposited), the thanatocoenose, or the biocoenose, the paleozoologist is
dealing with a sample regardless of whether or not the complete deposit has been
For more than 50 years, paleozoologists have suggested that probabilistic sampling
methods will produce “representative samples” (e.g., Gamble 1978; Krumbein 1965;
Voorhies 1970). These methods concern techniques to choose portions of the geo-
logical record to examine for faunal remains. There are many excellent discussions
quantitative paleozoology

of probabilistic sampling (e.g., Orton 2000), so methods of probabilistic sampling
are not discussed here. Instead the focus is on a couple of related sampling issues.
Choosing deposits to inspect for faunal remains is but one part of the sampling
problem. Another part concerns how faunal remains are retrieved or collected from
deposits chosen for inspection. If more sediment samples are chosen for inspection,
or more remains are recovered from the chosen sediments because of how remains
are retrieved, then the resultant sample is different (larger) than it might otherwise
have been.
In this chapter, two issues are of concern. One is collection or recovery technique.
Are faunal remains picked by hand from exposed sediments; are sediments passed
through hardware cloth (screens or sieves) and faunal remains that do not pass
through the cloth collected; are faunal remains collected from bulk samples, from
¬‚otation samples, or by some other means? Because the recovery methods used
in¬‚uence what is collected, efforts have been made to correct for these in¬‚uences,
and some of these correction procedures are reviewed here. Another issue discussed
in this chapter is sample size measured in either or both of two ways “ as amount of
sediment examined (either area or volume) and as amount of faunal material studied.
Both measures of sample size often correlate with the number of taxa recovered, the
relative abundances of those taxa, and the like. To make valid interpretations of
quantitative faunal data, we must understand both the nature of a sample and how
sampling techniques may in¬‚uence the faunal variables that we hope to measure.
All of the variables discussed here “ amount of sediment inspected, screen mesh
size, NISP “ are particular manifestations of sampling effort. Greater sampling effort
(however measured) will produce larger samples, but how sampling effort in¬‚uences
other characteristics of the sample is not always recognized.
One distinction that must be made at the start concerns the difference between
discovery sampling and statistical precision sampling (Nance 1983). Discovery sampling
concerns sampling designs built to discover new phenomena and the sampling effort
required to ¬nd various categories of phenomena. The more rare a kind of thing is in a
sampling universe, the more sampling effort required to ¬nd an instance of that kind.
Statistical precision sampling generates a sample that provides an accurate estimate
of a target variable. Whereas discovery sampling focuses on ¬nding examples of
rarely occurring kinds of phenomena, statistical precision sampling seeks to estimate
properties of commonly occurring categories of phenomena, whether abundances of
individual instances within each category, average size of members of each category,
or any of a plethora of other variables that might be measured. The distinction of
discovery sampling and statistical precision sampling will be important in this and
subsequent chapters.
sampling, recovery, and sample size 143


Many of the quantitative variables that we seek to measure with paleozoological
collections are often strongly in¬‚uenced by sampling effort (how ever such effort is
measured), itself a quantitative variable. In this chapter analytical techniques that
have been suggested for controlling those in¬‚uences when comparing samples of
markedly different sizes are outlined. These techniques are based on the assumption
that no other deposits will be inspected for faunal remains, and thus that no new
faunal remains will be added to the samples at hand. Another method that assumes
new specimens are forthcoming until a sample that is representative of the target
variable(s) is in hand is also described. This latter method can be implemented with
either or both of two distinct measures of sample size.
Paleozoologists typically collect a sample of faunal remains from a population of
remains. (For sake of discussion, the identity of the target variable “ taphocoenose,
thanatocoenose, biocoenose “ will be ignored.) The population may comprise all the
faunal remains encased within a stratum, or those within several strata thought for
non-faunal reasons to represent the same zoological property of interest and thus for
analytical purposes to be instances of the same population. Because paleozoologists
sample the depositional (geological) record for faunal remains, they generally collect
multiple samples. One sample may be collected today and another tomorrow; one
sample may be collected from a particular geographic and geological location and
another from a different location. In many cases, individual samples are collected over
multiple time periods, whether those periods are consecutive months or consecutive
annual ¬eld seasons. Because consecutively gathered samples from a deposit (from
what is thought to represent the same population) are cumulative, a basic method
of empirically assessing sample adequacy suggests itself.
Assume that a target variable has been speci¬ed by the research problem one is
attempting to solve. Let us say that the target variable requires measurement of the
number of mammalian taxa in a collection, generally known as taxonomic richness.
The acronym NTAXA for “number of taxa” will be used here. (NTAXA is used
by ecologists and archaeologists [e.g., Broughton and Grayson 1993] to measure
niche breadth [among other things].) How do we know when we have collected
enough faunal remains to have a sample that provides a relatively accurate estimate
of NTAXA? Archaeologist Robert Leonard (1987:499) suggested that one could sample
“to redundancy” and that the way to know when additional samples were redundant
with previous samples was simple; “plot the information gained against the number
of samples taken and determine if the curve is becoming asymptotic. It may then be
reasonable to assume that the sample is suf¬ciently representative with regard to that
quantitative paleozoology

Table 4.1. Volume excavated and NISP of mammals per annual ¬eld season at the
Meier site

Volume (m3 ) Deer NISP/m3
1973 11.0 519 16 276 25.1
1987 40.7 1,359 21 778 19.1
1988 31.2 1,232 22 756 24.2
1989 46.3 970 19 562 12.1
1990 29.2 956 18 570 19.5
1991 37.7 1,385 20 838 22.2

particular information.” In paleozoology, sample size can be measured one of two
ways “ either as amount excavated or as NISP.

Excavation Amount

Paleontologists have examined the in¬‚uence of sample size measured as amount of
sediment examined on NTAXA (e.g., Raup 1972). Efforts to correct for such continue
to this day (e.g., Crampton et al. 2003). Wolff (1975) used an empirical means to
determine if suf¬cient sediment had been examined to argue that his samples were
representative of NTAXA. He compiled data on cumulative NTAXA across increas-
ing amounts of sediment from which faunal remains had been extracted. When
his cumulative NTAXA curve leveled off across several additional units of sediment
volume, Wolff (1975) argued that his total sample was representative of that target
variable. With the cumulative NTAXA plotted on the vertical or y-axis of a bivariate
plot, and new unit volumes of sediment added along the horizontal or x-axis of the
plot, Wolff showed that taxa were initially added quickly by new samples, but as
the number of samples increased the rate of addition of new taxa slowed until it
leveled off across multiple new samples. The latter was taken by Wolff to mean that
he had sampled suf¬ciently to have a representative sample; Leonard (1987) would
say that Wolff had sampled to redundancy because faunal remains from additional
unit volumes of sediment failed to produce any new taxa.
The protocol is easy to illustrate with the data in Tables 4.1 and 4.2 for the Meier
site. If we use those data to construct a cumulative NTAXA curve based on volume
excavated, we obtain the result in Figure 4.1 . As the volume excavated from one
year to the next increased, NTAXA initially increased, but then it leveled off and no
sampling, recovery, and sample size 145

Table 4.2. Annual NISP samples of mammalian genera at the Meier site

Taxon 1973 1987 1988 1989 1990 1991 Total
Scapanus 4 4 3 4 1 2 18
Sylvilagus 2 3 1 1 10 1 18
Aplodontia 2 1 1 3 7
Tamias 1 1
Tamiasciurus 2 2
Thomomys 2 1 5 1 9
Castor 13 100 65 52 41 71 342
Peromyscus 4 12 12 4 3 35
Rattus 1 1
Neotoma 1 1
Microtus 15 25 34 15 11 100
Ondatra 37 97 55 59 74 52 374
Erethizon 1 1
Canis 2 25 13 16 11 25 111
Vulpes 3 1 1 5
Ursus 20 16 20 7 13 26 102
Procyon 15 79 51 35 43 64 287
Martes 1 6 1 1 11 20
Mustela 4 35 17 19 38 21 134
Mephitis 1 1 2 4
Lutra 6 12 6 2 11 14 51
Puma 4 1 3 1 9
Lynx 9 5 4 1 4 8 31
Phoca 3 6 5 10 6 13 43
Cervus 103 165 191 152 106 218 935
Odocoileus 276 788 756 562 570 838 3,780
Annual NISP 519 1,359 1,232 970 956 1,385 6,421
Annual NTAXA 16 21 22 19 18 20 26
Cumulative NISP 519 1,878 3,110 4,080 5,036 6,421 “
Cumulative NTAXA 16 21 24 26 26 26 “

new taxa were added after the ¬rst 129.2 m3 of sediment had been inspected. With
respect to cumulative volume of sediment excavated, the Meier site sample contains
representatives of at least the most common taxa (see the following section); very
rarely represented taxa may not be present in the collection, but the sampling to
redundancy procedure suggests that we have a statistically precise representation of
the common taxa.
quantitative paleozoology

figure 4.1. Cumulative richness of mammalian genera across cumulative volume (m3 )
of sediment excavated annually at the Meier site. Numbers adjacent to plotted points are
cumulative m3 . Data from Table 4.1 .

NISP as a Measure of Sample Redundancy

Retaining taxonomic richness or NTAXA as our target variable for illustrative pur-
poses, consider the Meier and the Cathlapotle collections. Meier was sampled over
a period of six annual ¬eld seasons (the last ¬ve were consecutive) by two archae-
ologists. Cathlapotle was sampled over a period of four annual ¬eld seasons by one
archaeologist, but early in the ¬rst annual ¬eld season recovery techniques varied
considerably from those used later that year, so the ¬rst year is split into two chrono-
logically consecutive samples for illustrative purposes. At both sites, each annual ¬eld
season spanned a period of 8 weeks. Annual NISP samples from Meier are described
in Table 4.2 and those for Cathlapotle are described in Table 4.3. Summed values
for Meier in Table 4.2 are larger than those given in Table 1.3 because an additional
sample analyzed in 1973 is included in the former table. Values for Cathlapotle in
Table 4.3 are greater than those given Table 1.3 because included in the former table
are specimens that could not be assigned to a temporal component and thus could
not be included in Table 1.3.
It has long been recognized that the order in which samples are added to cumulative
frequency curves can in¬‚uence the result (e.g., Kerrich and Clarke 1967). The total
sampling, recovery, and sample size 147

Table 4.3. Annual NISP samples of mammalian genera at Cathlapotle. The two 1993
samples represent different recovery techniques

Taxon 1993a 1993b 1994 1995 1996 Total
Didelphis 10 10
Scapanus 3 3
Sorex 4 4
Lepus 14 20 18 52
Aplodontia 2 18 41 42 33 136
Castor 1 32 123 185 51 392
Peromyscus 4 1 5
Microtus 1 12 16 39 68
Ondatra 19 34 32 21 106
Canis 4 27 5 3 39
Vulpes 1 3 1 5
Ursus 1 23 29 31 18 102
Procyon 1 57 59 70 20 207
Martes 2 2
Mustela 3 14 7 5 29
Mephitis 3 3
Lutra 14 19 13 19 65
Puma 5 3 3 1 12
Lynx 2 6 12 6 26
Phoca 1 19 41 4 65
Ovis 2 2
Cervus 16 462 879 1,184 683 3,224
Odocoileus 18 332 797 821 408 2,376
Equus 2 2 4
Annual NISP 40 973 2,091 2,488 1,345 6,937
Annual NTAXA 7 14 20 19 18 24
Cumulative NISP 40 1,013 3,104 5,592 6,937 “
Cumulative NTAXA 7 15 20 21 24 “

cumulative sample size at which the curve levels off and thus suggests that new
samples are providing no new information but instead only redundant information
can vary considerably depending on the order of sample addition. Thus, choice of the
order in which samples are added must be explicit and logical. Given that there is an
inherent (chronological) order to the annual samples from Meier and also to those
from Cathlapotle, it is logical to treat the samples as cumulative in the temporal order
in which they were collected. Doing so for the Meier annual samples produces the
quantitative paleozoology

figure 4.2. Cumulative richness of mammalian genera across cumulative annual samples
(NISP) from the Meier site. Numbers adjacent to plotted points are cumulative NISP. Data
from Table 4.2.

cumulative NTAXA curve shown in Figure 4.2; doing so for the Cathlapotle annual
samples produces the cumulative NTAXA curve shown in Figure 4.3 (both curves
are slightly different than those described in Lyman and Ames [2004] because all taxa
are included here; Lyman and Ames [2004] excluded historically introduced taxa).
What do those curves suggest?
On the one hand, the cumulative NTAXA curve for Meier levels off after the
addition of the fourth, or 1989, sample (Figure 4.2). Despite an addition of more than
2000 NISP, no new taxa are added with the 1990 and 1991 samples. These last two,
most recent samples are redundant with earlier samples in terms of their in¬‚uence
on the target variable of NTAXA. This suggests that the total Meier collection can
be treated as representative of the mammalian genera deposited at the site. The
cumulative NTAXA curve for the Cathlapotle sample, on the other hand, does not
level off but rises with the addition of each new sample (Figure 4.3). An argument
cannot be made that additional collection of faunal remains from this site will fail to
produce evidence of additional mammalian genera. The cumulative NTAXA curve
for Cathlapotle also suggests that the total sample, though it consists of nearly 7,000
NISP, does not represent all mammalian genera in the site deposits.
In the ecological literature, curves such as those illustrated in Figures 4.1 , 4.2 and
4.3 are sometimes referred to as “accumulation curves” (Gotelli and Colwell 2001 )
sampling, recovery, and sample size 149

figure 4.3. Cumulative richness of mammalian genera across cumulative annual samples
(NISP) from Cathlapotle. Numbers adjacent to plotted points are cumulative NISP. Data
from Table 4.3.

for an obvious reason. Sampling to redundancy has not been mentioned very often in
paleozoological research (e.g., Lyman 1995a; Monks 2000; Reitz and Wing 1999:107),
and used even less often (e.g., Butler 1990; Lyman and Ames 2004; Wolff 1975).
Many paleoethnobotanical examples are cases in which sampling effort is plotted
against richness, and the in¬‚uences of sample size differences are noted (Lepofsky
and Lertzman 2005). This underscores the ease with which a quantitative tool can
be misrepresented as doing one thing when in fact it is doing something else. We
return to this general kind of curve later in this chapter. Here it suf¬ces to note that
the curves in Figures 4.1 , 4.2 and 4.3 are but one kind of a more general kind of curve
that is used to examine the relationship between sample size and ecological variables
such as NTAXA.

Volume Excavated or NISP

The amount of sediment examined for faunal remains is one measure of sample size,
but the NISP per unit volume of sediment can vary considerably. This means that
correlations between sediment volume and, say, NTAXA, are likely to be less strong
quantitative paleozoology

figure 4.4. Relationship of mammalian genera richness (NTAXA) and sample size (NISP)
per annual sample at the Meier site. The relationship is described by the simple best-¬t

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