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6,001 “8,000 0 405 405
8,001 “10,500 186 102 288

bison and the number of assemblages per period (p > 0.5); there is no correlation
between the total ungulate NISP and bison NISP per temporal period (p > 0.5). The
abundance of bison remains does not seem to be a function of sampling intensity
or sample size. χ 2 analysis indicates there are signi¬cant differences in the relative
abundances of bison remains in the samples (χ 2 = 8291.5, p < 0.0001); the test for lin-
ear trends indicates there is a trend in the abundance of bison remains (χ 2 trend =
109.55, p < 0.0001). The data indicate an increase in bison over time. Grass was
least abundant in the geographic area of concern between 8,000 and 4,000 14 C
years ago, consistent with the few remains of bison; bison eat mostly grass. Bison
likely immigrated from Montana and Wyoming through southern Idaho, 2,500 years
ago or later, when ¬re frequencies increased (based on the amount of charcoal
deposited in lake sediments) and made the immigration route more hospitable
(Lyman 2004b). The graph in Figure 5.14 shows the history of the frequency of
bison remains in eastern Washington clearly. Similar graphs have been around in
paleozoology for several decades (e.g., Ziegler 1973; Stiner et al. 2000). The graph in
Figure 5.14 plots only the relative abundance of bison remains; most other graphs
plot multiple taxa simultaneously and thus such graphs can sometimes be dif¬cult to
Another way to graph taxonomic abundances that has seen some recent popularity
is of more deductive derivation. Popularized in the early 1990s, a group of paleozo-
ologists, many of whom work in the western United States, calculated indices of
measuring the taxonomic structure and composition 205

taxonomic abundance and plotted those index values against (usually) time or (less
often) space. The seminal work was Bayham™s (1979) plotting of the ratio of abun-
dances of large to small animals. His reasoning in doing so was that large animals
(grouped by taxon) were more ef¬ciently exploited (cost less in terms of energy
expended relative to energy earned) than were small animals given tenets of foraging
theory (see Stephens and Krebs [1986] for a theoretical statement). Bayham™s notion
and his method were re¬ned by Broughton (1994a, 1994b, 1999; see also James 1990)
in a series of studies on mammalian, piscean, and avian faunas from California, and
were subsequently used by a number of others working in both the New World (e.g.,
Butler 2000; Dean 2001 ; Lyman 2003a, 2003b, 2004d) and the Old World (e.g., Butler
2001 ; Grayson and Delpech 1998; Nagaoka 2001 , 2002; Stiner et al. 1999).
The sort of graph referred to is exempli¬ed in Figure 5.15. This is a simple bivariate
scatterplot of the abundance of North American elk (or wapiti, Cervus elaphus)
remains relative to the abundance of all ungulate remains in eighty-six assemblages
of mammalian remains from sites in eastern Washington State. In an earlier analysis,
I found that the absolute abundance of elk remains is not correlated with the total
ungulate sample size ( NISP) per assemblage (r = 0.16, p = 0.14) (Lyman 2004d);
removing the three largest collections (NISP > 1800), the correlation becomes weak
but signi¬cant (r = 0.33, p < 0.005). The relative abundance of elk per assemblage is
not correlated with assemblage age (r = 0.006, p > 0.9), and the slope of the simple
best-¬t regression line is not signi¬cantly different from zero. On this basis I suggested
that there is no evidence here that the abundance of elk relative to the abundance of
all ungulates changed over the 10,000 years represented (Lyman 2004d).
Since the earlier analysis, the χ 2 test for linear trends has been introduced to pale-
ozoology. That test suggests there is indeed a trend in the relative abundance of elk
remains over time (χ 2 trend = 112.96, p < 0.0001). The scatterplot in Figure 5.15
gives no indication of whether the trend is for elk remains to increase or decrease
over time. Thus one advantage of the sort of graph shown in Figure 5.15 is exempli-
¬ed by the included simple best-¬t regression line, which hints at a decrease in elk
abundance over time (despite it having a slope statistically indistinguishable from
no slope). Remember, however, that taxonomic abundance data are often at best
only ordinal scale data, and seldom are they ratio scale data. Therefore, the regres-
sion line in Figure 5.15 should not be interpreted literally as indicative of ratio scale
relative abundances of elk. Instead, that line assists with the identi¬cation of a trend
in (in this case) elk relative abundances. Consider another example, one that displays
a graphically visible trend.
The Emeryville Shellmound site on the shore of San Francisco Bay in Califor-
nia produced a large fauna from strati¬ed deposits. Paleozoologist Jack Broughton
quantitative paleozoology

figure 5.15. Bivariate scatterplot of elk abundances relative to the sum of all ungulate
remains in eighty-six assemblages from eastern Washington State. The simple best-¬t regres-
sion line is shown to assist with identifying trends in elk relative abundance.

(1999) analyzed those faunal remains and found a number of trends in taxonomic
abundances. One of the more interesting ones concerns the abundance of remains
of North American elk relative to the abundance of deer (Odocoileus sp.) remains.
To monitor change in the abundance of elk over time, Broughton calculated an
“elk’deer index” for each assemblage in each stratum (several strata produced more
than one assemblage). The index was calculated as elk NISP/ (elk NISP + deer
NISP + medium artiodactyl NISP), where it is very likely that all medium artiodactyl
remains are from deer. The data and index value for each assemblage are given in
Table 5.9. As shown in Figure 5.16, plotting the index value, which is effectively the
proportion of cervid remains that represent elk, against the stratum from which it
derives suggests that elk became less available to human occupants of the Emeryville
Shellmound site over time (stratum 1 is youngest, stratum 10 is oldest). That it is
indeed the case that elk availability decreased over time relative to deer is con¬rmed
by the simple best-¬t regression line through the point scatter (r = 0.62, p = 0.008).
The χ 2 test for trends also suggests that there is a trend in the relative abundance
of elk remains (χ 2 trend = 638.8, p < 0.0001), but does not indicate the direction of
change in abundance.
Changes in taxonomic abundances can be monitored more directly than with
the indices of relative elk abundances presented in Figure 5.16 as proportions of
some larger group of taxa. Table 5.10 lists the abundances of remains of two taxa of
measuring the taxonomic structure and composition 207

Table 5.9. Frequencies (NISP) of elk, deer, and
medium artiodactyl remains per stratum at Emeryville
Shellmound. Data from Broughton (1999)

Medium Elk-Deer
Stratum Elk Deer Artiodactyl Index
1 0 100 122 0.0
1 0 35 58 0.0
2 8 758 958 0.005
3 17 294 365 0.025
3 1 8 12 0.048
4 81 72 76 0.354
5 40 52 56 0.270
6 11 20 18 0.224
7 12 10 13 0.343
7 184 94 76 0.520
8 75 46 56 0.424
8 116 87 83 0.406
9 23 79 51 0.150
9 68 67 62 0.345
10 50 95 94 0.209
10 59 122 103 0.208
10 63 105 88 0.246

mammals recovered from the strati¬ed deposits of Homestead Cave in Utah State
(Grayson 2000). The deposits span the terminal Pleistocene and entire Holocene.
Based on pollen and plant macrofossil records, local climate shifted from cool and
moist relative to today, to more or less modern climate by about 8,000 years ago.
The two taxa were chosen from the several dozen represented in the site to illustrate
trends in abundance here; Neotoma cinerea prefers cool, moist conditions relative to
Dipodomys sp., which prefers warmer and drier conditions. The absolute abundance
of Neotoma cinerea is not correlated with the stratum total NISP (ρ = 0.13, p > 0.6);
the absolute abundance of Dipodomys sp. is correlated with the stratum total NISP
(ρ = 0.82, p = 0.0003), but given the exceptionally large abundances of remains in
all strata, I doubt that sample size is a problem.
Given the climatic preferences of the two taxa, and the environmental history
coincident with deposition of the strata in Homestead Cave, Neotoma cinerea should
decrease in abundance and Dipodomys sp. should increase. That is in fact precisely
quantitative paleozoology

figure 5.16. Bivariate scatterplot of elk“deer index against stratum at Emeryville Shell“
mound. The simple best-¬t regression line is shown to assist with identifying trends in elk
relative abundance. Data from Table 5.9.

what the relative abundances of remains of each taxon do. On the one hand, Neotoma
cinerea remains decrease in relative abundance during the terminal Pleistocene and
earliest Holocene (strata I, II, III) and virtually disappear after that (Figure 5.17; χ 2
trend = 13,034, p < 0.0001). Remains of Dipodomys sp., on the other hand, increase
rapidly during the terminal Pleistocene and earliest Holocene, and after about 8,000
BP (after the deposition of stratum VI), they comprise more than half the total NISP
per stratum (Figure 5.17; χ 2 trend = 25,457, p < 0.0001).
Two methods for examining trends in taxonomic abundances over time have been
described. One involves calculating an index of a taxon™s abundance within a lim-
ited set of taxa. The index can be expressed as a proportion or a percentage. The
other method involves calculating the proportion or percentage of a taxon™s abun-
dance within the entire assemblage. Broughton (1999) was interested in determining
whether elk availability was decreased by human predation and were replaced by deer
(Figure 5.16). Grayson (2000) was interested in the contribution of particular taxa
measuring the taxonomic structure and composition 209

Table 5.10. Frequencies (NISP) of two taxa of small mammal per stratum at
Homestead Cave. Remains from strata X, XIII, XIV, XV were not analyzed. Data
from Grayson (2000)

Neotoma Percent of Dipodomys Percent of Stratum
Stratum cinerea Total NISP sp. Total NISP Total NISP
I 2,577 25.1 360 3.5 10,275
II 1,508 19.2 1,329 16.9 7,855
III 306 10.6 1,056 36.6 2,884
IV 242 0.9 13,712 51.5 26,615
V 1 0.02 2,965 58.0 5,109
VI 5 0.02 15,173 62.4 24,330
VII 4 0.03 9,868 71.0 13,905
VIII 5 0.06 5,742 69.3 8,289
IX 1 0.005 15,477 70.1 22,088
XI 0 0 6,820 67.6 10,096
XII 0 0 16,753 73.3 22,860
XVI 0 0 4,371 69.4 6,296
XVII 9 0.06 10,418 67.0 15,548
XVIII 0 0 720 68.8 1,047

to the entire mammalian fauna. The choice of method was guided by the research
question being asked.


There are many reasons to compare the taxonomic abundances displayed by dif-
ferent collections. Simplistically, these can be reduced to two general categories of
questions “ those concerning paleoenvironmental conditions (was it hot or cool,
dry or moist?), and those concerning human or hominid adaptations (what did
they eat, and how much)? Those categories concern ultimate questions; they are
answered with detailed contextual, associational, and taphonomic analysis of tax-
onomic abundances. The concern of this chapter has been to describe ways that
taxonomic abundance data might be analyzed and studied, to answer more proximal
questions, questions closer to the quantitative data themselves. Toward that end,
diversity was de¬ned as a generic term for variation in taxonomic richness, even-
ness, and/or heterogeneity. Indices for each of the latter variables were described and
quantitative paleozoology

figure 5.17. Relative abundances of Neotoma cinerea and Dipodomys spp. at Homestead
Cave. Data from Table 5.10.

exempli¬ed. Two methods of monitoring trends in taxonomic abundances over time
were discussed. No doubt, there are other methods and indices that might be used.
Ecologists are regularly inventing new measures of taxonomic structure and compo-
sition, and re¬ning old ones. Paleozoologists should, and often do, pay attention to
those developments and adopt new indices and quantitative methods developed by
ecologists. In so doing, paleozoologists potentially adopt a family of problems the
identi¬cation of which is a good way to conclude this chapter.
Earlier the biological concept of community was de¬ned, and it was noted that
biological communities are sometimes dif¬cult to identify; the identi¬cation problem
is exacerbated when one seeks to identify a paleocommunity on the basis of the fossil
record (e.g., Bennington and Bambach 1996). This fact was explicitly dealt with more
than 50 years ago by paleozoologist J. Arnold Shotwell (1955, 1958) when he attempted
to use quantitative measures of skeletal completeness to distinguish taxa comprising
the proximal paleocommunity from taxa comprising distal (distant) communities.
Taphonomists and those with a quantitative bent were quick to point out some of the
analytical dif¬culties with what Shotwell proposed (Grayson 1978b and references
measuring the taxonomic structure and composition 211

therein). With the bene¬t of another couple decades of re¬‚ection, there is yet another
problem that attends Shotwell™s method, a problem that potentially plagues any and
all of the indices and measures of taxonomic abundances discussed in this chapter.
That problem is what is known as “time averaging.”
The temporal resolution available in the paleozoological record is seldom of the
¬ne scale, intrageneration resolution that is provided to zoologists. The temporal
acuity of the paleozoological record is such that, very often, any stratigraphically
bounded sample is a palimpsest or time-averaged collection representing multiple
generations, multiple seasons, multiple years, and typically multiple decades or even
centuries or millennia (Peterson 1977; Schindel 1980). This means that concepts such
as taxonomic richness, evenness, and heterogeneity, which derive from extant com-
munities, may never be of the same temporal resolution in the paleozoological record
as they are in the modern or extant zoological record (but see Olszewski and Kidwell
2007). Ecological time is seldom the same as paleozoological time (see also Grayson
and Delpech 1998). One result of recognition of this potential problem has been a
series of “¬delity studies,” introduced in Chapter 2 and de¬ned as “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). Many of these studies originate in taphonomic concerns regarding the
preservation of animal remains or the rate of input of those remains. Fewer concern
the difference between ecological time and paleontological time either studied empir-
ically or focusing on key quantitative concepts such as richness and evenness (see
Broughton and Grayson [1993], Lyman [2003b], and Olszewski and Kidwell [2007]
for exceptions). The critical point to contemplate is the relationship between the
property (richness, relative abundance, etc.) of a paleofauna that has been measured
and the temporal resolution of that value. Does it encompass a decade, a century,
more? And how might that in¬‚uence interpretations? An example will highlight the
signi¬cance of these questions.
If the elk abundance data for the eighty-six individual collections in Figure 5.15
are lumped into 500-year bins (1 “500 BP, 501 “1000 BP, etc.), and the elk index
recalculated using only elk and deer remains (bison, pronghorn, bighorn excluded),
the result is rather different than that shown in Figure 5.15. The resulting graph and
best-¬t regression line suggest there is a signi¬cant relationship between age and
the relative abundance of elk (r = 0.489, p = 0.064) (Figure 5.18). The slope of the
line suggests elk availability decreased over time. The χ 2 test for trends con¬rms
the trend in the relative abundance of elk remains (χ 2 trend = 9.67, p = 0.002;
including all ungulates, χ 2 trend = 42.5, p < 0.0001). Something not apparent in the
statistics is that elk seem least abundant between about 7,500 and 4,000 BP, precisely
quantitative paleozoology

figure 5.18. Bivariate scatterplot of elk abundances relative to the sum of all ungulate
remains in eighty-six assemblages from eastern Washington State summed by age for con-
secutive 500-year bins. The simple best-¬t regression line is shown to assist with identifying
trends in elk relative abundance. Compare with Figure 5.15. Note that there are no data for
the 6,001 “6,500, 7,001 “7,500, and 7,501 “8,000 bins.

when climate was least conducive to elk reproduction (Lyman 2004a, 2004d, and
references therein). Whatever the case, comparison of Figures 5.15 and 5.18 make it
clear that time averaging can in¬‚uence analytical results, as can the taxa included in
the measure of relative abundance.
Do not let the preceding mislead you. Time averaging may not always be a bad
thing. It has been suggested, for example, that either time averaged samples formed
by natural processes, or those formed by analytical lumping of assemblages may
serve to ¬lter out “noise” in a paleofaunal signal (Olszewski 1999; see also Muir and
Driver 2002). Whether time averaging is a good thing or a bad thing will depend
on the research question being asked and the attendant target variable that must be
measured or estimated in order to answer the research question. Similarly, lumping
assemblages from different spatial locations may also result in an averaging or muting
measuring the taxonomic structure and composition 213

of the paleofaunal signal (Lyman 2003b). Thus, one must be explicit about the spa-
tiotemporal coordinates (and their boundaries) pertinent to the research question
being asked. Either that, or we rewrite the ecological variables we seek to measure in
paleozoological spatiotemporal units. To reiterate, the research questions of interest
should dictate the temporal resolution necessary for a clear answer.
Skeletal Completeness, Frequencies
of Skeletal Parts, and Fragmentation

The minimum number of individuals (MNI) is typically de¬ned as something like
the most frequently occurring skeletal part (Table 2.4). Variation in how that def-
inition can be operationalized are differences in size, age, sex, or recovery context
(aggregation) considered renders MNI as a derived measure. But on a general, in
some ways less discriminating scale, how the basic de¬nition of MNI is operation-
alized is simply this: Given all the remains of a taxon in a collection (how the spa-
tiotemporal boundaries of that collection are de¬ned need not concern us initially),
redundant skeletal parts are each tallied as a single MNI. Redundant skeletal parts
means that specimens overlap anatomically. Two left femora of deer overlap anatom-
ically and are redundant with one another, just as are two upper right second molars,
three right distal humeri, and four left innominates. In the order listed, the MNI
values are 2, 2, 3, and 4. To reiterate, redundant that is, anatomically overlapping
skeletal parts each represent a unique individual or a tally of one MNI.
How MNI is operationalized on a general scale by redundant skeletal parts forces
us to recognize a previously unmentioned quantitative unit. That unit was not really
distinctively named until 1982, but it had played an important role in paleozoology
for decades prior to that time. Today that quantitative unit is known as the minimum
number of elements, or MNE. This unit not only is, in fact, the basis of MNI, it is also
the basis of another important quantitative unit that has at least two different names
(MAU,%survivorship), and it is, ¬nally, somewhat of a misnomer. The purposes of
this chapter are to make all of these points clear and to illustrate if and how MNE
might be analytically useful.
Another purpose of this chapter is to review the means to analytically determine,
and interpret, other quantitative variables that paleozoologists sometimes measure.
One concerns which parts or portions of the represented skeletons are present; are
those parts represented in abundances that reveal something of the taphonomic his-
tory of the collection, such as accumulation or preservation? Another concerns the
skeletal completeness, skeletal parts, and fragmentation 215

degree of skeletal completeness; how complete, on average, is each of the multiple
skeletons represented? The ¬nal variable that has been studied using MNE concerns
bone fragmentation. Techniques for quantifying the degree of fragmentation evi-
dent in a collection of faunal remains are reviewed, and pertinent concepts de¬ned.
Tallying the frequencies of skeletal parts, measuring skeletal completeness, and mea-
suring the degree of fragmentation all rest in one way or another on tallies of MNEi,
where i is a particular skeletal element, part, or portion. An historical overview of
MNE sets the stage for subsequent discussions of how it and its related quantitative
units have been and can be used. The overview provides the requisite background
to consideration of how skeletal completeness is measured and how fragmentation
is quanti¬ed.


When Chester Stock tallied up abundances of mammalian taxa represented by the
Rancho La Brea remains (Chapter 1 ), he determined the minimum number of indi-
viduals. To determine MNI, he tallied redundant or anatomically overlapping skeletal
parts; that is, he determined the MNE of each unique skeletal part whether ¬rst cervi-
cal vertebrae, left mandibles, right humeri, or left tibiae and used the largest number
as his MNI. All subsequent paleozoologists who have derived an MNI from a collec-
tion have ¬rst determined the MNE for at least the most common skeletal parts if
not all skeletal parts of a taxon, and then used the greatest MNE value as the MNI
value for that taxon. As put some years ago, MNE is the minimum number of skeletal
portions necessary to account for the specimens representing that portion (Lyman
1994c:102). How and why did explicit recognition of MNE emerge?
Traditionally, paleozoologists such as Chester Stock sought measures of taxonomic
abundances. Thus, MNI, biomass, NISP, and the like were designed to measure
those abundances. But with increases in our knowledge of how the paleozoological
record formed, taphonomic concerns came to the fore. Was, perhaps, taxon A more
abundant than taxon B in a collection because taxon A was more abundant on the
landscape than taxon B was at the time the remains of each were accumulated and
deposited? Or, did the agent or process of bone accumulation simply collect more
of taxon A than of taxon B? Or, did the agent or process of bone preservation (or
destruction) result in bones of taxon A being more frequently preserved than those of
taxon B? These were taphonomic questions that concerned skeletal-part abundances
and, thus, depending on their answers, could signi¬cantly in¬‚uence how taxonomic
abundance data were interpreted.
quantitative paleozoology

Taphonomists seek answers to questions that differ in kind and scale from those
traditionally asked by paleozoologists. (This is not meant to imply that paleozo-
ologists and taphonomists are two distinct sets of researchers; rather, it is meant
to underscore differences in the questions that are asked about a collection of fau-
nal remains.) Instead of asking how many or how much of each taxon contributed
to a collection what a paleozoologist would normally ask, although perhaps with
different target variables in mind (Figure 2.1 ) a taphonomist would ask why only
certain skeletal elements, individual organisms, or taxa are represented in a collec-
tion. Taphonomists attempt to measure and understand why paleozoologists do not
always ¬nd complete articulated skeletons. Rather, what they typically ¬nd are vari-
ously incomplete skeletons, often comprising broken skeletal elements. The questions
taphonomists ask, then, are focused more on the proximate causes for the existence
of a bone assemblage and why the assemblage is made up not only of the taxa that
it represents, but the skeletal parts and the taxonomic abundances that it is, as well
as such questions as why some bones are missing, others are broken, and still others
are abundant.
Taphonomists effectively shift the level of measurement from taxonomic abun-
dances to attributes of a collection of remains, such as skeletal-part frequencies, usu-

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