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pieces (fragments) that each skeletal element has been broken into or is represen-
ted by.
Paleozoologists have worried about the degree of fragmentation of faunal remains
for decades, as evidenced by their worries about intertaxonomic variation in frag-
mentation differentially skewing NISP measures of taxonomic abundances (Chap-
ter 2). Tallying MNE frequencies per taxon escapes that problem, but introduces
the problems attending derivation of MNE (aggregation, sample size, de¬nition).
Taphonomic questions about fracturing agents and processes have resulted in some
innovations in measuring fragmentation. Simply because taxon A has a greater NISP
value than taxon B does not mean that the remains of taxon A are more fragmentary
than those of taxon B. How might we determine which taxon™s remains are the more
anatomically complete and less fractured, and which taxon™s are more anatomically
incomplete and more fragmentary?



Fragmentation Intensity and Extent

Klein and Cruz-Uribe (1984) use the ratio NISP/MNI per skeletal element to measure
fragmentation for each taxon, but there is a potential problem with this measure.
NISP is the number of identi¬ed specimens, and a specimen is a bone or tooth
or fragment thereof. The last two words are emphasized for one simple reason. If,
say, many of the skeletal elements of taxon A are anatomically complete but a few
of each were broken into many (small) fragments, then the ratio NISP/MNI for
that taxon may be the same as that for taxon B all the remains of which are (large)
fragments. This suggests that there are two dimensions of fragmentation. The extent
skeletal completeness, skeletal parts, and fragmentation 251


of fragmentation is the dimension that signi¬es the proportion or percentage of
specimens in a collection that are anatomically incomplete, or its complement, the
percent of NISP that comprise anatomically complete specimens, or %whole (Lyman
1994b, 1994c). The intensity of fragmentation signi¬es how small fragments are or how
many pieces a kind of skeletal element has been broken into on average (Lyman 1994b,
1994c).
To calculate %whole or %fragmentary, tally up NISP for a taxon. Then, tally the
number that are anatomically complete or whole (how many are actually skeletal
elements rather than fragments of elements); this number will likely be (sometimes
quite signi¬cantly) smaller than the number of fragmentary specimens. Divide the
number of whole specimens by the total number of specimens (and multiply by 100)
to derive the %whole; or, subtract the number of whole specimens from the total
number of specimens, and divide the resulting number (number of fragments) by
the total NISP (and multiply by 100) to derive the %fragmentary.
In the collection of faunal remains from the sample of owl pellets (Table 2.9),
skulls of Microtus are not always complete. The total NISP of Microtus skulls is 110;
the number of complete skulls is 103; the %whole of Microtus skulls is 93.6 percent.
In that same collection, the total NISP of Peromyscus skulls is 206; the number of
complete skulls is 115; the %whole of Peromyscus skulls is 55.8 percent. The extent
of fragmentation of Microtus skulls is considerably less than is the extent of frag-
mentation of Peromyscus skulls. Why this difference should exist given the identical
taphonomic histories of the two may now be explored; it likely is a result of Peromyscus
skulls being much more fragile and of much more gracile structure than Microtus
skulls, which are larger and more robust.



The NISP:MNE Ratio

But what if, in a case like the skulls of the two taxa of rodents just described, the
specimens of the taxon with greater %whole are smaller than the fragments of the
taxon with lower %whole? This concerns fragmentation intensity and it is mea-
sured as the ratio of anatomically incomplete specimens to the MNE represented by
those specimens. (To calculate this ratio one must assume MNE values are not in¬‚u-
enced by aggregation, sample size, or de¬nition. Alternatively, one could assume the
in¬‚uences on MNE are randomly distributed across the collections compared such
that they do not skew the values in such a way as to in¬‚uence statistical interpreta-
tion.) Anatomically complete specimens are not included in the calculation because
(i) when they are included they decrease the ratio because they increase both values
quantitative paleozoology
252


Table 6.12. Ratios of NISP:MNE for four long bones of
deer in two sites on the coast of Oregon State. Data
from Lyman (1995b)

Skeletal element Umpqua/Eden site Seal Rock site
Humerus 1.14 1.75
Radius 2.00 1.89
Femur 1.50 2.67
Tibia 2.10 2.33


of the NISP:MNE ratio equally, and (ii) the intensity of fragmentation is meant to
capture the variable of fragment size. With respect to the ¬rst point, in an assemblage
of anatomically incomplete specimens, if NISP = 10 and MNE = 5, then the ratio is
2:1. If two anatomically complete specimens are included, NISP = 12, MNE = 7, and
the ratio is reduced to 1.71 :1. The more anatomically complete specimens, the less the
difference between NISP and MNE. With respect to the second point “ NISP:MNE
measures fragment size “ higher ratios suggest smaller fragments. A ratio of 2:1 sug-
gests elements were basically broken in half; a ratio of 15:1 suggests elements were
almost pulverized.
Let™s say we want to determine if the fragmentation of bones of a taxon differs
across two assemblages. (The remains of two taxa can be compared using the same
technique.) I did this for the four major long bones of deer (Odocoileus sp.) using the
remains from two sites on the coast of the state of Oregon (Lyman 1991 , 1995b). The
ratios (Table 6.12) suggest that, overall, long bones were less intensively fractured (bro-
ken into larger pieces) at the Seal Rock site than they were at the Umpqua/Eden site.
The average ratio at Seal Rock is 1.68 compared to an average ratio at Umpqua/Eden
of 2.16. Determination of the reason for this apparent difference in fragmentation
intensity requires other sorts of analyses. The NISP:MNE ratio allows one to rank-
order the elements from most intensively broken to least intensively broken. For Seal
Rock, that order is femur, tibia, radius, humerus; for Umpqua/Eden, that order is
tibia, radius, femur, humerus. Of course, variation in the NISP:MNE ratio can be
assessed and compared across different taxa as well.
Ratios of NISP:MNE have been used by zooarchaeologists in both the New World
(e.g., Wolverton 2002) and the Old World (e.g., Munro and Bar-Oz 2005) to measure
the intensity of fragmentation. But a property of the ratio needs to be identi¬ed.
The ISP of NISP concerns identi¬ed specimens, and to be identi¬ed a specimen
must retain suf¬cient anatomical and taxon-speci¬c features to be identi¬ed. As
skeletal completeness, skeletal parts, and fragmentation 253




figure 6.16. Model of the relationship between fragmentation intensity and NISP. The
value of Maximum and of N are unknown. Modi¬ed from Marshall and Pilgram (1993).

elements are broken into successively smaller and smaller fragments, the resulting
pieces become successively less likely to retain suf¬cient landmarks to permit their
identi¬cation. Thus, as Marshall and Pilgram (1993) pointed out some years ago,
fragmentation has the effect of ¬rst increasing the NISP represented by pieces of
any given skeletal element, but as fragmentation intensity increases beyond some
as yet unknown level of intensity, NISP will level off and then decrease because
the fragments are becoming so small as to be unidenti¬able (Figure 6.16). This
may be an interpretively treacherous property of fragmentation if some kinds of
skeletal elements are represented by only one identi¬able fragment and numerous
unidenti¬able small fragments. Each identi¬able fragment will represent an MNE of
1, and so the ratio for these would be 1 :1, or 1, but slightly larger and (thus) identi¬able
fragments will cause the ratio to be > 1.0.
The preceding leads to another observation. There is some threshold of fragment
size controlling whether or not a fragment is identi¬able. If the fragment is smaller
than the threshold size, it is not identi¬able. For the sake of illustration, grant the
(no doubt somewhat unrealistic) assumption that for any given skeletal element,
the element can be broken into some number of pieces of equal size. If we set that
threshold number of pieces at ¬fteen, such that if, say, a humerus is broken into ¬fteen
pieces, all can be identi¬ed (to skeletal element and to taxon), then if that humerus
is broken into sixteen pieces, none of them will be identi¬able (to skeletal element
or to taxon). The implication of this observation is graphed in Figure 6.17. That
quantitative paleozoology
254




figure 6.17. Model of the relationship between NISP and MNE. Observed values will
always fall on or below the diagonal (NISP ≥ MNE), but not in¬nitely far below the diagonal
because fragments that are too small will not be identi¬able. After Lyman (1994b).


graph suggests there will be a relatively strong correlation between MNE and NISP
per skeletal element simply because of constraints on the total NISP (identi¬able
fragments) that can be generated from any given set of fragments of multiple skeletal
elements. Again, that these two variables are often strongly correlated should come
as no great surprise given that whatever the greatest (left or right) MNE was for a
taxon, that value was the MNI for that taxon. Nevertheless, we need to examine the
relationship of these two variables in depth.



DISCUSSION


There have been subsequent phases to the history of MNE. One later phase was
the derivation of MAU and the related %MAU, along with the mathematically
equivalent %survivorship. Those units served as the basis for a large volume of
research on skeletal-part frequencies, and because they are ultimately based on MNE,
they also prompted a plethora of research projects on how to determine MNE in the
most accurate way possible. The former focused on what frequencies of skeletal
skeletal completeness, skeletal parts, and fragmentation 255


Table 6.13. African bovid size classes. After Brain (1974,
1981) and Klein— (1978, 1989)

Bovid size class Live weight
I (small) 0“23 kilograms (0“50 pounds)
II (small medium) 23“84 kilograms (50“200 pounds)
III (large medium) 84“296 kilograms (200“650 pounds)
>296 kilograms (>650 pounds)
IV (large)
V (very large)— ?


parts “ normed to the model of the MNI of complete skeletons “ meant with respect
to taphonomic agents and processes of dispersal (e.g., ¬‚uvial winnowing), accumu-
lation (e.g., nutritional value to carnivores and hominids), and destruction (e.g.,
carnivore gnawing) (see Lyman [1994c] for discussion of methods, and see the Jour-
nal of Taphonomy [2004: vol. 2] for more recent considerations). Earlier in this
chapter efforts to derive the most accurate MNE values possible were outlined.
Subsequent to those efforts, a new chapter or phase to the history of MNE was
written.
Grayson and Frey (2004) recently showed that the relationship between NISP
per skeletal element and MNE per skeletal element is strong; the two variables are
often tightly correlated. As indicated earlier in this chapter, that a strong relationship
exists between these two variables shouldn™t really be a surprise, given that NISP
and MNI are often tightly correlated and that MNI is operationalized as the largest
value of MNE (of left or right specimens) per taxon, and given the model in Fig-
ure 6.17. But the fact that people grappled with MNE and its derivatives for more
than twenty-¬ve years before the statistical and analytical signi¬cance of the cor-
relation of MNE and NISP was identi¬ed suggests that this signi¬cance should be
illustrated. The relationship is shown in Figures 6.1 and 6.2, but it warrants additional
discussion given the analytical weight placed on MNE abundances over the past two
decades.
Researchers have published both NISP and MNE data for collections from diverse
geographic locations and temporal periods. In one such presentation, Marean and
Kim (1998) described frequencies of skeletal parts for an assemblage of remains
representing several species of medium-small (size class II [Brain 1981 ]) bovids
and cervids. (Bovid size classes used in much of the following are summarized in
Table 6.13.) The remains originate from a Mousterian (Middle Paleolithic) deposit
in Kobeh Cave, located in the Zagros Mountains of Iran. The data are summarized
quantitative paleozoology
256


Table 6.14. NISP and MNE frequencies of skeletal parts of
bovid/cervid size class II remains from Kobeh Cave, Iran.
Data from Marean and Kim (1998)

Skeletal part/portion NISP MNE
Horn 43 20.00
Skull 60 19.00
Mandible 75 22.00
Upper teeth 46 29.60
Lower teeth 82 21.86
Atlas 5 0.90
Axis 1 0.40
Cervical 24 8.35
Thoracic 28 11.30
Lumbar 28 8.60
Sacrum 2 1.90
Ribs 266 30.80
Humerus 404 63.80
Radius 336 47.25
Ulna 127 25.10
Carpal 14 11.50
Metacarpal 319 37.95
Innominate 53 11.30
Femur 478 62.90
Tibia 665 95.70
Astragalus 3 3.00
Calcaneum 13 4.90
Metatarsal 307 35.85
Tarsal 10 7.85
Phalange 102 24.90
Sesamoid 7 6.00



in Table 6.14, and graphed in Figure 6.18. The two variables are strongly correlated
(r = 0.94, p < 0.0001), suggesting that the information regarding skeletal-part fre-
quencies provided by MNE is virtually identical to that provided by NISP.
The close relationship between NISP and MNE is widespread. Enloe et al. (2000)
described a large sample of saiga antelope (Saiga tatarica) remains from Prolom II
Cave, located on the Crimean Peninsula in the Ukraine. The material dates to the
Mousterian cultural period (Table 6.15). NISP and MNE are strongly correlated
(r = 0.92, p < 0.0001); the MNE values are redundant with the NISP values with
figure 6.18. Relationship between NISP and MNE values for size class II cervids and
bovids at Kobeh Cave, Iran. Best-¬t regression line (Y = ’0.015X0.692 ; r = 0.945) is signi¬-
cant (p = 0.0001). Data from Table 6.14.

Table 6.15. NISP and MNE frequencies of skeletal parts
of saiga antelope (Saiga tatarica) from Prolom II Cave,
Ukraine. Data from Enloe et al. (2000)

Skeletal part/portion NISP MNE
Maxilla 319 81
Mandible 477 56
Sacrum 3 3
Scapula 13 12
Humerus 33 22
Radius 112 46
Carpal 156 48
Metacarpal 138 82
Femur 22 16
Patella 4 4
Tibia 33 26
Lateral malleolus 9 9
Astragalus 82 81
Calcaneum 83 55
Naviculo cuboid 36 36
Cuneiform 18 17
Metatarsal 62 37
First phalanx 285 253
Second phalanx 114 109
Third phalanx 81 72
quantitative paleozoology
258




figure 6.19. Relationship between NISP and MNE values for saiga antelope at Prolom II
Cave, Ukraine. Best-¬t regression line (Y = 0.27X0.733 ; r = 0.922) is signi¬cant (p = 0.0001).
Data from Table 6.15.


respect to estimating the frequencies of skeletal parts (Figure 6.19). This is a com-
mon pattern. Table 6.16 summarizes the statistical relationships between NISP and
MNE for twenty-nine samples of faunal remains. In all but one case, r > 0.7, and
p < 0.0001 ; in twenty-¬ve of twenty-nine cases, r > 0.8. The value of MNE as a quan-
titative unit, even though it is explicitly designed to tally frequencies of skeletal parts,
seems redundant with NISP; MNE values for an assemblage can often be closely
predicted from the NISP values for that assemblage. In fact, Broughton et al. (2006)
found the correlation between the two variables to be perfect (r = 1.0, p < 0.001) in
a collection of ¬sh remains accumulated and deposited by an owl.
Earlier in this chapter it was argued that MNE is at best ordinal scale. This is
easily shown if we consider the relationship of MNE per skeletal part (or por-
tion) to MNI per skeletal part (or portion). Data revealing this relationship are,
like those revealing the relationship between NISP and MNE, also relatively com-
mon. We need only graph one data set to illustrate the relationship. Marshall and
Pilgram™s (1991 ; Pilgram and Marshall 1995) NISP and MNI data for caprine (Ovis
skeletal completeness, skeletal parts, and fragmentation 259


Table 6.16. Relationship between NISP and MNE in twenty-nine assemblages

Assemblage Relationship r p Reference
= 0.126X0.807
Meier deer Y 0.837 0.0001 This volume
= 0.063X0.766
Meier wapiti Y 0.883 0.0001 This volume
= “0.015X0.692
Kobeh Cave Y 0.945 0.0001 Marean and Kim (1998)
= 0.27X.0733
Prolom II Cave Y 0.922 0.0001 Enloe et al. (2000)
= 0.192X0.825
Garnsey (bison) Y 0.942 0.0001 Speth (1983)
= 0.162X0.738
Sjovold (bison) Y 0.939 0.0001 Dyck and Morlan (1995)
= 0.012X0.702
Twilight Cave BS1 “ size II Y 0.898 0.0001 Marean (1992)
= 0.029X0.786
Twilight Cave RBL2.1 “ size I Y 0.956 0.0001 Marean (1992)
= 0.081 X0.787
Twilight Cave RBL2.1 “ size II Y 0.950 0.0001 Marean (1992)
= 0.056X0.79
Twilight Cave RBL2.2 “ size I Y 0.948 0.0001 Marean (1992)
= 0.063X0.76
Twilight Cave RBL2.2 “ size II Y 0.937 0.0001 Marean (1992)
= 0.067X0.754
Twilight Cave RBL2.3 “ size I Y 0.914 0.0001 Marean (1992)
= 0.041 X0.739
Twilight Cave RBL2.3 “ size II Y 0.923 0.0001 Marean (1992)
= 0.088X0.772
Twilight Cave DBS “ size I Y 0.945 0.0001 Marean (1992)
= 0.108X0.741
Twilight Cave DBS “ size II Y 0.932 0.0001 Marean (1992)
= 0.036X0.932
Friesenhahn Cave (Homotherium) Y 0.957 0.0001 Marean and Ehrhardt (1995)
= “0.010X0.913
Friesenhahn Cave (proboscidean) Y 0.946 0.0001 Marean and Ehrhardt (1995)
= 0.001 X0.756
Kua Base Camp-size I Y 0.792 0.0001 Bartram and Marean (1999)
= 0.095X0.598
Kua Base Camp-size III Y 0.725 0.0001 Bartram and Marean (1999)
= 0.193X0.435
Kua Scavenged Kill-size III Y 0.661 0.0001 Bartram and Marean (1999)
= 0.02X0.519
Die Kelders-L. 10, size 1 Y 0.776 0.0001 Marean et al. (2000)
= “0.084X0.577
Die Kelders-L. 10, size 2 Y 0.789 0.0001 Marean et al. (2000)
= “0.173X0.592
Die Kelders-L. 10, size 3 Y 0.732 0.0001 Marean et al. (2000)
= “0.075X0.542
Die Kelders-L. 10, size 4 Y 0.835 0.0001 Marean et al. (2000)
= “0.914X1.256
Nahal Hadera V Y 0.911 0.0001 Munro and Bar-Oz (2005)
= “0.921 X1.292
Hefzibah Y 0.913 0.0001 Munro and Bar-Oz (2005)
= 0.046X0.763
Hayonim Cave-Early Natu¬an Y 0.815 0.0001 Munro and Bar-Oz (2005)
= “0.004X0.781
Hayonim Cave-Late Natu¬an Y 0.848 0.0001 Munro and Bar-Oz (2005)
= “0.358X1.008
el-Wad Terrace Y 0.823 0.0001 Munro and Bar-Oz (2005)


and Capra) remains from Ngamuriak, a Neolithic pastoral site in Kenya (Table 6.17),
are strongly related (Figure 6.20). Other assemblages from other places and times
display the same relationship between NISP and MNI per skeletal part or portion
as the Ngamuriak collection. Of the twenty-two assemblages listed in Table 6.18, the
relationship between NISP and MNI per skeletal part is rather strong (r > 0.7) in
twenty assemblages, and it is quite strong in ¬fteen assemblages (r > 0.8). Again, this
should come as no surprise given previous discussions and analyses presented in this
volume.
Table 6.17. NISP and MNI frequencies of skeletal parts of
caprines (Ovis and Capra) from Ngamuriak, Kenya. P,
proximal; D, distal. Data from Pilgram and Marshall (1995)

Skeletal part/portion NISP MNI
Tooth rows, lower 288 54
Innominate 133 28
Scapula 94 32
P humerus 30 11
D humerus 91 31
P radius 81 23
D radius 35 16
P metacarpal 50.5 12
D metacarpal 32.5 2
P femur 54 24
D femur 47 12
P tibia 18 6
D tibia 32 12
Calcaneum 65 17
P metatarsal 45.5 12
D metatarsal 29.5 1
First phalanx 83 4
Second phalanx 30 2

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