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MNI = ’0.114(NISP)0.58
45DO273 0.816 0.0136 84 8
MNI = 0.01 (NISP)0.36
45OK2A 0.849 0.0019 366 10
MNI = ’0.178(NISP)0.628
45DO282 0.875 0.0004 426 11
MNI = ’0.12(NISP)0.64 < 0.0001
45DO211 0.847 474 15
MNI = ’0.19(NISP)0.51
45DO285 0.721 0.0024 491 15
MNI = ’0.07(NISP)0.44
45DO214 0.765 0.0003 536 17
MNI = 0.02(NISP)0.3
45DO326 0.56 0.0242 640 16
MNI = ’0.093(NISP)0.4 < 0.0001
45DO242 0.89 673 13
MNI = ’0.04(NISP)0.21
45OK287 0.786 0.007 807 10
MNI = ’0.019(NISP)0.41
45OK250 0.776 0.003 1,077 12
MNI = ’0.072(NISP)0.48 < 0.0001
45OK4 0.881 1,108 15
MNI = ’0.158(NISP)0.4
45OK2 0.769 0.0002 2,574 18
MNI = ’0.124(NISP)0.5 < 0.0001
45OK11 0.849 3,549 24
MNI = ’0.094(NISP)0.47 < 0.0001
45OK258 0.863 4,433 21


and identi¬cation skills. What we don™t know, and can™t really know most of the time,
is whether MNI is a more accurate measure of taxonomic abundances than NISP for
any given assemblage of paleozoological remains. Hudson (1990) and Breitburg (1991)
knew that MNI provided more accurate measures of the thanatocoenosis because
they knew the original taxonomic abundances of the death assemblage. We don™t

Table 2.8. Maximum distinction (each pellet considered independently) and
minimum distinction (all pellets considered together) MNI values for six genera
of mammals in a sample of eighty-four owl pellets. The right femur is the most
abundant element for Microtus, and the left femur is the most abundant
element for Peromyscus in the minimum distinction column

Minimum Maximum
Taxon NISP distinction MNI distinction MNI
Sylvilagus 5 1 2
Reithrodontomys 19 5 5
Sorex 46 5 7
Thomomys 68 8 12
Microtus 705 104 118
Peromyscus 1,266 188 220
2,109 310 364
quantitative paleozoology
56




figure 2.8. Relationship between NISP and MNI data pairs for remains of six mammalian
genera in eighty-four owl pellets. The regression equation is MNI = “0.389(NISP)0.149 , and
the correlation coef¬cient of the simple best-¬t regression line is signi¬cant (r = 0.999, p <
0.0001). Data from Table 2.8.



know what the thanatocoenosis is in paleozoological contexts; it might be our target
variable.
That the relationship between NISP and MNI is particularistic and its precise
nature is dependent on the samples used is true. But the truth of that claim is
not a necessary basis for rejecting NISP in favor of MNI. This is so for several
reasons. First, as I noted earlier, NISP often contains virtually the same information
regarding taxonomic abundances as does MNI. Second, there are fewer analytical
steps in tallying NISP than in deriving MNI, so there are fewer layers (to borrow a
metaphor) in the house of cards upon which NISP rests than in the house of cards
upon which MNI rests. Do not misinterpret this second point; the simplest method
is not being advocated as the best just because it is simpler or easier or contains fewer
analytical steps. Rather, because NISP contains fewer steps and, more importantly,
fewer assumptions than MNI regarding taphonomy, recovery, identi¬cation skills,
and the like, perhaps NISP should be preferred. Finally, there is still problem seven,
which concerns how to aggregate faunal remains in order to produce MNI values.
No such problem exists with NISP, re¬‚ecting the fact that NISP is simply additive
and that MNI is not additive. It is time, then, to turn to what is likely the most serious
problem with MNI.
estimating taxonomic abundances: nisp and mni 57


Table 2.9. Adams™s (1949) data for calculating MNI values based on Odocoileus sp.
remains. MNI-I is equivalent to the MNI minimum distinction (one aggregate,
MNI = 118); MNI-II is equivalent to the MNI maximum distinction (¬ve aggregates,
MNI = 120)

Recovery Distal right Distal left Distal right Distal left
provenience humerus humerus femur femur MNI-II
A 38 42 10 11 42
B 5 12 1 1 12
C 30 42 10 10 42
D 11 9 3 5 11
E 9 13 2 7 13
MNI-I 93 118 26 34



Aggregation

Although MNI solves the problem of interdependence of specimens inherent to
NISP, MNI has its own signi¬cant problem. That problem is readily introduced by
considering the data that Adams (1949) presented when he determined the MNI
of deer (Odocoileus virginianus) per recovery provenience unit in the collection he
studied (Table 2.9). Adams distinguished what he referred to as “Minimums I”
and “Minimums II,” the individual column totals and the individual row totals,
respectively. I have substituted MNI for “Minimums” in Table 2.9 because MNI is
indeed what Adams meant. Notice that were one to ignore recovery provenience,
and just tally up the most frequently occurring skeletal part, distal left humeri would
be most abundant among the four skeletal parts, so the site-wide MNI “ or Adams™s
“MNI-I” “ is 118. But if the analyst were to tally up the most frequently occurring
skeletal part per unique recovery provenience, then distal left humeri would be the
most abundant skeletal part in four of the ¬ve recovery proveniences, but right distal
humeri would be the most abundant skeletal part in the ¬fth recovery provenience.
Thus the total MNI for the values summed over the ¬ve recovery proveniences “
Adams™s “MNI-II” “ is 120. Grayson (1984) later presented an example from a single
site in which differences between MNImni and MNImax values varied across nearly
two dozen taxa from 0 to 250 percent (the latter, MNImin = 15 and MNImax = 38).
It makes little difference whether Adams™s ¬ve distinct recovery proveniences are
horizontally distinct (like units in an excavation grid), vertically distinct (as with
strata), or both (as with grid units per stratum). His data illustrate the most sig-
ni¬cant problem that attends MNI. This problem was revealed by Adams (1949:24)
when he commented that one must assume “that parts of one individual are not
quantitative paleozoology
58


represented from more than one [recovery provenience].” He said this with spe-
ci¬c reference to his “MNI-II” values. But he only revealed the problem; he did not
explore its implications. This problem and its implications were later documented
at length by Grayson (1973, 1979, 1984). This problem is, in short, known as the
aggregation problem, where an aggregate is an assemblage or collection of faunal
remains the boundaries of which are chosen by the analyst, whether those bound-
aries correspond to stratigraphic boundaries or arbitrarily and arti¬cially bounded
excavation/collection units.
Grayson (1973) termed what Adams called “Minimums I” values the minimum
distinction method, and termed what Adams called “Minimums II” values the maxi-
mum distinction method. The former involves determination of MNI for the complete
assemblage considered as one aggregate; the latter involves determination of MNI
independently for each assemblage, each from a distinct recovery provenience speci-
¬ed by the analyst. The minimum distinction method is so-called because it produces
the lowest or smallest MNI values for a complete collection. The maximum distinc-
tion method is so-called because it produces the greatest or largest MNI values for
a collection (MNI values for all assemblages from unique recovery proveniences
are summed); it produces more than the minimum distinction method because it
considers a large number of (small) aggregates (or [sub]assemblages of remains).
The minimum distinction method considers only one large aggregate “ all remains
treated as a single collection. Adams did not care for either the minimum distinc-
tion method or the maximum distinction method because, despite the differences
in their results, both produced minimum numbers of individuals. Furthermore, the
maximum distinction method “ determining MNI based on individual recovery
proveniences “ required that one assume specimens in one provenience unit were
independent of all specimens in other provenience units, and Adams did not want
to make that assumption. It is ¬tting that we hereafter refer to this potential problem
of interaggregate interdependence of skeletal specimens as Adams™s dilemma.
That the aggregation problem is widespread is easy to show. Recall the collection
of remains of six genera of prey in eighty-four owl pellets; the NISP“MNI data pairs
for this collection are plotted in Figure 2.8. That ¬gure is based on the minimum
distinction method because all remains were lumped together to form one aggre-
gate. This means that only one skeletal element per taxon contributes to the MNI,
regardless of how many pellets contain remains of a taxon. What happens to the MNI
values for the taxa represented in the sample of eighty-four pellets when one shifts
from the minimum to the maximum distinction method is shown in Table 2.8. The
NISP values stay the same regardless of how MNI is determined “ whether the maxi-
mum or minimum distinction method is used. The MNI is greater in ¬ve of six taxa
estimating taxonomic abundances: nisp and mni 59


Table 2.10. Differences in site total MNI between the MNI minimum distinction results and
the MNI maximum distinction results

Richness Mean
N of (N of N taxa increase
Site assemblages NISP genera) MNImin MNImax increase per genus
45OK2A 4 366 10 30 39 4 of 10 0.9
45DO211 4 474 15 108 117 4 of 15 0.6
45DO285 4 491 15 66 102 12 of 15 2.4
45DO214 4 536 17 67 108 11 of 17 2.4
45DO326 4 640 16 53 81 14 of 16 1.75
45DO242 4 673 13 38 52 7 of 13 1.1
45OK250 3 1,077 12 62 79 8 of 12 1.4
45OK4 3 1,108 15 65 82 7 of 15 1.1
45OK2 4 2,574 18 66 105 13 of 18 2.2
45OK11 2 3,549 24 202 231 14 of 24 0.6
45OK258 2 4,433 21 117 139 10 of 21 1.0


when the maximum distinction method is used relative to the minimum distinction
method (Table 2.8). The ratio of Peromyscus to Microtus “ the subject of published
interpretations of this collection (Lyman et al. 2001, 2003) “ shifts from 1.81 :1 for
the minimum distinction MNI, to 1.86:1 for the maximum distinction MNI, to 1.80
for NISP. In this case, the differences are small, and statistically insigni¬cant; the
chi-square value is 0.41 if Sylvilagus is omitted so that the assemblage™s data pairs
meet the requirements of the test (p > 0.5). Even given the small differences in ratios
of Peromyscus to Microtus, the critical question is: Which ratio is correct? There is no
clear or obvious answer.
The aggregation problem is pernicious. Of the fourteen archaeological assemblages
summarized in Table 2.7, eleven have multiple components or temporally distinct
(sub)assemblages; the other three consist of only one assemblage. For purposes of
generating the regression equations in Table 2.7, I used the minimum distinction
MNI values for all fourteen sites. What happens to the MNI values for the eleven
sites with multiple (sub)assemblages if the maximum distinction method is used
and MNI is derived for each taxon in each (sub)assemblage independently? First, the
total MNI for each of the eleven sites increases when one shifts from MNImin(imum
distinction) to MNImax(imum distinction) (Table 2.10). Why? Because more kinds
of most common elements are speci¬ed in the latter than in the former.
Second, the total MNI for each site increases between nine and forty-one when
one shifts from MNImin to MNImax; the average increase is 23.7 individuals per
quantitative paleozoology
60



Number of Taxa




Amount of Increase in MNI
figure 2.9. Amount by which a taxon™s MNI increases if the minimum distinction MNI
is changed to the maximum distinction MNI in eleven assemblages (see Table 2.10 for other
data on these assemblages).


site (Table 2.10). This is not a lot in terms of absolute abundance, but think of it
this way: In site 45OK2A, MNImin is thirty and MNImax is thirty-nine; that is a
30 percent increase. In the sample of eleven sites, the site total MNImax increases
over MNImin from 8 percent (45DO211) to as much as 61 percent (45DO214); the
average increase is a bit more than 35 percent. The third thing to note regarding
the shift from MNImin to MNImax is that four to fourteen taxa per site increase in
abundance. Not all taxa increase, and any given taxon does not increase consistently
in all sites. Ratios of taxonomic abundances shift around rather unpredictably as a
result. Note, for example, that the amount by which any taxon™s MNI increases is one
to sixteen (Figure 2.9). Consider, for example, how the ratio of deer (Odocoileus spp.)
to gopher (Thomomys sp.) changes across all eleven sites when one uses MNImin
compared to when one uses MNImax (Figure 2.10). If the MNI of both taxa changed
consistently (say, all increase by 10 percent) when shifting from the minimum to the
maximum distinction method, the ratios would not change and all points would fall
on the diagonal in Figure 2.10. Instead, the eleven collections fall various distances
from that line, meaning that the ratios change more in some sites than in others; the
changes in most abundant skeletal parts are not patterned. There is marked variation
in which skeletal part de¬nes the MNI for either or both deer and gophers across the
(sub)assemblages.
estimating taxonomic abundances: nisp and mni 61



MNImax Ratio




MNImin Ratio
figure 2.10. Change in the ratio of deer (Odocoileus spp.) to gopher (Thomomys sp.)
abundances in eleven assemblages when MNImax is used instead of MNImin. If the ratios
did not change, all points should fall on the diagonal line rather than above and to the left,
or below and to the right of that line.

The most abundant skeletal part for each of the thirteen mammalian genera at
Cathlapotle (Table 1.3) that have more than 1 MNI in each of the two temporally
distinct (sub)assemblages are listed in Table 2.11 . Only three taxa (of a possible
thirteen) have more than one most abundant part (e.g., Castor in the postcontact
assemblage), indicating rather skeletally uneven representation of individual car-
casses. More importantly, it is virtually impossible to predict which part of a genus
will be most abundant in one (sub)assemblage based on which part of that genus is
most abundant in the other (sub)assemblage, particularly when left and right-side
designations are considered (Table 2.11 ). If the side designation is not considered,
then only four genera (Aplodontia, Castor, Microtus, Ondatra) out of thirteen are
represented by the same skeletal part in both (sub)assemblages. That two of these
four particular genera are the ones represented by the same skeletal part regardless
of side is, in this case, easy to explain. Only skulls and mandibles of Microtus were
identi¬ed among the mammal remains at Cathlapotle; postcranial remains of this
genus were not identi¬ed and this markedly increases the probability that the
same skeletal part (regardless of side) will be identi¬ed in both components. The
quantitative paleozoology
62


Table 2.11. The most abundant skeletal part representing thirteen mammalian
genera in two (sub)assemblages at Cathlapotle. When more than one skeletal
part represented the same MNI, all skeletal parts are listed. R, right; L, left

Taxon Precontact assemblage Postcontact assemblage
Lepus R proximal tibia R mandible
Aplodontia L mandible R mandible
Castor L femur R mandible, R femur
Microtus L mandible R mandible
Ondatra L mandible R mandible
Canis R P4 L dP4
Ursus L m2 R ulna
Procyon R proximal radius L m1
Mustela R mandible R distal humerus
Lutra R proximal radius R mandible, R distal humerus
Phoca L distal humerus R temporal
Cervus L astragalus L naviculo cuboid
Odocoileus R calcaneum R m3, R astragalus


mandible of Aplodontia is the most frequent skeletal part in both (sub)assemblages
because it was selectively retained by site occupants as a wood-working tool “ a
chisel or engraver (Lyman and Zehr 2003). It is unclear why the same skeletal part
provides the MNImax of Castor and Ondatra in both subassemblages, but those
parts are particularly robust and thus relatively immune to taphonomic attritional
processes.
The most frequent skeletal parts in Table 2.11 are from all parts of the skeleton “
the head (upper and lower teeth, mandibles), the forelimb, and the hindlimb. It is
likely, given what we know about taphonomy at this time, that this is the pattern that
will emerge in most cases. Because taphonomic processes in¬‚uencing the survival
and distribution of faunal remains are not perfectly correlated with remains that are
(or those that are not) taxonomically identi¬able (Lyman 1994c), it is unlikely that
we will ¬nd cases in which the MNImin and MNImax values for a given collection
will be perfectly correlated at a ratio scale. They might be correlated at an ordinal
scale, but it is quite likely even then that the correlation coef¬cient will be less than
1.0. Shifts in taxonomic abundances will likely not be uniform across all taxa when
one shifts from MNImin to MNImax.
Different aggregates of faunal materials making up a total collection will not only
produce different MNI values, but they will do so differentially across taxa. Let™s
say we have one taxon represented in a collection from a site, and that this taxon
is represented by twenty-¬ve left and thirty right distal humeri, the most common
estimating taxonomic abundances: nisp and mni 63


Table 2.12. Fictional data showing how the distribution of most abundant
skeletal elements of one taxon can in¬‚uence MNI across different
aggregates. If stratigraphic boundaries are ignored, a minimum of thirty
individuals is represented by thirty right humeri. Using stratigraphic
boundaries to de¬ne aggregates, the total MNI is forty-seven because the
most abundant element is left humeri in stratum 1, but the most
abundant element in strata 2 and 3 is left humeri

Left humeri Right humeri MNI per stratum
Stratum 1 22 5 22
Stratum 2 3 17 17
Stratum 3 0 8 8
MNI 25 30 47


skeletal part. Obviously, we have a MNImin of thirty (assuming that we ¬nd matches
in terms of age, sex, and size for all possible pairs of elements; i.e., the twenty-¬ve
left specimens all have matching right specimens). But there are also three strata (or
horizontally distinct recovery contexts, if you prefer) comprising the site, and the
humeri are distributed across those strata as indicated in Table 2.12. When we sum
the MNImax values in Table 2.12, we have a site total of MNI = 47. Why? Because
whereas with MNImin we had only one most common skeletal part in the form of
the right distal humeri ( = 30), we now have in Stratum 1 the left humerus as the
most common part whereas in Strata 2 and 3 the right humerus is the most common
part. The change from one kind of most common skeletal part to two kinds resulted
in an increase of 17 MNI (57 percent).
As a ¬nal example, let™s say we have two taxa. Taxon 1 is represented by the
remains of 7 individuals (= MNImin); those remains consist of 7 R humeri, 6 L
humeri, 6 R femora, and 5 L femora ( NISP = 24). Taxon 2 is represented by the
remains of 14 individuals (= MNImin); those remains consist of 14 R humeri, 7 L
humeri, 6 R femora, and 10 L femora ( NISP = 37). If we de¬ne faunal assemblages
stratigraphically, and there are three strata in the site, we may ¬nd the stratigraphic
distribution of skeletal parts indicated in Table 2.13. In that table the MNI for taxon
1 shifts from MNImin = 7 to MNImax = 10, and the MNI for taxon 2 does not shift
but rather both MNImin = 14 and MNImax = 14. The change in taxon 1 is the result
of changes in the number of most abundant skeletal parts de¬ned for this taxon as the
aggregates change. Most disconcerting is the fact that the ratio of taxon 1 to taxon 2
changes from 7:14 (or 1:2) to 12:14 (or 1:1.2) with a simple change in aggregates. Again,
these changes result from speci¬cation of different most common skeletal parts with
each different set of aggregates.
quantitative paleozoology
64


Table 2.13. Fictional data showing how the distribution of skeletal elements of
two taxa across different aggregates can in¬‚uence MNI. If stratigraphic
boundaries are ignored, there are only seven individuals (R humeri) of taxon 1,
and fourteen individuals (R humeri) of taxon 2. Aggregates de¬ned by
stratigraphic boundaries produce twelve individuals of taxon 1 and fourteen
individuals of taxon 2

Taxon 1 Taxon 2
Stratum 1 6 R humeri, 2 L humeri, 3 R femora, 4 R humeri, 1 L humerus, 4 L
3 L femora (MNImax = 6) femur (MNImax = 4)
Stratum 2 1 R humerus, 4 L humerus, 1 R 4 R humeri, 1 L humeri, 3 R
femora, 1 L femur (MNImax = 4) femora, 1 L femur
(MNImax = 4)
Stratum 3 1 L femur, 2 R femora 6 R humeri, 5 L humeri, 4 R
(MNImax = 2) femora, 4 L femora
(MNImax = 6)



Changes like those documented above are likely to occur more often than not. This
renders MNI a very unstable measurement unit. Of course, changes in aggregation
may not cause MNI values to ¬‚uctuate if the distribution of most abundant skeletal
parts is the same for each taxon. Consider, for example, the two-taxon ¬ctional data
given in the earlier example, but this time with similar distributions of most abundant
elements across the three strata, as shown in Table 2.14. The most abundant element
of both taxa (R humerus) has a similar distribution across all three strata and displays
its greatest frequency in Stratum 1. The ratio of taxon 1 to taxon 2 is 1 :2 in all three
strata by the MNImax method. The ratio of 1:2 is given by the MNImin method as
well.
Studying the distribution of most abundant elements per taxon across different
aggregates may reveal much about site formation and taphonomic history, as Grayson
(1979, 1984) noted years ago. I am, however, unaware of any such studies in the
literature. This is surprising given interest in site structure (e.g., O™Connell 1987).
Perhaps the lack of such studies is an instance of benign neglect. Whatever the case,
consideration of how aggregation in¬‚uences MNI deserves more study than it has
received because of the insight it will provide to MNI as a measure of taxonomic
abundance and also because of the insights it may grant to site structure. In such
studies, an aggregate of any kind might be de¬ned “ by a site as a whole, by a stratum,
by an archaeological feature (each pit, house ¬‚oor, hearth, etc.), by an arbitrary
excavation unit (say, 2 m — 2 m — 10 cm thick), or some combination thereof.
estimating taxonomic abundances: nisp and mni 65

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