Plains Indian Studies - Smithsonian Institution Libraries

164 SMITHSONIAN CONTRIBUTIONS TO ANTHROPOLOGY
use Statistical techniques to test for them empirically
(e.g., Binford, 1978:88; Reher, 1977:33, for
bison processing).
Grayson's (1973) contrast between minimum
and maximum distinction methods in the calculation
of MNI corrects for interdependence on a
locational rather than an anatomical basis. He
notes that MNI values for taxa in a whole sample
are larger when calculated by summing subtotal
MNI for each excavation unit than when calculated
by taking the whole site sample together.
By reducing the number of stratigraphic distinctions
used in making the calculation, the size of
the site area seen as likely to produce interdependent
specimens is increased. By making the
number of stratigraphic distinctions large, on the
other hand, the zooarcheologist implies his conviction
that interdependence is limited to small
site areas. This is precisely the operation Parmalee
is performing when he sums the MNI for birds
across sites. He implies a lack of interdependence
between sites but strong interdependence within
sites. Krantz (1968) also has proposed a method
for estimating species frequency by using a kind
of a measure of sample interdependence. He suggests
that the proportion of pairable right and
left bone fragments of the same element type
(e.g., the number of cases in which it can be
shown that pairs of right and left mandibles came
from the same individual) compared to the total
number of fragments of that element is related to
the proportion of the whole finds population that
is actually recovered. Krantz's equation relating
the number of pairs to the number of animals in
the finds collection is a hyperbolic relationship
(Casteel, 1977). At low levels of pairing, an enormous
change in the estimated number of individuals
is produced by a loss or gain of one pairing.
Since in practice it is extremely difficult to establish
pairs, the potential for error in a sample of
low interdependence is tremendous.
Considerable attention has been paid to the
relationship between MNI and total fragment
count E. For instance, Casteel (1976-1977) used
a sample of 610 pairs of data (MNI and E),
drawn from a wide variety of archeological and
paleontological studies. By plotting MNI against
E, he produced a curvilinear relationship when E
is less than 1000 specimens and a linear relationship
when E is greater than 1000 specimens.
Grayson (1978) and Ducos (1975:42, note 1) have
also reported a curvilinear relationship. Casteel
(1976-1977:142-145) has provided a succinct
summary of other analyses. King (1978) also plotted
the relationship of MNI to E for a wide
variety of sites but partitioned his sample into
subsamples composed of the values for cows, pigs,
and sheep (King, 1978, fig. 2).
This observation has led some workers to the
conclusion that MNI values cannot be compared
when the difference between the size of the samples
used to compute them is great. This conclusion
is in error. The nature of the MNI statistic
does not imply this curvilinear relationship. The
slope of the line that relates MNI and E for any
group of samples is controlled by the probability
of recovering the most common type of bone
element. In cases where only one element type
has distinctive morphological features permitting
the identification of the taxon, the slope of the
plot MNI to E for a group of samples of this
taxon is equal to 1. No matter how big or how
small the sample, each bone fragment identified
necessarily increases the MNI by 1. In taxa where
several element types have distinctive morphological
features the situation is more complex. The
upper limit of the slope is 1; the case where,
despite the fact that there are several potentially
recognizable bone element types, only one type is
actually recovered. The lower limit of the slope is
defined by the situation where each of the possible
element types are found in equal proportions. On
the average, one of each of the element types
accumulates in the process of identification before
the MNI increases by one. Figure 25 illustrates
this range of potential slopes for a species with 10
potentially identifiable element types. The upper
limit of the slope is shown by "a": each bone
fragment identified for the taxon is the same kind
of bone element. The lower limit is "b": all 10
element types are found in equal proportions. As
the number of identifiable bone elements in-