Journal of Archaeological Science 53 (2015) 291e296
Contents lists available at ScienceDirect
Journal of Archaeological Science
journal homepage: http://www.elsevier.com/locate/jas
On the variable relationship between NISP and NTAXA in bird remains
and in mammal remains
R. Lee Lyman
Department of Anthropology, University of Missouri, Columbia, MO 65211, USA
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 23 September 2014
Received in revised form
28 October 2014
Accepted 29 October 2014
It has long been recognized that the minimum number of individuals (MNI) and the number of taxa
identified (NTAXA) are both often tightly related to the number of identified specimens (NISP) in a
collection. The relationship between NISP and NTAXA has been suggested to vary between bird remains
and mammal remains for three reasons that concern the rate at which identifiable skeletal parts of each
are input to the zooarchaeological record. Rigorous testing of the relationship using 59 pairs of assemblages of bird and mammal remains confirms that the NTAXA of birds increases more rapidly per NISP
than does the NTAXA of mammals per NISP. Data also indicate that two of the three proposed reasons
(bird taxa outnumber mammal taxa on the landscape; each mammalian individual contributes more
NISP than each avian individual) are the likely causes for intertaxonomic variability in the relationship
between NISP and NTAXA. The third reason (fragmentation reduces identifiability of bird remains more
rapidly than it does mammal remains) has yet to be empirically evaluated but is logical.
© 2014 Elsevier Ltd. All rights reserved.
Keywords:
Bird remains
Mammal remains
Number of identified specimens (NISP)
Number of taxa (NTAXA)
Zooarchaeology
1. Introduction
The relationship between the number of identified specimens
(NISP) of faunal remains and more derived measures such as the
minimum number of individuals (MNI) or number of taxa identified (NTAXA) (also referred to as taxonomic richness) in zooarchaeological collections has been studied for some time (Casteel,
1977; Grayson, 1979, 1981, 1984; Grayson and Frey, 2004; Hesse,
1982; Lyman, 2008). The relationship is usually said to be an
expression of the speciesearea relationship (see Lyman and Ames
(2007) for discussion), meaning that the more identified bones
and teeth (the greater the NISP), or the larger the examined
geographic space (which typically results in more specimens
encountered and more taxa identified), the larger the value of the
derived variable, whether MNI, NTAXA, or something else (e.g.,
Leonard, 1989; Wolff, 1975). The relationship is thus often interpreted to be a causal one (Casteel, 1977; Grayson, 1984; Hesse,
1982; Klein and Cruz-Uribe, 1984; Lyman, 2008; Reitz and Wing,
1999), with sample size (measured as NISP, volume excavated, or
amount of geographic space sampled) being the independent variable and the derived variable being the dependent one.
But is the size of the sample the only variable that influences the
dependent variable? Grayson (1998), for instance, argued that the
E-mail address: [email protected].
http://dx.doi.org/10.1016/j.jas.2014.10.027
0305-4403/© 2014 Elsevier Ltd. All rights reserved.
variable relationship between NISP and NTAXA (both log transformed) in multiple sets of data was a result of variation in the rate
of input of faunal remains. He inferred that the variability in the
relationship ultimately represented variation in climate in one case
(Grayson, 1998) and variation in human diet breadth in another
(Grayson and Delpech, 1998). Although he provided no empirical
test demonstrating that the rate of NISP input in fact influenced
NTAXA, Grayson's reasoning in both concerned variables that
influenced the rate of input of identifiable skeletal parts per taxon.
A greater rate meant a less steep relationship in terms of a simple
best-fit regression line between NISP and NTAXA. This reasoning in
turn suggests that deep understanding of the relationship between
the two variables would be valuable in cases in which NTAXA is an
analytically important variable. In this paper, I explore several
causes for the relationship between the two variables, focusing
particularly on why the relationship between NISP and NTAXA in
avian remains tends to be different than that relationship in
mammalian remains.
2. Background
l (2007) examined the
Some years ago Bartosiewicz and Ga
statistical relationship between NISP and NTAXA among 35 assemblages of archaeological mammal bones, and 29 assemblages of
archaeological bird bones (see also Bartosiewicz et al., 2013). They
found that the relationship between NISP and NTAXA differed
292
R.L. Lyman / Journal of Archaeological Science 53 (2015) 291e296
significantly between the two taxonomic groups; the best-fit
regression line between the two was steeper for the bird assemblages than it was for the mammal assemblages. They suggested
three reasons for that difference, all of which concern the rate of
input of NISP to the paleozoological record. First, they observed that
there were more avian than mammalian taxa on the landscape for
prehistoric people to exploit. They argued that the slope of a
regression line between NISP (independent variable) and NTAXA
(dependent variable) has the potential to be greater in birds than in
mammals because NTAXA is greater in birds than in mammals.
l (2007) did not identify a more
Although Bartosiewicz and Ga
proximate cause for the relationship, such is readily apparent. The
greater the number of taxa available, the greater the likely value of
the dependent variable (NTAXA) and thus the greater the potential
steepness of the relationship between NISP and NTAXA. And, the
fewer taxa available, the more constrained and limited the
maximum possible NTAXA is and the less steep the possible relationship between NISP and NTAXA.
l (2007) observed that birds
Second, Bartosiewicz and Ga
generally have fewer bones per individual than mammals; in
particular, a bird's skeleton includes fewer identifiable bones than
does a mammal's skeleton. Thus they argued that it takes fewer
bones (less NISP) to make up an individual bird than a mammal in a
collection of skeletal remains, so individual bird taxa will be added
to the NTAXA of what is in a paleozoological collection more rapidly
than mammal taxa will be added. Thus the slope of the relationship
between the pair of variables for birds will be steeper than the slope
of the relationship between the pair of variables for mammals. And
l (2007) suggested that bird bones are
third, Bartosiewicz and Ga
less likely to break into taxonomically identifiable pieces than
mammal bones. More identifiable specimens (bone fragments) per
individual mammal therefore means that more skeletal specimens
will have to be added to find an additional taxon of mammal than
an additional taxon of bird. Whereas the second cause for the difference in the relationship between NISP and NTAXA for birds and
that relationship for mammals concerns fewer identifiable skeletal
elements in birds, the third cause concerns the fact that fragmentation increases the NISP of mammals more than it does for birds
(and may decrease the NISP of birds if bird bones are sufficiently
fragmented so as to be unidentifiable (Cannon, 2013)).
l (2007) made
Twenty-five years before Bartosiewicz and Ga
their observations, Hesse (1982) observed that a regression line
describing the relationship between NISP and MNI would be
steeper the fewer the bone types for a taxon; the regression line
would decrease in steepness as the number of identifiable bone
l (2007) do
types per taxon increased. Although Bartosiewicz and Ga
not cite Hesse (1982), Hesse's observation is the same as theirs and
concerns the fact that birds have fewer identifiable bones per individual (what Hesse termed the “effective number of elements”)
than mammals, and thus the regression line between NISP and MNI
(or NTAXA) for birds will be steeper than for mammals. Hesse
(1982) used Parmalee's (1977) data for prehistoric avian remains
from the North American Great Plains to show the steep relationship between the NISP per bird taxon and the MNI per taxon. The
relationship between the log10 values of NISP and MNI making up
Parmalee's (1977) data is graphed in Fig. 1 where it can be seen that
the relationship is strongly linear (Pearson's r ¼ 0.983) and there
are few outliers. The slope of the best-fit linear regression line is
relatively steep (slope ¼ 0.84).
The same tight linear relationship (Pearson's r ¼ 0.974) is
apparent in another set of zooarchaeological collections of avian
remains, this one from the North American Great Basin, also
identified by Parmalee (1980) (Table 1). The slope of the best-fit
regression line (¼ 0.72) is nearly as steep as that for the Great
Plains collection, suggesting Hesse's argument is correct. To insure
that the relationship between the NISP and MNI of birds is not a
function of the individual who did the identifications of the two
sets of remains (Parmalee), and not a function of the fact that both
collections include remains from multiple sites, consider the NISP
and MNI values for the bird remains identified by Emslie (1981) and
recovered from the Pottery Mound site in New Mexico (part of the
North American Southwest). This collection shows the same tight
relationship (Table 1; Pearson's r ¼ 0.928) as the first two and the
slope of the best-fit line is steep (¼ 0.537), though not as steep as
the first two. In sum the relationship between bird NISP and bird
MNI seems to not be a function of who did the identifications,
where the remains originated geographically, or whether the
collection is made up of remains from multiple sites or from one
site. The key question therefore is: Is the relationshipdthe slope of
the best-fit regression linedbetween NISP and MNI steeper in birds
than in mammals, as predicted by Hesse (1982)?
The relationships between NISP and MNI of mammals in three
collections are summarized in Table 1, along with those for the
three bird collections discussed in the two preceding paragraphs. A
graph of one of the mammal assemblages is shown in Fig. 2. In all
three cases for mammals, the relationship between NISP and MNI is
strong (r 0.86). More importantly, although the range of the
slopes of the best-fit regression lines for the three mammal collections overlap slightly with that range for the three bird assemblages (0.607e0.472, and 0.840e0.537, respectively), the average
Table 1
Relationships between log10 NISP and log10 MNI in three collections of bird remains,
and in three collections of mammal remains. Pearson's r and slope refer to relationship between the log10 of NISP and MNI in each of the six assemblages.
Taxa
NISP/MNI
a
Birds
Birdsc
Birds
Mammals
Mammals
Mammals
a
Fig. 1. Relationship between NISP and MNI of birds in a set of summed archaeological
collections. Data from Parmalee (1977).
b
c
3029/871
3136/863
3209/236
1822/178
5901/232
6190/209
NTAXA
23
72
53
18
25
22
b
Pearson's r
Slope
Reference
0.981
0.969
0.928
0.961
0.867
0.920
0.840
0.720
0.537
0.607
0.492
0.472
Parmalee 1977
Parmalee 1980
Emslie 1981
Pollock and Ray 1957
Lyman 2008
Lyman 2008
Sum of nine sites.
Taxonomic family (not genus/species).
Sum of 16 sites.
R.L. Lyman / Journal of Archaeological Science 53 (2015) 291e296
293
geographic area. I perform this test because if their reasons for the
variable relationship between NISP and NTAXA across taxa hold
true (they do), it will be important to understand the implications
of those reasons for future analyses and interpretations of
zooarchaeological collections.
3. Materials and methods
Fig. 2. Relationship between NISP and MNI of mammals in an archaeological site. Data
from Lyman (2008).
slope for mammals is less than that for birds (0.524 vs 0.699,
respectively). This suggests that Hesse (1982) was in fact correct.
On average, individuals will be added more quicklydMNI will increase more rapidlydamong collections of bird remains than
among collections of mammal remains. But is this in fact because,
as Hesse hypothesized, each bird skeleton produces fewer taxonomically identifiable bones than each mammal skeleton?
Logic suggests Hesse (1982) is correct. Recall that MNI is defined
as the most common skeletal element of a taxon in a collection
(Grayson, 1984; Lyman, 2008). MNI will increase more rapidly as
the number of kinds of bones that can be identified per individual
decreases simply because there are fewer kinds of potentially most
abundant elements that might define MNI. If one can identify humeri, radii, femora, and tibiae of taxon A, then there are eight
(assuming each element is bilaterally paired as a left and a right)
possible kinds of most abundant elements (and each individual
animal can contribute eight elements); if one can only identify
humeri and femora of taxon B, then there are only four possible
kinds of most abundant elements (and each individual animal can
contribute only four elements). A random sample of 40 NISP of
taxon A is likely to have fewer individuals represented than a
random sample of 40 NISP of taxon B simply because there could be
5 of each kind of element of taxon A but 10 of each kind of element
of taxon B. Taxon B would thus likely have a higher MNI (per NISP)
value than Taxon A.
Although Hesse (1982) was concerned with the relationship
between NISP and MNI, the logic behind his discussion is the same
l (2007) with respect to the
as that used by Bartosiewicz and Ga
relationship between NISP and NTAXA. The similarity between the
two resides in the fact that both concern the potential (and likely)
rate of input of identifiable specimens (partially dependent on the
number in an individual skeleton) to the paleozoological record. As
l (2007) suggested three reasons
noted earlier, Bartosiewicz and Ga
why the relationship between NISP and NTAXA would differ between birds and mammals, and they presented data suggesting
each reason was valid. Below I use another data set to test the
validity of two of the reasons. I examine the relationship between
NISP and NTAXA in birds and in mammals by performing a more
l's observations than they
rigorous test of Bartosiewicz and Ga
originally provided. Greater rigor comes from my use of a greater
number of samples for each taxon, greater taphonomic control of
the samples, and my samples originate in a different and larger
Bartosiewicz and G
al (2007) used 35 prehistoric assemblages of
mammal remains and 29 prehistoric avian assemblages. All of the
assemblages they included originated in Hungary, but apparently at
least some of the collections of birds and mammals did not originate in the same site or deposit. That is, each assemblage of bird
remains did not necessarily have an associated assemblage of
mammal remains from the same deposit. This is an important
consideration with respect to taphonomic influences on the collections of bones available and also on what could be identified. I
control for this here by including an assemblage of bird remains
only if it has an associated assemblage of mammal remains on the
assumption that bird and mammal remains from the same deposit
were subjected to similar diagenetic (if not biostratinomic) histories. In other words, each of the 59 assemblages of bird remains
has an associated assemblage of mammal remains; each pair of
assemblages was recovered from the same deposit in a site. Of
course, taphonomic histories may also vary from site to site and
deposit to deposit. To contend with this possibility, I use numerous
assemblages from varied depositional settings such that a great
deal of variability in taphonomic histories is included. In doing so, I
assume the large number of collections will mute any potential
taphonomic skewing of results emanating from one or a few
assemblages.
Taphonomic histories may also vary intertaxonomically given
differences between skeletons at the level of taxonomic class (Aves,
Mammalia). This is in fact an issue here, particularly with respect to
the influence of fragmentation on identifiability. As noted above,
l (2007) suggested fragmentationda taphoBartosiewicz and Ga
nomic resultdreduced identifiability of bird remains more rapidly
than a similar degree of fragmentation reduced the identifiability of
mammal remains. If so, this would enhance the differences between the relationship of NISP to NTAXA for bird remains and that
relationship for mammal remains. As indicated below, I cannot
directly assess the influence of fragmentation among the collections I use in the analyses for want of data. Instead, I assume that
the large number of assemblages included will mute any skewing
and taphonomic biases. Specifically, I find it unlikely that all the
included avian assemblages will be significantly more fragmented
(and thus have fewer identifiable specimens per taxon) than all of
the included mammalian assemblages.
All collections date to the Holocene, and all come from North
America (Supplementary Table 1). The assemblages originate in
Arizona (2), Arkansas (1), Florida (2), Illinois (9), Indiana (2),
Michigan (6), Minnesota (3), Missouri (9), Nevada (3), New Mexico
(8), South Carolina (1), South Dakota (1), Tennessee (4), Utah (1),
Wisconsin (5), Alberta (1) and Manitoba (1). Twenty-three analysts
identified the remains making up one or more of the collections
and wrote the reports. In some cases an analyst identified both the
bird and the mammal remains; in a few cases one analyst identified
the bird remains and another analyst identified the mammal remains. I believe that the analysts involved have not influenced in a
consistent or patterned way the relationship between NISP and
NTAXA across all 59 assemblages of either the birds or the mammals. My belief rests on the fact that multiple researchers identified
the remains, and in some cases the same researcher identified both
the bird and mammal remains. Had one set of analysts identified
the bird remains and another had identified the mammal remains,
294
R.L. Lyman / Journal of Archaeological Science 53 (2015) 291e296
then there would be cause for concern that any difference in the
relationship between NISP and NTAXA for birds relative to that for
mammals might be a function of the analysts involved.
I tallied NISP and NTAXA for birds and for mammals for each
assemblage. Only unique taxa were included; for example, if both
the subfamily Anatinae (ducks) and its included genus Anas sp.
were listed (not unusual), only data for the latter were recorded. If
some specimens were identified as, say, “dog or coyote; Canis
familiaris or Canis latrans” and other specimens were identified as
either or both of these species, only data for the latter were
recorded. This protocol insured that taxa were not counted twice
and thus did not artificially increase NTAXA. In some cases, NTAXA
of an assemblage might be slightly decreased by tallying, say, only
Canis sp. in one assemblage (NTAXA ¼ 1) and tallying C. latrans and
C. familiaris in another assemblage (NTAXA ¼ 2). I presume such
instances are too few to exert a strong influence on analytical
results.
The NISP of bird remains across the 59 assemblages ranges from
4 to 4988 and averages 354; the NTAXA of birds per assemblage
ranges from 3 to 59 and averages 18.2. The NISP of mammal remains across the 59 assemblages ranges from 23 to 18,376 and
averages 2158; the NTAXA of mammals per assemblage ranges from
5 to 45 and averages 18.8. Forty percent (73 of 181 species) of the
bird taxa occur in only one assemblage and 63.5% (115 of 181) occur
in three or fewer assemblages. This is in stark contrast to
mammalian taxa of which only 22.6% (28 of 124 species) occur in
only one assemblage and 46.0% (57 of 124) occur in three or fewer
assemblages. The turkey (Meleagris gallopavo) and Canada goose
(Branta canadensis) are the most ubiquitous bird species, occurring
in 43 and 42 assemblages, respectively. Deer (Odocoileus virginianus/hemionus) and domestic dogs (C. familiaris) are the most
ubiquitous mammals species, occurring in 56 and 43 assemblages,
respectively.
4. The relationship of NISP to NTAXA in birds and in
mammals
l (2007) showed that there were more bird
Bartosiewicz and Ga
than mammal species in the archaeological collections they
examined, just as was found on the modern landscape. According
to the Audobon Society, today there are more than 800 species of
birds in North America north of Mexico (birds.audubon.org/birdid;
Table 2
Avian skeletal elements illustrated in osteology guidesa and identified in a
zooarchaeological reportb. þ Indicates skeletal element is illustrated or identified.
Skeletal element (N)
Olsen 1972,
1979a
Skull (1)
Mandible (1)
Coracoid (2)
Furculum (1)
Sternum (1)
Scapula (2)
Humerus (2)
Radius (2)
Ulna (2)
Carpometacarpus (2)
First phalanx, 2nd digit (2)
Pelvis/Synsacrum (1)
Femur (2)
Fibula (2)
Tibiotarsus (2)
Tarsometatarsus (2)
Terminal foot phalanx (3)
SUM
þ
þ
þ
þ
þ
þ
þ
þ
þ
þ
17
Gilbert et al.
1981a
þ
þ
þ
þ
þ
þ
þ
þ
þ
þ
þ
þ
þ
þ
26
Broughton
2004b
þ
þ
þ
þ
þ
þ
þ
þ
þ
þ
þCarpal digit 2
þ
þ
þ
þ
þ
30
accessed Aug. 27, 2014). Today there are 462 species of mammals
known in North America north of Mexico (Kays and Wilson, 2009).
The number of distinct species identified in the 59 North American
samples of archaeological bird remains (N ¼ 181) is greater than the
number of distinct species identified in the 59 North American
samples of archaeological mammal remains (N ¼ 124). If
Bartosiewicz and G
al (2007) are correct in their surmise, the difference in taxonomic richness between North American birds and
mammals suggests the regression line between bird NISP and bird
NTAXA in the 59 North American assemblages should be steeper
than the regression line between mammal NISP and mammal
NTAXA.
l (2007) and Hesse (1982) indicated
Both Bartosiewicz and Ga
that the number of identifiable bones per individual skeleton is less
in a bird than in a mammal. That this is in fact so is easily
demonstrated in two ways. First, the number of kinds of skeletal
elements illustrated and described in zooarchaeological osteology
identification manuals tends to be greater for mammals than for
birds. For birds, the number is 17e26 (Table 2). The number is
difficult to estimate for mammals given that different taxa have
different numbers of teeth, metapodials, and the like. Conservatively, the number of mammal skeletal elements illustrated and
described in skeletal guides is 53e83 (Table 3). Second, the number
of kinds of skeletal elements (ignoring whether identified specimens are fragments or anatomically complete skeletal elements)
identified in a large collection of archaeological bird remains
(N ¼ 30) is smaller than the number of kinds of skeletal elements
identified in a large collection of archaeological mammal remains
(N ¼ 116) (Tables 2 and 3). These two observations suggest, just as
l (2007) proposed, that the regression line
Bartosiewicz and Ga
between bird NISP and bird NTAXA for the 59 North American assemblages will be steeper than the regression line between
mammal NISP and mammal NTAXA in those assemblages.
l (2007) suggested that the greater
Finally, Bartosiewicz and Ga
degree of identifiability of fractured (anatomically incomplete)
mammal bones relative to the identifiability of fractured bird bones
Table 3
Mammalian skeletal elements illustrated in zooarchaeology osteology guidesa and
identified in a zooarchaeological reportb. þ Indicates skeletal element is illustrated
or identified.
Skeletal element
Olsen 1964a
Gilbert 1990a
Grayson 1988b
Skull (1)
Mandible (2)
Teeth (16e40)
Atlas (1)
Axis (1)
Cervical 3e7 (5)
Thoracic (13)
Lumbar (6e7)
Clavicle (2)
Sacrum (1)
Scapula (2)
Humerus (2)
Radius (2)
Ulna (2)
Carpals (12)
Metacarpals (2e10)
Innominate (2)
Femur (2)
Tibia (2)
Fibula (2)
Astragalus (2)
Calcaneum (2)
Other tarsals (2e4?)
Metatarsal (2e10)
Phalange (24e60)
SUM
þ
þ
þ
þ
þ
þ
þ
þ
þ
þ
þ
þ
þ
þ
þ
þ
þ
þ
þ
þ
þ
þ
þ
þ
þ
þ
þ
þ
þ
þ
þ
þ
þ
~116
þ
þ
þ
þ
þ
þ
þ
þ
þ
þ
þ
þ
þ
þ
þ
þ
þ
þ
þ
þ
~53
þ
þ
~83
R.L. Lyman / Journal of Archaeological Science 53 (2015) 291e296
results in a generally greater ratio of NISP:NTAXA for mammal remains than for bird remains. This suggestion cannot be empirically
evaluated with the 59 North American collections because fragmentation data for them are unavailable. This is not, however, a
serious drawback because fragmentation will increase the NISP but
not the NTAXA for both birds and mammals. If bird bones more
rapidly become less identifiable with greater intensity of fragmentation than mammal bones, as suggested by Bartosiewicz and
l (2007), then the effect on the relationship between NISP and
Ga
NTAXA of mammals will be to make the regression line steeper for
birds than for mammals because there will be a lower rate of input
of bird NISP per taxon than that rate for mammals.
l's (2007) and Hesse's (1982)
In light of Bartosiewicz and Ga
reasoning, and given the three reasons for the relationship between NISP and NTAXA, the slope of the best-fit regression line
between the NISP and NTAXA of birds should be steeper than the
slope of the line between the NISP and NTAXA of mammals. That is
in fact precisely what is observed both graphically (Fig. 3) and
statistically for the 59 North American assemblages. The slope of
the best-fit linear regression line for birds is 0.409, and for mammals is 0.241. In both cases, the correlation of the two variables is
high, although it is higher for birds (r ¼ 0.841) than it is for
mammals (r ¼ 0.773). Thus variability in bird NISP explains almost
71% of the variability in NTAXA of birds whereas variability in
mammal NISP explains only 60% of the variability in NTAXA of
mammals. This is not unexpected either given that there are many
more kinds of bones that can be identified per individual of a
mammal taxon than there are kinds of bones that can be identified
per individual of a bird taxon.
5. Discussion
The preceding provides a more rigorous test of Bartosiewicz and
l's (2007) observations than they originally did for three reasons.
Ga
First, taphonomy is more tightly controlled by using 59 pairs of bird
and mammal assemblages, each pair recovered from the same
deposits or sites. Taphonomic, particularly diagenetic, differences
between deposits containing bird remains and those containing
mammal remains that might influence the relationship of NISP to
NTAXA are not possible. Second, the test described here is more
rigorous and more statistically powerful because a larger number of
assemblages for both taxa is used. And third, the assemblages I have
used derive from a larger geographic area and thus provide the
potential for a much greater suite of taxa and of taphonomic
Fig. 3. Relationship between NISP and NTAXA in 59 zooarchaeological assemblages of
bird bones, and in 59 zooarchaeological assemblages of mammal bones.
295
processes to influence both NISP and NTAXA. The analysis presented above therefore lends considerable strength to Bartosiewicz
and G
al's observations, and it also indicates that those observations
are very likely universal. But, one might ask, so what? In particular,
l's obserof what analytical significance are Bartosiewicz and Ga
vations? There are several responses to these questions.
Recall that I began with the observation that NTAXA was (and is)
often a function of NISP. The general cause of the relationship is
clear: as sample size (NISP) increases, so too does NTAXA. But,
l (2007)
importantly, Hesse (1982) and Bartosiewicz and Ga
observed that the relationship differs inter-taxonomically, at least
at the level of taxonomic class. In other words, the precise nature of
the relationship between NISP and NTAXA depends in part on
sample size and also in part on the particular taxa. One implication
of this observation concerns the fact that archaeologists and paleontologists sample deposits (e.g., Krumbein, 1965; Orton, 2000).
They are aware of the influences of sample size on derived measures such as NTAXA and sometimes use techniques such as rarefaction to control variability in sample sizes across multiple
samples (e.g., Barnosky et al., 2005; Lyman, 2014). Comparison of a
rarefaction curve for an assemblage of birds with a rarefaction
curve for mammals would, in light of Fig. 3, be unwise.
In addition, paleozoologists do not always rarify collections yet
continue to determine NTAXA (biodiversity), evenness and heterogeneity as measures of dietary breadth among prehistoric
humans (e.g., selected references in Lupo, 2007) or some aspect of
paleoecology (e.g., Barnosky et al., 2005; Faith, 2011). The implication of Fig. 3 is that if the taxa included in the analyses vary in
such a way as to influence the relationship between NISP and
NTAXA (e.g., number of effective elements per taxon), comparing,
say, the NTAXA of birds with the NTAXA of mammals would be
unwise. Previously, one might argue that the indices could be
compared if the samples upon which they were based were similar
in size. Fig. 3 indicates that even if the sample of bird remains is the
same size as the sample of mammal remains, differences in richness are to be expected simply because fewer bones are required to
produce a particular NTAXA value for birds than are required to
produce that same NTAXA for mammals.
A second implication concerns the influence of the number of
kinds of skeletal elements (or fragments thereof) that can be
identified per taxon. For example, if all the skeletal elements listed
in Table 3 are identified for one collection or taxon but only, say,
mandibles, maxillae and teeth are identified for another collection
or taxon, then, as noted in the immediately preceding paragraph,
indices of faunal structure such as NTAXA, evenness, and heterogeneity for those two faunas can only be compared with explicit
recognition that those taxon free indices will be differentially
influenced by the rate of skeletal part input. Paleozoologists have
long been aware of this pitfall, expressing it as the lack of comparability of taxonomic abundances determined on the basis of taxa
with different numbers of identifiable bones per taxon or different
degrees of fragmentation of bones per taxon (e.g., Chaplin, 1971;
Holtzman, 1979; Shotwell, 1955, 1958). The potential magnitude
of the effect is clearly demonstrated in Fig. 3. A potentially important follow-up study along lines similar to the study reported here
would involve generating a graph like that in Fig. 3 comparing the
relationships between the NISP and NTAXA of rodentsdof which
teeth, skulls, and mandibles are typically the elements identifieddwith that for artiodactylsdof which nearly all teeth and
bones, cranial and post-cranial, are identified.
Finally, given the variable relationships shown in Fig. 3 both
between birds and mammals and within birds and mammals, the
issue of how large a representative sample must be is underscored.
The scatterplots in Fig. 3 emphasize that the relationship of NISP
and NTAXA varies considerably (the data points fall various
296
R.L. Lyman / Journal of Archaeological Science 53 (2015) 291e296
distances from the best-fit regression line) for a number of reasons.
This makes a standard representative sample size for all collections
impossible to determine because it is quite improbable. Sampling
to redundancy (Lyman and Ames, 2004, 2007) is a logical technique
for monitoring sample adequacy or representativeness because it is
case specific and can (and should) be empirically determined on a
case-by-case basis.
6. Conclusion
In the few studies of which I am aware wherein the varied relationships between NISP and NTAXA across multiple assemblages
are interpreted to signify changes in climate (Faith, 2011; Grayson,
1998; Lyman, 2012, 2014) or changes in human diet breadth
(Grayson and Delpech, 1998), the variable relationship is said to be
a function of varied rates of skeletal part input. Those interpretations have a firm foundation because data and analyses
presented here show that the relationship between NISP and
NTAXA is indeed influenced by the rate of skeletal part input. And
we now know that rate is determined by such things as taxonomic
richness on the landscape and the effective number of elements (to
borrow Hesse's (1982) term) per taxon, both the number of identifiable bones in an individual and the number of identifiable
fragments into which the bones of a skeleton can be broken.
The rarity with which knowledge of the varied relationship
between NISP and NTAXA has been used to solve analytical problems suggests that we still have a lot to learn about the basic
quantitative units that underpin much zooarchaeological analysis
(Grayson, 1984; Lyman, 2008). Increased computing power and
greater access to large data sets will facilitate meta-analyses that
should be directed toward revealing new aspects of the relationships between zooarchaeological variables as well as enhancing our
understanding of known relationships. Greater knowledge and
understanding should result in more refined and insightful analyses and interpretations.
Acknowledgments
This analysis grew from my chance reading of the thoughtful
2007 paper by Bartosiewicz and G
al. The comments of two anonymous reviewers were helpful.
Appendix A. Supplementary data
Supplementary data related to this article can be found at http://
dx.doi.org/10.1016/j.jas.2014.10.027.
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