Journal of Archaeological Science 33 (2006) 1256e1265
http://www.elsevier.com/locate/jas
Identifying bilateral pairs of deer (Odocoileus sp.) bones: how
symmetrical is symmetrical enough?
R. Lee Lyman
Department of Anthropology, University of MissouridColumbia, 107 Swallow Hall, Columbia, MO 65211, USA
Received 9 November 2005; received in revised form 22 December 2005; accepted 3 January 2006
Abstract
Identifying bilaterally paired bones in zooarchaeological collections rests on the assumption that left and right skeletal elements from the
same organism will be symmetrical. Bilaterally paired bones in an individual are, however, typically asymmetrical to some degree, demanding
that the question ‘‘How symmetrical is symmetrical enough to identify a bilateral pair?’’ be answered with control data. The degree of symmetry
chosen, or tolerance, will influence both how many true pairs in an archaeological collection are not identified (type I error) and how many false
pairs are identified (type II error). Bivariate measures of 60 pairs of astragali and 48 pairs of distal humeri of deer (Odocoileus virginianus and
O. hemionus) indicate that both sorts of error are frequent even when a conservative level of tolerance (average asymmetry) is used. Simulation
of an archaeological collection indicates that as sample size increases, frequencies of both kinds of error increase. Application of the matching
criteria and tolerance level to an archaeological collection underscores that the analytical requirements of identifying paired bones are steep.
Ó 2006 Elsevier Ltd. All rights reserved.
Keywords: Anatomical refitting; Bilateral symmetry; Deer
1. Introduction
Various analytical techniques in zooarchaeology require that
bilaterally paired bones such as left and right femora, left and
right humeri, and the like be identified among commingled
left and right skeletal elements representing multiple individuals. These include estimation of the number of individual animals represented using the Lincoln index (e.g., [1,5,11,35,38]),
and measuring the dispersal of the bones of individual carcasses
to detect natural site formation processes or hominid behaviors
involving butchering and food sharing (e.g., [3,8e10,32,37]).
Analytical identification of bilaterally paired bones rests on
the assumption that the members of a pairdthe left and right
matesdare bilaterally symmetrical. Members of bilateral pairs
are, however, typically asymmetrical to some degree. It is
therefore critical to determine how asymmetrical paired bones
are in order to conclude that two bones that might be paired
E-mail address: [email protected]
0305-4403/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved.
doi:10.1016/j.jas.2006.01.002
are indeed paired, or are from the same individual animal.
Some have argued that determination of how symmetrical is
symmetrical enough is a slippery issue because symmetry
varies within a species from nearly perfect to somewhat asymmetric [12]. Indeed, temporally fluctuating asymmetry has in
the past few decades become a very important research topic
in biology ([18,28] and references therein) in which metrical
(size) bilateral symmetry is usually measured [27].
Early on, some paleozoologists suggested that it is fairly
straightforward to establish how symmetrical is symmetrical
enough to identify a bilateral pair (e.g., [17]). The general
procedure is to establish the range of variation in (a)symmetry
for particular skeletal elements within a species (e.g., [10,13,
24,32,33]). But the specific procedure followed when deciding
how similar is similar enough to conclude that a bilateral pair
has been identified among archaeological specimens is typically obscure (e.g., [4,10,13,24,32,33,37]).
Nichol and Creak [25, p. 15] state that the more possible
pairs in an archaeological collection, the more likely that pairs
will be found and the smaller the ‘‘error margin needed to
R.L. Lyman / Journal of Archaeological Science 33 (2006) 1256e1265
allow all the bones from one side to be accommodated by
those from the other.’’ This assumes that every left element
will have a matching right element within a collection. This
assumption may be reasonable when one searches for bilateral
pairs among skeletal elements that were accumulated and deposited together, such as individual skeletal elements that
make up a large portion of the skeleton and that can be assumed to have been regularly accumulated as a unit. An example is the numerous individual elements that comprise a fish
head, precisely the elements that Nichol and Creak [25] examined. It seems progressively less reasonable to make this assumption as the size of the animal increases and as the
natural anatomical propinquity of the paired elements decreases. If the elements of a bilateral pair are large, and are anatomically not near each other within a body, such as with the
humeri of an ungulate carcass too large to be transported as
a complete unit, then they are easily disassociated anatomically and are potentially accumulated and deposited independently of one another. If the elements are relatively small and
are anatomically interdependent (articulated or within the
same anatomical region), such as with left and right mandibles
of a rabbit, then they are likely to be accumulated and deposited interdependently.
Nichol and Creak [25, p. 8] referred to the maximum allowable difference (or degree of asymmetry) between bilateral
pair mates as the ‘‘tolerance.’’ Tolerance should be empirically
determined from a set of known reference specimens, but in
doing so, several things must be acknowledged. The tolerance
level will depend on the attributes chosen. Genetic and environmental conditions influence the degree of (a)symmetry in
anatomical attributes differentially [18]. Further, different populations will display different degrees of asymmetry in the
same attribute [18]. Thus the degree of symmetry necessaryd
the tolerancedto identify pairs determined on the basis of
a modern reference collection will be to some unknown degree
specific to that collection. The average degree of asymmetry in
an attribute displayed by a modern population may or may not
be equal to the average asymmetry manifest in a prehistoric
population.
Another thing requiring acknowledgment is the analyst’s
willingness to make identification errors. Regardless of the
chosen tolerance level, a left and a right element might be misidentified as not a pair when in fact they are a true pair (type I
error), and a match might be identified when in fact the left
and right elements do not represent a true pair (type II error).
A tolerance level that minimizes both type I and type II errors
in matching must be empirically established by using museum
skeletons, regardless of the anatomical criteriadmetric (size),
morphological (shape), meristic (frequency)dused to identify
bilaterally paired skeletal elements. This simple yet central
point of all bilateral refitting methods is illustrated in the
remainder of this paper.
2. Materials and methods
The astragalus and the distal humerus are two compact,
dense skeletal parts that survive in measurable condition
1257
despite many sorts of taphonomic processes [6,19,20]. By
choosing two skeletal parts, I hoped to avoid the problem of
using one among the specimens of which it might be difficult
to identify bilateral pairs. Results for astragali and distal humeri are very similar and strengthen the conclusions drawn.
Deer (Odocoileus spp.) are widely distributed prehistorically across much of the Americas, their remains are frequent
in archaeological contexts, and numerous modern skeletons
are housed in museums. I measured museum specimens of
two species of deerdwhite-tailed deer (O. virginianus) and
mule deer (O. hemionus)dcollected from the western United
States. A total of 60 pairs of astragali (left and right elements)
from adult (all epiphyses fused or fusing, skeletal elements of
adult size) museum specimens was measured; 17 pairs are of
white-tailed deer, and 43 pairs are of mule deer. A total of 48
pairs of distal humeri from some of the same adult museum
skeletons was measured; 17 pairs of white-tailed deer, 30 pairs
of mule deer, and 1 hybrid of the two species. Based on recent
research both skeletal parts can now often be distinguished as
to species based on morphological features [14,15], and these
features were used to taxonomically distinguish specimens in
the archaeological collection [21].
I focus here on linear measurements rather than, say, rugosity of muscle attachment scars and number of foramina (e.g.,
[29]). Two measurements were taken on each astragalus and
each distal humerusdboth museum specimens and archaeological specimensdto the nearest 0.02 mm with sliding calipers. The two measurements of astragali were the (greatest)
distal breadth (Db [7]) and the (greatest) lateral length (GLl
[7]). The two measurements of distal humeri were the anterior
breadth of the distal trochlea (DBt) and the minimum (anteroposterior) diameter of the (latero-medial) center of the distal
trochlea (MNd). Some archaeological specimens of astragali
and of distal humeri that could be identified to species were
not measurable and some specimens that were measured could
not be identified to species; various specimens were broken or
weathered and lacked taxonomically diagnostic features;
others displayed taxonomically ambiguous features. Thus the
frequencies of specimens identified to species reported here
are different than those reported elsewhere [21].
Use of two measurements rather than one should make any
effort to identify bilateral mates more accurate because specimens must be relatively symmetrical in two dimensions rather
than just one. Given how the two measures are analyzed (see
below), specimens could be assessed for symmetry of shape.
Minimizing measurement error is critical to studies of (a)symmetry [27]. I measured a sample of astragali (5 lefts, 5 rights,
no bilateral pairs) once each day over a period of 3 days. The
average difference in measurements approximates measurement error. The tolerance level should exceed the measurement error to insure true pairs are not overlooked because of
measurement error. Measurement error of astragalus distal
breadth was 0.062 0.06 mm, and of greatest lateral length
was 0.073 0.05 mm.
Measurements of all 60 astragalus pairs (Table 1) and measurements of all 48 pairs of distal humeri were compiled
(Table 2). To establish how symmetrical was symmetrical
R.L. Lyman / Journal of Archaeological Science 33 (2006) 1256e1265
1258
Table 1
Metric data for 60 pairs of museum specimens of deer (Odocoileus sp.)
astragali
Taxon
Sex
Right, Db
Right, GLl
Left, Db
Left, GLl
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
M
?
M
?
F
?
F
M
M
M
M
F
M
?
M
M
M
F
M
M
M
M
M
F
F
M
?
F
M
M
F
M
M
M
F
M
M
F
F
F
F
M
?
F
M
M
M
F
M
F
F
M
F
F
M
M
M
M
M
M
25.36
26.28
28.04
24.18
23.92
28.90
24.84
25.70
25.26
26.70
26.32
26.76
27.30
25.12
26.68
26.16
26.68
27.22
25.70
28.28
29.56
27.36
28.76
29.04
26.80
27.24
29.74
25.56
26.28
24.84
24.48
26.46
27.62
28.40
26.40
28.46
27.76
26.80
24.86
26.78
26.08
28.46
28.06
25.32
28.28
25.50
26.34
25.90
27.90
27.26
25.66
28.12
25.70
27.06
27.70
24.78
29.60
28.52
29.80
28.04
38.78
40.38
43.10
39.90
36.84
43.74
38.94
42.76
38.94
43.74
42.86
41.72
41.80
37.44
39.70
40.88
40.52
40.90
39.60
42.70
44.18
45.04
42.18
45.30
41.88
41.82
44.22
41.92
41.74
38.24
37.06
39.76
42.50
42.56
41.94
45.62
40.94
39.98
39.20
43.26
38.56
41.18
44.62
39.76
43.10
39.12
40.66
41.10
43.00
42.14
39.02
42.02
40.68
41.30
40.18
38.78
42.74
43.38
44.24
41.74
25.56
25.80
28.02
24.38
24.08
29.26
25.04
26.02
25.50
26.72
26.28
26.50
27.08
25.16
26.54
26.38
26.86
27.56
26.16
28.46
29.46
27.22
28.38
28.80
26.30
27.24
29.62
25.88
26.68
24.94
24.90
26.54
27.88
28.40
26.66
28.66
27.58
26.70
25.12
26.92
26.10
28.18
28.26
25.30
28.36
25.34
26.50
26.10
28.06
26.86
25.60
28.14
26.16
27.30
27.62
24.78
28.78
28.70
29.86
28.38
38.36
40.08
42.86
40.00
36.74
43.32
38.88
42.44
38.38
43.46
42.94
41.36
41.92
37.54
39.82
40.72
40.38
41.20
39.40
42.84
44.16
45.18
41.92
45.82
41.58
42.28
43.98
41.74
40.86
38.52
36.96
38.76
42.32
42.96
41.66
45.20
40.52
39.80
38.96
42.60
38.40
41.08
44.50
39.38
43.30
38.94
40.72
40.98
43.08
42.04
38.92
42.00
40.42
41.16
40.12
38.92
42.60
43.12
44.34
41.68
virginianus
virginianus
virginianus
virginianus
virginianus
virginianus
virginianus
virginianus
virginianus
virginianus
virginianus
virginianus
virginianus
virginianus
virginianus
virginianus
virginianus
hemionus
hemionus
hemionus
hemionus
hemionus
hemionus
hemionus
hemionus
hemionus
hemionus
hemionus
hemionus
hemionus
hemionus
hemionus
hemionus
hemionus
hemionus
hemionus
hemionus
hemionus
hemionus
hemionus
hemionus
hemionus
hemionus
hemionus
hemionus
hemionus
hemionus
hemionus
hemionus
hemionus
hemionus
hemionus
hemionus
hemionus
hemionus
hemionus
hemionus
hemionus
hemionus
hemionus
Table 2
Metric data for 48 pairs of museum specimens of adult deer (Odocoileus sp.)
distal humeri
Taxon
Sex
Right, DBt
Right, MNd
Left, DBt
Left, MNd
O. virginianus
O. virginianus
O. virginianus
O. virginianus
O. virginianus
O. virginianus
O. virginianus
O. virginianus
O. virginianus
O. virginianus
O. virginianus
O. virginianus
O. virginianus
O. virginianus
O. virginianus
O. virginianus
O. virginianus
O. hemionus
O. hemionus
O. hemionus
O. hemionus
O. hemionus
O. hemionus
O. hemionus
O. hemionus
O. hemionus
O. hemionus
O. hemionus
O. hemionus
O. hemionus
O. hemionus
O. hemionus
O. hemionus
O. hemionus
O. hemionus
O. hemionus
O. hemionus
O. hemionus
O. hemionus
O. hemionus
O. hemionus
O. hemionus
O. hemionus
O. hemionus
O. hemionus
O. hemionus
O. hemionus
Hybrid
M
?
?
?
M
M
?
F
M
M
M
F
M
?
F
M
M
M
M
M
M
M
F
M
F
F
M
M
F
?
M
F
F
F
F
M
M
M
F
M
M
M
M
M
F
M
F
M
37.38
33.88
37.56
37.38
40.14
37.82
36.04
35.62
37.08
39.40
41.58
38.24
37.96
34.76
38.68
39.86
37.64
42.02
43.20
46.08
38.30
41.62
38.80
42.80
37.94
38.50
38.50
36.34
39.34
43.18
40.30
38.96
38.34
37.70
38.00
42.20
38.96
41.94
36.50
40.44
41.20
37.48
35.92
37.78
39.58
44.64
40.78
40.66
21.56
19.58
22.38
20.82
22.12
22.38
20.86
21.18
21.58
24.26
22.24
21.26
21.60
20.78
21.18
22.94
22.98
23.78
24.46
24.34
22.52
23.48
21.06
22.96
21.80
22.56
22.62
19.86
22.00
23.08
22.48
21.68
22.46
21.78
20.76
20.78
21.76
23.36
20.72
23.20
22.76
20.64
19.94
20.22
20.26
24.30
22.28
23.44
37.42
34.14
37.76
37.60
39.04
37.14
35.60
35.12
37.46
39.92
39.28
38.94
38.26
35.14
37.90
39.60
37.74
42.34
43.76
46.34
38.72
41.60
38.96
42.60
38.30
39.18
38.18
37.48
39.38
42.86
40.54
38.46
38.20
37.66
38.52
41.62
39.16
41.14
36.44
40.76
41.66
37.34
36.28
38.82
39.46
44.24
40.18
40.68
21.70
19.48
22.00
20.62
22.42
22.42
21.16
21.10
21.62
24.50
22.10
24.42
21.52
20.58
21.12
23.10
22.52
24.58
24.72
24.44
22.48
23.48
20.82
22.88
21.60
22.36
22.38
19.90
21.72
22.68
22.46
21.18
22.58
21.70
20.88
21.22
22.18
23.24
20.74
23.00
22.38
20.40
20.04
20.54
20.10
24.50
22.54
23.76
enough in a collection of known pairs, conceive of the absolute value of the difference between the two measurements
(on left and right mates) of one dimension (whether of astragali or distal humeri) as defining the length of one side of
the right angle of a right triangle (side a in Fig. 1, upper),
and the absolute difference between the two measurements
(on left and right mates) of the other dimension as defining
the length of the other side of the right angle of the right triangle (side b in Fig. 1, upper). The Pythagorean theorem
(a2 þ b2 ¼ c2) is used to find how asymmetrical the left and
right specimens are in terms of the two dimensions (Fig. 1,
R.L. Lyman / Journal of Archaeological Science 33 (2006) 1256e1265
b
a
c
a2 + b2 = c2
7
R
6
L
Dimension 2
5
4
l
3
2
r
1
0
0
1
2
3
4
5
6
7
Dimension 1
Fig. 1. A model of how two dimensions of a bone can be used simultaneously
to measure the degree of (a)symmetry between bilaterally paired left and right
elements. Upper, the Pythagorean theorem describing how the lengths of the
three sides of a right triangle are related; lower, the model of how two measurements (dimensions) on each of two elements (L and R; l and r) considered
together define a right triangle. The length of the hypotenuse (c-value in the
text) is a measure of how (a)symmetrical two specimens are; specimens L
and R are more symmetrical than specimens l and r.
lower). If the left and right specimens are perfectly symmetrical, then the hypotenuse (side c) of the right triangle will be
zero because a ¼ 0 and b ¼ 0. What is hereafter referred to
as the c-value (the length of the hypotenuse) is, then, a measure
of (a)symmetry. The c-value by itself suggests symmetry in
terms of size. A graph of the right triangles formed by left
and right mates suggests symmetry in terms of shape because
both dimensions are considered simultaneously. I nevertheless
focus on size.
There was no statistically significant difference between the
astragalus mean c-values of the two species (white-tailed deer,
0.315 0.164; mule deer, 0.359 0.217; Student’s t ¼ 0.757;
p ¼ 0.45), so the mean of all 60 pairs was determined
(0.347 0.203). This grand mean c-value indicates how symmetrical astragali are in deer in terms of the two dimensions
measured. Using both species as the basis for a tolerance level,
most conservatively, any left astragalus of a species that produces a c-value the grand mean c-value (0.347) with a right
astragalus of the same species could be a match. This value is
the conservative matching statistic. It exceeds the measurement
error of a c-value (approximately 0.1). Further, any left
1259
astragalus of a species that produces a c-value within the
mean þ one standard deviation (0.347 þ 0.203 ¼ 0.55) of
a right astragalus of the same species could be a match. This
value is the liberal matching statistic. Applying both the conservative and the liberal matching statistics to known pairs
from which they were derived will reveal how varying tolerance levels influence the magnitude of type I and type II errors.
There was no statistically significant difference between
mean c-values for distal humeri of the two deer species
(white-tailed deer, 0.753 0.81; mule deer, 0.467 0.282;
Student’s t ¼ 1.771; p > 0.08), so the grand mean was determined; c-value ¼ 0.561 0.541. The conservative tolerance
level or matching statistic is (c-value ¼) 0.561; the liberal
matching statistic is 1.102.
The archaeological collection originated in the site of Cathlapotle (45CL1), in southwestern Washington State [2,21,23].
The site was visited by Meriwether Lewis and William Clark
in March of 1806 as they led the Corps of Discovery eastward.
At that time the site comprised several large cedar-plank
houses and associated midden deposits [2]. Radiocarbon dates
indicate the main occupation began about AD 1450. Ceramic
trade goods indicate abandonment circa AD 1834. I identified
all mammalian remains. Site deposits were designated as exterior or interior depositsdoutside or inside of a house, respectively. Exterior ‘‘midden’’ deposits have very high organic
contact, lenses of fresh-water mussel shells, and other indications that they formed as primary or secondary dumps [2]. Exterior yard deposits are generally broad sheet-like deposits that
contain intact hearths, activity areas, pits, evidence of small
structures, and so forth. They lack the very high organic content of middens. Interior deposits were variously assigned to
walls, benches (deposits below the 2 m wide sleeping benches
or platforms that ran along the interior side of the house walls),
storage pits, and hearth areas. The houses had extensive subfloor storage features that are about 2 m wide by 2 m deep located below the sleeping platforms that line the interior walls
of the houses.
Most mammalian remains from Cathlapotle were recovered
from storage pits and exterior midden deposits. Site deposits
are distributed over an area about 200 50 m. Less than 2%
of this area has been excavated [2]. No change in the size of
the deer bones over time is evident [22] so I treat the deer
remains as a single assemblage. Metric and general provenience data for deer astragali from Cathlapotle are described
in Table 3.
3. Results using museum specimens
3.1. Initial results by species
The bivariate scatterplot of the 17 white-tailed deer astragalus pairs (Fig. 2) from museum collections indicates that simple visual inspection of this graph, were it based on an
archaeological collection, might provide sufficient resolution
to allow some astragali to be correctly paired. But there is
a cluster of three left and three right astragali, and another
cluster of four left and four right astragali within each of
R.L. Lyman / Journal of Archaeological Science 33 (2006) 1256e1265
1260
Table 3
Archaeological astragali of deer (Odocoileus sp.) from Cathlapotle
Spec.
Side
Db
GLl
Species
North
West
Level
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
L
L
R
R
R
L
L
L
L
R
L
R
L
L
L
R
R
L
L
L
R
R
R
R
L
R
R
L
L
L
L
L
L
L
L
R
L
R
L
R
L
L
R
R
R
L
25.84
28.72
25.68
30.24
29.76
27.04
25.38
25.82
27.50
25.36
22.80
27.84
25.30
25.08
26.86
26.12
25.88
24.48
27.70
23.78
26.50
27.54
27.94
27.38
25.28
27.56
26.18
27.00
26.76
30.12
24.86
24.72
26.54
23.46
28.76
28.06
26.28
23.90
25.28
24.40
24.56
26.94
25.98
27.24
28.38
25.38
40.86
41.80
40.98
45.44
42.84
43.16
40.54
40.00
42.22
38.42
39.64
40.66
41.54
40.64
41.48
40.32
40.60
37.94
42.78
37.66
42.40
42.28
43.96
44.28
37.90
40.44
42.40
41.18
41.24
43.38
39.54
38.30
42.02
38.52
44.86
41.48
41.46
39.06
41.08
37.46
39.86
41.46
40.46
41.86
44.28
38.10
hemionus
hemionus
hemionus
hemionus
hemionus
hemionus
?
?
?
?
?
?
?
?
virginianus
virginianus
virginianus
virginianus
virginianus
virginianus
virginianus
virginianus
virginianus
virginianus
virginianus
virginianus
virginianus
virginianus
virginianus
virginianus
virginianus
virginianus
virginianus
virginianus
virginianus
virginianus
virginianus
virginianus
virginianus
virginianus
virginianus
virginianus
virginianus
virginianus
virginianus
virginianus
107e109
107e109
107e109
120e122
159e160
159e160
159e160
107e109
106e107
106e107
124e126
153e155
159e160
159e160
159e160
52e54
75e77
75e77
107e109
120e122
120e122
120e122
130e132
132e134
138e140
138e140
147e149
149e151
153e155
155e157
155e157
155e157
155e157
159e160
159e160
159e160
159e160
159e160
160e162
160e162
160e162
160e162
160e162
160e162
160e162
107e109
98e100
98e100
98e100
96e98
103e107
103e107
91e95
98e100
77e81
77e81
96e98
86e88
103e107
103e107
91e95
103e105
76e78
76e78
98e100
96e98
96e98
96e98
99e101
96e98
86e88
86e88
86e88
84e86
86e88
84e86
84e86
84e86
84e86
103e107
95e99
83e107
103e107
103e107
84e86
84e86
84e86
90e92
90e92
90e92
90e92
98e100
13
18
14
6
15
10
9
12
7
5
5
3
7
5
14
12
10
11
12
6
3
5
2
10
8
7
2
3
7
6
10
9
9
8
9
4
15
14
3
3
4
9
5
8
8
10
which it would be difficult to identify true pairs. The conservative pair statistic does not help identify pairs in either cluster. Both clusters are near the center of the plot. The GLl and
Db values of all deer are normally distributed (do not differ
significantly from a Gaussian distribution; p > 0.1). It is in
the center of a distribution of points (Fig. 2) where type II errors (false pairs identified) would be most likely to occur and
these would also likely influence the magnitude of type I error
(e.g., if a false pair is identified and the true mate of one of the
members of that pair occurs in the assemblage).
Both probability theory and the empirical data in Fig. 2 indicate that true pairs will be most obvious at the extremes of
the point scatter (upper right, lower left) where few specimens
occur in normally distributed variables. But at these extremes
the conservative pair statistic would not identify three of the
seven pairs plotted (all in the upper right portion of the graph)
if only that statistic was used to identify pairs. In this case, the
graph rather than the statistic helps avoid type I error (failure
to identify a true pair). This is likely because in this case, the
conservative pair statistic indicates that the left and right members of a pair must display a c-value 0.366; the liberal pair
statistic indicates that the left and right members of a pair must
display a c-value 0.563 (¼0.366 þ 0.197). But that is all
those statistics indicate. They do not indicate where in a population (as represented by all the points in Fig. 2) any given possible pair falls.
The bivariate scatterplot of the 43 mule deer astragalus
pairs (Fig. 3) from museums indicates that with a sample of
R.L. Lyman / Journal of Archaeological Science 33 (2006) 1256e1265
30
Distal Breadth [Db] (mm)
Study of bilateral pairs of astragali of each species suggests
that as the absolute size of the archaeological sample of possible pairs increases, the probability of committing some
type II error (and related type I error) will increase as well.
As more possibly matching archaeological specimens are included in an analysis, it will be much more difficult to identify
true pairs. The number of matches will increase only if the distinction of type I and type II errors is ignored. Earlier analysts
seem to have recognized this problem regarding large samples,
though their wording was inexplicit (e.g., [36, p. 311]). Later
commentators were more explicit [11]. Nichol and Wild [26,
p. 36e37], for instance, noted that
+ Right
Left
29
+
+
28
+
27
+
+
+
+
+
+
+
26
+
++
+
+
25
24
+
+
1261
23
36
37
38
39
40
41
42
43
44
Greatest Lateral Length [GLl] (mm)
Fig. 2. Left and right pairs of museum white-tailed deer astragali. See text for
discussion of clusters circled by a dashed line. Data from Table 1.
this size, the conservative matching statistic (c-value ¼ 0.359)
should be preferred over the liberal matching statistic (cvalue ¼ 0.576 [¼0.359 þ 0.217]) because otherwise many
left astragali have multiple potential matching right astragali.
Again, probability theory and these empirical data indicate
that the potential to commit a type II error increases as the frequency of specimens and thus the frequency of potential
matches increases. Even using the conservative matching statistic, many lefts have several possible right mates. Further,
unlike with the 17 pairs comprising the white-tailed deer
data (Fig. 2), with 43 pairs, even the true pairs at the extremes
of the point scatter are difficult to perceive. Note the cluster of
three pairs in the upper right portion of Fig. 3. The possibility
of committing a type II error (identifying a false pair) increases as the sample size increases. Adding the white-tailed
deer specimens would increase the number of possible
matches and thus increase the probability of committing
a type II error because those specimens would both increase
the sample size (create a more normally distributed population) and they would also provide a wider range of tolerance
in both the conservative matching statistic (c-value ¼ 0.347)
and the liberal matching statistic (c-value ¼ 0.55 [¼0.347 þ
0.203]).
‘‘it is much harder to identify the extra unmatchable elements in a collection of bones from a larger number of animals of a species than it is in a smaller collection. For
example, if there are 100 lefts and 100 rights of a bone,
it will be rather difficult to produce an estimate of MNI
much greater than 100, whether 100 or 200 animals are represented, while it may be very easy to see that a single left
and a single right come from different individuals.’’
Consider Fig. 4, which shows the 48 pairs of museum distal
humeri from some of the same deer that provided the astragali
data. Notice that the points representing three lefts overlap the
points representing three rights in Fig. 4. But none of the true
pairs are actually symmetrical (Table 2). The three pairs of
overlapping points all represent false pairs. And, the tight clustering of points in the middle of the graph suggests that other
false pairs would likely be identified even were the conservative matching statistic used.
3.2. Simulating an archaeological collection
Simulating an archaeological collection using a set of
known pairs allows evaluation of how many instances of type I
error and how many instances of type II error occur when different tolerance levels are used. I drew a random sample of 60
astragali (without replacement) from among the 120 comprising the collection of museum specimens. (Astragali were numbered from 1 through 120 in the order listed in Table 1.
Members of the first pair of astragali are numbered,
Distal Breadth [Db] (mm)
+
29
Right
Left
Minimum Diameter of Trochlea
[MNd] (mm)
25
30
++
+
+
+
+
+
++
+
28
+
+
+
+
+
+
+
+
25
+
+
+
+
+
+
+
+ +
+
++
+
26
+
+
+
27
+
+
+
+
+
+
+
+
24
+
Right
Left
+
+
24
+
+
+
23
+
+
+++
++ +
22
+
+ +
+
+
+
+
+
+
20
+
+
+
+ +
+
+
+
+
+
+ +
+
+
++
++ +
21
++
+
+
+ +
+
19
36
37
38
39
40
41
42
43
44
45
46
Greatest Lateral Length [GLl] (mm)
Fig. 3. Left and right pairs of museum mule deer astragali. See text for discussion of the cluster circled by the dashed line. Data from Table 1.
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
Breadth of Trochlea [DBt] (mm)
Fig. 4. Left and right pairs of museum distal humeri. Specimens of both mule
deer and white-tailed deer are included. Data from Table 2.
R.L. Lyman / Journal of Archaeological Science 33 (2006) 1256e1265
1262
respectively, 1 and 2, members of the last pair are 119 and
120; right astragali all have odd numbers, left astragali all
have even numbers.) I initially ignored species designations
because until a few years ago the two deer species could
not be distinguished among zooarchaeological remains and,
as noted earlier, some astragali cannot be identified to species even today. The sample of 60 astragali included 28
left elements and 32 right elements, meaning there were 28
possible pairs; 16 true pairs were included. The bivariate
scatterplot of the sample (Fig. 5) reveals many of the problems with metrically identifying bilateral pairs, even with explicit tolerance limits.
Of the 16 true pairs, only four (astragali 7e8, 13e14, 59e60,
83e84) would be identified if the conservative matching statistic were used (c-value ¼ 0.347). But use of that conservative
statistic would also result in the identification of seven false
pairs (5e98, 6e97, 20e79, 30e63, 32e93, 36e73, 104e
119). Using the liberal matching statistic would add three true
pairs (55e56, 71e72, 99e100). The conservative matching
statistic creates a plethora of problems many of which would
be exacerbated were the liberal matching statistic used. The
conservative matching statistic results in ignoring six true pairs
(5e6, 19e20, 35e36, 73e74, 79e80, 97e98). The conservative matching statistic does not help sort out the cluster of points
in the lower left portion of the graph (Fig. 5). That cluster consists of several true pairs (1e2, 13e14, 59e60, 91e92), only
one (59e60) or two (59e60, 91e92) of which would be identified depending on whether or not one seeks to identify the
maximum possible number of pairs. One possible solution concerning this point cluster would identify three pairs (17e92,
91e102, 59e60), only one of which was a true pair; another
solution would identify four pairs (17e78, 91e92, 1e102,
59e60), only two of which were true pairs.
If species are recognized among the astragali, fewer errors
occur but a significant number remain. Five of the seven false
pairs would not be identified, but two would still be identified.
All 6 true pairs not recognized by the conservative matching
statistic would still not be identified. The cluster of points in
the lower left of Fig. 5 would sort out better, but at least
one false pair would remain (91e102) and a true pair (1e2)
would be missed if the conservative matching statistic were
used. As noted earlier, and as can be imagined by inspection
of Fig. 4, similarly messy results are produced by the distal
humerus data.
4. Results with an archaeological collection
Does the difficulty of identifying bilateral pairs attend study
of a real archaeological collection? The mule deer astragali
and the deer of unknown species (Odocoileus sp.) astragali
from Cathlapotle are plotted in Fig. 6. The latter are those
that did not clearly display morphological criteria diagnostic
of either species, thus they may represent either species. Using
the conservative matching statistic, there seems to be one pair
of left and right astragali in this setdspecimens 1 and 3 (cvalue ¼ 0.2). Both members of the pair clearly represent
mule deer based on morphological features. There are no pairs
among the specimens identified only as deer using either the
conservative or the liberal matching statistic for mule deer.
None of the specimens identified only to genus pair up with
the specimens identified as mule deer, thus the former will
be compared to those astragali representing white-tailed deer.
The white-tailed deer and the deer astragali from Cathlapotle are plotted in Fig. 7. As noted earlier, the latter are included
because they may represent white-tailed deer although they
did not display the diagnostic morphology of either species
represented in the collection. Using the conservative matching
statistic for white-tailed deer (c-value ¼ 0.315), there are two
pairs of left and right astragali; specimen 9 matches with specimen 22 (c-value ¼ 0.072), and specimen 10 matches with
specimen 46 (c-value ¼ 0.321). The liberal matching statistic
(c-value ¼ 0.479) suggests there may be two more pairs, specimens 21 and 33 (c-value ¼ 0.362), and specimens 8 and 16
(c-value ¼ 0.439).
31
+
Left - Mule deer
30
12
29
83
84
28
109 74 73
36
35
27
30
63
26
58
32
93
95
10291 37
1 92
17
14 78
59 60
11113
2
25
62
36
37
71
85
44
80
7920 19
21
50
56
55
15
38
39
28
27
1
26
+
3
25
24
8
7
10
24
65
100
72
+
+
Right - Deer
Left - Deer
29
47
68
98
6 5
97
104
119
51 99
54 53
41
Distal Breadth [Db] (mm)
Distal Breadth [Db] (mm)
30
Right - Mule deer
40
23
41
42
43
44
45
46
Greatest Lateral Length [GLl] (mm)
22
38
39
40
41
42
43
44
45
46
Greatest Lateral Length [GLl] (mm)
Fig. 5. Simulated archaeological assemblage of astragali. Each number signifies a particular astragalus listed in Table 1; odd numbers are right astragali,
even numbers are left astragali (see text for explanation). Some numbers have
been moved slightly to enhance legibility.
Fig. 6. Cathlapotle mule deer (O. hemionus) and deer (Odocoileus sp.) astragali. The single bilateral pair identified using the conservative matching statistic is circled with a dashed line, and specimen numbers (Table 3) are included.
R.L. Lyman / Journal of Archaeological Science 33 (2006) 1256e1265
31
+
30
Right - Deer
Left - Deer
29
Distal Breadth [Db] (mm)
Right - White-tailed deer
Left - White-tailed deer
+
28
+
22
+
+
+
+
+ 9
27
26
33
16
++
+
8
46
+ 21
+
10
25
+
24
+
23
22
37
38
39
40
41
42
43
44
45
Greatest Lateral Length [GLl] (mm)
Fig. 7. Cathlapotle white-tailed deer (O. virginianus) and deer (Odocoileus sp.)
astragali. Bilateral pairs identified using the matching statistics are circled with
dashed lines, and specimen numbers (Table 3) are included.
5. Discussion
Common sense suggests, and analyses presented above
confirm that the tolerance level chosen will influence which bilateral pairs, both true and false, are identified. Among the
Cathlapotle assemblage an analyst would identify three pairs
of astragali using the conservative matching statistic, or five
pairs using the liberal matching statistic, out of a possible 21
(counting those specimens not identified to species twice because they could match with astragali of either species).
Only 14.3% or 23.8%, respectively, of all possible matches
were in fact made. These results may be small because so little
of the site has been excavated (<2%); if more had been excavated, then other matches likely would have been found presuming a small degree of taphonomic interdependence of
left and right astragali. Do the results repay the effort?
The MNI of deer at Cathalpotle is 41 if a traditional ‘‘most
common element’’ definition (e.g., [4]) is used. For mule deer
astragali, there are 9 lefts, 5 rights, and 1 pair. For white-tailed
deer astragali, there are 24 lefts, 16 rights, and 3 pairs. Plugging
these values into the Lincoln index of (LR)/P, where L is the
number of lefts, R is the number of rights, and P is the number
of pairs [11,35], estimates of 45 individual mule deer and 128
individual white-tailed deer are derived. The estimated number
of individual mule deer is less than the estimated number of individual white-tailed deer. The number of identified specimens
(NISP) of all bones identified for these two species is 23 for
mule deer and 154 for white-tailed deer [21]. Given that taxonomic abundances are at best rank-order or ordinal scale [12],
we have not gained any resolution by identifying bilateral pairs
among the deer remains at Cathlapotle.
The mean distance between bilaterally matched bison (Bison antiquus) long bones at the Horner bison kill site is about
1e2 m, and conjoined fragments of skeletal elements are
about the same distance apart [33]. The conjoined fragments
of skeletal elements of both bighorn sheep (Ovis canadensis)
and bison (Bison bison) at the Bugas-Holding site average
1263
1 m apart [30]. At the Jones-Miller bison (Bison sp.) kill
site, conjoined fragments average about 2 m apart [34].
Based on Waguespack’s [37, p. 411] map and tabular summary of refits at a habitation site, I estimated the distance between 17 bilateral refits. For those that seemed to occupy the
same horizontal position (n ¼ 7), I assumed specimens making
up a pair were 0.25 m apart. The 17 bilateral refits are, on average, about 4.9 m apart. This is more than twice as far apart
as bilaterally refitting bones in kill sites. Enloe [9, p. 15] found
portions of a single carcass to be separated by as much as 63 m
in the Upper Paleolithic habitation site of Pincevent. Thomas’s
[31, p. 367] 35-year-old assumption that ‘‘the dietary practices
of man tend to destroy and disperse the bones of his prey-species’’ is confirmed and expanded. Bones of a carcass are likely
to be more dispersed (farther apart) within a habitation site
than the bones of a carcass of that taxon at a kill or procurement site.
But, consider each of the five pairs identified at Cathlapotle.
According to the excavator, K.A. Ames, both members of the
1e3 pair (Table 3) come from a sheet midden; the specimens
are about one meter apart horizontally and could well represent a true pair. Specimen 10 comes from the single unit excavated inside House 2 and its mate, specimen 46, comes from
a sheet midden outside of House 2 such that the two specimens
were 20 m apart; Ames suggests the probability that these
specimens represent a true pair is remote. Specimen 9 comes
from House 2 and specimen 22 from House 4; they were about
21 m apart and if a true pair, then represent interhouse sharing.
Both specimens of the 8e16 pair came from midden deposits
and were 55 m apart; there is no clear evidence of post-depositional disturbance so they may represent a true pair. Finally,
specimen 21 came from the floor of House 4 and its mate,
specimen 33, came from a storage pit inside of House 1; the
two specimens were 60 m apart and likely represent a false
pair. Given the absence of clear ethnoarchaeological indications of the amount of dispersal to expect at habitation sites,
the lack of evidence corroborating suspected pairs, and the difficulty of identifying pairs exemplified here, I am hesitant to
say much else about these five pairs.
6. Conclusion
Chaplin [4, p. 70] noted that ‘‘the right and left bones of
[an] animal are not always the same size.’’ Winder [38, p.
116] indicated that ‘‘the reliable recognition of [bilateral] pairs
in real assemblages may be difficult.’’ Fieller and Turner [11,
p. 57] emphasized that identifying pairs could present an ‘‘immense problem’’ if the sample of possible pairs was large. I
have shown that the sample size need not be very large before
the immensity of the matching problem arises. A mere 15 possible pairs presents what may be insurmountable difficulties,
in part because the rules for determining how similar is similar
enough are analytical choices. Consideration of two dimensions simultaneously and use of a tolerance level in the form
of a conservative matching statistic does not make things easier. Nor do these aspects of analytical protocol reduce type I or
type II error.
1264
R.L. Lyman / Journal of Archaeological Science 33 (2006) 1256e1265
Many researchers cited here use metric symmetry to provide an initial indication of possible pairs. Enloe and David
[10, p. 297] found that size variables identified multiple possible mates for individual bones, and that confirmation of a pair’s
validity depended on ‘‘morphological symmetry, architecture
of the bones, and the development of muscle and ligament attachment points.’’ With large samples made up of several
dozen specimens of each side of multiple skeletal elements,
the requisite metric data become numerous, the time necessary
to visually compare morphologies becomes long, laboratory
layout space requirements increase, and the like. Biologists
are developing multivariate techniques for comparing shapes
of paired bones (e.g., [16]) that demand statistical sophistication. Any effort to identify bilaterally paired bones, regardless
of the criteria and methods used, must be attended by explicit
recognition of the necessity of simultaneously reducing both
type I and type II error. In light of the analyses described
above, future identifications of bilateral pairs should be attended by steep data and analytical requirements.
Acknowledgments
Excavations at Cathlapotle were supported by the U.S. Fish
and Wildlife Service and the Friends of the Wapato Valley.
Anan Raymond, Regional Archaeologist for the U.S.F.W.S.
and his staff, the staff of the Ridgefield Wildlife Refuge, and
the people of Ridgefield, Washington, supported excavations
in diverse ways. The Chinook Tribe also provided support and
keen interest, and actively participated in the project. Analysis
of the Cathlapotle mammalian fauna was partially funded by the
College of Arts and Science of the University of MissouridColumbia. Support for the collection of metric data was provided
by the Chancellor’s Office, University of MissouridColumbia,
and Barbara M. Lyman. Kristen Fuld suggested the term ‘‘cvalue.’’ Helpful comments on an early draft were provided by
D.K. Grayson and two anonymous reviewers.
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