Journal of Archaeological Science 33 (2006) 847e861 http://www.elsevier.com/locate/jas

A crossbeam co-ordinate caliper for the morphometric analysis of lithic nuclei: a description, test and empirical examples of application Stephen J. Lycett*, Noreen von Cramon-Taubadel, Robert A. Foley Leverhulme Centre for Human Evolutionary Studies, University of Cambridge, Fitzwilliam Street, Cambridge, United Kingdom Received 5 June 2005; received in revised form 25 October 2005; accepted 31 October 2005

Abstract Over the last four decades, there has been surprisingly little advance in the quantitative morphometric analysis of Palaeolithic stone tools, especially compared to that which has taken place in biological morphometrics over a comparable time frame. In Palaeolithic archaeology’s sister discipline of palaeoanthropology, detailed quantitative morphometric, geometric morphometric, and even 3D geometric morphometric analyses are now seen almost as routine. This period of relative methodological stasis may have been influenced by the lack of homologous landmarks on many lithic tools (essential for any comparative analysis), especially core-based technologies of the Lower Palaeolithic. Archaeological field conditions may also prohibit the use of expensive and delicate precision instruments in certain cases. Here we present a crossbeam co-ordinate caliper that e crucially e both geometrically locates and measures distances between morphologically homologous landmarks upon lithic nuclei via a single protocol. Intra- and inter-observer error tests provide evidence that error levels associated with the instrument fall within acceptable ranges. In addition, we present empirical examples of application in the form of a multivariate analysis of 55 discrete morphometric variables, and a 3D geometric morphometric analysis of co-ordinate landmark configurations derived from Pleistocene lithic nuclei (i.e. ‘cores’ sensu lato). We also introduce to lithic studies some techniques for the study of shape variation that have previously been used with success in biological morphometric analyses. We conclude that use of an instrument such as the crossbeam co-ordinate caliper may provide a useful adjunct to traditional techniques of lithic analysis, particularly in developing a quantitative morphometric approach. Ó 2005 Elsevier Ltd. All rights reserved. Keywords: Lithics; Morphometrics; Landmarks; Geometric mean; Size-adjustment; Semi-landmarks; 3D geometric morphometrics

1. Introduction An interest in the variation of stone tool form (morphology) has long been a central theme of Palaeolithic archaeology. Such concerns play a fundamental role both in the establishment of typological distinctions, and in assessments of their validity and meaning. During the Plio-Pleistocene especially, it is the variation in shape of cores and core-tools (i.e. polyhedrons, discoids, Acheulean handaxes, cleavers, etc.) that form * Corresponding author. Leverhulme Centre for Human Evolutionary Studies, University of Cambridge, The Henry Wellcome Building, Fitzwilliam Street, Cambridge, CB2 1QH, United Kingdom. E-mail address: [email protected] (S.J. Lycett). 0305-4403/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.jas.2005.10.014

the basis of many typological and descriptive schemes (e.g. [6,8,27]), and discussion of such variation in terms of cultural traditions, hominin biomechanical and cognitive capacities, raw material factors, etc. (e.g. [33,56,60 and references therein, 65]). However, since the seminal work of Bordes [6], Roe [48,49] and Isaac [23] there has been surprisingly little advance in the quantitative morphometric analysis of such artefacts, especially compared to that which has taken place in biological morphometrics (e.g. [4,5,20,29,42,43,67]). Others [2,53] have suggested that quantitative techniques of shape analysis employed in biology have moved on to such a great extent in recent decades, that a veritable ‘revolution’ has taken place. In recent years, developments have been made toward the goal of a productive science of lithic shape analysis (e.g.

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[10,18,32,34,40,54,55,65]). However, compared with other academic arenas it may reasonably be averred that this goal remains largely unrealised to date. One potential factor that may have inhibited the development of quantitative approaches to lithic variation is the lack of morphologically homologous landmarks that can be identified on hominin-modified stone nuclei. (The term ‘nuclei’ here refers to lithic pieces possessing negative flake scars, the size of which, indicate the piece could at least potentially have functioned as a ‘core’ for utilizable flake tools, held in the hand or between fingers.) A lack of homologous landmarks tends to restrict lithic quantitative variables to a small number of basic measurements (e.g. length, width, and thickness) on a limited number of regions; most commonly resulting in a data set comprised of
11 primary variables (e.g. [7,36,39]). Moreover, applications of these measurements have generally been limited to bifacial technologies (e.g. [10,23,32,49]) and rarely involve the simultaneous analysis of a wide range of disparate lithic ‘morphs’. Conversely, most biological morphometric approaches can readily employ a range of morphologically homologous points (e.g. suture junctions, projections, foramina, etc.) that allow either Euclidean distances to be calculated between pairs of points, or for landmark configurations to be determined. These data are then readily amenable to a battery of multivariate statistical approaches, geometric approaches and, most recently, 3D geometric morphometric techniques. Moreover, these techniques can be applied across a broad range of species variation, enabling both intra- and inter-specific comparative analyses to be undertaken. Considering the above issues, the approach taken by Dibble and Chase [12] remains one of the most interesting regarding potential solutions to the problems of lithic morphometrics. Dibble and Chase presented a simple device for capturing a series of 22 bilateral outline measurements from artefacts such as bifaces or flakes. However, while a high proportion of flake and biface variability could potentially be described from outline data alone, it is worth emphasizing that lithic nuclei are 3D and important shape information may be under-utilized. This latter point is particularly important if analyses are to move away from the traditional trend of comparing bifacial assemblages alone, and a broader array of lithic forms are to be incorporated within analyses. Although instruments designed to accurately record the location of pre-defined and readily visible landmarks are now available (e.g. Microscribe MXÔ, Immersion Corp., San Jose, CA.), such instruments cannot, in themselves, locate landmarks; the very problem that may currently be hindering morphometric lithic research. Moreover, such instruments present attendant problems associated with electrical circuitry and delicate mechanics that may be an impediment to those working under archaeological field conditions [35]. Here we present a crossbeam co-ordinate caliper that e crucially e both geometrically locates and measures distances between morphologically homologous landmarks upon lithic nuclei via a single protocol. In addition, we present empirical examples of application in the form of a multivariate analysis of 55 discrete morphometric variables, and a 3D geometric

morphometric analysis of co-ordinate landmark configurations derived from hominin-modified Pleistocene lithic nuclei. We also introduce to lithic studies some techniques for the study of shape variation that have previously been used with success in biological morphometric analyses. 2. Crossbeam co-ordinate caliper design description and specifications The crossbeam co-ordinate caliper (hereafter, CCC) essentially consists of a base with marked scales and axes, two upright supports and rulers, and a crossbeam linking the two uprights, which also has a marked scale along its length (Fig. 1). All the materials employed are readily available. Base: the base we used had scales 300 mm in total length, which together form the four sides of a grid to be utilized as a co-ordinate system (Fig. 2). These were marked as zero at the distal and proximal ends of the length axis running down the centre of the ‘grid’, as well as at the left and right lateral ends of the width axis. Hence, the intersection of the length and width axes at the very centre of the base occupies a zeroezero co-ordinate position. Axes of 45  were also marked on the base (Fig. 2). The CCC base shown here was made on a plain background for clarity of illustration, but could also be manufactured on graph-lined paper to assist with the positioning and measuring of nuclei. Lamination of the base also aids positioning of nuclei and adds strength for extended use. Uprights: the uprights consist of two magnets, of a type designed for use in metal-welding (Fig. 1). Within these were set two steel rules (300 mm in length and 40 mm in width) obtained from engineer’s squares. The use of magnetic bases enables metal plates to be placed beneath the base for extra stability during use of the CCC. Slots (4 mm wide and 280 mm long) were cut into the upright scaled rulers in order to accommodate attachment of the adjustable, sliding crossbeam. Crossbeam: the crossbeam consists of two half-square, angled alloy strips, each of which measures 10 mm wide, 10 mm deep and 400 mm long. Placed together as they would in position during use of the CCC, they form a T-shape in cross-section.

Fig. 1. The crossbeam co-ordinate caliper.

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150mm

150mm

0

0

0

150mm

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0

Fig. 2. Schematic illustration of base with length, width and 45  axes depicted. Note that the four sides of the base are each 300 mm in length and form the basis of a grid that can be utilized as a co-ordinate system. The scales are marked as 0 mm in the centre and 150 mm at the extremities of their range. The intersection of the axes occupies a zeroezero co-ordinate position.

Holes (4 mm in diameter) drilled into either end of the crossbeam allow it to be bolted to the uprights. The bolts themselves are 4 mm in diameter and 35 mm in length. Thin nylon washers were placed directly on either side of the uprights upon the bolts, so as to aid smooth operation of the CCC when moving the crossbeam. Springs (18 mm long) placed on either side of the bolts prior to tightening, ensure the two sections of the crossbeam are firmly squeezed together which assists in accurate measuring when steel rulers are placed between them (see below). A millimetre scale (300 mm) was placed on the top portion of one of the crossbeam elements. As with the scales on the base, this was marked as zero at the centre and 150 mm at either end. When all the elements are together (i.e. base, uprights, crossbeam) the entire CCC weighs 917 g. 2.1. Protocol for orientation of nuclei prior to use of CCC Prior to the recording of measurements using the CCC it is essential that all nuclei are orientated in a standard fashion,

A

Width axis

Height axis

B

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such that morphologically homologous features may be compared across different specimens. The protocol employed is essentially a three-stage process and proceeds as follows. 2.1.1. Orientation and positioning protocol stage 1: standard orientation of nuclei Each nucleus is hierarchically oriented firstly by its ‘height’, secondly by its ‘width’ and thirdly by its ‘length’, each being orthogonal to each other and intersecting at the centre of the nucleus (Fig. 3A, B). The height of a nucleus is defined as the minimum distance in any orientation passing through the centre of its volume. In most cases this primary axis is readily identifiable. In a minority of cases (e.g. certain polyhedral type nuclei) this may need to be verified instrumentally via the use of spreading calipers normally applied in craniometric analyses. The width axis of a nucleus is orthogonal to its height and is defined as the next most minimal distance through the centre of its volume in the correct orthogonal orientation. In turn, the length of a nucleus is defined as the axis orthogonal to both the height and width axes. 2.1.2. Orientation and positioning protocol stage 2: identification of superior and inferior surfaces, and identification of distal and lateral portions of nuclei To identify the superior surface of the nucleus, it is held with one end of the height axis facing directly upward, and the ‘poles’ of the width and length axes all held in a level plane. With the nucleus positioned in this manner and a line of sight taken directly over the top of the nucleus, a view can be seen which is directly analogous to that which would appear in a 2D photographic reproduction, with the (hypothetical) end of the height axis pole appearing in the centre of the photograph. This procedure is repeated for each end of the height axis. The superior surface is defined on the basis of the view that has the least amount of cortex visible in the overhead view. Where both sides have approximately equal cortex remaining, or where no cortex is present, the superior surface is defined as the most intensely flaked surface. This is identified by counting the number of all visible negative flake scars (1 cm in length  0.5 cm in width) removed on each surface, whether complete or truncated by other flake scars. The upper surface is that with the highest number of visible flakes removed. The logic underlying both these criteria is that, on average, the most intensely flaked surface will be Height axis

Length axis

Fig. 3. Standard orientation of nuclei. Each nucleus is hierarchically orientated first by minimum height, second by width (A), and third by length (B). Each axis is orthogonal and intersects at the centre of the nucleus’ volume.

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that more extensively modified by hominin agency, and forms the focal surface for the example analyses detailed below. Once the superior surface of the nucleus has been identified the opposing surface is referred to as the inferior surface. To assist the labelling of metric variables the left side of the nucleus will be referred to as the left lateral portion, and the right side referred to as the right lateral (Fig. 4A). The position of maximum width (directly parallel to the width axis) on the correctly orientated nucleus defines its proximal end if it falls toward one end of the nucleus away from the width axis, with the opposing end of the nucleus referred to as the distal end (Fig. 4B). If maximum width happens to fall directly on the width axis line (as it might in a perfectly ovate biface) the proximal end is defined as that which has the greatest sum of all left and right lateral measurements taken on either side of the length axis line (see below, and Fig. 6). In a minority of cases where this is not readily appreciable by eye, this may prohibit firm identification of the proximal and distal aspects of the nucleus until the first series of lateral measurements have been determined. However, since these are always the first measurements to be taken, it is then a simple matter to define the left/right lateral portions and proximal/distal portions of the nucleus on the observations derived from these first measurements. 2.1.3. Orientation and positioning protocol stage 3: positioning and zeroing a nucleus upon the CCC for data collection The nucleus is positioned on the base of the CCC with the superior pole of the height axis facing directly upward, and the poles of the width and length axes all held in a level plane. It is important that the imaginary height pole of the nucleus be kept directly vertical with at least one point of the inferior surface of the core in contact with the base of the CCC, even if this is not the point at which the imaginary height pole would exit the nucleus itself. In this position the poles of both the width and length axes should be equidistant from the flat surface of the CCC base. This orientation is then held firmly in position and the nucleus is secured to the base of the CCC with plasticine, in a manner analogous to that employed routinely by

A

researchers undertaking 3D geometric morphometric analyses of biological material (e.g. [63]). It is important that the plasticine does not protrude from the maximum extremities of the nucleus (when viewed from directly overhead) in a manner that may interfere with the taking of measurements around the perimeter of a nucleus. The nucleus is then ‘zeroed’ such that the distances between the extremities of the distal/proximal and left/right lateral portions of the nucleus are minimized exactly. This is achieved by positioning the CCC over the nucleus and ensuring, with the aid of steel rulers (Fig. 5), that the distal and proximal extremities of the nucleus are equidistant from the intersection of the length/width lines on the CCC base. This is repeated for the left/right lateral extremities of the nucleus (Fig. 5). This procedure may have to be repeated several times, switching between the width and length axes of the base, until the extremities of the distal/proximal and left/right lateral portions of the nucleus are minimized to an accuracy of the nearest millimetre. It obviously assists the zeroing procedure if this stage is achieved as far as possible by eye, prior to the final stage of instrumental zeroing. It is important that the ends of the imaginary length/width poles identified in the orientation phase (step 1) of the protocol are kept equidistant from the base of the CCC, and the imaginary height pole is kept exactly vertical during the zeroing phase. 2.2. Taking measurements with the CCC The recording of data with the CCC operates on the principles of cartesian co-ordinate geometry. That is, distances between points of known geometric location can be recorded and related to the overall dimensions and shape of a lithic nucleus. With a nucleus correctly orientated and secured on the base, it is possible to position the crossbeam over the nucleus and take a series of bilateral measurements from the length line, which bisects the nucleus, to its lateral margins (Fig. 6A, B). This is achieved with the aid of a steel ruler

B

Distal end

Distal portion Left lateral

Right lateral Proximal portion

Proximal end Fig. 4. Standard morphological terminology is applied to each orientated nucleus. The left half of the nucleus is referred to as the left lateral portion, and the right half as the right lateral (A), distal and proximal portions of the core are defined accordingly (B) (see text for further explanation).

Fig. 5. Zeroing a nucleus by width. Use of steel rules and the scale along the crossbeam ensures that extremities of the nucleus are equidistant from zero.

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A

851

B

Fig. 6. Bilateral measurements taken from the length axis of the base. A total of 26 measurements were taken at percentage points left (A) and right (B) of this line.

inserted between the sections of the crossbeam (Fig. 5). The crossbeam should be set at an arbitrary level height (this can be kept precise throughout using the scaled uprights) such that the crossbeam has ample clearance as it passes down the length of the nucleus. The steel ruler should be set upright, flush with the extremity of the nucleus’ margin at a pre-designated percentage point along the length line. Thereafter, the distance from the centre (zero) line to the left and right lateral margins of the nucleus may be read and recorded using the millimetre scale along the crossbeam. It is essential that the end of the ruler is flat with the base and hence at 90  during this procedure. This can be repeated at a series of percentage points along the length line (Fig. 6A, B). It should be noted that bilateral measurements can be taken at any number of percentage points if deemed necessary for a particular research design. In the example analyses that follow, we take all measurements at the percentage points illustrated in the appropriate diagrams for each measurement description. Since zero occupies the mid-point of the scale on the crossbeam, it is necessary only to calculate percentages for one half of the length, as these will be replicated on the opposing portion of the nucleus. The crossbeam is positioned using the scales along the sides of the base, against which, the uprights are positioned (Fig. 7). The use of setsquares assists and lends greater precision to this procedure (Fig. 7). With a repositioning of the crossbeam, this entire procedure may be repeated for a series of longitudinal measurements taken from the width line of the base, thus capturing data regarding the extremities of the distal and lateral portions of the nucleus (Fig. 8A, B). All measurements are rounded up to the nearest whole millimetre. It is also possible to obtain data regarding the surface morphology of a nucleus, thus enabling substantial data from all three of its dimensions to be gained. Surface data is collected by aligning the crossbeam along one of the four major axis lines drawn on the base, and lowering the beam to a level height in contact with the surface of the nuclei in at least one place, whereupon the height of the crossbeam is recorded.

Fig. 7. Using setsquares to accurately align and position uprights along the scales of the base.

Thereafter, ‘depth’ measurements may be obtained with specially modified steel rules (Fig. 9) at percentage points along the length of the particular axis under examination (Fig. 10A). A small metal block is used to ensure that the steel rule is kept at the 90  angle required for accurate measurements (Fig. 9). For ease, measurements are read from the top of the bar and rounded up to the nearest whole millimetre (Fig. 11A). Reading from the top of the bar requires that 10 mm (the thickness of the bar) be removed from the raw data prior to analysis. At the edges of the core, depth measurements are taken to the lowest point that would be in contact with a steel ruler if held vertically aside its edge (Fig. 11B). In the example analyses that follow, measurements were taken at the same percentage points indicated in Fig. 10A, B. Depth measurements were also taken along the 45  e225  axis and 135  e315  axis (Fig. 10B). When taking the latter series of measurements, the nucleus remains secured in its original position, but the crossbeam is placed (with the aid of steel rules)

A

B

10 20 25 30 40 50 60 70 75 80 90 10 20 25 30 40 50 60 70 75 80 90

Fig. 8. Longitudinal measurements taken from the width axis of the base. A total of 22 measurements were taken at percentage points distal (A) and proximal (B) of this line.

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Fig. 9. Taking depth measurements using modified steel rules. Note that one corner of steel rule has been removed to enable easier access to any depressions in the nucleus surface. Also note the use of a small steel block to ensure the steel rule is kept at 90  throughout measurement procedure in order to increase precision.

such that the zero mark of the scale along the top of the crossbeam is located centrally along the ‘length’ of the nucleus in that particular axis. These metric data, which in their raw form are essentially distances (i.e. dimensions) between cartesian co-ordinate points, may be adjusted and manipulated (see Section 4.1.2) such that they more effectively express the shape characteristics of lithic nuclei specimens. 3. Intra- and inter-observer error assessment Methodologies with low intrinsic error and high degrees of replicability are a fundamental goal of quantitative analyses. An assessment of intra- and inter-observer error was achieved following the protocol of White and Folkens [64, p. 307], which operates on the coefficient of variation (CV) statistic. A CV is calculated by dividing the standard deviation of

a data set by its mean, and multiplying the result by 100 in order to express deviations from the mean in terms of a percentage [59]. Firstly, to assess intra-observer error levels one of us (SJL) measured all the attributes described in the previous section on three different lithic nuclei a total of three times, with one week elapsed between each measuring session. Thereafter, CVs were calculated from these three measuring sessions for each individual measurement. For the purposes of this error assessment a lava polyhedral core from Bed II, Olduvai Gorge (Tanzania), an unprovenanced quartzite Acheulean handaxe, and a chert Clactonian polyhedral core from Lion Point, Essex (England) were analysed. These three nuclei were specifically chosen for their disparity of shape, morphology and raw material. The measurement procedure for these nuclei was repeated once more by a further observer (NvCT) for comparison with each of those taken by the first observer. In this case, a CV for each measurement was calculated for the mean observation of the first observer and the measurement recorded for that particular attribute obtained by the second observer. By convention, error rates
5% are generally deemed to be acceptable in such assessments. CVs obtained by the first observer for the lava core from Olduvai ranged from 0 to 4.56, with a mean CV of 2.47 for the total data. When data were compared with the observations of the second observer this produced CVs ranging from 0.49 to 4.95, with a mean CV of 2.59. Although the mean interobserver error was higher than mean intra-observer error, differences between the two series of CV values were not found to be significant when CV groups were compared statistically by Wilcoxon’s signed ranks test (exact p ¼ 0.716) [14,26]. CVs obtained by the first observer for the unprovenanced handaxe ranged from 0 to 4.88 with a mean CV of 2.39. When these data were compared with observations by the second observer this produced CVs ranging from 0 to 4.76, with a mean of 2.42. Although the mean inter-observer error was again higher than mean intra-observer error, differences between the two series of CV values were not significant when subjected to Wilcoxon’s signed ranks test (exact p ¼ 0.822). CVs obtained by the first observer for the Clactonian polyhedral nucleus ranged from 0 to 4.92 with a mean CV of 3.03. When these data were compared with observations by the second observer this produced CVs ranging from 1.03 to 4.95, with a mean of 2.89. Hence, in contrast to the previous nuclei,

A

B 0

10

20 25 30 35 40

50

60 65 70 75 80

90 100

0 10 20 25 30 40

50

60 70 75 80 90 100

Fig. 10. (Schematic) Depth measurements taken from the crossbeam to the superior surface of nucleus. A total of 15 measurements were taken at percentage points along the length axis of the base (A) and 13 depth measurements were taken for the additional three axes of the base (B).

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A

853

B

Fig. 11. (Schematic) (A) Depth measures are taken with the crossbeam level and in contact with superior surface of nucleus. Measurements are read from the top of the crossbeam. (B) Taking depth measurements at the edges of nuclei. Measurements are taken at the lowest point in direct contact with steel ruler held vertically against this edge.

mean inter-observer error was found to be lower than mean intra-observer error. However, differences between the two series of CV values were again found not to be significant when assessed statistically (exact p ¼ 0.10). In sum, both intra- and inter-observer error fell within acceptable limits, and even when inter-observer error comparisons produced higher mean CVs than intra-observer assessments, there is no evidence that such differences produce statistically significant effects. Such consistency is perhaps not surprising when the simplicity of operating the CCC is taken into consideration. All an observer needs to do is to be able to co-ordinate two metric rulers at one time, ensure some basic controls are adhered to (e.g. that rulers are always at 90  ), and read-off the measurements accordingly. 4. Discriminant function analysis of morphometric variables derived from the crossbeam co-ordinate caliper In order to illustrate some of the potential utility of variables captured by the CCC for the comparison of lithic nuclei variability, we undertook two separate analyses. 4.1. Materials and methods A total of 85 hominin-modified lithic nuclei dating from the Pleistocene were analysed from three different localities. Thirty nuclei were bifacial handaxes made on quartzite cobbles and large flakes from Attirampakkam, Tamil Nadu, southeast India [11,45]. A further 30 handaxes, made on chert, came from Saint Acheul, France. Typologically, both the Attirampakkam and St. Acheul material would be assigned to the Mode 2 technocomplex if Clark’s [8] terminology were employed. The remainder of the sample was comprised of 25 non-handaxe specimens consisting of ‘chopper’ cores (n ¼ 4), polyhedral cores (n ¼ 16) and crude discoidal-type cores (n ¼ 5). All were made on quartzite cobbles and collected from the Soan River Valley (Siwalik Hills), northern Pakistan [11]. Employing Clark’s [8] terminology, this assemblage may collectively be assigned to a Mode 1 techno-complex.

The limited sample sizes, and perhaps even the collection history of these lithic artefacts, place constraint upon the nature of interpretations that may be made in the light of the following analyses. However, they do allow statements to be made regarding the comparative morphologies of the nuclei that have been measured and the groups concerned, at least as we have partitioned them for the analyses (i.e. by locality). The main issue is whether these analyses suggest that employment of the CCC provides data that may be useful in future analyses of lithic nuclei of the general type examined here. All the material analysed is under the care of the Cambridge University Museum of Archaeology and Anthropology, Cambridge, UK. 4.1.1. Discriminant function analysis (DFA) DFA is a multivariate technique that is used to provide a set of weightings (i.e discriminant functions) that most effectively discriminate between groups that have been defined a priori; these weightings are linear combinations of the independent variables [21,22,46]. The weightings maximise the probability of correctly assigning individuals within each group to their respective groups, thus potentially allowing individuals of unknown group assignation to be grouped with a probability estimation of accuracy. It is also possible to test the effectiveness of the discriminant function in producing significant differences between the groups, using the Wilks’ lambda statistic [26]. Additionally, DFA ranks variables according to their relative effectiveness in discriminating between groups. Hence, DFA can be employed to identify which independent variables are most important in assigning individuals to groups. The DFA was undertaken using SPSS v.12.0.1. 4.1.2. Compilation of the metric data set Metric measurements were recorded as described in Section 2.2 and compiled into a data set composed of 55 variables. This data set contained 49 size-adjusted Euclidean distance variables, four ‘coefficients of surface curvature’, a ‘coefficient of edge point undulation’ and an ‘index of symmetry’ for each

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of the 85 lithic nuclei analysed. The computation and adjustment of these variables are described in the following sections. 4.1.2.1. Size-adjustment of Euclidean distance variables. The left/right lateral and distal/proximal measurements taken either side of the length and width axes of the CCC base (Figs. 6 and 8), created a total of 49 Euclidean distance variables. These data were size-adjusted in order to emphasize (allometric) shape differences between individual specimens. Previous work by Crompton and Gowlett [10,18,19] has shown that many Acheulean bifaces exhibit allometric (i.e. size-related) shape differences. An important corollary of this is that attempts to examine shape differences in lithic products should attempt to account for the effects of isometric size prior to the analysis of shape [10,33]. Although lithic archaeologists have given relatively little concern to such matters, attempts to remove the effects of isometric scaling in order to compare allometrically-scaled shape differences are now routine in biological morphometric analyses [15,24]. However, some popular methods for size-adjustment have received criticism. Dividing each variable by a single measurement designated to represent ‘size’ (such as maximum length or height of an individual) has been criticized since it has been shown not to fully remove correlations with size [47]. McPherron [33] highlighted the problems of such a method as employed by Wynn and Tierson [65] during their study of handaxe morphology. Regression-residual based methods that observe deviations from an allometric regression line based upon a proxy ‘size’ variable, have also been heavily criticized on the grounds that they are biased by the composition of the data set [3], adversely affected by outliers [15] and by the particular line-fitting technique employed to obtain the initial best-fit regression line [3,31]. Given the problems associated with these methods, geometric mean size-adjustment was selected here. This method isometrically corrects for size enabling direct comparison of allometric shape variation yet, unlike regression based methods, is not dependent upon the composition of the data set. Size-adjustment via this method has become increasingly popular in biological morphometric analyses of shape (e.g. [1,9,28,62]). The geometric mean is one of the Mosimann family of size variables [37,38]. Like the arithmetic mean, the geometric mean provides a measure of central tendency, but it is not as strongly influenced by outliers or deviations from the modal data. The geometric mean ðGMx Þ may be computed as: sffiffiffiffiffiffiffiffiffiffi n Y n GMx ¼ xi

ð1Þ

i¼1

where xi ¼ individual variables to be size-adjusted, and n ¼ number of individual variables to be size-adjusted. Simply, the geometric mean is the nth root of the product of all n variables [24,59]. Size-adjustment of the data proceeds on a specimen-by-specimen basis, dividing each variable in turn by the geometric mean of all variables for that individual specimen.

This procedure effectively equalizes the volume of all specimens in a sample, creating a dimensionless scale-free variable while maintaining the original shape information of the data [15,24]. Size-adjusted Euclidean distance data were supplemented by additional variables labelled and calculated as described in the following sections. 4.1.2.2. Coefficient of surface curvature. A ‘coefficient of surface curvature’ was calculated by taking the standard deviation of the depths along an axis, and dividing this by the length of that axis. Hence, the coefficient of surface curvature emphasizes relative variation over the length of each axis. This measure is necessary since the raw individual depth measures along each axis are not necessarily correlated with the size of each nucleus as in the case of the inter-landmark Euclidean distances. This is readily appreciable conceptually if one visualizes the case of a large flat nucleus with a high geometric mean yet which, due to its flat superior surface, has relatively small depth measures. Such a situation can be contrasted with the case of a far smaller nucleus, which is highly domed on its superior surface and hence has relatively high depth measures. Four coefficients of surface curvature were calculated here for the length, width, 45  e225  and 135  e315  axes. 4.1.2.3. Coefficient of edge point undulation. A ‘coefficient of edge point undulation’ was determined by computing the standard deviation of the depths at the endpoints of the length, width, 45  e225  and 135  e315  axes (i.e. eight variables in total) and dividing this by the geometric mean of the lengths of the four axes. (Note that any differences between the height settings of the bar when taking the initial endpoint depth measurements across each axis (see Section 2.2) need to be determined and accounted for prior to calculation of the coefficient of edge point undulation.) 4.1.2.4. Index of symmetry. Symmetry is not a major focus here, for which rigorous methodologies (at least for biface outlines) are now available [54]. However, it is possible to create an ‘Index of Symmetry’ from the data collected here that, as part of a multivariate analysis, allows relative bilateral symmetry to be assessed. The index of symmetry may be computed as: 0qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 2 n X ðXi  Yi Þ @ A Xi þ Yi i¼1

ð2Þ

where Xi ¼ the width value left of the length line taken at a particular percentage point, Yi ¼ the width value right of the length line taken at the corresponding percentage point, and n ¼ the number of percentage points at which Xi and Yi are taken. Hence, a value of zero would correspond to perfect bilateral symmetry. 4.2. Results of DFA

for

Fig. 12 shows a plot of the DFA scores (functions 1 and 2) individual lithic nuclei from the Soan Valley,

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a quantitative manner. These results suggest that important aspects of shape variation in lithic nuclei are not being quantitatively analysed by traditional methodologies. DFA (along with other related multivariate techniques such as principal components analysis and canonical variates analysis) is the type of methodology that, despite being widespread in other sciences and morphometric analyses, has infrequently been applied to morphometric variables of lithic nuclei. This may be due to a paucity of such variables captured by traditional techniques, especially outside of bifacial assemblages. However, the DFA performed here employing the CCC, provides more than enough hints that future analyses of these types of data would be fruitful. It is important to note that data obtained from the CCC could also be supplemented by data taken by traditional methods (e.g. flake scar counts, flake scar size, position and percentage of cortex, etc.). The introduction of new metric variables should be seen as useful adjuncts to traditional data, not necessarily as direct replacements [12].

4

2

0

Function 2

855

-2

-4

-6 -6

-4

-2

0

2

4

6

8

Function 1 Fig. 12. Discriminant functions plot for 55 variables recorded on material from Soan Valley, Pakistan (B), Attirampakkam, India (>) and St. Acheul, France (*). Differences between centroids (-) are significant (Wilks’ lambda ¼ 0.21, df ¼ 108, p < 0.0001) on DF 1. The six variables most highly correlated with DF 1 were the coefficient of surface curvature along the width axis, the index of symmetry, the left lateral measure at 40% of width, left lateral measure at 35% of width, the coefficient of edge point undulation, and the coefficient of surface curvature for the 135  e315  axis.

Attirampakkam and St. Acheul. Under the DFs produced, 98.8% of the nuclei would be correctly assigned to their a priori defined group. On the first DF (88.4% of variation) the centroid of the Soan Valley Mode 1 cores is clearly differentiated from those of the Attirampakkam and St. Acheul Acheulean bifaces. Differences between centroids on this DF are significant (Wilks’ lambda ¼ 0.21, df ¼ 108, p < 0.0001). Differences between centroids on the second DF (11.6% of variation) were not significant (Wilks’ lambda ¼ 0.338, df ¼ 53, p ¼ 0.231). The six variables most highly correlated with DF 1 were the coefficient of surface curvature along the width axis, the index of symmetry, the left lateral measure at 40% of width, left lateral measure at 35% of width, the coefficient of edge point undulation, and the coefficient of surface curvature for the 135  e315  axis. 4.3. Discussion of DFA It is notable that at least three of the variables out of the top six that load most highly on DF 1 are precisely the type of variables that have not previously been quantitatively examined in lithic nuclei (i.e. the coefficient of surface curvature along the width axis, the coefficient of edge point undulation, and the coefficient of surface curvature for the 135  e315  axis). Even an attribute such as symmetry, the second most highly correlated variable with DF 1, has not previously been examined between Mode 1- and Mode 2-type assemblages in

5. 3D geometric morphometric analysis of surface morphology Given the protocol for acquiring Euclidean distance measures from lithic nuclei described above, it is possible to extend the methodology to derive 3D cartesian co-ordinates from the raw data collected using the CCC. The dearth of landmarks available on lithic nuclei is particularly problematic in the case of 3D co-ordinate analyses that crucially depend on such data. Even a traditional measurement, such as ‘maximum width’, which may be considered a homologous feature when employed as a Euclidean distance, does not provide two discrete homologous landmarks at each of its termini if the relative position of the measurement can vary widely, or can occur at different points along a nuclei and hence is not represented by a unique pair of landmarks [4 (p. 2),66 (pp. 174, 178, 179)]. In such circumstances, only geometrically defined landmarks that remain morphologically homologous to each other regardless of shifting morphology can be employed in 3D analyses. Such geometrically defined landmarks would be termed ‘semi-landmarks’ under Bookstein’s [5] revised landmark terminology. Fig. 13 illustrates 51 landmarks on the lithic nuclei for which information on their location in 3D space can be derived. The principle of deducing (x, y, z) co-ordinates (hereafter referred to as ‘landmarking’) using the CCC is based on the understanding that the origin (0, 0, 0) lies at the intersection of the orientation lines on the base of the CCC. The X-axis follows the width line of the CCC base (i.e. the 90  e270  line), which bisects the nucleus into its proximal and distal portions The Y-axis follows the length line of the base (i.e. the 0  e180  line), dividing the nucleus bilaterally into its left and right halves. The Z-axis projects orthogonal to these from the base and is assumed to bear positive values when landmarking the superior surface of the lithic nucleus. The X- and Y-axes bear both positive and negative values, as in traditional geometric axis (see Fig. 13). The 45  e225  line on the base also yields geometric landmarks and is read from the right distal quadrant to the left proximal one (following

S.J. Lycett et al. / Journal of Archaeological Science 33 (2006) 847e861

856

Positive

Conversely, landmark co-ordinates are zero-dimensional and only contain information on form when presented and analysed as a configuration, where relative positioning of landmarks holds useful ‘shape’ information. 5.2. Materials and methods

Negative

Y 0.00

ve ati

g Ne

Z ive sit Po

0.0

0

Negative

0.00

X

Positive

Fig. 13. Configuration of 51 landmarks employed for the 3D analysis of nuclei surface morphology. All landmarks are located in 3D space along four lines of CCC base orientation, where X ¼ 0 (width), Y ¼ 0 (length) and two axes where X ¼ Y (45  e225  ; 315  e135  ). Landmark 8 occupies the X, Y origin (0, 0, Z ) and is derived from measurements taken along the 0  e180  length axis. The core can be divided into four 2D quadrants, based on segments left and right of the Y-axis, and proximal and distal to the X-axis.

nucleus orientation rules). Similarly, the 135  e315  line is read from the left distal quadrant to the right proximal one. 5.1. Geometric morphometrics Geometric morphometrics is an analytical approach to shape analysis that operates on co-ordinate data in a nonEuclidean shape-space [25] for which the geometric and statistical properties are well defined ([43] and references therein). Co-ordinate based shape analysis has already gained widespread support and recognition amongst biologists and palaeontologists. Therefore, a detailed explanation of the methodologies involved will not be given here. Those unfamiliar with geometric morphometrics should find the following publications of interest [4,13,29,30,42e44,50e52,67]. Geometric approaches offer advantages in terms of statistical robusticity [50,51] over other methodologies including the multivariate analysis of morphological variables such as outlines (Elliptical Fourier analysis) and Euclidean distances. However, data of the latter varieties contain information on the dimensions of an object and therefore represent discrete morphological properties. Discrete data may be especially important in some types of analysis if specific elements of nuclei shape need to be compared directly in a particulate manner.

The 85 nuclei employed in the previous DF analysis were utilized for the 3D analysis (see Section 4.1). Employing the same positional and depth data as that collected for the previous analysis, x, y and z co-ordinates were determined for each of the 51 landmarks illustrated in Fig. 13 using the protocol described in Appendix. The raw (x, y, z) co-ordinates for the 85 lithic nuclei were compiled into a single input file for the geometric morphometrics package Morphologika, available online at http://www.york.ac.uk/res/fme/resources/software.htm [41,42,44]. This software minimizes scaling, translational and rotational differences by Generalised Procrustes Analysis (GPA) [4,16,17,44,52] and conducts a Principal Components Analysis (PCA) on landmark residuals. PCA is a multivariate procedure that identifies and extracts uncorrelated variables (i.e. principal components) from a set of inter-correlated raw variables, such that the major variation between specimens can be described and quantified [14,46,57]. Of the principal components extracted, each consecutive PC explains less of the original variation. 5.3. Results of 3D geometric morphometric analysis Fig. 14 shows the plot of the first two principal components (PCs) from the 3D geometric analysis of the Soan Mode 1 assemblage, Attirampakkam handaxes and the St. Acheul handaxes. The wireframe diagrams at the termini of the PC axes illustrate the ‘shape’ occupying the extreme position in PC shape-space and do not necessarily refer to any specific nucleus morphology. By moving along an axis it is possible to visually detect the shape changes that characterise the particular PC. In PC1 (36.8% of the total variation), the extreme negative terminus of the axes is characterised by domed and more circularshaped nuclei, while the extreme positive end is occupied by very flat and pointed nuclei. PC2 (17.5% of total variation) also contains considerable information about the shape differences amongst these assemblages. The negative end of this range is characterised by flat, rounded nuclei and is dominated by specimens belonging to the Mode 1 Soan assemblage, while the positive end is dominated by domed and pointed individuals belonging to the handaxe assemblages. It is interesting to note that the two bifacial assemblages differ more on PC2 than on PC1, indicating a slight separation between individuals that are relatively more ovate and flat, compared with individuals pointed in outline and more domed in crosssection. Fig. 15 illustrates PC1 against PC3 from the same analysis. PC1 contains exactly the same information as in the previous figure, but PC3 (8.3% total variation) appears to exhibit differential bilateral asymmetry. The negative terminus of PC3 expresses lateral flattening towards the left side of nuclei,

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857

0.18 0.16

PC2

0.14 0.12 0.10 0.08 0.06 0.04

PC1 -0.28

-0.24

0.02 -0.20

-0.16

-0.12

-0.08

-0.04 -0.02

0.04

0.08

0.12

0.16

0.20

-0.04 -0.06 -0.08 -0.10 -0.12 -0.14 -0.16 -0.18

Fig. 14. Plot of PC1 and PC2 for the 3D geometric morphometrics analysis of 51 surface landmarks. Soan Mode 1 (B), Attirampakkam handaxes ( ), St. Acheul (A). Superior and lateral views of wireframe diagrams representing the extreme shapes at termini of axes are included to aid interpretation of shape differences between groups.

whereas the positive end describes lateral flattening on the right side of nuclei. While both the Soan assemblage and the bifacial assemblages occupy some space on PC3, the Soan assemblage occupies a much greater range, indicating a greater tendency for these nuclei to exhibit bilateral asymmetry. Although the bifacial assemblages also exhibit some degree of asymmetry, they do so to a lesser degree indicated by their clustering around the low positive and low negative values of PC3. However, PC3 contains additional information regarding edge points that would account for the source of this asymmetry that could not be expressed by outline analysis alone. This is visible in the side-view wireframe diagrams for PC3 (Fig. 15), which indicates that the left and right lateral flattening of outline appears to correlate with relatively lower edge points. 5.4. Discussion of 3D geometric morphometric analysis The changes along each of the PCs derived from the 3D geometric morphometric analysis essentially reflect the morphological variables that best distinguish individual nuclei and, ultimately, assemblages. Hence, the Soan Mode 1 nuclei are broadly distinguishable from the bifacial assemblages by being more domed in terms of their surface convexity and being round in their general outline profile on PC1. In contrast, bifaces are generally much flatter and more elongate. The handaxe assemblages appear to vary between relatively more ovate and flat surfaces at one extreme of their morphological

range, to pointed outlines and more rounded surface morphologies at the opposite end of their shape variation (PC2). PC3 appears to account for bilateral asymmetry due to a flattening of outline profile, that also appears to be explained by a correlation between flatness of outline and relatively lower edge points along the sides of the nuclei. Such quantification procedures, both within and between assemblages of these types, may have implications in more detailed analyses, which attempt to investigate potential relationships between shape variation in lithic nuclei and factors such as raw material, reduction intensity, regional differences, etc. In future studies, this protocol could be extended in a number of ways. For instance, it is possible to acquire more information along any of the four base axes described here by further sub-division into more percentage points. Moreover, by recording the edge-point depths of the lateral measurements from the length and width lines, it would be possible to gain more detailed outline information. Such additional landmarks may prove useful to researchers interested in outline symmetry, outline regularity and/or undulation across specimens. Finally, by recording Euclidean distances on the inferior side of the nucleus, it is possible to combine data from the superior and inferior surface in a cross-platform morphometrics software program such as Morpheus [58] to create an entire 3D representation of any lithic artefact. One such representation, employing the latter two of these potential methodological extensions, was created for 118 landmarks

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858

0.12 0.10

PC3

0.08 0.06 0.04 0.02

PC1 -0.28

-0.24

-0.20

-0.16

-0.12

-0.08

-0.04 -0.02

0.04

0.08

0.12

0.16

0.20

-0.04 -0.06 -0.08 -0.10 -0.12 -0.14 -0.16 -0.18

Fig. 15. Plot of PC1 and PC3 for the 3D geometric morphometrics analysis of 51 surface landmarks. Soan Mode 1 (B), Attirampakkam handaxes ( ), St. Acheul (A).

recorded on both the superior and inferior surfaces of a handaxe from St. Acheul, and is illustrated in Fig. 16. Although this is included here for purely graphical purposes, extension of the geometric methodology could result in full-scale analyses of the 3D morphology of lithic nuclei. Moreover, with this type of methodological extension it would be

Y

0.00

Z

X 0.00

Y

X

Z

Fig. 16. Full-scale 3D representation of a St. Acheul biface, combining a total of 118 landmarks on both the superior and inferior surface of the lithic nucleus.

possible to conduct a 3D investigation of biface (a) symmetry, which has hitherto been impossible. 6. Discussion and conclusions D’Arcy Thompson [61, p. 269], one of the pioneers of biological morphometrics, once stated that in science ‘‘we begin by describing the shape of an object in the simple words of common speech: we end by defining it in the precise language of mathematics; and one method tends to follow the other in strict scientific order and historical continuity’’. We suggested at the outset of this paper that a fully developed and productive science of quantitative lithic shape analysis was still far from realised. While there are encouraging recent signs of development in lithic circles, it is doubtful whether the same degree of revolutionary advancement has taken place in our own field as that of other disciplines. Indeed, it may even be argued that much of lithic shape analysis remains rooted in the potentially ambiguous language of qualitative description (i.e. the earliest stage of D’Arcy Thompson’s sequence of scientific development). The example multivariate and 3D geometric morphometric analyses we present here suggest that interesting aspects of shape variation in Pleistocene lithic nuclei could be collected and analysed by employing a device such as the CCC. Such attributes are largely unanalysed via traditional methodologies of data collection, yet remain important in testing ideas concerning the potential significance of lithic shape variation, be it due to cultural differences, raw material, reduction intensity, etc. Moreover, the instrument we describe is lightweight,

S.J. Lycett et al. / Journal of Archaeological Science 33 (2006) 847e861

portable, inexpensive, easy to operate, and yet accurate enough to recover meaningful and interpretable results. The methodology for data collection is flexible enough to be adjusted to collect a greater or lesser quantity of data, or target more attributes in detail, if specific research aims deemed this appropriate. It is worth repeating that any data collected by the CCC can be augmented by additional data collected by traditional techniques of lithic analysis. It may even be possible for researchers working in different regions to build directly comparable quantitative databases of lithic attributes, enabling greater scope for inter-regional or inter-continental research programmes to be undertaken. Acknowledgments We are especially indebted to Norbert von Cramon-Taubadel for helping to turn our paper scribbles and ramblings into material reality. Chris Clarkson, Mark Collard and Marta Mirazo´n Lahr provided valuable conversations. We are also grateful to Parth Chauhan and John Grattan for helpful and perceptive comments. Access to lithic material and hospitability during data collection was gratefully received from Anne Taylor, Assistant Curator, Cambridge University Museum of Archaeology and Anthropology. SJL is supported by a Trinity College, University of Cambridge Research Scholarship. NvCT is supported by St John’s College, University of Cambridge and a Gates Trust Scholarship. Appendix A. Deriving landmarks 0  e180  Landmarks 1e15 lie along the length line of the base (0  e 180  ), which corresponds to the Y-axis (see Fig. 13). Hence, they all have x-values of 0. The y-values are the actual percentage values along the length line and the z-values can be calculated from the depth measurements recorded below the crossbeam at those percentage points. For example, if the overall length of a nucleus were 120 mm, then landmark 2 (corresponding to 10%) would lie at 12 mm along the line. This landmark might have a depth of 3 mm below the crossbeam, positioned at 60 mm above the base. The x-value in this case is 0; the y-value is 12 and the z-value can be computed as: 60  3 ¼ 57, giving a co-ordinate of (0, 12, 57). Landmark 8, which lies at the X, Y intersection, has x- and y-values of 0, and a z-value calculated from the depth measurement at that point. Landmarks 9e15 differ by having negative y-values. 90  e270  Landmarks 16e27 lie along the width line of the base (90  e270  ), corresponding to the X-axis (Fig. 13). They all have y-values of 0. The x- and z-values for these landmarks are calculated as before, with x-values corresponding to the percentage values along the width line and z-values being computed from depth measurements as above. In this case landmarks 16e21 have negative x-values.

859

45  e225  and 135  e315  The 45  e225  and 135  e315  base line landmarks (28e 51) differ slightly from the other landmarks in their deduction protocol. This is because the nucleus is zeroed relative to the length (Y-axis) and width (X-axis) lines only (see Section 2.1.3). When the depths are taken along the 45  e225  and 135  e315  lines, the CCC crossbeam is moved relative to the base, such that the zero of the crossbeam and the intersection of the base axes no longer align. This movement of the CCC along these base axes must be accounted for when deriving the landmark co-ordinates. The following protocol is followed: (1) The CCC is lined up along the 45  e225  (or 135  e315  ) line such that the zero of the crossbeam and the intersection of the base axes are aligned. The distance to both edges of the nucleus edges along the 45  e225  (or 135  e315  ) line are recorded. (2) The CCC is moved along the 45  e225  (or 135  e315  ) line such that the nucleus edges (corresponding to landmarks 28/39 or 40/51) are equidistant from the zero of the crossbeam. Percentages along the total length are calculated and the depth values at these percentages are recorded. (3) The x- and y-values for the distal endpoints (landmarks 28 and 40) are calculated first and then all other landmarks along the line can be deduced. Any point which lies on a line at a 45  angle to the X, Y plane, has equal x and y co-ordinate values, assuming equal scaling of the axes. The length of a line from a point (xi, yi) to the origin (0, 0) in 2D space is equal to:

D¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 ðxi  0Þ þðyi  0Þ

But since xi ¼ yi on the 45  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 D ¼ ðxi  0Þ þðxi  0Þ qffiffiffiffiffiffiffiffiffiffiffiffi D ¼ 2ðxi Þ2 2

D ¼ 2ðxi Þ

ðA1Þ

2

D2 ¼ x 2 i 2 rffiffiffiffiffiffi D2 xi ¼ 2 where D equals the distances from the zero of the crossbeam to the distal edge of the nucleus prior to equalizing the distances (as in step 2 above). Example. If the distal edge corresponding to landmark 28, is 60 mm distant from the zero of the crossbeam prior to realigning p ffiffiffiffiffiffiffiffiffiffiffiffi the CCC, the x- and y-values of landmark 28 are 602 =2 ¼ 42:43. The z-value will be the depth measurement taken at the edge. Therefore, if its value is a depth of 15 mm taken from a crossbeam at a height of 63 mm the z-value will

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be 48. Given that X ¼ þY in the right distal quarter, the coordinate for this landmark is (42.43, 42.43, 48). (4) Once the distal edge landmark has been calculated (where xi ¼ yi), the (x, y) co-ordinates for all other percentage points (x) along the 45  e225  (or 135  e315  ) line are computed as: sffiffiffiffiffiffiffiffiffiffiffiffi ðaDÞ2 x¼  xi 2

ðA2Þ

where D ¼ total length of the 45  e225  (or 135  e315  ) line from endpoint to endpoint. a ¼ percentage point along the axis line as a decimal (e.g. 10% ¼ 0.1) As before, the z-values are calculated as the height of the crossbeam in that orientation minus the depth taken at that percentage point. The only other aspect of the protocol is to assess whether X ¼ Y in that quarter (see Fig. 13), and thereby assign negative or positive prefix signs to the x- and y-values. References [1] R.R. Ackermann, Ontogenetic integration of the hominoid face, Journal of Human Evolution 48 (2005) 109e217. [2] D.C. Adams, F.J. Rohlf, D.E. Slice, Geometric morphometrics: ten years of progress following the ’revolution’, Italian Journal of Zoology 71 (2004) 5e16. [3] L.C. Aiello, Allometry and the analysis of size and shape in human evolution, Journal of Human Evolution 22 (1992) 127e147. [4] F.L. Bookstein, Morphometric Tools for Landmark Data, Cambridge University Press, Cambridge, 1991. [5] F.L. Bookstein, Landmark methods for forms without landmarks: localizing group differences in outline shape, Medical Image Analysis 1 (1997) 225e243. [6] F. Bordes, Typologie du Pale´olithique Ancien et Moyen, Me´moires de l’Institut Pre´historiques de l’Universite´ de Bordeaux 1, Delmas, Bordeaux, 1961. [7] P. Callow, A comparison of British and French Acheulean bifaces, in: S.N. Collcutt (Ed.), The Palaeolithic of Britain and its Nearest Neighbours: Recent Trends, University of Sheffield, Sheffield, 1986, pp. 3e7. [8] G. Clark, World Prehistory: A New Outline, second ed. Cambridge University Press, Cambridge, 1969. [9] M. Collard, B. Wood, How reliable are human phylogenetic hypotheses? Proceedings of the National Academy of Sciences USA 97 (2000) 5003e 5006. [10] R.H. Crompton, J.A.J. Gowlett, Allometry and multidimensional form in Acheulean bifaces from Kilombe Kenya, Journal of Human Evolution 25 (1993) 175e199. [11] H. De Terra, T.T. Paterson, Studies on the Ice Age in India and Associated Human Cultures, Carnegie Institute, Washington, DC, 1939. [12] H.L. Dibble, P.G. Chase, A new method for describing and analyzing artifact shape, American Antiquity 46 (1981) 178e187. [13] I.L. Dryden, K.V. Mardia, Statistical Shape Analysis, John Wiley, London, 1998. [14] C. Dytham, Choosing and Using Statistics: A Biologist’s Guide, second ed., Blackwell Science, Oxford, 2003. [15] A.B. Falsetti, W.L. Jungers, T.M. Cole III, Morphometrics of the callitrichid forelimb: a case study in size and shape, International Journal of Primatology 14 (1993) 551e572. [16] C.R. Goodall, Procrustes methods and the statistical analysis of shape, Journal of the Royal Statistical Society B 53 (1991) 285e340.

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