Computational protocol: Relative Importance of Modularity and Other Morphological Attributes on Different Types of Lithic Point Weapons: Assessing Functional Variations

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[…] The sample used here is an extension of the one used on a previous paper, and consists of Late Holocene lithic points (n = 118) from southern Patagonia(southern Santa Cruz Province, Argentina and Magallanes, Chile) .Projectile points were classified as Bird IV–Vtypes by their own discoverers (see ref. 9), except 14 pieces corresponding to sitesstudied by one of us (JC, Cóndor cave 1, Norte 2, Laguna Azul, and Laguna Cóndor) or belonging to previous collections that were reanalyzed to recover geometric-morphometric data. Further details regarding the archaeological, geological, and bio-anthropological context for this sample are provided in ref. 9.Photographs were taken on completed points by one of us (JC) in surface and subsurface archaeological surveys along the region, and on digitized images of points published in the literature. Lithic points were assigned to two different typological categories according to Bird's – pioneering classification (see a detailed review of this classification system in ref. 9). Classification under the different criteria as well as further qualitative and quantitative data of each point is presented on .Only complete, non fragmentary points were taken into account. Small damages (≤3 mm) were tolerated and the shape was rebuilt from the adjacent planes of the piece. Illustrations and photographs were scanned in a digitizing tablet, keeping constant the digitizing scale (100% in cm), resolution (100 dpi), and point orientation (the tip towards the upper border). The raw images were compiled and scaled in the TpsUtil and TpsDig2 programs respectively , . A total of seven landmark and 17 semi-landmark coordinates were digitized on the contour of the points in order to achieve a good representation of its size and shape (). Landmark configurations were superimposed using a Generalized Procrustes Analysis (GPA, 28, 29), and sliding semi-landmarks were relaxed following the minimum bending energy criterion implemented in the TPSRelw (version 1.45) software . GPA removes the effects of translation, rotation, and scaling , , . After superimposition, pure shape information is preserved in the specimens' aligned landmarks. Size is calculated as the centroid size, the square root of the summed distances between each landmark coordinate and the centroid . Subsequent analyses were done with the complete, 24-landmark configuration, or else with partial configurations consisting of blade-alone landmarks (1 to 9 and 17 to 24 in ), or stem-alone landmarks (10 to 16 in ).The Procrustes superimposed coordinates were further used to obtain angle measurements, proportions, and asymmetry values for each point. Specifically, we computed the tip angle (TA, in plain view), the ratio of blade length to stem length (IBS), and asymmetry values (AS) as indicated in . Tip angle and the index blade-stem length were chosen because previous experimental and comparative studies (reviewed in ref. 9) have shown that, given that the major size and shape changes associated to successive cycles of use and resharpening occur in the point blade, mainly in its length and tip angle –, then they can be considered as reliable reduction estimators. In some specific analyses, we attempt to minimize the effects of reduction on shape by regressing the shape coordinates on IBS and/or TA. Departing from previous comparative and experimental studies (see a review on ref. 9), and assuming that IBS or TA are good proxies to represent reduction phases, then the residuals of the regression of shape on IBS/TA can be seen as the portion of shape variation that is preserved in the data when the effects of reduction are removed.Asymmetry individual scores quantify the individual asymmetries of shape (as deviations from the mean asymmetry) by using Mahalanobis distances, which are scaled relative to the variation of asymmetry in the sample.The analysis of the point modularity was done considering the hypothesis that the blade and the stem are distinct modules. If this hypothesis is true, each of these regions should be highly integrated internally and relatively independent to the other region. Modularity can be assessed by analyzing covariation among subsets of landmarks , . Since a strong covariation within modules does not contribute to covariation between subsets, a weak covariation among hypothetical modules is expected if the subconfigurations of landmarks closely resemble the true ones , . Conversely, if the blade and stem do not fit to the true modules, the weak within-module integration contributes to the covariation among sub-configurations that will therefore be stronger. Overall, it is expected that covariation among subsets is weaker for subsets corresponding to the true modules than for other partitions of the landmarks into subsets . To assess the hypothesis of blade versus stem modularity, we computed the multisetRV coefficient . The RV coefficient is a measure of the strength of internal (within module) covariance relative to external covariance. Then, the analysis compares the RV coefficient or multi-set RV coefficient for the partition of the landmark configuration into the hypothesized modules with alternative partitions into subsets of the same numbers of landmarks . The multiset RV coefficient was computed from the Procrustes-aligned coordinates of the landmarks of the blade and stem, before and after correcting for the effects of size, IBS and TA, and for 10,000 random partitions of the total set into random subsets containing the corresponding numbers of landmarks. Size-, IBS- and TA-corrected shape data was obtained by using the residuals of the multivariate regression of the Procrustes aligned shape coordinates against the centroid size, IBS and TA respectively.The complete configuration, as well as the blade and stem sub-configurations, was submitted to three independent Principal Component analyses (PCA) of shape in order to obtain axes of maximum shape variation for the whole points, the blades, and the stems. The first PCs of each analysis, depicting the main trend of shape variation on each configuration, along with the tip angle (TA), the index blade length/stem length (IBS), the point size (cs), and the asymmetry scores (AS) were collectively submitted to a further Principal Component analysis in order to synthesize data and explore the relative contribution of each trait to the total variation observed in the sample. Since the different attributes are measured on different scales, the matrix of correlation was used as the basis to perform the composite PCA. Even though TA and IBS are indeed shape indicators, we have decided to include it on the composite PCA along with the pure shape variables (first PC of the Procrustes coordinates) because TA and IBS refer to specific shape attributes that have been previously used to control the effects of reduction. There are other portions of shape variation that, with some probability, does not respond to resharpening effects. In consequence, the necessity of maintaining it separated from the complete approach to shape (PCs of shape coordinates) respond to enable comparisons with previous using of TA and IBS as reduction-dependant variables. Note that the intention of the composite PCA is to collectively and simultaneously explore the full shape variation, specific shape variation previously associated to reduction (IBS, TA), asymmetry, and size. Of course, any correlation among the behaviour of these variables will be accounted for the composite PCA, for instance, by sorting correlated traits along the same PC. […]

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