As many of you know, we have slowly been scanning (3D) all of the dart points from the United States Forest Service (USFS) collections in East Texas. We still have a ways to go yet; however, using the geomorph package in R, we have begun to make our way through a few initial iterations of that analysis, and–as always–would like to hear your thoughts regarding how we might better our efforts (my email = email@example.com).
We are scanning the points in 3D; however, while thinking through the analysis I usually begin in 2D–particularly since I want a landmark configuration that can be used for both 2D and 3D data; similar to the approach we are using for ceramics (like ceramics, there are no shortages of 2D images of lithics in the gray literature that I would like to enlist for the analysis). In this initial iteration, the landmarks can be divided into two components (base and blade) and two sides (left/right). Each of the four sections includes 25 equidistant semi-landmarks along the curvature of the spline (and one landmark at each of the divisions).
The base and blade were separated in an effort to explore correlation between base shape and blade shape. The two sides (left/right) were separated to allow us to explore differences in directional and fluctuating asymmetry. A total of 25 landmarks (equidistant) were generated for each of the four sections of the spline, and four landmarks were placed at the intersection of the four splines.
We began our effort by superimposing the landmarks from each of the dart points (below) by means of a generalized Procrustes analysis (GPA). It is important to remember that within studies of geometric morphometrics, shape (shape only) is not the same thing as form (shape + centroid size, in this case). While we are recording centroid size for use within discussions of allometry (or variation in size), form is not used for the principal components analysis (PCA) below.
Results of generalized Procrustes analysis (superimposition).
Once superimposed, the landmarks were used in a Principal Components Analysis (PCA); again, for shape–not form. While this does help to illustrate some of the variation in shape, there is much more that we can (and should) do with these data.
Principal Component Analysis of shape.
One example of this might be to explore whether there is significant correlation between blade shape and base shape; which appears to be true for this (small and preliminary) sample.
For each of the following analyses, the data (rows) were shuffled (x 1000) to ensure that the results were not influenced by sample order.
Two-block partial least squares for blade shape/base shape.
Moving to an analysis of allometry (size variation), we used the PredLine and common allometric component (CAC) functions in geomorph to illustrate the range of size variation in the sample. The PredLine function can also be used to plot variable allometry for each of the point types–something we are working through currently.
PredLine (top) and CAC (bottom).
It will be interesting to explore (when all scans are complete, and types are taken into consideration) whether there are similar trajectories (parallelism), whether those trajectories end in similar points (convergence), or whether they start in similar and end in different points (divergence).
We also use two-block partial least squares to test whether there is a significant correlation between centroid size and dart point shape.
Two-block partial least squares for centroid size/shape.
Shifting to yet another topic, it is possible to use this same landmark configuration to analyze deviations from symmetry; in other words, asymmetry. For this section, I use a sample from an additional collection of dart points that we have been working with (also from East Texas, but a private collection).
Using the same landmark configuration, we employed the landmarks from the left and right sides to analyze variability in directional and fluctuating asymmetry. It should be noted here that while these results are significant (there are differences between the left and right sides), a larger sample is needed for the final analysis (which will be aimed at highlighting asymmetry in specific types); however, we thought it worth mention (and illustrating).
Directional (top) and fluctuating (bottom) asymmetry.
From these very basic examples, we see much promise for extending our geometric morphometric studies to include dart points. It should be noted that it is possible to include qualitative measures (type, raw material, qualitative measures of retouch, etc.) in each of the analyses above to further highlight the dynamic variation in the shape and form of dart points. We have collected those metrics for this sample as we continue to work toward the 3D geometric morphometric analysis, which should–at least in theory–be a bit more dynamic than the 2D approach.
Similar to our efforts with ceramics, we are hoping to capitalize on both 2D and 3D data from across the East Texas region (prior to synthesizing these data in a larger network analysis), since there is a veritable wealth of readily accessible data available in the published–and gray–literature. While we have conducted a few small-scale (site specific) tests of correlation between the 2D /3D ceramic data with good results, more studies of this kind are needed as we continue to work through the various benefits and limits of the analytical approach.
Note: For those of you grumbling about retouch and resharpening, that is an additional issue that we are exploring (phenotypic trajectory analysis), and are working through the details of our approach to that analysis currently. Once the full collection is scanned, we will likely pursue an analysis of 2D morphometrics prior to moving into the 3D realm; particularly since we hope to use both 3D and 2D data in future analyses.