PermuTree

Python program for performing a permutational regression analysis on trees. It takes a NEWICK string file and a CSV file of a single continuous variable and tests for significant correlation between phenotypic and phylogenetic distances. Please note that this script was written in Python version 2.7, thus some commands may not run properly (e.g., print function). In addition, the script requires the tree.py module to run, which can be downloaded through Peter Beerli's website (see README), as well as matplotlib and scipy Python packages

Pairwise interspecimen shape distances from the single species sample with size removed.

<p>The interspecimen Procrustes surface metric values for a GPSA superimposition are plotted against the interspecimen Procrustes distance values for a GPA superimposition. There is a slight positive correlation.</p

Comparison of superimpositions for the single species sample with size removed.

<p>Top: GPA superimposed skulls from the front and side. Bottom: GPSA superimposed skulls from the front and side. Note that there is virtually no visible difference between the two superimpositions.</p

A Landmark-Free Method for Three-Dimensional Shape Analysis

<div><p>Background</p><p>The tools and techniques used in morphometrics have always aimed to transform the physical shape of an object into a concise set of numerical data for mathematical analysis. The advent of landmark-based morphometrics opened new avenues of research, but these methods are not without drawbacks. The time investment required of trained individuals to accurately landmark a data set is significant, and the reliance on readily-identifiable physical features can hamper research efforts. This is especially true of those investigating smooth or featureless surfaces.</p><p>Methods</p><p>In this paper, we present a new method to perform this transformation for data obtained from high-resolution scanning technology. This method uses surface scans, instead of landmarks, to calculate a shape difference metric analogous to Procrustes distance and perform superimposition. This is accomplished by building upon and extending the Iterative Closest Point algorithm. We also explore some new ways this data can be used; for example, we can calculate an averaged surface directly and visualize point-wise shape information over this surface. Finally, we briefly demonstrate this method on a set of primate skulls and compare the results of the new methodology with traditional geometric morphometric analysis.</p></div

Landmark and surface point distributions for a single specimen.

<p>Foreground: A single specimen with the landmarks highlighted. Background: The same specimen rendered only as the points making up the surface. Note the relatively high density of points in the surface scan and the uneven distribution of landmarks.</p

The heat maps of the two samples, with and without size.

<p>Blue indicates low values, red indicates high values. Top left: The single species sample with size removed. Top right: The single species sample with size restored. Bottom left: The multiple species sample with size removed. Bottom right: The multiple species sample size restored.</p

A heat map of the variance from the prototype for the single species sample with size removed.

<p>Blue indicates low values, red indicates high values. These values are calculated from the covariance matrix of the set of nearest neighbor points for each point on the prototype. Note the high variance region in the center of the neurocranial region in the side view. One specimen had a large hole in this region, which is reflected in the heat map.</p

Graphs comparing GPSA to GPA for the two samples, with and without size.

<p>Top left: The single species sample with size removed. Top right: The single species sample with size restored. Bottom left: The multiple species sample with size removed. Bottom right: The multiple species sample size restored. As expected, the two methods become more correlated with increasing shape and form variability.</p

Principal axes of shape variation for the mixed-species data.

<p>Top shows the axis of greatest (I) and second greatest (II) variance (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0150368#pone.0150368.s001" target="_blank">S1 Appendix</a> for details). Lower left panel shows visualization of specimen surface with lowest projection (specimen 12, score ≈ -82.6) on axis I. Lower right panel shows the same for the specimen with the highest projection (specimen 6, score ≈ 28.5). Coloring indicates magnitude of displacements due to the vertex regression coefficients. Mean surface is shown in semi-transparent gray for comparison.</p

Graphs comparing aspects of GPA and GPSA for the single species sample with size removed.

<p>Top left: GPSA and GPA superimpositions compared using Procrustes distance. Note the high correlation. Top right: The two superimpositions compared using Procrustes surface metric. Note the high correlation. Bottom left: Procrustes surface metric and Procrustes distance measures compared using GPA superimposition. Note the low correlation. Bottom right: The shape distance measures compared using GPSA superimposition. Note the low correlation.</p