morphometrics -drafts-

A total of 20 individuals belonging to Quercus pubescens (blue) and Quercus macranthera (green) were sampled at a mixed population. Mean leaf shape for each individual tree was calculated using the generalized Procrustes analysis on outline configurations of ten leaves selected randomly from each tree.

Shape variation between these individuals was determined with generalized Procrustes analysis on the mean outline configurations. Following superimposition, principal component analysis was performed on the covariance matrix of Procrustes residuals.

First six PC’s and orthogonal shape models were shown in the figures. In the first three figures, results of standard methods were shown. In the following figures “outalign” method were presented.

In the first three figures, mean configurations and the following Procrustes pca were calculated with the use of 180 equally-spaced outline points:

(Click each to see image in original size)

In the following three figures, leaf outlines were aligned by using “outalign algorithm” prior to calculate each mean outline configuration. This produces outlines with different lengths. Before the Procrustes pca, each mean outline configuration was resampled to create 180 equidistant outline points. Note that, outalign algorithm reduces mismatches between outline points; this increases the amount of shape variation captured by initial generalized Procrustes analysis. However local shape features in the sample mean and the related model deformations are lost due to the resampling:

(Click each to see image in original size)

In the last three figures, again, leaf outlines were aligned by using “outalign algorithm” prior to calculate each mean outline configuration and each mean outline was resampled to create 180 equidistant outline points. However, before the Procrustes pca, final outline configurations (mean shapes) were also aligned by using “outalign algorithm”. Note that, this increases the amount of shape variation captured by the Procrustes pca. The sample mean shape and the model deformations is much more localized:

(Click each to see image in original size)