Further Applications of EDMA - An Invariant Approach to Statistical Analysis of Shapes - page 277

shared-derived aspects might constitute “key adaptations” for the
group. Of course, if we are interested in adaptation, we might also be
very interested in cases where there is a strong signal that does not
reflect genealogy. Instead, there might be a strong “alternative” signal
that reflects similarity resulting from something other than genealogy
(as seen in the example below).
When we compare morphometric classifications with a genealogical
hypothesis, we are comparing patterns of hierarchical relationships.
The goal is to determine whether or not there is some hierarchical
structure in the morphometric data. If a hierarchical structure exists
for the data, we must then determine whether it matches the structure
of the cladogram that is constructed from other data. To examine hier-
archical structure in the data, we require a measure of dissimilarity
between taxa. One possible dissimilarity measure that we can use with
landmark data is a statistic defined by Richtsmeier et al., (1998:69):
where FDM( A,B ) ij refers to all of the below-diagonal elements of the
form-difference matrix between taxa A and B . If F =0, then A and B
have identical forms. F will become increasingly positive as differ-
ences between taxa become more pronounced. To compare multiple
taxa, all of the pairwise F statistics can be placed into a dissimilarity
matrix. This matrix is then subjected to a hierarchical cluster analysis
(e.g., UPGMA; Sneath and Sokal, 1973). The morphometric and cladis-
tic trees can be compared using any of a large variety of
tree-comparison and consensus statistics.
Because morphometric data vary within samples, our estimates of
mean forms are always made with some sampling error. This sampling
error carries through our computations of form-difference matrices,
dissimilarity measures, hierarchical clustering, and tree comparisons.
In other words, within-sample variation always influences our classifi-
cations that are based on morphometrics, as well as our subsequent
comparisons with trees built with other data. Using the bootstrap, our
knowledge of within-sample variation can be used to assess the effects
of variation on our tree comparisons.
The bootstrap was first used in phylogenetic analysis by Felsenstein
(1985), and most phylogenetic applications since have used the same
method. The data consist of a matrix of taxa (rows) and character states
(columns), which are used to generate an empirical phylogenetic tree
(usually using maximum parsimony). The matrix is then resampled