Further Applications of EDMA - An Invariant Approach to Statistical Analysis of Shapes - page 278

using a bootstrapping algorithm that selects characters (columns) ran-
domly and with replacement. With each resampling, a bootstrap tree is
constructed. When a large sample of bootstrap trees has been generat-
ed, each node in the empirical cladogram is assigned a bootstrap
proportion . The bootstrap proportion for a node indicates the propor-
tion of resamplings where the included taxa were grouped together in
the bootstrap trees (regardless of the clades' internal structures). If
there is a strong phylogenetic signal in the data, the bootstrap proba-
bilities should be close to 100%. If there is little or no signal, the
bootstrap probabilities will be closer to 0%, because the tree structure
is unlikely to be reproduced during resampling.
We would like to conduct similar analyses with morphometrics.
However, our application of the bootstrap is somewhat different.
Felsenstein's (1985) method, and subsequent applications of it,
assumes that characters are invariant within taxa. In addition, there
is an assumption that the characters are independent. With morpho-
metric characters, it is obvious that neither of these assumptions is
met. In addition, we want to avoid any subjective “coding” of the data,
where continuous distributions are transformed into ordinal character
states. Finally, our application will differ from most in that we do not
use the data to construct the cladogram; we are simply evaluating the
fit between a hierarchical structure identified in our morphometric
data and a cladogram that is established ahead of time, using other
sources of data.
Our solution is to use a combination of parametric bootstrapping
and hierarchical cluster analysis. Parametric bootstrapping assumes a
model of variation, and generates random data sets under that model.
Similar approaches have been used before with models of molecular
sequence data (Huelsenbeck et al., 1996). We assume a general pertur-
bation model and estimate the mean forms and variance-covariance
matrices for each taxon under that model (Lele, 1993 and Chapter 3 of
this topic). Then, assuming multivariate normal perturbations, we can
generate bootstrap samples under the model (Lele and Cole, 1996). The
bootstrap samples are used to construct a sample of trees. We then
compare their topologies (cluster structures) to the cladogram to see
how often the genealogical relationships are reflected by the morpho-
metric data.
As an illustration of the method, we analyzed the form of the mid-
facial skeleton in a sample of adult, female ateline primates (Cole et
al., 2000). The atelines are a class of New World primates that are
characterized by large body size (6 to 15 kg) and fully prehensile tails