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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

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