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transformations in shape. However, finding (and tracking) shape characters, and recon-
structing the evolution of shape, are different exercises. When looking for characters, par-
ticular features of the whole are selected as informative, making no effort to provide a
complete description of the changes in shape (or of the ancestral shape). Consequently,
characters usually comprise a subset of the features that evolve, and tracing characters on
a cladogram does not fully reconstruct the evolution of shape. For example, all members
of a particular group might have a shallow body compared to the other species, and “shal-
low body” is then selected as a character. But, no inference is made concerning amount of
change in body depth or how shallow their ancestor was, or what the ancestor's head
shape was. In contrast, reconstructing the evolution of shape requires an inference of the
ancestral configuration of landmarks as well as the direction and magnitude of change in
the complete configuration along each branch.
Of the three types of questions, only those relating to taxonomic discrimination are so
straightforward that they require nothing more than standard morphometric tools. This
does not mean taxonomic discrimination is easy; on the contrary, it can be very difficult.
However, the difficulties of taxonomic discrimination pale in comparison to the problems
of finding characters or reconstructing the evolution of shape. Because taxonomic discrimi-
nation is a straightforward problem, our discussion of it focuses on some of the practical
issues that complicate its application to shape data.
The problems of evolutionary analysis, on the other hand, raise questions that are
largely outside the scope of morphometric theory. The methods used to infer evolutionary
transformations of shape either (1) minimize a distance or squared distance over the clado-
gram (which, in our case, would be a Procrustes distance); or (2) use an explicit model of
the evolutionary process and estimate values of the model's parameters that maximize the
likelihood of the data, given the model (an accessible, general overview of these
approaches can be found in Felsenstein, 2002, and a discussion of them in context of geo-
metric shape data can be found in Rohlf, 2002). Whatever the model, when these methods
are used to infer shape evolution, the whole shape (the complete set of shape variables) is
always used. The primary issue facing users of these methods is to choose (or develop) a
realistic, justifiable model of shape evolution
a matter that involves considerations of
evolutionary biology rather than morphometrics. Accordingly, we do not discuss this topic
beyond a brief listing of the models that could be used.
Unlike the taxonomic and evolutionary questions, phylogenetic analysis using shape
continues to raise profound methodological questions with no satisfying answers. The cen-
tral problem is that there is no generally accepted method for finding characters in shape
data, and it is not even clear what a method of character discovery would look like. For
systematists, the lack of progress in this area since the first edition will mean that this
remains a disappointing chapter. However, we chose to use the opportunity of the second
edition to clarify some important points that we made in the first edition. The most impor-
tant of these is that decomposing shapes into variables that will be treated as independent
traits is a fundamentally flawed approach to inferring phylogenetic relationships from
shape data. It does not matter whether the decomposition is into partial warps or principal
components or any other means of defining vectors in a shape space or its tangent spaces.
This flaw lies at the heart of multiple methods of character analysis, including the
approach previously offered by us (Fink and Zelditch, 1995; Zelditch et al., 1995). The
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