Biology Reference
In-Depth Information
variation within species in more than two or three dimensions at a time, but doing so may
be important for deciding whether species are similar enough to code their features as
homologous.
The appropriateness of coding is, itself, a subject of debate. Not only are methods for
coding controversial, even the idea of coding is. As mentioned earlier in this chapter, there
are methods for inferring the evolution of shape that do not require coding characters.
Some apply the trait values themselves, without coding, in standard tree construction
algorithms (Farris, 1970; Goloboff et al., 2006). Others take a very different approach to the
problem. In particular, they do not make preliminary hypotheses of homology, then for-
malize them by codes, then infer the phylogeny that minimizes the net number of extra
steps (a step is considered “extra” if it means that a putatively homologous character is
reinterpreted as arising more than once). Instead, they use explicit models of the evolu-
tionary process, among which are:
1.
Randomly varying directions of natural selection in different lineages
2.
Random genetic drift of species around a single, stable optimum
3.
Randomly wandering optima
4.
Constrained wandering of optima
5.
Wandering optima whose paths have a correlation that diminishes over time
6.
Bursts of change around the time of speciation with little or no change thereafter.
(For a more detailed synopsis of the models, see Felsenstein, 2002.) Using one of these
approaches avoids the whole issue of coding, but instead requires one to confront the
problem of deciding which model is reasonable and justifiable. Such models have not
been widely used to infer cladograms from morphological data and, like the methods
which minimize a net morphometric distance (linear or squared) over a tree, model-based
methods might best be considered as methods for reconstructing the evolution of shape
given a cladogram.
SUMMARY
At present, no method is tailored to the problem of finding characters in morphometric
data, and the available methods are cumbersome and involve an uncomfortable degree of
subjectivity. Each could be improved by refining the part of the procedure that involves
making linear combinations of variables, such as combining PC1, PC2 and PC3 to see
whether similarities inferred from scores on one component are belied by scores on others.
However, rather than improving methods that were devised to use standard morphomet-
ric techniques, it might be better to start at the beginning and develop a method tailored
to our purposes. Doing so will require refining the statement of the problem. Currently,
we cannot state the problem in mathematical terms, and that is necessary before we can
find a mathematical solution. Our original statement of the problem focused on one partic-
ular element of it: finding characters without having to dissect organisms arbitrarily into
parts prior to the phylogenetic analysis. However, that dissection need not be an integral
part of a method for finding characters. We could instead use partial least squares analysis
(Chapter 7) to test the hypothesis that the blocks of landmarks do not covary; if they do
