Biology Reference
In-Depth Information
determine the spatial location and extent of a difference captured by these data, even
using multivariate analyses, uncovers one of the most severe limitations of traditional
morphometric data
their poor ability to localize morphological differences.
A further obstacle to finding characters in shape data is that neither the magnitude of
the difference, nor the magnitude of its spatial extent, are relevant to its utility as a charac-
ter. Small magnitude differences (so long as they are big enough to be considered a differ-
ence at all) count as much as large magnitude ones, and small-scale differences (such as
the tip of an appendage) count as much as large-scale ones (perhaps spanning the whole
organism). Consequently, neither the Procrustes distance between taxa nor the bending
energy of the transformation has any relevance to the problem. This is one of the reasons
why the problem is so difficult to solve
neither of the metrics used in geometric mor-
phometrics is germane to the problem, and if there is a relevant metric, it has yet to be
defined.
When we first approached this problem, we focused on one major limitation of conven-
tional (qualitative) approaches: that organisms are often dissected arbitrarily, along lines
of convention. Conventional anatomical subdivisions are often not biologically meaningful
except in the context of a particular problem. For example, if we are interested in locomo-
tion and foraging, we can subdivide an organism into parts that are used in locomotion
and parts that are used in foraging. Alternatively, if we are interested in development, we
can subdivide the organism into parts that have a common germ-layer origin, or that
develop from the same type of bone, or that undergo the same kinds of epigenetic interac-
tions, etc. These subdivisions have long been regarded as arbitrary, except to the extent
that they are useful in a particular investigation. These subdivisions often are not
suitable for dissecting an organism in systematic studies because what differs between
taxa may cross several such divisions, and may not be wholly within any them. Our goal
in using partial warps was to find a more objective basis for dissection. We did not suc-
ceed (for reasons discussed below), but the problem we defined remains a fundamental
and unresolved difficulty for character analysis. Our method had fatal flaws, but so do
others that require us to decompose the organism using biologically arbitrary mathemati-
cal rules.
The approach we took is similar to one that is standard in cladistic studies using mor-
phometric data. We defined a set of variables
a priori
, and compared taxa with respect to
them. A similar tactic is applied to conventional morphometric variables, when a set of
lengths or ratios is defined and measured on taxa, then the values of those lengths or
ratios is compared among the taxa. Most attention has focused on the problem of coding
those variables, but coding is the least of the problems. Such variables do not solve the
problems we had hoped to address, but share with them the flaw that we inadvertently
introduced: they score taxa on arbitrarily selected components of shape, one component at
a time.
Why Not to Use Partial Warps as Characters
Even though partial warps have a geometric scale, are a function of homologous
landmarks, and do not emphasize differences of large magnitude at the expense of
