Introduction - Geometric Morphometrics for Biologists - page 2

Indeed, the pioneering work in modern geometric morphometrics (the focus of this topic)
had nothing at all to do with organismal morphology; the goal was to answer a question
about the alignment of megalithic “standing stones” like Stonehenge ( Kendall and
Kendall, 1980 ). Nevertheless, morphometrics can be as much a branch of morphology as it
is a branch of statistics. It is that when the tools of shape analysis are turned to organismal
shapes, illustrating and even explaining shape differences that have been mathematically
analyzed.
The tools of geometric shape analysis have a tremendous advantage when it comes
to these purposes: not only because it offers precise and accurate description, but also
because it enables rigorous statistical analyses and serves the important purposes of
visualization, interpretation and communication of results. Geometric morphometrics
allows us to visualize differences among complex shapes with nearly the same facility
as we can visualize differences among circles, kidneys and letters of the alphabet (and
mittens).
In emphasizing the biological component of morphometrics, we do not discount the
importance of its mathematical component. Mathematics provides the models used to
analyze data, both the general linear models exploited in statistical analyses and the alge-
braic models underlying exploratory methods such as principal components analysis.
Additionally, mathematics provides a theory of measurement that we use to obtain the
data in the first place. It may not be obvious that any theory governs measurement
because very little theory (if any) underlays traditional measurement approaches. Asked
the question “What are you measuring?”, we could give many answers based on our
biological motivation for measurement

such as (1) “functionally important characters”;
(2) “systematically important characters”; (3) “developmentally important characters”;
or (4) “size and shape”. However, when asked “what do you mean by “character” and
how is that related either mathematically or conceptually to what you are measuring?” or
if asked “what do you mean by “size and shape”?”, it was difficult to provide coherent
answers. A great deal of experience and tacit knowledge went into devising measurement
schemes, but that knowledge and experience had very little to do with any general theory
of measurement. Rather than being grounded in a general theory of measurement,
each study appeared to devise its approach to measurement according to the biological
questions at hand, as guided by the particular tradition within which that question arose.
There was no general theory of shape nor were there any analytic methods adapted to the
characteristics of shape data.
Owing largely to developments in measurement theory over the past two decades, there
has been remarkable progress in morphometrics. That progress resulted from first pre-
cisely defining “shape” and then pursuing the mathematical implications of that defini-
tion. We therefore now have a theory of measurement. Below we offer a critical overview
of the recent history of measurement theory, presenting it first in terms of exemplary data
sets and then in more general terms, emphasizing the core of the theory underlying
geometric morphometrics the definition of shape. We conclude the conceptual part

of this Introduction with a brief discussion of methods of data analysis. The rest of the
Introduction is concerned with the organization of this topic and where you can find more
information about available software and other resources for carrying out morphometric
analyses.