Summary of current research.

The
field of morphometrics is concerned with methods for capturing
information on the size and shape of biological structures and the
analysis of shape change and shape variation in populations. **Geometric
morphometrics** is a relatively new approach that takes into account the
geometrical relationships among the features (positions of the landmarks
and shapes of outlines, *etc.*) rather than just measured distances
or angles. This new approach was made possible by some recent
mathematical breakthroughs (Kendall’s shape space) that make it possible
to deal with shape as a single mathematical object. In the past ad hoc
methods have been used.

My current research is concerned with the
development, evaluation, and application of **new statistical methods** for
use in geometric morphometrics. Over the last few years I have written
papers demonstrating how standard statistical methods such as principal
components analysis, canonical variates analysis, multiple regression,
and other methods can be adapted for the analysis of shape (by
approximating the non-Euclidean shape space by a tangent space
approximation). An important aspect of this new approach is that it is
possible to visualize the results of many types of statistical analyses
by generating shapes of hypothetical organisms. A current application involves
the visualization of estimates of ancestral species.

An important side project at the moment is an investigation of the
statistics of the **comparative method** (methods to analyze variation
sampled across a phylogeny rather than independent samples as assumed by most
statistical methods). Two papers have been published in this area and others
are in preparation.

My work also emphasizes the development of
interactive **computer software** to perform the unique computations needed
in geometric morphometrics. This software also provides the special
interactive graphical displays to enable users to visualize shapes.
This software is very important since it has made it possible for these
new methods to be applied routinely by many biologists.

I also have a continuing interest in the development
and evaluation of **numerical taxonomic methods** (*e. g.*, cluster and
ordination methods for applications in ecology, systematics, and
functional morphology).

I also support the Stony Brook Morphometrics www pages that serve as the principal locus for the exchange of software, example datasets, directory of interested workers, and information on meetings and workshops relevant to the field of geometric morphometrics.

Due to the unfamiliarity of most biologists with the
types of mathematics needed to understand the methods used in geometric
morphometrics, many 1 to 2-week **workshops** have been held to teach the
necessary techniques and to give potential users a chance to collect
data, learn how to use the software, and to interpret the results. I
have often organized or been a principle lecturer at such workshops.
These include the Univ. of Mich. Stony Brook University, Iowa State University
in
the
US
and
one or more workshops in Austria, Chile, Italy, France, Spain, Sweden, Taiwan,
and
Turkey.
The
first formal **course in geometric morphometrics** was held here at SB in
1994 (it is now offered in the Fall of even numbered years).
Visitors often travel to SB to take the course
and to work in my lab while they are here.