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 (Kendallís 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.