N.A.T.O. Advanced Study Institute, "Advances in Morphometrics" 18-30 July 1993 and Contributions to Morphometrics, edited by L. F. Marcus, E. Bello, and A. Garcia-Valdecasas, Monografias del Museo Nacional de Ciencias Naturales, Madrid 1993.

T. A. Dickinson, Associate Curator-in-Charge, Department of Botany, Royal Ontario Museum (tim@utstat.toronto.ca)

The NATO ASI, "Advances in Morphometrics," held this summer at Il Ciocco (Lucca), Italy was an opportunity for participants from a wide range of disciplines (physical anthropology, botany, cardiology, computer science, coral population ecology, entomology, herpetology, ichthyology, mammalogy, neuroanatomy, ornithology, paleontology, primatology) to come to grips with some of the latest approaches to, in the words of the ASI diploma, the analysis of "size and shape of organisms using Geometric Morphometrics." Contributions to Morphometrics ("the black book") was one of two books distributed to the participants (the other was "the blue book," Proceedings of the Michigan Morphometrics Workshop, Rohlf and Bookstein 1990) together with reprints of Rohlf and Marcus (1993; "A revolution in morphometrics") and Bookstein (1989; "`Size and shape': a comment on semantics") and two diskettes of compressed software for a wide range of morphometric and related techniques. I was one of the participants in the NATO ASI, and what follows is a review of both that workshop and Contributions to Morphometrics.

The synthesis of biological morphology with geometry, mathematics, and statistics, that has emerged during the past 15 years as "Geometric Morphometrics" is due particularly to Fred Bookstein and his students and collaborators at the University of Michigan and elsewhere. Bookstein's orange book (1991) provides a summation of this synthesis that is not for the faint-hearted. The blue and black books referred to above, together with an earlier red one (Bookstein, Chernoff et al. 1985) represent stages in the progressive refinement of this synthesis and especially its exposition to the biological community by Bookstein and other practitioners. Of the latter three books, I suspect that ordinarily the black one, Contributions to Morphometrics, is least likely to be seen by North American workers, despite being written entirely in English. This is unfortunate, since it represents an interesting stage in the exposition of the synthesis, and it contains valuable presentations ranging from the historical and theoretical to the extremely practical.

Geometric morphometrics distinguishes and analyzes differences in size and shape based on the Cartesian coordinates of discrete landmarks the location of which can be unambiguously determined in all of the objects under study. The first section of the book, "History, concepts, discussion and criticism," contains an essay by Bookstein in which geometric morphometrics is firmly placed at the intersection of two morphometric traditions: a graphical one emphasizing visual comparisons of shape and connecting Albrecht Durer with Francis Galton and D'Arcy Thompson, and another, based on measurements of unitary forms and their analysis (independent of their geometric relationships) and employing multivariate statistical methods. The essay goes on to describe the frustrations stemming from the failure to understand "what constituted the data" of morphometric analyses, and the breakthroughs made by C. R. Goodall, D. G. Kendall, K. V. Mardia and Bookstein in defining not only those data, and methods for summarizing them, but also the relevant statistical theory. In view of the critical importance of landmarks, the other chapter in this section, by V. Louise Roth, is appropriately a discussion of how landmarks are to be identified on three dimensional objects. This essay focuses less on issues like homology than it does on the hidden assumptions potentially associated with the use of two- dimensional projections of three-dimensional objects, choices of landmarks, and selection of variables.

The second section, "Data acquisition" comprises a single chapter by Jose M. Becerra, Bello, and Garcia-Valdecasas, "Building your own machine image system for morphometric analysis: a user point of view." The juxtaposition with Roth's chapter is significant. Until very recently, automated acquisition of morphometric data has been based almost exclusively on interactions with two-dimensional images, regardless of the dimensionality of the objects under study. The authors discuss critical issues involved in assembling a microcomputer-based system for video image capture and analysis: hardware and software selection, image storage, resolution, precision, and accuracy.

Three chapters present "Methodology and software" ranging from multivariate statistics (Marcus) to thin plate splines (F. J. Rohlf) and fractal analysis (D. Slice). The first of these is a useful introduction to methods for summarizing multivariate data both graphically and numerically. Principal components analysis (PCA) is emphasized, especially the use of singular value decomposition to obtain the results, and Gabriel's biplot to display them. A more comprehensive introduction is provided in the author's contribution to the blue book (Marcus 1990).

The chapter by Rohlf is extremely important, as it provides the most accessible presentation available of the methods based on the thin plate spline metaphor for quantifying and visualizing shape change that Bookstein has been developing (1990; Bookstein 1990; 1991). The matrix algebra underlying this metaphor and its extension to "relative warps" is presented clearly, making reference to parallel analytical approaches in conventional multivariate analysis. "Partial warps" are, in effect, quantitative descriptions of the deformation of the landmark plane required to transform a reference configuration of landmarks into the configuration seen in a sample object. Partial warps provide, in a manner analogous to Fourier analysis, a decomposition of this deformation into trends in shape variation at different scales. Relative warps are principal components of the partial warps. In a series of programs for MS-DOS computers described in this chapter and elsewhere, Rohlf has programmed not only the underlying computations but also a range of sophisticated graphic displays of the results that clearly relate them to the original landmark data. This software gives users the opportunity to visualize their data in the tradition of Durer and D'Arcy Thompson, while at the same time extracting numerical parameters for shape contrasts that can be used in multivariate analyses. As pointed out repeatedly by Rohlf and Bookstein, however, the parameters obtained for each sample object's configuration of landmarks relate only to the pairwise comparison between it and the single reference configuration used in the analysis.

Slice's contribution supplies the only botanical application in the book: an analysis of variation in fractal dimension between samples of leaves from five Acer species. Unfortunately, while this example illustrates fractal analysis, it fails to demonstrate that fractal analysis yields unique insights into shape variation unobtainable by other less complex means.

The concluding two chapters ("Applications") demonstrate the utility of landmark data (even those extracted exclusively from two-dimensional images) not only for summarizing the size and shape variation of mature structures (skulls of moles) but also in analyzing allometric changes in body form during the ontogeny of unitary organisms (threespine sticklebacks).

Finally, an appendix by Becerra introduces the reader to BITNET and INTERNET, and the use of FTP. A second appendix, by Marcus, describes the software provided on the diskette that accompanies the book. Programs provided by Rohlf for resistant fit and thin plate spline methods have since been superceded by versions made available at Il Ciocco and now by FTP to SBBIOVM.SUNY.EDU (in the directory BIOSTAT.192). For readers having access to the program MATLAB (Mathworks, Inc.) Marcus provides a set of command scripts to implement both the graphical analyses in his chapter and the thin plate spline methods described by Rohlf. For some readers, however, the most useful item may be a utility program provided by Becerra for converting MorphoSys image files to TIFF ones and viceversa. This greatly increases the capability of simple image analysis systems based on the PCVision Plus frame grabber (Imaging Technologies, Inc.) and the inexpensive MorphoSys program (Meacham and Duncan 1991).

The books described above, together with Bookstein (1991), set the stage for the NATO ASI in Italy this summer. It was held at Il Ciocco, a convention center and resort hotel in Tuscany, in the hills outside Lucca. The organizers were able to provide not only an extremely comfortable setting but also a very business-like one. In addition to a lecture hall, two large rooms were filled with microcomputers, mostly MS-DOS machines, but also some Macs and an IBM RISC 6000 workstation. The workshop consisted of lectures in the morning, increasingly interspersed with accounts of applications of the methods described, and related topics. Afternoons were mostly dedicated to allowing participants an opportunity to try out the methods in the computer lab, using a wide range of programs and data-capture hardware.

Lectures covered a sequence of topics similar to that in Bookstein (1991). Bookstein usually started, providing the theoretical framework for a particular approach. The same and additional topics were then developed further by Rohlf and others, sometimes in the context of particular software implementations of the methods being discussed. The data for morphometric analyses are the coordinates of landmarks. Size variation is then describable as "centroid size," the magnitude of the root-mean- square of the centroid-landmark distances. Size-independent variation in shape is then analyzed using the "shape coordinates" for each object (cf. Appendix 4 in Bookstein et al. 1985, and Sanfilippo and Riedel 1990). These are obtained by rescaling the raw landmark coordinates so that the endpoints of a particular baseline have the coordinates (0,0) and (0,1). This is a departure from the emphasis, in the past (e.g. Bookstein et al. 1985), on analysis of interlandmark distances; ASI participants who had originally obtained (x,y) coordinates of two-dimensional specimens (such as leaves, or projections of three-dimensional specimens) mostly were able to go back to those data. Others who had calipered hundreds or thousands of specimens to obtain such distances understandably felt annoyed at the shift and consequent need to recover coordinate data using trigonometric methods. Rotational- fit methods with which to obtain consensus configurations of landmarks were compared using Slice's program GRF (Rohlf and Slice 1990). These average shapes provide the reference configuration needed for some of the thin plate spline methods. Like Rohlf's programs for splines and warps described above, GRF displays its results graphically, as well as providing numerical output.

In addition to the software by Rohlf and Slice (the latter's includes powerful utilities for digitizing and for converting between diffent data formats), a number of other programs were demonstrated and made available to participants. Two programs are available for calculating shape coordinates, centroid size, and other parameters. Garcia- Valdecasas and J. Elvira provided a program with which to explore digital image formats and processing as an accompaniment to the former's lecture on image analysis. Possibly the most imaginative program made available is D'ARCYGRAPH by D. Rasskin-Gutman. It enables the user to create shapes as configurations of landmarks (or import them from files), rotate them, stretch them, and then save the new configurations as files of (x,y) coordinates that can be analyzed by other programs. Demonstrations (but not the software) were provided for general purpose data analysis and graphics programs like MATLAB and IBM's Data Explorer (S-Plus, developed from Bell Labs' S, unfortunately failed to materialize). The latest version of Rohlf's NTSYS-pc package was installed on the ASI computers and provided a common computational platform for ordinations and other multivariate methods (as well as another means of carrying out shape coordinate and thin plate spline calculations).

The ASI not only introduced participants to analytical tools and the software with which to employ them. The organizers also ensured that a sampling of state-of-the-art hardware for capturing coordinate data from specimens was on hand. Video systems demonstrated programs from Hungary and the United States for acquisition of two- dimensional data. For acquisition of three-dimensional data there was a British Reflex microscope, an Italian laser-scanning device, and a U.S. Polhemus electromagnetic system. It was out of the question to bring in CATscan or MRI devices, but participants got a taste of the power of these technologies from lectures and poster presentations describing studies of fossil primates. For example, the inner ear from a Neanderthal skull has been digitally reconstructed from CAT data by C. P. E. Zollikofer and M. Ponce de Leon. As yet, however, none of these systems appears to have the resolution necessary for studies of small, three-dimensional subjects like flowers.

Throughout the ASI, but more especially toward the end, many of the participants were concerned to explore the wider significance of morphometric data, the acquisition and analysis of which we were being taught. Some were concerned to be able to refine taxonomic decisions in relation to conservation issues. Others wished to understand the relationship of geometric morphometrics to phylogenetic studies. Bookstein suggested that geometric morphometrics could only provide a posteriori explanations of extrinsically derived phylogenies. Nevertheless, some thin plate spline comparisons of ichthyosaur skulls presented in passing by R. Reyment were highly suggestive of a possible role in generating phylogenetic hypotheses (if not in the actual reconstruction of cladistic relationships). Obviously, geometrically sound and statistically valid morphometrics is essential for definition of meaningful character states in some situations, but this was expressed only as an article of faith by one of the lecturers, without any examples.

Any pedagogical undertaking, however successful overall, is bound to have its weak points, and the ASI was no exception. Lectures were at times used to convey information that would have been better committed to printed notes. Difficulties stemming from the great variance in accent and presentation style inevitable in an international effort were compounded by the lack of a device as simple as a common data set to be subjected to every analytical technique discussed. Instead, participants found their own solutions to the difficulty of the subject matter, each of us explaining something to someone else at one time or another. The anarchy of being able to see perhaps a few dozen different data sets being analyzed in one room was in itself exciting and instructive.

Finally, it remains to be seen whether the organizers will be able to capture in any official summary of the ASI the ferment resulting from presenting a body of new thinking to a group of more or less critically thinking colleagues. Some of this ferment doubtless came from the diversity of disciplines represented by the participants, and the feeling that geometric morphometrics as presented failed to address particular problems of concern to some. There may be real difficulties in acquiring data, such as when landmarks are lacking, or when their number and position are inconsistent, or biologically equivocal, due to ontogenetic processes. More important, perhaps, is the possibility that geometric morphometrics, however complete and powerful, does not necessarily capture everything that humans usefully recognize as "shape" or "form" when trying to understand organic evolution. Highly characteristic leaf outlines may be the result of variation at more than one scale in ways that are not captured by geometric morphometrics. Similarly, variation in radially symmetric structures, or patterns of reticulation, may not be adequately represented. Despite these problems, however, the overwhelming lesson of the ASI was nevertheless that geometric morphometrics offers anthropologists, biologists, and others powerful tools with which to compare forms. Considerable opportunity remains for adepts to expand not only on applications of these tools, but also on the existing methods of analysis and visualization that are the tools themselves.

Bookstein, F. L. 1989. "`Size and Shape': A comment on semantics." Systematic Zoology 38: 173-180.

Bookstein, F. L. 1990. Chapter 11. "Higher-order features of shape change for landmark data." Pp. 237-250 in Proceedings of the Michigan Morphometric Workshop. Special Publication No. 2. Ann Arbor MI, The University of Michigan Museum of Zoology.

Bookstein, F. L. 1990. Part II. "Analytic Methods. Introduction and overview: geometry and biology." Pp. 61-76 in Proceedings of the Michigan Morphometric Workshop. Special Publication No. 2. Ann Arbor MI, The University of Michigan Museum of Zoology.

Bookstein, F. L. 1991. Morphometric tools for landmark data. Cambridge, Cambridge University Press.

Bookstein, F. L., Chernoff, B. C., Elder, R. L., Humphries, J. M., Smith, G. R., and Strauss, R. E. 1985. Morphometrics in evolutionary biology. Special Publication 15. Philadelphia, Academy of Natural Sciences of Philadelphia.

Marcus, L. F. 1990. Chapter 4. Traditional morphometrics. Pp. 77-122 in Proceedings of the Michigan Morphometric Workshop. Special Publication No. 2. Ann Arbor MI, The University of Michigan Museum of Zoology.

Meacham, C. A. and Duncan, T. 1991. MorphoSys 1.29. Berkeley CA, Regents of the University of California.

Rohlf, F. J. and Bookstein, F. L., Ed. 1990. Proceedings of the Michigan Morphometrics Workshop. Special Publication No. 2. Ann Arbor, The University of Michigan Museum of Zoology.

Rohlf, F. J. and Marcus, L. F. 1993. "A revolution in morphometrics." TREE 8: 129-132.

Rohlf, F. J. and Slice, D. 1990. "Extensions of the Procrustes method for the optimal superimposition of landmarks." Systematic Zoology 39: 40-59.

Sanfilippo, A. and Riedel, W. R. 1990. Chapter 19. Morphometric analysis of evolving Eocene Podocyrtis (Radiolaria) morphotypes using shape coordinates. Pp. 345-362 in Proceedings of the Michigan Morphometric Workshop. Special Publication No. 2. Ann Arbor MI, The University of Michigan Museum of Zoology.