In the series of workshops (Ann Arbor, May 1988; Stony Brook, June 1990) on the newly emerging consensus in morphometrics, there is now a European version (50 Hz 220 volts). The meeting took place at the Centre Nacional de Education Ambientale en la Naturaleza, Valsain (Segovia), Spain, from May 28 through June 2, 1991. The instructors, all veterans of the Battle of Stony Brook, were Jim Rohlf, Fred Bookstein, Leslie Marcus, Antonio G.-Valdecasas, Marco Corti, Anna Loy, and Dennis Slice. The 36 student participants were from Spain, Portugal, France, Czechoslovakia, and Maine. We were produced and directed by Valdecasas with spectacular logistical support by Elisa Bello and hardware and software support by Jose Becerra of the Museo Nacional de Ciencias Naturales, Madrid.

The workshop emphasized methods for analysis of landmark data. After overviews by Rohlf and Bookstein, there were lectures by Bookstein on landmarks as data, by Rohlf on analysis of images and of outlines, by Bookstein on the general approach to the statistics and the features of shape comparisons by landmarks, by Marcus on the interrelation of multivariate statistics and morphometric data (a subject we decided should no longer be referred to as "traditional morphometrics"), and by Rohlf on the steps involved in analysis of intergroup differences and intragroup variability by thin-plate splines. Interspersed among these lectures were afternoon demonstrations of software for data acquisition from calipers, digitizing tablets, and images, for fractal and Fourier analysis of outlines, for various versions of Procrustes analysis and the visualization of their residuals, and for Rohlf's thin- plate spline programs TPSPLINE and TPSRW, which were released in several time-stamped versions throughout the course of the workshop. On the last day all of us joined in a lively and thought-provoking four-hour free-for-all regarding scientific strategies, limits of landmark data and of the Cartesian model, limits of morphometric inference in systematics, relations to other channels of measurement, and many other fundamental matters. All time not otherwise accounted for was spent in independent work by the students, or by student-instructor pairs, at one of the 14 computers scattered around the workroom. These activities often persisted past 10 p.m., the usual Spanish dining hour.

Your three lecturers (Rohlf, Bookstein, Marcus) have now team-taught most of three workshops of this sort, totalling some 100 hours at the front of rooms of various shapes. We think the format of the last workshop was the best so far, and is worth imitating a few more times, until the methods it is promulgating become established. Perhaps it would be appropriate to recount our experiences in support of this recommendation.

1. SYLLABUS. In their present states of advancement, one cannot cover both outline methods and landmark methods to equivalent depth. The Valsain workshop emphasized landmark methods, and, within that domain, the pair of thin- plate spline methods recently developed by Bookstein for between-group and within-group analyses. The combination was convenient for intensive group instruction in that the techniques overlap with each other, and with the core of the multivariate statistics of landmark configurations, in their glossaries, formulas, graphics, significance tests, and software modules. Thus over the course of the workshop a few technical terms became familiar from the indefinite repetition of verbal and graphical contexts: Centroid size, Affine transformations, Thin-plate splines, Bending energy, Principal, Partial, and Relative warps, and Uniform components and factors of shape variation. It would be helpful if subsequent workshops distributed an illustrated Glossary of these and similarly crucial terms prior to the outset of instruction.

Data acquisition can be taught "in theory" by lectures in a similar format, but it is unwise to allow students to pursue it during the workshop. In earlier workshops, students were assigned the task of collecting real data and working up their analysis for presentation, all in ten days or less. However, the effort of data acquisition would typically expand to fill nearly the full duration of the workshop, whereupon the pressure and anxiety of impending presentations would take over, leaving little opportunity or energy for serious play with any of the analytic methods. Paradoxically, we find that a four-day workshop prohibiting serious data collection seems to result in more learning of morphometrics than does a ten-day workshop that actually encourages data collection. Of course, this requires that a variety of annotated data sets (real landmarks from real groups) be made available in advance, by the organizers or perhaps by some of the more advanced students, for explaining all the principal techniques being taught.

2. READINGS. It is important to have background readings and completely worked examples available in advance. Best would be a potpourri from earlier workshops along these lines--the Proceedings of the Michigan Morphometrics Workshop (for sure), the Proceedings of the Valsain workshop as they are likely to appear in 1992. As long as the morphometric consensus remains novel, students will need multiple exposures to master it. (See also under "teaching" below.) Do not distribute technical mathematicostatistical texts (e.g. Bookstein's monograph) or highly technical research papers. It is not possible for the student to find quick answers to questions in these sources, and so they serve mainly as a depressant on student enthusiasm. The really useful handouts are the guides to stepping through interactive programs (i.e., "if your graphical output looks like this, here is what you might look at next...").

3. TEACHING. Lectures should always focus on exposition and comparison of existing methods, not the presentation of research results or of methods new to the other instructors. The lecturers should intentionally overlap in their coverage. In particular, each lecturer should be capable of answering most questions generated by the others' lectures, as it is in the answers to these questions of interrelation that the typical student will finally achieve enlightenment about the semantics of new concepts. Examples in the course of lectures should emphasize the understanding of method, especially the relations between different computations upon the same data, rather than detailed findings about creatures. All such exemplary data should be available for students so that they may reproduce the entire analysis, including all interpretative choices, on their own.

It is particularly important that students leave the workshop capable of explaining and defending the fundamentals of what they were taught to others who did not have the benefit of asking questions of their own. Therefore, lecturers should carefully draw and explain the distinctions between findings that depend on arbitrary aspects of the techniques taught and findings that are held in common, to various degrees of approximation, among all methods of a larger class. For instance, all efficient approaches to testing the "statistical significance" of a group difference of mean shape for landmark data are essentially the same--there is no argument remaining about the linearized statistics of shape space, or about its subspace of linear (uniform) transformations. It is these commonalities, agreed upon by the three instructors and also by interested statisticians such as Mardia, Kendall, Goodall, and Sampson, that constitute the "morphometric consensus" to which we have referred. But when significant differences are found, the choice of a particular basis for expressing those differences remains arbitrary, especially as regards the nonuniform features (residuals from the various uniform fits). Some displays, such as the partial warps, are global; these need to be supplemented by local displays, such as residual vectors from the various Procrustes fits. Depending on the example, some of these displays will be more interpretable than others even though anything you see in one diagram of one graphical style can be found, if you know how to look, in some combination of the full stack of diagrams (along with their covariances) generated according to another graphical style. Likewise, while the choice of a distance function between outlines lacking landmarks is essentially arbitrary, once that choice is made the resulting ordination of specimens is essentially fixed regardless of the basis selected for the representation of that ordination; and so on. Such an understanding, separating the necessary choices from the contingent, will ease the student's reconstruction, some weeks or months afterward, of the logic of what was taught so intensively at one burst.

4. COMPUTING. The essential activity of these workshops is not listening but computing. To that end, there should be one fast PC for every two or three students. (As of July 1991, that entails a 386-based machine with math coprocessor and VGA-level graphics.) The workshop will also require preloaded software including good flexible editors, printers and plotters that can handle bitmapped graphics, at least one device for the projection of screen demonstrations, ample spare floppies, and so on. There should be considerable physical space around each machine, as while some sessions are observed only by the student controlling the keyboard, others are watched by up to ten spectators (one teaching, one arguing, all the others leaving fingermarks on the screen). When some participants bring their own laptops or notebook machines, it is easy for discussions to continue late at night, over meals, or under a tree. The resulting variety of platforms also makes it likelier that participants can gain access to the familiar comforts of their favorite editor.

An unfortunate aspect of the Valsain workshop was the propagation of a virus into some of the software that was distributed. We learned the hard way that all disks involved in any such conference should be disinfected beforehand by a good commercial package.

There seems to be no point to the distribution of software that is not graphical or that has inconvenient user interfaces. Students can be expected to notice which programs are simpler to use, and will allocate their energies accordingly, regardless of the content of the lectures. Thus all relevant software should be rebuilt as necessary, even heroically during the workshop, to encourage masses of analytic plots and biplots, geometric graphics, graphical animation whenever possible, and diagnostics. This is morphometrics, after all; the student will most easily understand displays that look like the organisms they understand. In this connection we are very pleased to note that one inadequate program from the 1988 and 1990 workshops is already officially obsolete. Bookstein's program for computing relative warps has been replaced by Rohlf's vastly superior version of the same algorithm.

5. STUDENTS should be of diverse ages, sexes, nationalities, and taxonomic specialties. Each should bring a little data set, if only copies of published figures, and should run its landmarks or outlines through every program to which the format (inter- or intragroup) is suited. Other programs can be explored using the same demonstration data underlying the lectures. When techniques are novel or use neologisms (e.g., the various kinds of "warps"), the student should be aggressive enough to ask for clarification and differentiation as many times as necessary, of any lecturer or more advanced student, until enlightenment is obtained. At Valsain, the best (i.e. most fruitful) interchanges with the lecturers often began when a student said, "...But that can't be right, because ... ." Through the dissection of the semantics of these buried presumptions there can emerge an adequate understanding of the logical partition of information between assumptions and data, which is what is actually being taught. This can happen only if students are willing to confront lecturers sharply with the unconformities between their mental maps and the actual domain of landmark methods.

6. MISCELLANY. We cast a last few recommendations into the imperative verb form. Require instructors to disagree somewhat but never to contradict each other. Carry an umbrella at all times. Have a device for reproducing images from blackboards. Don't expect to sleep much. When you go home, insist that this sort of workshop be repeated: it is the best mode we have ever seen for disseminating new biometric technology.

Fred L. Bookstein, Leslie A. Marcus, F. James Rohlf, Antonio G.-Valdecasas. July 1, 1991