It is far from obvious that outside of highly specialized domains such as commercial agriculture, the methodology of biometrics—quantitative comparisons over groups of organisms—should be of any use in today’s bioinformatically informed biological sciences. The methods in our biometric textbooks, such as regressions and principal components analysis, make assumptions of homogeneity that are incompatible with current understandings of the origins of developmental or evolutionary data in historically contingent processes, processes that might have come out otherwise; the appropriate statistical methods are (...) those suited to random walks, not normal distributions. A valid methodology would further require that especially close attention be paid to the difference between aspects of processes that are plastic, those that encode their own histories or biographies, and the very small fraction of quantifications that can usefully and realistically be modeled as varying by colored noise around a central tendency that itself has some quantitative meaning. This point of view—that only a vanishingly small fraction of the quantitative information borne by any living organism is worth quantifying—is illustrated by some data on a human birth defect, namely, fetal alcohol syndrome. In a suggestive metaphor, the biometrician is like the pilgrim in Friedrich’s painting Der Wanderer über dem Nebelmeer, uncertain as to whether to measure the mountains or the clouds. The mountains stand for contingent history, the clouds for the subset of the data most closely matching controlled experiments suitable for quantitative biometric summary. Biometrics applies to the clouds, not the mountains. The success of statistical methods comes at the expense of all the theories that we simultaneously hold to be true about the biological materials to which they both pertain. Biometrics is thus complementary to all of the emerging reductionist sciences of biological structure. (shrink)

The current literature that attempts to bridge between geometric morphometrics (GMM) and finite element analyses (FEA) of CT-derived data from bones of living animals and fossils appears to lack a sound biotheoretical foundation. To supply the missing rigor, the present article demonstrates a new rhetoric of quantitative inference across the GMM–FEA bridge—a rhetoric bridging form to function when both have been quantified so stringently. The suggested approach is founded on diverse standard textbook examples of the relation between forms and the (...) way strains in them are produced by stresses imposed upon them. One potentially cogent approach to the explanatory purposes driving studies of this class arises from a close scrutiny of the way in which computations in both domains, shape and strain, can be couched as minimizations of a scalar quantity. For GMM, this is ordinary Procrustes shape distance; in FEA, it is the potential energy that is stored in the deformed configuration of the solid form. A hybrid statistical method is introduced requiring that all forms be subjected to the same detailed loading designs (the same “probes”) in a manner careful to accommodate the variations of those same forms before they were stressed. The proper role of GMM is argued to be the construction of regressions for strain energy density on the largest-scale relative warps in order that biological explanations may proceed in terms of the residuals from those regressions: the local residual features of strain energy density. The method, evidently a hierarchical one, might be intuitively apprehended as a geometrical approach to a formal allometric analysis of strain. The essay closes with an exhortation. (shrink)