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)

Complexity in our universe, Herbert Simon once noted, generally takes a hierarchical, nearly decomposable form. If our purpose as biologists is to "carve Nature at the joints," then the quantitative biologist's pattern questions must embody some tentative claim of where the explanatory joints are—only after meaningful qualifications can notions of variance and covariance make sense. In morphometrics, specimens and variables alike can be "carved at the joints," with a correspondingly great gain in explanatory power in both versions. Simon's advice is (...) that the competent biologist's measurements should lie entirely within a single organismal component or else deal entirely with one of the joints. In either context, our best contemporary rhetorics of explanation in biology may resemble morphometrics in their frank combination of carefully supervised parallel quantifications that, taken together, result in new qualifications, leading in turn to new quantifications, and so on. In short, the relation between qualitative and quantitative in the organismal biological sciences is not an opposition but a complementarity, and the modern biometrical statistics of organismal form may be a particularly apposite praxis for exploring it. (shrink)

Back in 1987 the physicist/theoretical biologist Walter Elsasser reviewed a range of philosophical issues at the foundation of organismal biology above the molecular level. Two of these are particularly relevant to quantifications of form: the concept of ordered heterogeneity and the principle of nonstructural memory, the truism that typically the forms of organisms substantially resemble the forms of their ancestors. This essay attempts to weave Elsasser’s principles together with morphometrics for one prominent data type, the representation of animal forms by (...) positions of landmark points. I introduce a new spectrum of pattern descriptors of the shape variation of landmark configurations, ranging from the most homogeneous through growth gradients and focal features to a model of totally disordered heterogeneity incompatible with the rhetoric of functional explanation. An investigation may end up reporting its findings by one of these descriptors or by several. These descriptors all derive from one shared diagrammatic device: a log–log plot of sample variance against one standard formalism of today’s geometric morphometrics, the bending energies of the principal warps that represent all the scales of variability around the sample average shape. The new descriptors, which I demonstrate over a variety of contemporary morphometric examples, may help build the bridge we urgently need between the arithmetic of today’s burgeoning image-based data resources and the rhetoric of biological explanations aligned with the principles of Elsasser along with an even earlier philosopher of biology, the Viennese visionary Hans Przibram. (shrink)