Reflections on a Biometrics of Organismal Form

Abstract

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 (the biometrics of organismal form) 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 (uniform shears) 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.