Biology subjects

Bookstein, F. L.

Publications and source records attributed to Bookstein, F. L..

3 recordsLinked to original sources

bioRxiv2024

Bridging geometric morphometrics to medical anatomy: An example from an experimental study of the human smile

The method of Cartesian transformations introduced by DArcy Thompson a century ago in his celebrated book On Growth and Form precipitated an important development in 20th-century biometrics: a fusion of the geometrical and biological approaches to morphology. Some decades later this fusion, in turn, spun off another multidisciplinary focus, statistical shape analysis, that bridges between biostatistics and biomedical imaging. Our article is intended to seed a complementary focus: a bridge between biostatistics and medical anatomy, a field that has to this day remained mainly verbal rather than quantitative. Specifically, we are proposing a novel methodology for arriving at anatomical interpretations of statistical findings about large-scale contrasts of organismal morphology or its dynamics by combining two toolkits hitherto separate in their notation and their disciplinary housing: morphometrics and psychometrics. A contemporary morphometric analysis deals with patterns of shape coordinate covariation in terms of their geometric adjacency; psychometric factor analysis, the same patterns of covariation in terms of simplicity of interpretation. By combining these tools we account for the dynamics of a facial expression in terms of the actions of the underlying muscles, thereby realizing Thompsons original metaphor, the "origins of form in force," for systems that "vary in a more or less uniform manner." This paper reviews the history of Thompsons metaphor and then the current literature quantifying smiles, in order to set the stage for the combination of scaling analysis and factor analysis that we are putting forward. We demonstrate the new approach by reanalyzing a data set of ten landmarks around the vermilion borders of the human lip contrasting the dynamics of two socially stereotyped physiological cycles, the open-lip smile and the closed-lip smile, over a sample of 14 normal faces. Our analysis centers on just two dimensions of statistical shape space, those of largest geometrical scale, which can be identified with the action of two different muscles, orbicularis oris and zygomaticus major. The two smiles differ radically in their achieved deformations. Furthermore, while the closed-lip smiles arrived at their final forms along similar shape trajectories, the open-lip smiles did not. Our closing discussion explores some aspects of morphodynamics that are illuminated by the example here.

physiology↗

bioRxiv2023

Quadratic trends: a morphometric tool both old and new

The original exposition of the method of "Cartesian transformations" in DArcy Thompsons great essay On Growth and Form of 1917 is still its most cited. But generations of theoretical biologists have struggled ever since to invent a biometric method aligning that approach with the comparative anatomists ultimate goal of inferring bio-logically meaningful hypotheses from empirical geometric patterns. Thirty years ago our community converged on a common data resource, samples of landmark configurations, and a currently popular biometric toolkit for this purpose, the "morphometric synthesis," that combines Procrustes shape coordinates with thin-plate spline renderings of their various multivariate statistical comparisons. But because both tools algebraically disarticulate the landmarks in the course of a linear multivariate analysis, they have no access to the actual anatomical information conveyed by the arrangements and adjacencies of these locations as they combine in pairs or higher numbers into substructures. This paper explores a geometric approach circumventing these fundamental difficulties: an explicit statistical methodology for the simplest nonlinear patterning of these comparisons at their largest scale, their fits by what Sneath (1967) called quadratic trend surfaces. After an initial quadratic regression of target configurations on a template, the proposed method ignores individual shape coordinates completely, replacing them by a close reading of the regression coefficients accompanied by several new diagrams, notably the exhaustive summary of each regression by an unfamiliar biometric ellipse, its circuit of second-order directional derivatives. These novel trend coordinates, directly visualizable in their own coordinate plane, do not reduce to any of the usual Procrustes or thin-plate summaries. The geometry and algebra of these second-derivative ellipses seem a serviceable first approximation for applications in evo-devo studies and elsewhere. Two examples are offered, one the classic growth data set of Vilmann neurocranial octagons and the other the Marcus groups data set of midsagittal cranial landmarks over most of the orders of the mammals. Each analysis yields startling new findings inaccessible to the current GMM toolkit. A closing discussion suggests a variety of ways by which innovations in this spirit might burst the current strait-jacket of Procrustes coordinates and thin-plate splines that together so severely constrain the conversion of landmark locations into understanding across our science.

evolutionary biology↗

bioRxiv2019

Pathologies of Between-Groups Principal Components Analysis in Geometric Morphometrics

Good empirical applications of geometric morphometrics (GMM) typically involve several times more variables than specimens, a situation the statistician refers to as \"high p/n,\" where p is the count of variables and n the count of specimens. This note calls your attention to two predictable catastrophic failures of one particular multivariate statistical technique, between-groups principal components analysis (bgPCA), in this high-p/n setting. The more obvious pathology is this: when applied to the patternless (null) model of p identically distributed Gaussians over groups of the same size, both bgPCA and its algebraic equivalent, partial least squares (PLS) analysis against group, necessarily generate the appearance of huge equilateral group separations that are actually fictitious (absent from the statistical model). When specimen counts by group vary greatly or when any group includes fewer than about ten specimens, an even worse failure of the technique obtains: the smaller the group, the more likely a bgPCA is to fictitiously identify that group as the end-member of one of its derived axes. For these two reasons, when used in GMM and other high-p/n settings the bgPCA method very often leads to invalid or insecure bioscientific inferences. This paper demonstrates and quantifies these and other pathological outcomes both for patternless models and for models with one or two valid factors, then offers suggestions for how GMM practitioners should protect themselves against the consequences for inference of these lamentably predictable misrepresentations. The bgPCA method should never be used unskeptically -- it is never authoritative -- and whenever it appears in partial support of any biological inference it must be accompanied by a wide range of diagnostic plots and other challenges, many of which are presented here for the first time.

evolutionary biology↗