Several papers have appeared in the recent literature of forensic anthropology exploring the possibility that surface measurements of a cadaver's pubic symphysis might be converted by linear statistics (correlation-based methods) into a numerical estimate of its age at death. In its logic this maneuver would be an instance of an inverse regression, a "prediction" from an effect to its presumed cause. From the statistical literature of the 1940s and 1950s we retrieve a mandatory requirement that a data set must satisfy if this estimation is to be performed by a regression: the average prediction afforded by both regression lines, the one predicting from cause to effect and the one "predicting" from effect to cause, must closely match the average of the data being predicted along every bin of that predictor's length—either regression must be least squares not only at large scale but at the smallest scales. Evidence from yesterday's and today's forensic literature demonstrates unequivocally that this requirement cannot be met. It follows that it is impossible to fulfill the forensic assignment validly by linear methods such as regression or correlation no matter how sophisticated the geometric morphometrics on which they are based. In their stead we propose borrowing an alternative, Rasch scaling, from the methodological literature of developmental psychology. Any such protocol would require the arithmetical fusion of indicia of multiple processes of development and multiple processes of aging, each one measured separately based on rigorous analysis of the forward predictions from age to morphometrics, predictions that themselves must satisfy similarly rigorous requirements.

It is a classic aim of quantitative and evolutionary biology to infer genetic architecture and potential evolutionary responses to selection from the variance-covariance structure of measured traits. But a meaningful genetic or developmental interpretation of raw covariances is difficult, and classic concepts of morphological integration do not directly apply to modern morphometric data. Here, we present a new morphometric strategy based on the comparison of morphological variation across different spatial scales. If anatomical elements vary completely independently, then their variance accumulates at larger scales or for structures composed of multiple elements: morphological variance would be a power function of spatial scale. Deviations from this pattern of "variational self-similarity" (serving as a null model of completely uncoordinated growth) indicate genetic or developmental coregulation of anatomical components. We present biometric strategies and R scripts for identifying patterns of coordination and compensation in the size and shape of composite anatomical structures. In an application to human cranial variation, we found that coordinated variation and positive correlations are prevalent for the size of cranial components, whereas their shape was dominated by compensatory variation, leading to strong canalization of cranial shape at larger scales. We propose that mechanically induced bone formation and remodeling are key mechanisms underlying compensatory variation in cranial shape. Such epigenetic coordination and compensation of growth are indispensable for stable, canalized development and may also foster the evolvability of complex anatomical structures by preserving spatial and functional integrity during genetic responses to selection.

This article exploits a method recently incorporated in the geometric morphometric toolkit that complements previous approaches to quantifying the facial features associated with specific body characteristics and trait attribution during social perception. The new method differentiates more globally encoded from more locally encoded information by a summary scaling dimension that is estimated by fitting a line to the plot of log bending energy against log variance explained, partial warp by partial warp, for some sample of varying shapes. In the present context these variances come from the regressions of shape on some exogenous cause or effect of form. We work an example involving data from male faces. Here the regression slopes are steepest, and the sums of explained variances over the uniform component, partial warp 1 and partial warp 2 are greatest, for the conventional body mass index, followed by cortisol and, lastly, perceived health. This suggests that physiological characteristics may be represented at larger scale (global patterns), whereas cues in perception are of smaller scale (local patterns). Such a polarity within psychomorphospace, the global versus the focal, now has a metric by which patterns of morphology can be modeled in both biological and psychological studies.

Searchable abstracts of presentations at key conferences on calcified tissues ISSN 2052-1219 (online)

The biologist examining samples of multicellular organisms in anatomical detail must already have an intuitive concept of morphological integration. But quantifying that intuition has always been fraught with difficulties and paradoxes, especially for the anatomically labelled Cartesian coordinate data that drive today's toolkits of geometric morphometrics. Covariance analyses of interpoint distances, such as the Olson–Miller factor approach of the 1950's, cannot validly be extended to handle the spatial structure of complete morphometric descriptions; neither can analyses of shape coordinates that ignore the mean form. This paper introduces a formal parametric quantification of integration by analogy with how time series are approached in modern paleobiology. Over there, a finding of trend falls under one tail of a distribution for which stasis comprises the other tail. The null hypothesis separating these two classes of finding is the random walks, which are self-similar, meaning that they show no interpretable structure at any temporal scale. Trend and stasis are the two contrasting ways of deviating from this null. The present manuscript introduces an analogous maneuver for the spatial aspects of ontogenetic or phylogenetic organismal studies: a subspace within the space of shape covariance structures for which the standard isotropic (Procrustes) model lies at one extreme of a characteristic parameter and the strongest growth-gradient models at the other. In-between lies the suggested new construct, the spatially self-similar processes that can be generated within the standard morphometric toolkit by a startlingly simple algebraic manipulation of partial warp scores. In this view, integration and "disintegration" as in the Procrustes model are two modes of organismal variation according to which morphometric data can deviate from this common null, which, as in the temporal domain, is formally featureless, incapable of supporting any summary beyond a single parameter for amplitude. In practice the classification can proceed by examining the regression coefficient for log partial warp variance against log bending energy in the standard thin-plate spline setup. The self-similarity model, for which the regression slope is precisely $$-1,$$ corresponds well to the background against which the evolutionist's or systematist's a-priori notion of "local shape features" can be delineated. Integration as detected by the regression slope can be visualized by the first relative intrinsic warp (first relative eigenvector of the nonaffine part of a shape coordinate configuration with respect to bending energy) and may be summarized by the corresponding quadratic growth gradient. The paper begins with a seemingly innocent toy example, uncovers an unexpected invariance as an example of the general manipulation proposed, then applies the new modeling tactic to three data sets from the existing morphometric literature. Conclusions follow regarding findings and methodology alike.

Cimpian & Salomon (C&S) appear to characterize the inherence heuristic and essentialism as unwise or childish aspects of human reasoning. But actually, these cognitive modes lie at the core of statistical analysis across all of the quantitative sciences, including the developmental cognitive psychology in which the argument here is couched. Their whole argument is as much an example of its topic as an analysis of it.

Most biologists are familiar with principal component analysis as an ordination tool for questions about within-group or between-group variation in systems of quantitative traits, and with multivariate analysis of variance as a tool for one useful description of the latter in the context of the former. Less familiar is the mathematical approach of relative eigenanalysis of which both of these are special cases: computing linear combinations for which two variance–covariance patterns have maximal ratios of variance. After reviewing this common algebraic–geometric core, we demonstrate the effectiveness of this exploratory approach in studies of developmental canalization and the identification of divergent and stabilizing selection. We further outline a strategy for statistical classification when group differences in variance dominate over differences in group averages.

The ontogenetic development of the mental region still poses a number of unresolved questions in human growth, development and phylogeny. In our study we examine the hypotheses of DuBrul & Sicher (1954) (The Adaptive Chin. Springfield, IL: Charles) and Enlow (1990) (Facial Growth, 3rd edn. Philadelphia, PA: Saunders) to explain the presence of a prominent mental region in anatomically modern humans. In particular, we test whether the prominence of the mental region and the positioning of the teeth are both correlated with the developmental relocation of the tongue and the suprahyoid muscles inserting at the lingual side of the symphysis. Furthermore, we test whether the development of the mental region is associated with the development of the back of the vocal tract. Using geometric morphometric methods, we measured the 3D mandibular and tooth surfaces in a cross-sectional sample of 36 CT-scanned living humans, incorporating the positions of the tongue and the geniohyoid and digastric muscle insertions. The specimens' ages range from birth to the complete emergence of the deciduous dentition. We used multivariate regression and two-block partial least squares (PLS) analysis to study the covariation among the mental region, the muscle insertions, and the teeth both across and within age stages. In order to confirm our results from the 3D cross-sectional sample, and to relate them to facial growth and the position of the cervical column and the hyoid bone, we used 46 lateral radiographs of eight children from the longitudinal Denver Growth Study. The 3D analysis demonstrates that the lingual side of the lower border of the symphysis develops downwards and forwards. These shape changes are significantly correlated with the relocation of muscle insertion sites and also with the vertical reorientation of the anterior teeth prior to emergence. The 2D analysis confirms the idea that as the mental region prominence develops, the space of the laryngopharynx becomes restricted due to upper mid-face retraction and the acquisition of upright body posture. In agreement with the hypotheses of DuBrul & Sicher (1954) and Enlow (1990), our results suggest that the presence of a prominent mental region responds to the space restriction at the back of the vocal tract, and to the packaging of the tongue and suprahyoid muscles in order to preserve the functionality of the laryngopharynx during respiration, feeding and speech.

The present study investigates whether the human mandible is sexually dimorphic during early postnatal development and whether early dimorphic features persist during subsequent ontogeny. We also examine whether mandibular dimorphism is linked to dimorphism of dental development. Dense CT-derived mandibular meshes of 84 females and 75 males, ranging from birth to adulthood, were analyzed using geometric morphometric methods. On the basis of the specimen's chronological ages and mineralization stages of the deciduous and permanent teeth, we compute dental age as proxy for dental development by the additive conjoint measurement method. By birth, males have, on average, more advanced age-specific shapes than females. However, sex differences decrease quickly as females catch up via a different association between shape and size. This leads to an almost complete reduction of sexual dimorphism between the ages of 4 and 14. From puberty to adulthood, males are characterized by allometric shape changes while the shape of the female mandible continues to change even after size has ceased to increase. Dimorphism of dental maturation becomes visible only at puberty. Sexual dimorphism, concentrated at the ramus and the mental region during the earliest ontogenetic stages and again at adulthood, is not associated with the development of the teeth. At puberty there is a simultaneous peak in size increase, shape development, and dental maturation likely controlled by the surge of sex hormones with a dimorphic onset age. We argue that the infant and adult dimorphism of the mental region may be associated with the development of supralaryngeal structures.

Morphometrics of the molar crown is based traditionally on diameter measurements but is nowadays more often based on 2D image analysis of crown outlines. An alternative approach involves measurements at the level of the cervical line. We compare the information content of the two options in a three-dimensional (3D) digital sample of lower and upper first molars (M(1) and M(1) ) of modern human and Neanderthal teeth. The cervical outline for each tooth was created by digitizing the cervical line and then sectioning the tooth with a best fit plane. The crown outline was projected onto this same plane. The curves were analyzed by direct extraction of diameters, diagonals, and area and also by principal component analysis either of the residuals obtained by regressing out these measurements from the radii (shape information) or directly by the radii (size and shape information). For M(1) , the crown and cervical outline radii allow us to discriminate between Neanderthals and modern humans with 90% and 95% accuracy, respectively. Fairly good discrimination between the groups (80-82.5%) was also obtained using cervical measurements. With respect to M(1) , general overlap of the two groups was obtained by both crown and cervical measurements; however, the two taxa were differentiable by crown outline residuals (90-97%). Accordingly, while crown diameters or crown radii should be used for taxonomic analysis of unworn or slightly worn M(1) s, the crown outline, after regressing out size information, could be promising for taxonomic assignment of lower M1s.

Title: Localized differences in caudate and hippocampal shape are associated with schizophrenia but not antipsychotic type Article Type: Archival Report Abstract: Background: Differences in the volume of the caudate and hippocampus in patients with schizophrenia are associated with disease and antipsychotic treatment. The relationship between alterations in caudate and hippocampal shape with disease and antipsychotic treatment has not been thoroughly examined. Methods: Schizophrenia patients, randomly assigned to haloperidol and olanzapine treatment, underwent longitudinal MRI scans at 3, 6, and 9 months. The caudate and the hippocampus were, bilaterally, segmented from high-resolution brain MRI with an automated technique. The shape of the caudate and the hippocampus were represented as a medial representation (M-rep), a mesh structure derived from these segmentations. The shape of the caudate and hippocampus were derived from the M-repusing two quantitative measures: local width and local deformation. A novel nonparametric statistical method, called adjusted exponentially tilted (ET) likelihood, was used to compare the measures of caudate and hippocampus shape across the three groups, while controlling for covariates of interest. Results: Contrary to our a priori hypothesese, longitudinal shape change was not observed in the hippocampus or caudate when the haloperidol-treated, olanzapine-treated, and healthy controls were examined in a global analysis. Contrary to our a priori hypothesese, no longitudinal shape change was observed when the three groups were examined individually. Consistent with our a priori hypothesise, both baseline and repeated measures analysis showed differences in local caudate and hippocampal size between haloperidol-treated and olanzapine treated patients and controls. Also consistent with our a priori hypothesise, baseline and repeated-measures cross-sectional analysis, showed no consistent differences in hippocampal or caudate shape between the haloperidol-treated and olanzapine-treated patients. Conclusions: Regionally specific differences in local hippocampal and caudate shape are present in schizophrenic patients. Longitudinal shape change was not observed haloperidol-and olanzapine-treated patients within the observed time frame in our sample. Regionally specific shape differences between in schizophrenia patients and controls: suggests that the M-reps method is valid and reliable, and; provides additional evidence for the presence of disrupted cortico-basal ganglia-thalamo-cortical circuits in schizophrenia. These results should be confirmed with replication in a different sample, using a study design that controls for confounding factors.-while surely an expert in shape analysis, he has quite uncommon & strong opinions about the shape analysis often not shared by rest of the community-lack of knowledge in schizophrenia Editorial Office of Biological Psychiatry Please accept the submission of …