Morphometric Variation at Different Spatial Scales: Coordination and Compensation in the Emergence of Organismal Form.

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.[Cranial shape; developmental canalization; evolvability; morphological integration; morphometrics; phenotypic variation; self-similarity.].

Correlation of the human pubic symphysis surface with age-at-death: a novel quantitative method based on a bandpass filter.

Age-at-death estimation from skeletal remains typically utilizes the roughness of pubic symphysis articular surfaces. This study presents a new quantitative method adapting a tool from geometric morphometrics, bandpass filtering of partial warp bending energy to extract only age-related changes of the surfaces. The study sample consisted of 440 surface-scanned symphyseal pubic bones from men between 14 and 82 years of age, which were landmarked with 102 fixed and surface semilandmarks. From the original sample, 371 specimens within Procrustes distance of 0.05 of the side-specific average were selected. For this subsample, age was correlated with total bending energy (calculated as summed squared partial warps amplitudes) for a wide range of plausible bandpass filters. For our subsample's 188 right-side surfaces, the correlation between age and bandpass filtered versions of bending energy peaks relatively sharply at r = -0.648 for ages up through 49 years against the first seven partial warp amplitudes only. The finding for left symphyses is similar. The results demonstrate that below the age 50, the symphyseal surface form changes most systematically related to age may be best detected by a lowpass-filtered version of bending energy: signals at the largest geometric scales of roughness rather than its full spectrum. Combining this method with information from other skeletal features could further improve age-at-death estimation based on the symphyseal pubic surface.

How not to answer interdisciplinary "Why?" questions.

The book under review tries to link the economic concept of "reward," or, more accurately, "capture rate," to the experimental literature of various neuroscientific quantities dealing with motor control. But this reviewer argues that such a linkage requires a richer language of quantification than the book actually affords: a language not just of "greater" or "less," but of how much greater or less. Without such a methodology, the arguments here cannot be persuasive.

Variation of 3D outer and inner crown morphology in modern human mandibular premolars.

OBJECTIVES: This study explores the outer and inner crown of lower third and fourth premolars (P3 , P4 ) by analyzing the morphological variation among diverse modern human groups. MATERIALS AND METHODS: We studied three-dimensional models of the outer enamel surface and the enamel-dentine junction (EDJ) from µCT datasets of 77 recent humans using both an assessment of seven nonmetric traits and a standard geometric morphometric (GM) analysis. For the latter, the dental crown was represented by four landmarks (dentine horns and fossae), 20 semilandmarks along the EDJ marginal ridge, and pseudolandmarks along the crown and cervical outlines. RESULTS: Certain discrete traits showed significantly different regional frequencies and sexual dimorphism. The GM analyses of both P3 s and P4 s showed extensive overlap in shape variation of the various populations (classification accuracy 15-69%). The first principal components explained about 40% of shape variance with a correlation between 0.59 and 0.87 of the features of P3 s and P4 s. Shape covariation between P3 s and P4 s expressed concordance of high and narrow or low and broad crowns. CONCLUSIONS: Due to marked intragroup and intergroup variation in GM analyses of lower premolars, discrete traits such as the number of lingual cusps and mesiolingual groove expression provide better geographic separation of modern human populations. The greater variability of the lingual region suggests a dominance of functional constraints over geographic provenience or sex. Additional information about functionally relevant aspects of the crown surface and odontogenetic data are needed to unravel the factors underlying dental morphology in modern humans.

A method of factor analysis for shape coordinates.

Currently the most common reporting style for a geometric morphometric (GMM) analysis of anthropological data begins with the principal components of the shape coordinates to which the original landmark data have been converted. But this focus often frustrates the organismal biologist, mainly because principal component analysis (PCA) is not aimed at scientific interpretability of the loading patterns actually uncovered. The difficulty of making biological sense of a PCA is heightened by aspects of the shape coordinate setting that further diverge from our intuitive expectations of how morphometric measurements ought to combine. More than 50 years ago one of our sister disciplines, psychometrics, managed to build an algorithmic route from principal component analysis to scientific understanding via the toolkit generally known as factor analysis. This article introduces a modification of one standard factor-analysis approach, Henry Kaiser's varimax rotation of 1958, that accommodates two of the major differences between the GMM context and the psychometric context for these approaches: the coexistence of "general" and "special" factors of form as adumbrated by Sewall Wright, and the typical loglinearity of partial warp variance as a function of bending energy. I briefly explain the history of principal components in biometrics and the contrast with factor analysis, introduce the modified varimax algorithm I am recommending, and work three examples that are reanalyses of previously published cranial data sets. A closing discussion emphasizes the desirability of superseding PCA by algorithms aimed at anthropological understanding rather than classification or ordination.

Reconsidering "The inappropriateness of conventional cephalometrics".

Of all the articles on cephalometrics this journal has published over the last half-century, the one most cited across the scientific literature is the 1979 lecture "The inappropriateness of conventional cephalometrics" by Robert Moyers and me. But the durable salience of this article is perplexing, as its critique was misdirected (it should have been aimed at the craniometrics of the early twentieth century, not merely the roentgenographic extension used in the orthodontic clinic) and its proposed remedies have all failed to establish themselves as methods of any broad utility. When problems highlighted by Moyers and me have been resolved at all, the innovations that resolved them owe to tools very different from those suggested in our article and imported from fields quite a bit farther from biometrics than we expected back in 1979. One of these tools was the creation de novo of a new abstract mathematical construction, statistical shape space, in the 1980s and 1990s; another was a flexible and intuitive new graphic, the thin-plate spline, for meaningfully and suggestively visualizing a wide variety of biological findings in these spaces. On the other hand, many of the complaints Moyers and I enunciated back in 1979, especially those stemming from the disarticulation of morphometrics from the explanatory styles and purposes of clinical medicine, remain unanswered even today. The present essay, a retrospective historical meditation, reviews the context of the 1979 publication, its major themes, and its relevance today. This essay is dedicated to the memory of Robert E. Moyers on the 100th anniversary of the American Journal of Orthodontics and Dentofacial Orthopedics.

Variability of Australopithecus second maxillary molars from Sterkfontein Member 4.

The question of how many Australopithecus species lived at Sterkfontein Member 4 and Makapansgat continues to be controversial inasmuch as the fossils are poorly preserved, the stratigraphy is difficult to interpret, and the cranial, dental, and postcranial remains are mostly not associated. To proceed we applied the most intensive modern methods of 3D geometric morphometrics to dental form, specifically the shapes of the upper second molars (M(2)s) in a sample combining 13 Australopithecus, 11 Paranthropus, and 23 Homo. We analyzed outer and inner crown surfaces, as well as crown and cervical outlines both separately and together, using a total of 16 landmarks, 51 curve semilandmarks, and 48 pseudolandmarks over the four structures. Outer and inner enamel surfaces are highly correlated in this dataset, while crown outline is the least informative of the four structures. Homo was easily distinguished from both Australopithecus and Paranthropus by these methods, likewise Homo sapiens from Homo neanderthalensis. There were, however, no stable classes within the Australopithecus sample or between Australopithecus and Paranthropus. Instead, there was a gradient along which Australopithecus prometheus and Australopithecus africanus lie toward the extremes, with Paranthropus overlapping both. If there are indeed different species at this site, then either their M(2) morphologies are uninformative or else the present sample is too small to make an accurate assessment. Our findings suggest that the variability of the Australopithecus specimens will be difficult to interpret authoritatively, independent of the method used.

The psychology of inherence is self-referential (and that is a good thing).

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.

"The map is not the territory".

Bentley et al.'s claim that their "map … captures the essence of decision making" (target article, Abstract) is deconstructed and shown to originate in a serious misunderstanding of the role of principal components and statistical graphics in the generation of pattern claims and hypotheses from profile data. Three alternative maps are offered, each with its radiation of further investigations.

Analysis of the human female foot in two different measurement systems: from geometric morphometrics to functional morphology.

The relationship of geometric morphometrics (GMM) to functional analysis of the same morphological resources is currently a topic of active interest among functional morphologists. Although GMM is typically advertised as free of prior assumptions about shape features or morphological theories, it is common for GMM findings to be concordant with findings from studies based on a-priori lists of shape features whenever prior insights or theories have been properly accounted for in the study design. The present paper demonstrates this happy possibility by revisiting a previously published GMM analysis of footprint outlines for which there is also functionally relevant information in the form of a-pri-ori foot measurements. We show how to convert the conventional measurements into the language of shape, thereby affording two parallel statistical analyses. One is the classic multivariate analysis of "shape features", the other the equally classic GMM of semilandmark coordinates. In this example, the two data sets, analyzed by protocols that are remarkably different in both their geometry and their algebra, nevertheless result in one common biometrical summary: wearing high heels is bad for women inasmuch as it leads to the need for orthotic devices to treat the consequently flattened arch. This concordance bears implications for other branches of applied anthropology. To carry out a good biomedical analysis of applied anthropometric data it may not matter whether one uses GMM or instead an adequate assortment of conventional measurements. What matters is whether the conventional measurements have been selected in order to match the natural spectrum of functional variation.

Infant growth patterns of the mandible in modern humans: a closer exploration of the developmental interactions between the symphyseal bone, the teeth, and the suprahyoid and tongue muscle insertion sites.

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.

Technical note: a novel geometric morphometric approach to the study of long bone shape variation.

Procrustes-based geometric morphometrics (GM) is most often applied to problems of craniofacial shape variation. Here, we demonstrate a novel application of GM to the analysis of whole postcranial elements in a study of 77 hominoid tibiae. We focus on two novel methodological improvements to standard GM approaches: 1) landmark configurations of tibiae including 15 epiphyseal landmarks and 483 semilandmarks along articular surfaces and muscle insertions along the tibial shaft and 2) an artificial affine transformation that sets moments along the shaft equal to the sum of the moments estimated in the other two anatomical directions. Diagrams of the principal components of tibial shapes support most differences between human and non-human primates reported previously. The artificial affine transformation proposed here results in an improved clustering of the great apes that may prove useful in future discriminant or clustering studies. Since the shape variations observed may be related to different locomotor behaviors, posture, or activity patterns, we suggest that this method be used in functional analyses of tibiae or other long bones in modern populations or fossil specimens.

Early modern human diversity suggests subdivided population structure and a complex out-of-Africa scenario.

The interpretation of genetic evidence regarding modern human origins depends, among other things, on assessments of the structure and the variation of ancient populations. Because we lack genetic data from the time when the first anatomically modern humans appeared, between 200,000 and 60,000 years ago, instead we exploit the phenotype of neurocranial geometry to compare the variation in early modern human fossils with that in other groups of fossil Homo and recent modern humans. Variation is assessed as the mean-squared Procrustes distance from the group average shape in a representation based on several hundred neurocranial landmarks and semilandmarks. We find that the early modern group has more shape variation than any other group in our sample, which covers 1.8 million years, and that they are morphologically similar to recent modern humans of diverse geographically dispersed populations but not to archaic groups. Of the currently competing models of modern human origins, some are inconsistent with these findings. Rather than a single out-of-Africa dispersal scenario, we suggest that early modern humans were already divided into different populations in Pleistocene Africa, after which there followed a complex migration pattern. Our conclusions bear implications for the inference of ancient human demography from genetic models and emphasize the importance of focusing research on those early modern humans, in particular, in Africa.

A new OH5 reconstruction with an assessment of its uncertainty.

The OH5 cranium, holotype of Paranthropus boisei consists of two main portions that do not fit together: the extensively reconstructed face and a portion of the neurocranium. A physical reconstruction of the cranium was carried out by Tobias in 1967, who did not discuss problems related to deformation, although he noted a slight functional asymmetry. Nevertheless, the reconstructed cranium shows some anomalies, mainly due to the right skewed position of the upper calvariofacial fragment and uncertainty of the relative position of the neurocranium to the face, which hamper further quantitative analysis of OH5's cranial geometry. Here, we present a complete virtual reconstruction of OH5, using three-dimensional (3D) digital data, geometric morphometric (GM) methods and computer-aided design (CAD) techniques. Starting from a CT scan of Tobias's reconstruction, a semi-automatic segmentation method was used to remove Tobias's plaster. The upper calvariofacial fragment was separated from the lower facial fragment and re-aligned using superposition of their independent midsagittal planes in a range of feasible positions. The missing parts of the right hemiface were reconstructed using non-uniform rational basis-spline (NURBS) surface and subsequently mirrored using the midsagittal plane to arrive at a symmetrical facial reconstruction. A symmetric neurocranium was obtained as the average of the original shape and its mirrored version. The alignment between the two symmetric shapes (face and neurocranium) used their independent midsagittal plane and a reference shape (KNM-ER 406) to highly reduce their degrees of freedom. From the series of alternative reconstructions, we selected the middle of this rather small feasible range. When reconstructed as a range in this way, the whole cranial form of this unique specimen can be further quantified by comparative coordinate-based methods such as GM or can be used for finite element modeling (FEM) explorations of hypotheses about the mechanics of early hominin feeding and diets.

Sexual dimorphism of the human mandible and its association with dental development.

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.

Socioeconomic status, marital status and childlessness in men and women: an analysis of census data from six countries.

This study compares the effects of two distinct forms of human capital - income and education - on marital status and childlessness separately by sex in six different countries. Nearly 10 million individual records on individuals aged 16 to 50 were used from censuses from Brazil, Mexico, Panama, South Africa, USA and Venezuela dating from 2000 or later, to analyse the relationship between education, income and marital status and childlessness in men and women. Regarding income, the findings for both outcome variables are strongly consistent across all six countries. Highest-income males and lower-income females have the highest proportion of ever-married and the lowest proportion of childlessness (using a proxy for childlessness: own children in the household or not). There is no corresponding consistency of findings as regards education either between the sexes or among the countries. To conclude, a lower percentage of low-income men are selected by females, because for women male status and resources provided by men are important criteria in mate selection. Therefore a higher proportion of low-income men remain unmarried and childless. Thus selection seems to play a role in modern societies.

Fetal and infant growth patterns of the mandibular symphysis in modern humans and chimpanzees (Pan troglodytes).

Comparison of the early development of the mandibular symphysis between primates and modern humans is of particular interest in human palaeontology. Using geometric morphometric methods, we explored and compared the ontogenetic shape changes of 14 chimpanzee mandibles (Pan troglodytes) against 66 human CT-scanned mandibles over the age range from fetal life to the complete emergence of the deciduous dentition in a visualization incorporating the deciduous tooth arrangement. The results reveal that the symphysis is anteriorly inclined in the youngest chimpanzee fetuses but develops an increasingly vertical orientation up until birth. At the same time, the anterior teeth reorient before a vertical emergence, and a symphyseal tuber appears on the labial side. When the deciduous canine emerges, the symphysis inclines anteriorly again, exhibiting the adult characteristic slope. These two phases are characterized by a repositioning of the simian shelf. Unlike chimpanzees, the human symphysis remains vertical throughout fetal development. However, the combination of morphological changes observed in chimpanzee fetuses is similar to that of modern humans after birth, as the mental region projects forward. By elongating the alveolar process, the inclination of the chimpanzee symphysis could be a key event for emergence of the deciduous canine, as space is lacking at the alveolar ridge in a vertical symphysis once the deciduous incisors and molars have emerged. The repositioning of the simian shelf suggests that the suprahyoid muscles have a significant influence on the anterior growth of the symphysis. The anteroposterior positioning of the basal symphysis in both species may be related to hyoid bone position during ontogeny.

Socioeconomic status, education, and reproduction in modern women: an evolutionary perspective.

Although associations between status or resources and reproduction are positive in premodern societies and also in men in modern societies, in modern women the associations are typically negative. We investigated how the association between socioeconomic status and reproductive output varies with the source of status and resources, the woman's education, and her age at reproductive onset (proxied by age at marriage). By using a large sample of US women, we examined the association between a woman's reproductive output and her own and her husband's income and education. Education, income, and age at marriage are negatively associated with a woman's number of children and increase her chances of childlessness. Among the most highly educated two-thirds of the sample of women, husband's income predicts the number of children. The association between a woman's number of children and her husband's income turns from positive to negative when her education and age at marriage is low (even though her mean offspring number rises at the same time). The association between a woman's own income and her number of children is negative, regardless of education. Rather than maximizing the offspring number, these modern women seem to adjust investment in children based on their family size and resource availability. Striving for resources seems to be part of a modern female reproductive strategy--but, owing to costs of resource acquisition, especially higher education, it may lead to lower birthrates: a possible evolutionary explanation of the demographic transition, and a complement to the human capital theory of net reproductive output.

Anatomical similarity between the Sost-knockout mouse and sclerosteosis in humans.

Sclerosteosis, a rare autosomal recessive genetic disorder caused by a mutation of the Sost gene, manifests in the facial skeleton by gigantism, facial distortion, mandibular prognathism, cranial nerve palsy, and, in extreme cases, compression of the medulla oblongata. Mice lacking sclerostin reflect some symptoms of sclerosteosis, but this is the first report of the effect on the facial skeleton. We used geometric morphometrics (GMM) to analyze the deformations of the murine facial skeleton from the wild-type to the Sost gene knockout. Landmark coordinates were obtained by surface reconstructions from micro-computed tomography. Centroid size, principal component scores in shape space and form space, and asymmetry were computed by the standard GMM formulas, and dental and skeletal jaw lengths were examined as ratios. We show here that, compared to wild type controls, mice lacking Sost have larger centroid size (effect size, p-value: 4.59, <.001), higher mean asymmetry (1.14, .065), dental and skeletal mandibular prognathism (1.36, .010 and 5.92, <.001), a smaller foramen magnum (-1.71, .015), and calvaria that are more highly curved (form space p = 4.09, .002; shape space p = 12.82, .002). These features of mice lacking sclerostin largely correspond to the changes of the facial skeleton observed in sclerosteosis. This alignment further supports claims that the Sost gene plays a fundamental role in bony facial development in rodents and humans alike.

Principles for the virtual reconstruction of hominin crania.

Fossils are usually discovered broken or distorted, therefore reconstruction is inevitably the first step towards any comparative analysis. We outline a general methodological framework by which missing information about biological specimens can be estimated using geometric morphometric methods and discuss how this relates to effective paleoanthropological use of incomplete and distorted crania. Combining digital data resources with geometric morphometrics, we go beyond the assembly of fragments on the computer. As in a three-dimensional jigsaw puzzle, we first assemble the virtual pieces manually. Then we use landmarks, several hundred semilandmarks, and information from complete specimens to estimate missing coordinates and correct for distortion simultaneously. One can thus incorporate information from incomplete specimens in a comparative morphometric analysis while keeping track of the uncertainties that result from partial preservation or deformation. We exemplify our approach by reconstructing the fossil crania Arago XXI, Taung, and KNM-WT 15000. As different assumptions and algorithms lead to different estimations, there exists no "all-purpose" reconstruction. Instead one creates multiple reconstructions-a posterior distribution in a Bayesian sense. This distribution reflects uncertainty due to missing data values and sensitivity to prior assumptions. While there will typically be shape differences among equally plausible reconstructions, these different estimates might still support a single conclusion.