Elliptical Fourier analysis: fundamentals, applications, and value for forensic anthropology

Human identification: an investigation of 3D models of paranasal sinuses to establish a biological profile on a modern UK population

Medical imaging is a valuable source for facilitating empirical research and provides an accessible gateway for developing novel forensic anthropological methods for analysis including 3D modelling. This is especially critical for the United Kingdom (UK), where methods developed from modern UK populations do not currently exist. This study introduces a new approach to assist in human identification using 3D models of the paranasal sinuses. The models were produced from a database of 500 modern CT scans provided by University College London Hospital. Linear measurements and elliptic Fourier coefficients taken from 1500 three-dimensional models across six ethnic groups assessed by one-way ANOVA and discriminant function analysis showed a range of classification rates with certain rates reaching 75-85.7% (p < 0.05) in correctly classifying age and sex according to size and shape. The findings offer insights into the potential for employing paranasal sinuses as an attribute for establishing the identification of unknown human remains in future crime reconstructions.

Sox21b underlies the rapid diversification of a novel male genital structure between Drosophila species

The emergence and diversification of morphological novelties is a major feature of animal evolution.1,2,3,4,5,6,7,8,9 However, relatively little is known about the genetic basis of the evolution of novel structures and the mechanisms underlying their diversification. The epandrial posterior lobes of male genitalia are a novelty of particular Drosophila species.10,11,12,13 The lobes grasp the female ovipositor and insert between her abdominal tergites and, therefore, are important for copulation and species recognition.10,11,12,14,15,16,17 The posterior lobes likely evolved from co-option of a Hox-regulated gene network from the posterior spiracles10 and have since diversified in morphology in the D. simulans clade, in particular, over the last 240,000 years, driven by sexual selection.18,19,20,21 The genetic basis of this diversification is polygenic but, to the best of our knowledge, none of the causative genes have been identified.22,23,24,25,26,27,28,29,30 Identifying the genes underlying the diversification of these secondary sexual structures is essential to understanding the evolutionary impact on copulation and species recognition. Here, we show that Sox21b negatively regulates posterior lobe size. This is consistent with expanded Sox21b expression in D. mauritiana, which develops smaller posterior lobes than D. simulans. We tested this by generating reciprocal hemizygotes and confirmed that changes in Sox21b underlie posterior lobe evolution between these species. Furthermore, we found that posterior lobe size differences caused by the species-specific allele of Sox21b significantly affect copulation duration. Taken together, our study reveals the genetic basis for the sexual-selection-driven diversification of a novel morphological structure and its functional impact on copulatory behavior.

Investigating intentional cranial modification: A hybridized two-dimensional/three-dimensional study of the Hirota site, Tanegashima, Japan

Intentional cranial modification has a long history, being a ubiquitous practice in many cultures around the world for millennia. The crania excavated at the Hirota site on Tanegashima Island, Kagoshima Prefecture, Japan, has been previously noted to have a marked tendency toward a short head and a flattened occipital bone, which has been suggested to be the result of artificial cranial deformation. However, whether this deformation was intentional or caused by unintentional habits remains unclear. This study aimed to investigate the characteristics of the cranial shape of the Hirota site to clarify whether the crania were intentionally modified. In the examination of Hirota crania, Kyushu Island Jomon and Doigahama Yayoi crania were added as comparative data and contrasted with three-dimensional (3D) surface scan imaging and two-dimensional outline-based geometric morphometric analysis, combined with objective assessments of potential cranial modification. The results showcased Hirota's short and flattened cranial morphology, indicating clear alignment with our hypothesis that Hirota samples are morphologically different from Doigahama and Jomon samples. No sex-based differences were found. Morphological abnormalities in cranial sutures were visually assessed utilizing novel 3D visualization methods of cranial outer surfaces. Based on a comprehensive review of the results, we concluded that Hirota site crania were intentionally modified. Although the motivation of the practice is unclear, the Hirota people may have deformed their crania to preserve group identity and possibly aid in the long-distance trade of shellfish, as seen archaeologically.

Knuckle-walking in Sahelanthropus? Locomotor inferences from the ulnae of fossil hominins and other hominoids

Because the ulna supports and transmits forces during movement, its morphology can signal aspects of functional adaptation. To test whether, like extant apes, some hominins habitually recruit the forelimb in locomotion, we separate the ulna shaft and ulna proximal complex for independent shape analyses via elliptical Fourier methods to identify functional signals. We examine the relative influence of locomotion, taxonomy, and body mass on ulna contours in Homo sapiens (n = 22), five species of extant apes (n = 33), two Miocene apes (Hispanopithecus and Danuvius), and 17 fossil hominin specimens including Sahelanthropus, Ardipithecus, Australopithecus, Paranthropus, and early Homo. Ulna proximal complex contours correlate with body mass but not locomotor patterns, while ulna shafts significantly correlate with locomotion. African apes' ulna shafts are more robust and curved than Asian apes and are unlike other terrestrial mammals (including other primates), curving ventrally rather than dorsally. Because this distinctive curvature is absent in orangutans and hylobatids, it is likely a function of powerful flexors engaged in wrist and hand stabilization during knuckle-walking, and not an adaptation to climbing or suspensory behavior. The OH 36 (purported Paranthropus boisei) and TM 266 (assigned to Sahelanthropus tchadensis) fossils differ from other hominins by falling within the knuckle-walking morphospace, and thus appear to show forelimb morphology consistent with terrestrial locomotion. Discriminant function analysis classifies both OH 36 and TM 266 with Pan and Gorilla with high posterior probability. Along with its associated femur, the TM 266 ulna shaft contours and its deep, keeled trochlear notch comprise a suite of traits signaling African ape-like quadrupedalism. While implications for the phylogenetic position and hominin status of S. tchadensis remain equivocal, this study supports the growing body of evidence indicating that S. tchadensis was not an obligate biped, but instead represents a late Miocene hominid with knuckle-walking adaptations.

Does sternal body shape reflect family relationships? A study on a genealogically documented Central European osteological sample (19th-20th centuries)

In forensic contexts, sternal anatomical varieties represent useful tools for the identification of an individual, either by comparison of ante-mortem and post-mortem data, or by potential comparison of data from biologically related individuals. Sternal body variation is also used to detect the biological affinity of individuals in bioarchaeology. However, no study has been made available to date on the degree to which the overall shape of the sternal body reflects the degree of biological relatedness. We, therefore, analyzed the sternal body shape of 10 individuals with known genealogical data, members of one family over three generations including inbred individuals (19th-20th centuries, Bohemia, Czech Republic), and a control sample of 12 biologically unrelated individuals. First, closely biologically related individuals were compared with unrelated individuals based on 10 variables expressing the morphological characteristics of the sternum, and then all individuals were compared based on Fourier analysis depending on their degree of relationship. The results showed that there is a greater degree of shape similarity in biologically related individuals than in unrelated individuals, and variability decreases with an increasing degree of relatedness. Inbred individuals showed the lowest sternum-shape distances and degree of variability, while unrelated individuals, showed the highest distances and variability. Moreover, in some cases, the documented relationships were also supported by a similar morphology of the ossified and fused xiphoid process. Thus, sternal shape analysis expands the possibilities for individual identification and the detection of the biological affinity of individuals for both the forensic sciences and bioarchaeology.

Ontogenetic changes in the tooth morphology of bull sharks (Carcharhinus leucas)

Teeth are an integral component of feeding ecology, with a clear link between tooth morphology and diet, as without suitable dentition prey cannot be captured nor broken down for consumption. Bull sharks, Carcharhinus leucas, undergo an ontogenetic niche shift from freshwater to marine habitats, which raises the question: does tooth morphology change with ontogeny? Tooth shape, surface area and thickness were measured using both morphometrics and elliptic Fourier analysis to determine if morphology varied with position in the jaw and if there was an ontogenetic change concordant with this niche shift. Significant ontogenetic differences in tooth morphology as a function of position in the jaw and shark total length were found, with upper and lower jaws of bull sharks presenting two different tooth morphologies. Tooth shape and thickness fell into two groupings, anterior and posterior, in both the upper and lower jaws. Tooth surface area, however, indicated three groupings, mesial, intermediate and distal, in both the upper and lower jaws. While tooth morphology changed significantly with size, showing an inflection at sharks of 135 cm total length, each morphological aspect retained the same tooth groupings throughout. These ontogenetic differences in tooth morphologies reflect tooth strength, prey handling and heterodonty.

Testing inter-observer error under a collaborative research framework for studying lithic shape variability

Evaluating error that arises through the aggregation of data recorded by multiple observers is a key consideration in many metric and geometric morphometric analyses of stone tool shape. One of the most common approaches involves the convergence of observers for repeat trails on the same set of artefacts: however, this is logistically and financially challenging when collaborating internationally and/or at a large scale. We present and evaluate a unique alternative for testing inter-observer error, involving the development of 3D printed copies of a lithic reference collection for distribution among observers. With the aim of reducing error, clear protocols were developed for photographing and measuring the replicas, and inter-observer variability was assessed on the replicas in comparison with a corresponding data set recorded by a single observer. Our results demonstrate that, when the photography procedure is standardized and dimensions are clearly defined, the resulting metric and geometric morphometric data are minimally affected by inter-observer error, supporting this method as an effective solution for assessing error under collaborative research frameworks. Collaboration is becoming increasingly important within archaeological and anthropological sciences in order to increase the accessibility of samples, encourage dual-project development between foreign and local researchers and reduce the carbon footprint of collection-based research. This study offers a promising validation of a collaborative research design whereby researchers remotely work together to produce comparable data capturing lithic shape variability.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s12520-022-01676-2.

Ontogenetic patterns in human frontal sinus shape: A longitudinal study using elliptical Fourier analysis

Frontal sinus morphology is highly variable across individuals, but little is known regarding how or at what age that variation is reached. Existing ontogenetic studies are conflicting and often cross-sectional in nature, limiting understanding of individualistic growth. Studies investigating sinus growth with longitudinal series often focus on lateral cephalograms and consequently do not capture the sinus morphological features that are most relevant to clinical and medicolegal settings (e.g., arcade/scalloping, width-to-height dimensions, asymmetry). Longitudinal analysis of sinus morphology from frontal radiographs is important to understand when sinus morphology stabilizes. The purpose of this study was to investigate at what age the frontal sinus attains its final shape, and whether sex-based differences in ontogeny are evident, using a longitudinal sample of posterior-anterior (PA) frontal radiographs from the AAOF Legacy Collection. Frontal sinus outlines were manually traced in 935 radiographs from 111 individuals (55F/56M) spanning 8-29 years of age. Outlines were subjected to elliptical Fourier analysis (EFA) and underwent principal components analysis (PCA). PC1 (51.02% of variation) appears to represent the relative height and breadth of the sinus, PC2 (11.73%) and PC3 (10.03%) captures the degree of relative complexity in the outlines. Individual PC scores were plotted against age-in-months with individual Loess growth curves. Overall, younger individuals typically display relatively shorter, flatter sinuses, increasing in vertical complexity with age. Mixed-effect models on PC1 indicate significant effects for the repeated measure of years (p < 0.001). Within individuals, Euclidean distances of PCs between each sinus outline and their oldest-age outline (i.e., final morphology) were calculated and plotted against age-in-months with Loess growth curves. The results indicate that final frontal sinus morphology is mostly attained by 20 yoa regardless of sex. There is sexual dimorphism in ontogenetic trajectories: females attain frontal sinus shape earlier than males. Specifically, Loess growth curves of the Euclidean distances to final sinus shape indicate that female shape shows decreased development at 14-16 yoa, with males approaching stabilization at 18-20 yoa. These trends were supported by paired t-tests on PC1 between each year and the oldest age, whereby significant differences end for females starting at 15 and 18 yoa for males. The timing of shape-stabilization in the current study closely aligns with previous studies on linear and size dimensions, indicating a close relationship between the ontogeny of frontal sinus shape and size. This research has several implications in diverse fields. Documenting ontogenetic patterns in modern humans could lead to more accurate interpretations of frontal sinus variation in hominin lineages. Understanding the age at which frontal sinus shape and size stabilizes in pediatric populations has important clinical implications, with future studies needed to investigate if/how sinus development directly relates to sinonasal disease susceptibility (e.g., sinusitis), surgical complications, and/or expected trauma patterns. For forensic practitioners utilizing frontal sinus comparisons for decedent identifications, it is important to know at what age these features stabilize to understand how much change may be expected between antemortem and postmortem radiographs.

Thirty years of geometric morphometrics: Achievements, challenges, and the ongoing quest for biological meaningfulness

The foundations of geometric morphometrics were worked out about 30 years ago and have continually been refined and extended. What has remained as a central thrust and source of debate in the morphometrics community is the shared goal of meaningful biological inference through a tight connection between biological theory, measurement, multivariate biostatistics, and geometry. Here we review the building blocks of modern geometric morphometrics: the representation of organismal geometry by landmarks and semilandmarks, the computation of shape or form variables via superimposition, the visualization of statistical results as actual shapes or forms, the decomposition of shape variation into symmetric and asymmetric components and into different spatial scales, the interpretation of various geometries in shape or form space, and models of the association between shape or form and other variables, such as environmental, genetic, or behavioral data. We focus on recent developments and current methodological challenges, especially those arising from the increasing number of landmarks and semilandmarks, and emphasize the importance of thorough exploratory multivariate analyses rather than single scalar summary statistics. We outline promising directions for further research and for the evaluation of new developments, such as "landmark-free" approaches. To illustrate these methods, we analyze three-dimensional human face shape based on data from the Avon Longitudinal Study of Parents and Children (ALSPAC).

A Novel Approach for the Shape Characterisation of Non-Melanoma Skin Lesions Using Elliptic Fourier Analyses and Clinical Images

The early detection of Non-Melanoma Skin Cancer (NMSC) is crucial to achieve the best treatment outcomes. Shape is considered one of the main parameters taken for the detection of some types of skin cancer such as melanoma. For NMSC, the importance of shape as a visual detection parameter is not well-studied. A dataset of 993 standard camera images containing different types of NMSC and benign skin lesions was analysed. For each image, the lesion boundaries were extracted. After an alignment and scaling, Elliptic Fourier Analysis (EFA) coefficients were calculated for the boundary of each lesion. The asymmetry of lesions was also calculated. Then, multivariate statistics were employed for dimensionality reduction and finally computational learning classification was employed to evaluate the separability of the classes. The separation between malignant and benign samples was successful in most cases. The best-performing approach was the combination of EFA coefficients and asymmetry. The combination of EFA and asymmetry resulted in a balanced accuracy of 0.786 and an Area Under Curve of 0.735. The combination of EFA and asymmetry for lesion classification resulted in notable success rates when distinguishing between benign and malignant lesions. In light of these results, skin lesions’ shape should be integrated as a fundamental part of future detection techniques in clinical screening.

Age-at-Death Estimation of Fetuses and Infants in Forensic Anthropology: A New "Coupling" Method to Detect Biases Due to Altered Growth Trajectories

Simple Summary

In forensic anthropology, estimating the age-at-death of young juvenile skeletons is crucial as a direct determinant of legal issues in many countries. Most methods published for this purpose are based on either maturation or growth processes (two essential components of development) and focus on “normal” (i.e., nonpathological) growth. However, when the osseous remains available for study are from an individual that experienced an altered growth process, age estimation may be biased, and accounting for this would be helpful for potentially avoiding inaccuracies in estimation. In this research, we developed a method based on the combined evaluation of both maturation and growth. Maturation is evaluated by the conformation of the pars basilaris, a bone at the skull base that provides an indirect estimate of brain maturation, while growth is assessed using femoral biometry. The method was tested on two medical validation samples of normal and pathological individuals. The results show that it was possible to identify “uncoupling” between maturation and growth in 22.8% of the pathological individuals. Highlighting potential uncoupling is therefore an essential step in assessing the confidence of an age estimate, and its presence should lead experts to be cautious in their conclusions in court.

Abstract

The coupling between maturation and growth in the age estimation of young individuals with altered growth processes was analyzed in this study, whereby the age was determined using a geometric morphometrics method. A medical sample comprising 223 fetuses and infants was used to establish the method. The pars basilaris shapes, quantified by elliptic Fourier analysis, were grouped into consensus stages to characterize the maturation process along increasing age groups. Each pars basilaris maturation stage was “coupled” to biometry by defining an associated femur length range. The method was tested on a validation sample of 42 normal individuals and a pathological sample of 114 individuals whose pathologies were medically assessed. Couplings were present in 90.48% of the normal sample and 77.19% of the pathological sample. The method was able to detect “uncoupling” (i.e., possibly altered growth) in more than 22.8% of samples, even if there was no visible traces of pathology on bones in most cases. In conclusion, experts should be warned that living conditions may cause alterations in the development of young individuals in terms of uncoupling, and that the age-at-death estimation based on long bone biometry could be biased. In a forensic context, when age has been estimated in cases where uncoupling is present, experts should be careful to take potential inaccuracies into account when forming their conclusions.

The Effects of Cranial Orientation on Forensic Frontal Sinus Identification as Assessed by Outline Analyses

Simple Summary

Frontal sinus patterns are unique amongst individuals. When faced with an unknown decedent, investigators can compare the frontal sinus pattern observed in postmortem radiographs to antemortem radiographs of the suspected individual to make a positive identification. Ideally, the antemortem and postmortem radiographs are oriented in the same exact position, but this can be challenging. This study investigates how slight variations in radiographic orientation affect sinus outlines and potentially impact identification. Frontal sinus models were created from CT scans (21 individuals) and digitally oriented across three clinically relevant views. From each standard orientation (looking straight ahead), eight 5° deviations were obtained in horizontal (left/right), vertical (up/down), and diagonal (e.g., left-up vs. right-down) directions. Within and between individual differences in sinus size and outline shape were assessed. Sinus breadth remained relatively stable across deviations, while sinus height was affected by small vertical deviations. Although radiographic vertical deviations resulted in statistical differences, impacts on outline matches were minimal. However, practitioners need to take particular care in matching radiographic orientation for smaller and/or discontinuous (right and left sides separated) sinuses, which are more likely to lose part of the sinus in more inferiorly oriented views and, thus, could affect various methods of sinus identification.

Abstract

The utility of frontal sinuses for personal identification is widely recognized, but potential factors affecting its reliability remain uncertain. Deviations in cranial position between antemortem and postmortem radiographs may affect sinus appearance. This study investigates how slight deviations in orientations affect sinus size and outline shape and potentially impact identification. Frontal sinus models were created from CT scans of 21 individuals and digitally oriented to represent three clinically relevant radiographic views. From each standard view, model orientations were deviated at 5° intervals in horizontal, vertical, and diagonal (e.g., left-up) directions (27 orientations per individual). For each orientation, sinus dimensions were obtained, and outline shape was assessed by elliptical Fourier analyses and principal component (PC) analyses. Wilcoxon sign rank tests indicated that sinus breadth remained relatively stable (p > 0.05), while sinus height was significantly affected with vertical deviations (p < 0.006). Mann–Whitney U tests on Euclidean distances from the PC scores indicated consistently lower intra- versus inter-individual distances (p < 0.05). Two of the three orientations maintained perfect (100%) outline identification matches, while the third had a 98% match rate. Smaller and/or discontinuous sinuses were most problematic, and although match rates are high, practitioners should be aware of possible alterations in sinus variables when conducting frontal sinus identifications.

Shape-changing chains for morphometric analysis of 2D and 3D, open or closed outlines

Morphometrics is a multivariate technique for shape analysis widely employed in biological, medical, and paleoanthropological applications. Commonly used morphometric methods require analyzing a huge amount of variables for problems involving a large number of specimens or complex shapes. Moreover, the analysis results are sometimes difficult to interpret and assess. This paper presents a methodology to synthesize a shape-changing chain for 2D or 3D curve fitting and to employ the chain parameters in stepwise discriminant analysis (DA). The shape-changing chain is comprised of three types of segments, including rigid segments that have fixed length and shape, scalable segments with a fixed shape, and extendible segments with constant curvature and torsion. Three examples are presented, including 2D mandible profiles of fossil hominin, 2D leaf outlines, and 3D suture curves on infant skulls. The results demonstrate that the shape-changing chain has several advantages over common morphometric methods. Specifically, it can be applied to a wide range of 2D or 3D profiles, including open or closed curves, and smooth or serrated curves. Additionally, the segmentation of profiles is a flexible and automatic protocol that can consider both biological and geometric features, the number of variables obtained from the fitting results for statistical analysis is modest, and the chain parameters that characterize the profiles can have physical meaning.

Assessing the patterns and drivers of shape complexity in the amblypygid pedipalp

Amblypygi is an arachnid order possessing a unique pair of spined pedipalps: appendages that perform in prey capture, courtship, and contest. Pedipalp length, hypothesized to be under sexual selection, varies markedly across amblypygid species, and pedipalp spination, thought to reflect selection for function in prey capture, also differs interspecifically. Differences in pedipalp shape between species may indicate that the relative strength of selection for prey capture and sexual selection vary across the group. However, interspecific differences in pedipalp shape have not been quantified, due to difficulties in identifying homologous features. For the first time, we quantify trends in amblypygid pedipalp shape complexity. We use elliptical Fourier analysis to quantify 2D complexity in pedipalp outlines across eleven species and six genera. We find that complexity significantly decreases as pedipalp length increases. This appears to be driven by relative spine length, suggesting that a trade-off exists between pedipalp length and spination. Furthermore, significant female-biased sexual dimorphism in shape complexity is present in the tibial segment of the amblypygid pedipalp. Our results provide novel insights into the drivers of amblypygid pedipalp evolution and suggest that a functional trade-off between performance in prey capture and other functions under sexual selection exist in this enigmatic structure.

Comparing maxillary first molar crown shape using elliptical Fourier analysis in the Late Neolithic cave burials of Belgium

The Belgian Meuse karstic basin holds more than 200 Late Neolithic collective burials. Four of the largest include Hastière Caverne M, Hastière Trou Garçon C, Sclaigneaux and Bois Madame. The remains from these caves are commingled and fragmentary. However, in situ maxillary molars are well preserved permitting an investigation of molar crown shape within and across sites.

Crown outlines from the burials are compared using elliptical Fourier analysis to capture shape distinctions in the relatively numerous first maxillary molars (n = 27). Elliptical Fourier analysis is designed to compare deviations between each shape outline and an idealized ellipse, recorded as amplitudes of the harmonics which are reduced to principal components (PC) scores. We expect individuals from each site will be more similar to one another than to other internments in PC scores, and that the sites will be distributed along PC axes according to differences in chronology and geographic location.

Principal components analysis reveals that individuals tend to cluster together based on cave burial as well as time period. Geographic distance only differentiates the final/late Neolithic cave burials. The earliest of the sites, Hastière Caverne M, is distinctive and includes multiple outliers. Hastière Trou Garçon C from earlier in the Late Neolithic does not cluster with Hastière Caverne M as expected. Instead, this cave burial groups with Sclaigneaux, the most geographically distant site but chronologically the closest to Hastière Trou Garçon C. Although the limited sample sizes for each site must be considered, it appears that early farmers of the Belgian Meuse basin exhibited intricate human population dynamics which may have included small, semi-isolated groups early in the Late Neolithic and larger communities with greater contact toward the onset of the northern European Bronze Age.

Next-generation osteometric sorting: Using 3D shape, elliptical Fourier analysis, and Hausdorff distance to optimize osteological pair-matching

Determining which bilateral bones belong to the same person based on shape and size similarity is called pair-matching and it is instrumental for sorting commingled skeletons. To date, pair-matching has popularly been accomplished by visual inspection and/or linear caliper measurements; however, attention is turning increasingly to computational analysis. In this paper, we investigate a fast three-dimensional (3D) computerized shape-analysis method for whole-bone pair-matching using a test sample of 14 individuals (23 femora, 26 humeri, and 26 tibiae). Specifically, the method aims to find bilateral pairs using, as the shape signature criterion, a single 3D outline that snakes around each bone's perimeter as described by a 3D elliptical Fourier analysis function. This permits substantial 3D-point-cloud data reduction, that is, to 0.02% of the starting c.500,000 point cloud or just 100 points, while preserving key 3D shape information. The mean Hausdorff distance (Hd) was applied to measure the distance between each mirrored right-side outline to every left-side outline in pairwise fashion (132, 168 and 169 comparisons, respectively). Both thresholds and lowest Hd were investigated as pair-match criteria, with the lowest Hd producing the best performance results for searches jointly utilizing right-left and left-right directions for comparison: true positive rates of 1.00 (10/10), 1.00 (12/12), and 0.92 (11/12) for the femora, humeri, and tibiae, respectively. The computational time to calculate 469 pairwise 3D comparisons on a single stock-standard Intel^® Core™ i7-4650U CPU @ 1.70 GHz was 5 s. This short data processing time makes the method viable for real-world application.

Definitions of frontal bone inclination: Applicability and quantification

In sex determination from crania, a "vertical" forehead is considered a female feature, while a "sloping" forehead is considered a male feature. Precise description of frontal inclination with a quantitative measure like an angle is considerably more difficult as it requires accurate identification of clearly defined craniometric points. In the literature, the morphognostic terms "frontal bone inclination," or "frontal profile," are defined in numerous ways. The aim of this study was to determine which of these frontal inclination definitions is best suited for sex estimation. In a study in the context of the digital forensic osteology project, 10 of the frontal angle definitions described in the literature were assessed for their usefulness in sex determination on 211 virtual crania, reconstructed from postmortem CT-data. Custom-developed software was used for the automated measurement of frontal bone inclination angles from lateral-profile, volume-rendered 3D cranial images in which 10 anthropometric landmarks had been manually marked. Discriminant function analysis was performed to determine if satisfactory accuracy rates for the classification of sex could be achieved with defined variables. Four of the ten examined definitions were found to be highly significant for sex determination; three of these, also provided satisfactory intra- and inter-observer reliability. The frontal angle according to Schwalbe provided the best accuracy rate of 75.4% and a critical discriminatory value (separation value) of 88.6°: angles greater than this, suggest female sex; angles smaller than this, suggest male sex. Further, the open-source, custom-developed software introduced here proved compatible with commonly used image-processing and statistical programs and allowed quick, automated, valid measurement of numerous cranial angles. Other craniometric angles can, thus, also be quickly and easily determined with this software.

Of fractal and Fourier: A measure for local shape complexity for neurological applications

BACKGROUND

Local shape complexity can be biologically meaningful as a marker of disease, trauma, or change in brain structure over time. Fractal dimensionality (FD) is currently the dominant measure of local shape complexity used in neuroimaging but its limitations are not well understood.

NEW METHOD

Elliptical Fourier harmonic power requirement (HPR) may provide complementary information to FD. We benchmarked the performance of FD and HPR on a series of simulated shapes, systematically manipulating aspects of local shape complexity, and a series of clinical contours (glioma tumour cores and stroke lesions from the BRATS and ATLAS datasets). HPR was calculated as the point of 99.9% harmonic power. FD was calculated at six resolutions (8 × 8, 16 × 16, 32 × 32, 64 × 64, 128 × 128, and 256 × 256), by using an approach which computationally indexes the complexity of the shape boundary (i.e. the number of cells defining the contour) relative to the total grid size.

RESULTS AND COMPARISON WITH EXISTING METHODS

PR and FD were moderately positively correlated (r ≈ 0.2 to 0.8 depending on shape properties), and both were sensitive to the frequency and amplitude of local complexity. FD was most biased by rotation, while HPR was more biased by global shape features such as deep invaginations. FD indicated an aggregate measure of complexity across the whole contour, while HPR indicated the point of highest complexity.

CONCLUSIONS

The HPR index provides conceptually distinct local complexity information from the current FD standard. Future research will benefit from using these complementary measures.

Maturation of the human foetal basioccipital: quantifying shape changes in second and third trimesters using elliptic Fourier analysis

During prenatal development, the brain is considered the best maturation criterion for the estimation of foetal physiological age, regardless of the conditions of pregnancy. Unfortunately, the brain lyses very quickly after death, but fortunately, the brain also has a major influence over osseous structures of the cranial base during development. Therefore, we considered the osseous structures of the cranial base potential indirect maturation indicators of foetal age. Because of its early formation and robustness, the basioccipital is a cranial base bone that is often used for studies in biological anthropology. Studies generally use conventional morphometry and bone size ratio to highlight morphological changes occurring during the foetal period and to create age estimation methods. These methods usually define thresholds beyond which the morphology of the basioccipital changes, but do not fully consider the form that might be valuable precisely to visualize its development or improve age estimation methods. Using geometric morphometric methods, the present study aims to analyse the development of the basioccipital during the second and third trimesters of foetal life by quantifying and visualizing shape changes in the inferior view. Basioccipital shapes are used as direct indicators of the maturation of the cranial base and as indirect indicators of the maturation of the brain and, by extension, the whole body. A sample of 221 anonymized computed tomographic (CT) scans of normal foetuses, ranging from 18 to 41 gestational weeks (GW), was used. Elliptic Fourier analysis (EFA) was used to quantify the basioccipital outline, and maturation stages were established to visualize shape changes with a principal component analysis. Our study allowed us precisely to quantify and continuously visualize shape changes occurring during prenatal life. Additionally, this study provides the first evidence of two distinct linear shape trajectories of the basioccipital. Foetuses aged between 18 and 26 GW have a rapid shape change with well-individualized stages, whereas shape changes are less visible in the second trajectory (27-41 GW). Furthermore, intra-stage shape variation is higher for the basioccipital at the beginning of the second and third trimesters than at the first trimester. By using geometric morphometric methods and EFA, this study shows that it was possible to go beyond classical methods. Indeed, the developed methodology enabled the first quantification of the overall shape changes of the basioccipital between gestational ages. The morphological shape changes throughout the foetal period can be useful for anthropological studies and provide new perspectives for immature age estimation methods.

Female genitalia can evolve more rapidly and divergently than male genitalia

Male genitalia exhibit patterns of divergent evolution driven by sexual selection. In contrast, for many taxonomic groups, female genitalia are relatively uniform and their patterns of evolution remain largely unexplored. Here we quantify variation in the shape of female genitalia across onthophagine dung beetles, and use new comparative methods to contrast their rates of divergence with those of male genitalia. As expected, male genital shape has diverged more rapidly than a naturally selected trait, the foretibia. Remarkably, female genital shape has diverged nearly three times as fast as male genital shape. Our results dispel the notion that female genitalia do not show the same patterns of divergent evolution as male genitalia, and suggest that female genitalia are under sexual selection through their role in female choice.

Although male genital shape is known to evolve rapidly in response to sexual selection, relatively little is known about the evolution of female genital shape. Here, the authors show that across onthophagine dung beetles, female genital shape has diverged much more rapidly than male genital shape.

An Automated Two-dimensional Pairwise form Registration Method for Pair-matching of Fragmented Skeletal Remains

This study introduces an automated pairwise method for osteological pair-matching of fragmented skeletal remains using two-dimensional fragmented outlines extracted from photographs. The form data are used in pairwise iterative closest point registrations with rigid transformations. A modified version of the average Hausdorff distance is calculated to remove any coordinate correspondences with outline fracture margins, which allow the distance analysis of fragmented outlines. A dilation modification to the Hausdorff distance is proposed creating a greater separation between true- and false-pairs. The sample consists of 122 calcanei (61 pairs) from the UI-Stanford collection. Performance statistics are provided for simulated fragmented and complete assemblages. Results indicate up to 98% accuracy for fragmented and complete assemblages. The dilated Hausdorff distance performed similarly across assemblages, but showed a slight decrease in performance for the complete assemblage. This approach provides a useful short listing tool to reduce the number of visual comparisons required in large commingled assemblages.