What does geometric mean, mean geometrically? Assessing the utility of geometric mean and other size variables in studies of skull allometry

Primate body mass and dietary correlates of tooth root surface area

OBJECTIVES

This study aims to examine primate postcanine tooth root surface area (TRSA) in the context of two ecological variables (diet and bite force). We also assess scaling relationships within distinct taxonomic groups and across the order as a whole.

MATERIALS AND METHODS

Mandibular postcanine TRSA was measured using a three-dimensional computed tomography (CT) method for catarrhine (N = 27), platyrrhine (N = 21), and strepsirrhine (N = 24) taxa; this represents the first sample of strepsirrhines. Two different body size proxies were used: cranial geometric mean (GM) using nine linear measurements, and literature-derived body mass (BM).

RESULTS

TRSA correlated strongly with body size, scaling with positive allometry or isometry across the order as a whole; however, scaling differed significantly between taxa for some teeth. Among Strepsirrhini, molar TRSA relative to GM differed significantly between folivores and pliant-object feeders. Additionally, P₄ TRSA relative to BM differentiated folivores from both hard- and pliant-object feeders. Among Cercopithecoidea, P₄ TRSA adjusted by GM differed between hard- and pliant-object feeders.

DISCUSSION

Dietary signals in TRSA appear primarily driven by high frequency loading experienced by folivores. Stronger and more frequent dietary signals were observed within Strepsirrhini relative to Haplorhini. This may reflect the constraints of orthognathism within the latter, constraining the adaptability of their postcanine teeth. Finally, because of the strong correlation between TRSA and BM for each tooth locus (mean r²  = 0.82), TRSA can be used to predict BM in fossil primates using provided equations.

Covariation between the cranium and the cervical vertebrae in hominids

The analysis of patterns of integration is crucial for the reconstruction and understanding of how morphological changes occur in a taxonomic group throughout evolution. These patterns are relatively constant; however, both patterns and the magnitudes of integration may vary across species. These differences may indicate morphological diversification, in some cases related to functional adaptations to the biomechanics of organisms. In this study, we analyze patterns of integration between two functional and developmental structures, the cranium and the cervical spine in hominids, and we quantify the amount of divergence of each anatomical element through phylogeny. We applied these methods to three-dimensional data from 168 adult hominid individuals, summing a total of more than 1000 cervical vertebrae. We found the atlas (C1) and axis (C2) display the lowest covariation with the cranium in hominids (Homo sapiens, Pan troglodytes, Pan paniscus, Gorilla gorilla, Gorilla beringei, Pongo pygmaeus). H. sapiens show a relatively different pattern of craniocervical correlation compared with chimpanzees and gorillas, especially in variables implicated in maintaining the balance of the head. Finally, the atlas and axis show lower magnitude of shape change during evolution than the rest of the cervical vertebrae, especially those located in the middle of the subaxial cervical spine. Overall, results suggest that differences in the pattern of craniocervical correlation between humans and gorillas and chimpanzees could reflect the postural differences between these groups. Also, the stronger craniocervical integration and larger magnitude of shape change during evolution shown by the middle cervical vertebrae suggests that they have been selected to play an active role in maintaining head balance.

Scaling of linear anthropometric dimensions in living humans

OBJECTIVES

Some previous studies suggest that humans do not conform to geometric similarity (isometry) in anthropometric dimensions of the upper and lower limbs. Researchers often rely on a single statistical approach to the study of scaling patterns, and it is unclear whether these methods produce similar results and are equally robust. This study used one bivariate and one multivariate method to examine how linear anthropometric dimensions scale in a sample of adult humans.

MATERIALS AND METHODS

Motion capture marker data from 104 adults of varying height and mass were used to calculate anthropometric dimensions. We analyzed scaling patterns in pooled and separate sexes with two methods: (1) bivariate log-log regression and (2) multivariate principal component analysis (PCA). We calculated 95% highest density/confidence intervals for each method and defined positive/negative allometry as estimates lying outside those intervals.

RESULTS

Results identified isometric scaling of the upper arm, thigh, and shoulder, positive allometry of the forearm and shank, and negative allometry of the pelvis in the pooled sample using both statistical methods. Patterns of allometry in the pooled sample were similar between methods but differed in magnitude. Sex-specific results differed in both pattern and magnitude between log-log regression and PCA. Only one measurement (shoulder width) departed from isometry in the sex-specific log-log regressions.

DISCUSSION

Our findings suggest that especially in sex-specific analyses, the pattern and magnitude of allometry are sensitive to statistical methodology. When body mass was selected as the size variable, most human linear anthropometric dimensions in this sample scaled isometrically and were therefore geometrically similar within sexes.

Analysis of morphological variability and heritability in the head of the Argentine Black and White Tegu (Salvator merianae): undisturbed vs. disturbed environments

The heterogeneity of biotic and abiotic factors influencing fitness produce selective pressures that promote local adaptation and divergence among different populations of the same species. In order for adaptations to be maintained through evolutionary time, heritable genetic variation controlling the expression of the morphological features under selection is necessary. Here we compare morphological shape variability and size of the cephalic region of Salvator merianae specimens from undisturbed environments to those of individuals from disturbed environments, and estimated heritability for shape and size using geometric morphometric and quantitative genetics tools. The results of these analyzes indicated that there are statistically significant differences in shape and size between populations from the two environments. Possibly, one of the main determinants of cephalic shape and size is adaptation to the characteristics of the environment and to the trophic niche. Individuals from disturbed environments have a cephalic region with less shape variation and also have a larger centroid size when compared to individuals from undisturbed environments. The high heritability values obtained for shape and size in dorsal view and right side view indicate that these phenotypic characters have a great capacity to respond to the selection pressures to which they are subjected. Data obtained here could be used as an important tool when establishing guidelines for plans for the sustainable use and conservation of S. merianae and other species living in disturbed areas.

Interferon regulatory factor 6 variants affect nasolabial morphology in East Asian populations

OBJECTIVE

The interferon regulatory factor 6 gene (IRF6) is one of the most conspicuous genes among a large number of candidate risk genes for non-syndromic cleft lip with or without cleft palate, which is considered to be a multifactorial defect. Variants of IRF6 are also suggested to affect normal craniofacial variations, especially in the area of the nose and the upper lip. In the present study, we used lateral cephalograms to establish the relationship between IRF6 and sagittal nasolabial morphology in healthy East Asian subjects.

DESIGN

Genomic DNA was extracted from 215 Japanese and 226 Korean individuals, and genotyped for five IRF6 single nucleotide polymorphisms (SNPs): rs17389541, rs642961, rs2013162, rs2235371, and rs7802. These SNPs were tested by multiple regression analyses for their association with craniofacial measurements obtained from lateral cephalometrics.

RESULTS

We detected a significant association between the derived variants, rs2013162 and rs2235371 and the distances between a facial bone plane indicated by distance from Nasion and Point A (NA plane) to soft tissue landmarks; the Subalare (NA-Sbal) and the Subnasale (NA-Sn) in the sagittal plane.

CONCLUSION

Our results indicate that IRF6 variants play an important role in the normal range of variation in nasolabial soft-tissue morphology.

Facing the facts: The Runx2 gene is associated with variation in facial morphology in primates

The phylogenetic and adaptive factors that cause variation in primate facial form-including differences among the major primate clades and variation related to feeding and/or social behavior-are relatively well understood. However, comparatively little is known about the genetic mechanisms that underlie diversity in facial form in primates. Because it is essential for osteoblastic differentiation and skeletal development, the runt-related transcription factor 2 (Runx2) is one gene that may play a role in these genetic mechanisms. Specifically, polymorphisms in the QA ratio (determined by the ratio of the number of polyglutamines to polyalanines in one functional domain of Runx2) have been shown to be correlated with variation in facial length and orientation in other mammal groups. However, to date, the relationship between variation in this gene and variation in facial form in primates has not been explicitly tested. To test the hypothesis that the QA ratio is correlated with facial form in primates, the current study quantified the QA ratio, facial length, and facial angle in a sample of 33 primate species and tested for correlation using phylogenetic generalized least squares. The results indicate that the QA ratio of the Runx2 gene is positively correlated with variation in relative facial length in anthropoid primates. However, no correlation was found in strepsirrhines, and there was no correlation between facial angle and the QA ratio in any groups. These results suggest that, in primates, the QA ratio of the Runx2 gene may play a role in modulating facial size, but not facial orientation. This study therefore provides important clues about the genetic and developmental mechanisms that may underlie variation in facial form in primates.

The role of allometry and posture in the evolution of the hominin subaxial cervical spine

Cervical vertebrae not only protect the spinal cord but also are the insertion and origin points for muscles related to the movement of the head, upper limb, and trunk, among others, and are thus important elements in primate evolution. While previous work has been undertaken on the first two cervical vertebrae, there is a dearth of studies on the subaxial cervical spine in hominines. In this paper, we provide detailed morphological information on two important aspects of the subaxial cervical vertebrae (C3 - C7): mid-sagittal morphology and superior facet orientation. We studied large samples of African apes including modern humans and the most complete fossil hominin subaxial cervical vertebrae using both traditional and geometric morphometrics. There are significant differences between extant hominoids related to the relative length and orientation of the spinous process as well as to the orientation of the articular facets, which are related to size, locomotion, and neck posture. In fact, fossil hominins do not completely conform to any of the extant groups. Our assessment of mid-sagittal morphology and superior articular facet orientation shows that australopiths have more Homo-like upper subaxial cervical vertebrae coupled with more "primitive" lower cervical vertebrae. Based on these results, we hypothesize that those changes, maybe related to postural changes derived from bipedalism, did not affect the entire subaxial cervical spine at once. From a methodological point of view, the combination of traditional and geometric morphometric data provides a more integrative perspective of morphological change and evolution, which is certainly useful in human evolutionary studies.

Skull 5 from Dmanisi: Descriptive anatomy, comparative studies, and evolutionary significance

A fifth hominin skull (cranium D4500 and mandible D2600) from Dmanisi is massively constructed, with a large face and a very small brain. Traits documented for the first time in a basal member of the Homo clade include the uniquely low ratio of endocranial volume to basicranial width, reduced vertex height, angular vault profile, smooth nasal sill coupled with a long and sloping maxillary clivus, elongated palate, and tall mandibular corpus. The convex clivus and receding symphysis of skull 5 produce a muzzle-like form similar to that of Australopithecus afarensis. While the Dmanisi cranium is very robust, differing from OH 13, OH 24, and KNM-ER 1813, it resembles Homo habilis specimens in the "squared off" outline of its maxilla in facial view, maxillary sulcus, rounded and receding zygomatic arch, and flexed zygomaticoalveolar pillar. These characters distinguish early Homo from species of Australopithecus and Paranthropus. Skull 5 is unlike Homo rudolfensis cranium KNM-ER 1470. Although it appears generally primitive, skull 5 possesses a bar-like supraorbital torus, elongated temporal squama, occipital transverse torus, and petrotympanic traits considered to be derived for Homo erectus. As a group, the Dmanisi crania and mandibles display substantial anatomical and metric variation. A key question is whether the fossils document age-related growth and sex dimorphism within a single population, or whether two (or more) distinct taxa may be present at the site. We use the coefficient of variation to compare Dmanisi with Paranthropus boisei, H. erectus, and recent Homo sapiens, finding few signals that the Dmanisi sample is excessively variable in comparison to these reference taxa. Using cranial measurements and principal components analysis, we explore the proposal that the Dmanisi skulls can be grouped within a regionally diverse hypodigm for H. erectus. Our results provide only weak support for this hypothesis. Finally, we consider all available morphological and paleobiological evidence in an attempt to clarify the phyletic relationship of Dmanisi to Homo species evolving >2.0 to 1.0 Ma.

Trabecular bone structure in the primate wrist

Trabecular (or cancellous) bone has been shown to respond to mechanical loading throughout ontogeny and thus can provide unique insight into skeletal function and locomotion in comparative studies of living and fossil mammalian morphology. Trabecular bone of the hand may be particularly functionally informative because the hand has more direct contact with the substrate compared with the remainder of the forelimb during locomotion in quadrupedal mammals. This study investigates the trabecular structure within the wrist across a sample of haplorhine primates that vary in locomotor behaviour (and thus hand use) and body size. High-resolution microtomographic scans were collected of the lunate, scaphoid, and capitate in 41 individuals and eight genera (Homo, Gorilla, Pan, Papio, Pongo, Symphalangus, Hylobates, and Ateles). We predicted that particular trabecular parameters would 1) vary across suspensory, quadrupedal, and bipedal primates based on differences in hand use and load, and 2) scale with carpal size following similar allometric patterns found previously in other skeletal elements across a larger sample of mammals and primates. Analyses of variance (trabecular parameters analysed separately) and principal component analyses (trabecular parameters analysed together) revealed no clear functional signal in the trabecular structure of any of the three wrist bones. Instead, there was a large degree of variation within suspensory and quadrupedal locomotor groups, as well as high intrageneric variation within some taxa, particularly Pongo and Gorilla. However, as predicted, Homo sapiens, which rarely use their hands for locomotion and weight support, were unique in showing lower relative bone volume (BV/TV) compared with all other taxa. Furthermore, parameters used to quantify trabecular structure within the wrist scale with size generally following similar allometric patterns found in trabeculae of other mammalian skeletal elements. We discuss the challenges associated with quantifying and interpreting trabecular bone within the wrist.

Trabecular bone structure correlates with hand posture and use in hominoids

Bone is capable of adapting during life in response to stress. Therefore, variation in locomotor and manipulative behaviours across extant hominoids may be reflected in differences in trabecular bone structure. The hand is a promising region for trabecular analysis, as it is the direct contact between the individual and the environment and joint positions at peak loading vary amongst extant hominoids. Building upon traditional volume of interest-based analyses, we apply a whole-epiphysis analytical approach using high-resolution microtomographic scans of the hominoid third metacarpal to investigate whether trabecular structure reflects differences in hand posture and loading in knuckle-walking (Gorilla, Pan), suspensory (Pongo, Hylobates and Symphalangus) and manipulative (Homo) taxa. Additionally, a comparative phylogenetic method was used to analyse rates of evolutionary changes in trabecular parameters. Results demonstrate that trabecular bone volume distribution and regions of greatest stiffness (i.e., Young's modulus) correspond with predicted loading of the hand in each behavioural category. In suspensory and manipulative taxa, regions of high bone volume and greatest stiffness are concentrated on the palmar or distopalmar regions of the metacarpal head, whereas knuckle-walking taxa show greater bone volume and stiffness throughout the head, and particularly in the dorsal region; patterns that correspond with the highest predicted joint reaction forces. Trabecular structure in knuckle-walking taxa is characterised by high bone volume fraction and a high degree of anisotropy in contrast to the suspensory brachiators. Humans, in which the hand is used primarily for manipulation, have a low bone volume fraction and a variable degree of anisotropy. Finally, when trabecular parameters are mapped onto a molecular-based phylogeny, we show that the rates of change in trabecular structure vary across the hominoid clade. Our results support a link between inferred behaviour and trabecular structure in extant hominoids that can be informative for reconstructing behaviour in fossil primates.

Anatomical Correlates to Nectar Feeding among the Strepsirrhines of Madagascar: Implications for Interpreting the Fossil Record

One possible ecological scenario for the origin of primates is the archaic pollination and coevolution hypothesis. Its proponents contend that the consumption of nectar by some early primates and the resulting cross-pollination is an example of coevolution that drove adaptive radiations in some primates. This hypothesis is perhaps ecologically sound, but it lacks the morphology-behavior links that would allow us to test it using the fossil record. Here we attempt to identify cranial adaptations to nectar feeding among the strepsirrhines of Madagascar in order to provide such links. Many Malagasy strepsirrhines are considered effective cross-pollinators of the flowers they feed from, and nectar consumption represents as much as 75% of total feeding time. Previous studies identified skeletal correlates to nectar feeding in the crania of nonprimate mammals; from these, nine cranial measurements were chosen to be the focus of the present study. Results indicate that Cheirogaleus, Varecia, and Eulemur mirror other nectar-feeding mammals in having elongated crania and/or muzzles. These strepsirrhines might be effective cross-pollinators, lending support to the coevolution hypothesis.

Allometry and apparent paradoxes in human limb proportions: Implications for scaling factors

It has been consistently demonstrated that human proximal limb elements exhibit negative allometry, while distal elements scale with positive allometry. Such scaling implies that longer limbs will have higher intralimb indices, a phenomenon not borne out by empirical analyses. This, therefore, creates a paradox within the limb allometry literature. This study shows that these apparently conflicting results are the product of two separate phenomena. First, the use of the geometric mean of limb elements produces allometry coefficients that are not independent, and that when using ordinary least squares regression must yield an average slope of one. This phenomenon argues against using the geometric mean as a size variable when examining limb allometry. While the employment of relevant dimensions independent of those under analysis to calculate the geometric mean--as suggested by Coleman (Am J Phys Anthropol 135 (2008) 404-415)--may be a partial method for resolving the problem, an empirically determined, independent and biologically relevant size variable is advocated. If stature is used instead of the geometric mean as an independent size variable, all major limb elements scale with positive allometry. Second, while limb allometry coefficients do indicate differential allometry in limb elements, and thus should lead to some intralimb index allometry, this pattern appears to be attenuated by other sources of limb element length variation.

Correlations between auditory structures and hearing sensitivity in non-human primates

Primates show distinctions in hearing sensitivity and auditory morphology that generally follow phylogenetic patterns. However, few previous studies have attempted to investigate how differences in primate hearing are directly related to differences in ear morphology. This research helps fill this void by exploring the form-to-function relationships of the auditory system in a phylogenetically broad sample of non-human primates. Numerous structures from the outer, middle, and inner ears were measured in taxa with known hearing capabilities. The structures investigated include the overall size and shape of the pinna, the areas of the tympanic membrane and stapedial footplate, the masses and lever arm lengths of the ossicles, the volumes of the middle ear cavities, and the length of the cochlea. The results demonstrate that a variety of auditory structures show significant correlations with certain aspects of hearing (particularly low-frequency sensitivity). Although the majority of these relationships agree with expectations from auditory theory, some traditional (and possibly outdated) ideas were not supported. For example, the common misconception that higher middle ear transformer ratios (e.g., impedance transformer ratio) result in increased hearing sensitivity was not supported. Although simple correlations between form and function do not necessarily imply causality, the relationships defined in this study not only increase our understanding of auditory patterns in extant taxa but also lay the foundation to begin investigating the hearing in fossil primates.