Midsagittal cranial shape variation in the genus Homo by geometric morphometrics

Midsagittal profiles of crania referred to different taxa of the genus Homo have been analyzed by geometric morphometric techniques. Comparisons between single specimens using the thin-plate-spline function suggest a generalized reduction of the lower face, associated with antero-posterior development of the braincase occurring (possibly in parallel evolution) along distinct human lineages. Furthermore, Neandertals display a projection of the midface, and modern humans show a derived globularity of the vault associated with midsagittal parietal bulging. Principal Component Analysis demonstrates a bimodal pattern of variation, which describes an "archaic" pole (rather heterogeneous in terms of taxonomy) clearly distinguishable from the modern one. The first two principal components - that explain together 80% of the total variance in shape - involve respectively fronto-parietal expansion and midfacial prognathism. These results contribute to identify different structural patterns in human evolution, supporting discontinuity rather than continuity of cranial shape among different taxa of the genus Homo, especially when considering the differences between Neandertals and early modern humans.     

Inter- and intraspecific variation in grass phytolith shape and size: a geometric morphometrics perspective

Background and AimsThe relative contributions of inter- and intraspecific variation to phytolith shape and size have only been investigated in a limited number of studies. However, a detailed understanding of phytolith variation patterns among populations or even within a single plant specimen is of key importance for the correct taxonomic identification of grass taxa in fossil samples and for the reconstruction of vegetation and environmental conditions in the past. In this study, we used geometric morphometric analysis for the quantification of different sources of phytolith shape and size variation.MethodsWe used landmark-based geometric morphometric methods for the analysis of phytolith shapes in two extant grass species (Brachypodium pinnatum and B. sylvaticum). For each species, 1200 phytoliths were analysed from 12 leaves originating from six plants growing in three populations. Phytolith shape and size data were subjected to multivariate Procrustes analysis of variance (ANOVA), multivariate regression, principal component analysis and linear discriminant analysis.Key ResultsInterspecific variation largely outweighed intraspecific variation with respect to phytolith shape. Individual phytolith shapes were classified with 83 % accuracy into their respective species. Conversely, variation in phytolith shapes within species but among populations, possibly related to environmental heterogeneity, was comparatively low.ConclusionsOur results imply that phytolith shape relatively closely corresponds to the taxonomic identity of closely related grass species. Moreover, our methodological approach, applied here in phytolith analysis for the first time, enabled the quantification and separation of variation that is not related to species discrimination. Our findings strengthen the role of grass phytoliths in the reconstruction of past vegetation dynamics.     

Three-dimensional geometric morphometrics of Arvicanthis: implications for systematics and taxonomy

Arvicanthis is an African murid, found throughout sub-Saharan Africa, Sudan and Egypt. Although in the past 10 years several studies have been carried out to assess its systematics, there is still a need for a general revision of the genus. In this study the morphometric relationships between 71 populations throughout the range were investigated. A three-dimensional geometric morphometric approach was used to assess differences in the size and shape of the skull. These were related to the different biogeographical domains characterizing the range of the genus and to molecular and karyotypic phylogenies. Results agree only in part with phylogeny, and show a close relationship with the environmental backgrounds of each species. It is therefore suggested that the adaptation of Arvicanthis to local environment has played an important role in the phenotypic evolution of the skull. This leads to problems in taxonomic definitions based on morphometrics, which should not be used without comparison with other independently derived characters such as the DNA and the karyotype.     

Methods for studying allometry in geometric morphometrics: a comparison of performance

Evolutionary Ecology - Allometry has been the focus of growing interest in studies using geometric morphometric methods to address a wide range of research questions at the interface of ecology and...     

Using geometric morphometrics to determine the “fittest” floral shape: A case study in large-flowered,buzz-pollinated Meriania hernandoi

Premise

Floral shape (relative arrangement and position of floral organs) is critical in mediating fit with pollinators and maximizing conspecific pollen transfer particularly in functionally specialized systems. To date, however, few studies have attempted to quantify flowers as the inherently three-dimensional (3D) structures they are and determine the effect of intraspecific shape variation on pollen transfer. We here addressed this research gap using a functionally specialized system, buzz pollination, in which bees extract pollen through vibrations, as a model. Our study species, Meriania hernandoi (Melastomataceae), undergoes a floral shape change from pseudocampanulate corollas with more actinomorphically arranged stamens (first day) to open corollas with a more zygomorphic androecium (second day) over anthesis, providing a natural experiment to test how variation in floral shape affects pollination performance.

Methods

In one population of M. hernandoi, we bagged 51 pre-anthetic flowers and exposed half of them to bee pollinators when they were in either stage of their shape transition. We then collected flowers, obtained 3D flower models through x-ray computed tomography for 3D geometric morphometric analyses, and counted the pollen grains remaining per stamen (male pollination performance) and stigmatic pollen loads (female pollination performance).

Results

Male pollination performance was significantly higher in open flowers with zygomorphic androecia than in pseudo-campanulate flowers. Female pollination performance did not differ among floral shapes.

Conclusions

These results suggest that there is an “optimal” shape for male pollination performance, while the movement of bees around the flower when buzzing the spread-out stamens results in sufficient pollen deposition regardless of floral shape.

     

Bias and error in estimates of mean shape in geometric morphometrics

Sampling experiments were performed to investigate mean square error and bias in estimates of mean shape produced by different geometric morphometric methods. The experiments use the isotropic error model, which assumes equal and independent variation at each landmark. The case of three landmarks in the plane (i.e., triangles) was emphasized because it could be investigated systematically and the results displayed on the printed page. The amount of error in the estimates was displayed as RMSE surfaces over the space of all possible configurations of three landmarks. Patterns of bias were shown as vector fields over this same space. Experiments were also performed using particular combinations of four or more landmarks in both two and three dimensions.It was found that the generalized Procrustes analysis method produced estimates with the least error and no pattern of bias. Averages of Bookstein shape coordinates performed well if the longest edge was used as the baseline. The method of moments (Stoyan, 1990, Model. Biomet. J. 32, 843) used in EDMA (Lele, 1993, Math. Geol. 25, 573) exhibits larger errors. When variation is not small, it also shows a pattern of bias for isosceles triangles with one side much shorter than the other two and for triangles whose vertices are approximately collinear causing them to resemble their own reflections. Similar problems were found for the log-distance method of Rao and Suryawanshi (1996, Proc. Nat. Acad. Sci. 95, 4121). These results and their implications for the application of different geometric morphometric methods are discussed.     

Correction to: Methods for studying allometry in geometric morphometrics: a comparison of performance

Evolutionary Ecology -     

A non‐invasive geometric morphometrics method for exploring variation in dorsal head shape in urodeles: sexual dimorphism and geographic variation in Salamandra salamandra

The study of morphological variation among and within taxa can shed light on the evolution of phenotypic diversification. In the case of urodeles, the dorso‐ventral view of the head captures most of the ontogenetic and evolutionary variation of the entire head, which is a structure with a high potential for being a target of selection due to its relevance in ecological and social functions. Here, we describe a non‐invasive procedure of geometric morphometrics for exploring morphological variation in the external dorso‐ventral view of urodeles' head. To explore the accuracy of the method and its potential for describing morphological patterns we applied it to two populations of Salamandra salamandra gallaica from NW Iberia. Using landmark‐based geometric morphometrics, we detected differences in head shape between populations and sexes, and an allometric relationship between shape and size. We also determined that not all differences in head shape are due to size variation, suggesting intrinsic shape differences across sexes and populations. These morphological patterns had not been previously explored in S. salamandra , despite the high levels of intraspecific diversity within this species. The methodological procedure presented here allows to detect shape variation at a very fine scale, and solves the drawbacks of using cranial samples, thus increasing the possibilities of using collection specimens and alive animals for exploring dorsal head shape variation and its evolutionary and ecological implications in urodeles. J. Morphol. 278:475–485, 2017. © 2017 Wiley Periodicals, Inc.     

Quantification of age-related shape change of the human rib cage through geometric morphometrics

The aim of this study is to quantify patterns of age-related shape change in the human thorax using Procrustes superimposition. Landmarks (n=106) selected from anonymized computed tomography (CT) scans of 63 adult males free of skeletal pathology were used to describe the form of the rib cage. Multivariate linear regression was used to determine a relationship between landmark location and age. Linear and quadratic models were also investigated. A permutation test employing 1×10⁵ random trials was used to assess the model significance for both model formulations. Linear relationships between the centroid size (CS) of a landmark set and the corresponding individual's height, weight, and BMI were conducted to enable scaling of the dimensionless results from the Procrustes analysis. A significance level of =0.05 was used for all tests. The average age of the study subjects was 57.0±17.3 years. Complete landmark sets were obtained from most of the scans (44 of 63). The quadratic relationship between the age and landmark location was found to be significant (p=0.037), thereby establishing a relationship between the age and thoracic shape change. The linear relationship was mildly significant as well (p=0.073). Significant relationships between the centroid size of the dataset and subject weight, height and BMI were determined, with the best-correlated value being weight (p=0.002, R²=0.22). Landmark datasets calculated using the quadratic model exhibited shape change consistent with the clinical observations (increasing kyphosis and rounding of the thoracic cage). Procrustes superimposition represents a potential improvement in the approach used to generate computational models for injury biomechanics studies. The coefficients from the quadratic model are provided and can be used to generate the complete set of model landmark data points at a given age.     

Principles and methods of geometric morphometrics

The basic concepts, notions and methods of geometric morphometrics (GM) are considered. This approach implies multivariate analysis of landmark coordinates located following certain rules on the surface of a morphological object. The aim of GM is to reveal differences between morphological objects by their shapes as such, the "size factor" being excluded. The GM is based on the concept of Kendall's space (KS) defined as a hypersphere with points distributed on its surface. These points are the shapes defined as aligned landmark configurations. KS is a non-Euclidian space, its metrics called Procrustes is defined by landmark configuration of a reference shape relative to which other shapes are aligned and compared. The differences among shapes are measured as Procrustes distances between respective points. For the linear methods of multivariate statistics to be applied to comparison of shapes, the respective points are projected onto the tangent plane (tangent space), the tangent point being defined by the reference. There are two principal methods of shape comparisons in GM: the Procrustes superimposition (a version of the least squares analysis) and thin-plate spline analysis. In the first case, Procrustes residuals are the outcome shape variables which remain after isometric alignment of the shapes being compared. Their summation over all landmarks yields Procrustes distances among these shapes. The Procrustes distances can be used in multivariate analyses just as the Euclidian distances. In the second case, the shapes are fitted to the references by stretching/compressing and shearing until complete identity of their landmark configurations. Eigenvectors of resulting bending energy matrix are defined as new shape variables, principal warps which yield another shape space with the origin defined by the reference. Projections of the shapes being compared onto principal warps yield partial warps, and their covariance matrix decomposition into eigenvectors yields relative warps which are similar to principal components (in particular, they are mutually orthogonal). Both partial and relative warps can be used in many multivariate statistic analyses as quantitative shape variables. Results of thin-plate spline analysis can be represented graphically by transformation grid which displays type, amount and localization of the shape differences. Basis rules of sample composition and landmark positioning to be used in GM are considered. At present, rigid (with minimal degrees of freedom) 2D morphological objects are most suitable for GM applications. It is important to recognize three type of real landmarks, and additionally semi-landmarks and "virtual" landmarks. Some procedures of thin-plate spline analysis are considered exemplified by some study cases, as well as applications of some standard multivariate methods to GM results. They make it possible to evaluate correlation between different shapes, as well as between a shape and some non-shape variables (linear measurements etc); to evaluate the differences among organisms by shape of a morphological structure; to identify landmarks which most accounted for both correlation and differences between the shapes. An annotated list of most popular softwares for GM is provided.     

Multivariate and geometric morphometrics in the analysis of sexual dimorphism variation in Podarcis lizards

Podarcis bocagei and P. carbonelli are two closely related lacertid species, very similar morphologically and ecologically. We investigated sexual dimorphism patterns presented by both species in allopatry and in sympatry. Sexual size and shape dimorphism patterns were analyzed using both multivariate and geometric morphometric techniques. Multivariate morphometrics revealed a marked sexual dimorphism in both species--males being larger with more robust habitus and females presenting a longer trunk. General patterns of sexual size dimorphism are not modified in sympatry, although there is evidence for some morphological change in male head size. The application of geometric morphometrics offered a more detailed image of head shape and revealed that males present a more developed tympanic area than do females, while females have a more rounded head. Differences in the degree of sexual shape dimorphism were detected in sympatry, but no consistent patterns were observed. From the results of the study, and based on previous knowledge on the populations studied, we conclude that the morphological differences observed are probably not caused by exploitative competition between the species, but rather appear attributable to the modification of the relative influence of sexual and natural selection on both sexes.     

From floral induction to floral shape

The initial emphasis in molecular-genetic studies of flower development was on homeotic genes that control organ identity, which is rather invariant between different species. Studies in flower development during the past three years have dealt with more diverse aspects of flower development, including floral induction and floral shape. Genes identified in the respective pathways might hold clues to the diversity of modern angiosperms.