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.     

apTreeshape: statistical analysis of phylogenetic tree shape

apTreeshape is a R package dedicated to simulation and analysis of phylogenetic tree topologies using statistical imbalance measures. It is a companion library of the R package 'ape', which provides additional functions for reading, plotting, manipulating phylogenetic trees and for connecting to public phylogenetic tree databases. One strength of the package is to include appropriate corrections of classical shape statistics as well as new tests based on the statistical theory of likelihood ratios.     

Developmental plasticity, morphological variation and evolvability: a multilevel analysis of morphometric integration in the shape of compound leaves

The structure of compound leaves provides flexibility for morphological change by variation in the shapes, sizes and arrangement of leaflets. Here, we conduct a multilevel analysis of shape variation in compound leaves to explore the developmental plasticity and evolutionary potential that are the basis of diversification in leaf shape. We use the methods of geometric morphometrics to study the shapes of individual leaflets and whole leaves in 20 taxa of Potentilla (sensu lato). A newly developed test based on the bootstrap approach suggests that uncertainty in the molecular phylogeny precludes firm conclusions whether there is a phylogenetic signal in the data on leaf shape. For variation among taxa, variation within taxa, as well as fluctuating asymmetry, there is evidence of strong morphological integration. The patterns of variation are similar across all three levels, suggesting that integration within taxa may act as a constraint on evolutionary change.     

Analysis of body shape for differentiating among species of rajids

This study sought to differentiate the species of skates encountered in Gulf St Vincent (GSV), South Australia using normalized elliptical Fourier analysis of body shape. Significant intraspecific variation was observed among whole body shapes. This was overcome by limiting subsequent analyses to the anterior snout region, where significant differences in shape were detected among the species examined and provided a high degree of classification success for the skates of GSV. More generally, this approach has the potential to provide a cost‐ and time‐efficient means of discrimination among species of skates. Further research is required to investigate the potentially confounding effects of sexual dimorphism and ontogenetic variation in growth to improve the efficacy of the body shape analysis of the skates and batoids species in general. In addition, this approach requires considerable development to facilitate implementation in a fishery setting.     

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.     

ShapeR: An R Package to Study Otolith Shape Variation among Fish Populations

ShapeR is an open source software package that runs on the R platform and is specifically designed to study otolith shape variation among fish populations. The package extends previously described software used for otolith shape analysis by allowing the user to automatically extract closed contour outlines from a large number of images, perform smoothing to eliminate pixel noise, choose from conducting either a Fourier or Wavelet transform to the outlines and visualize the mean shape. The output of the package are independent Fourier or Wavelet coefficients which can be directly imported into a wide range of statistical packages in R. The package might prove useful in studies of any two dimensional objects.     

3D surface analysis and classification in neuroimaging segmentation

This work emphasizes new algorithms for 3D edge and corner detection used in surface extraction and new concept of image segmentation in neuroimaging based on multidimensional shape analysis and classification. We propose using of NifTI standard for describing input data which enables interoperability and enhancement of existing computing tools used widely in neuroimaging research. In methods section we present our newly developed algorithm for 3D edge and corner detection, together with the algorithm for estimating local 3D shape. Surface of estimated shape is analyzed and segmented according to kernel shapes.     

Allometric scaling and morphological variation in sinking rate of phytoplankton

Since the first decades of the last century, several hypotheses have been proposed on the role of phytoplankton morphology in maintaining a favorable position in the water column. Here, by an extensive review of literature on sinking rate and cell volume, we firstly attempted to explore the dependency of sinking rate on morphological traits using the allometric scaling approach. We found that sinking rate tends to increase with increasing cell volume showing the allometric scaling exponent of 0.43, which is significantly different than the Stokes’ law exponent of 0.66. The violation of the 2/3 power rule clearly indicates that cell shape changes as size increases. Both size and shape affect how phytoplankton sinking drives nutrient acquisition and losses to sinking. Interestingly, from an evolutionary perspective, simple and complex cylindrical shapes can get much larger than spherical and spheroidal shapes and sink at similar rates, but simple and complex cylindrical shapes cannot get small enough to sink slower than small spherical and spheroidal shapes. Cell shape complexity is a morphological attribute resulting from the combination of two or more simple geometric shapes. While the effect of size on sinking rate is well documented, this study deepens the knowledge on how cell shape or geometry affect sinking rates that still needs further consideration.     

Measurement of biophysical properties of red blood cells by resistive pulse spectroscopy: volume, shape, surface area, and deformability

This paper presents a simple, new approach to the determination of size, shape, surface area, and deformability information for cells, notably red blood cells. The results are obtained by combining experimental measurements from resistive pulse spectroscopy (an extension of electronic cell-sizing methodology) with theoretical calculations for model cell systems. Assuming constancy of surface area and approximating red cell shapes by both prolate and oblate ellipsoids of revolution, values are determined for cell shape factor and volume under a variety of conditions. For red blood cells under low-stress conditions, shape factor, volume, and surface area results are found to be consistent with those available from the literature, when the oblate model is used. The applicability of this approach for determination of red cell properties under altered conditions is demonstrated by results for cell volume, at varying osmotic pressure and mechanical shear (tensile) stress. By quantitating the change in cell shape with stress, a new numerical scale for measuring cell deformability is also obtained, and data are presented on its variation for red cells at different osmolalities, over the range of 140 to 500 mOsm.     

Phenotypic convergence of artificially reared and wild trout is mediated by shape plasticity

Phenotypic plasticity can be viewed as the first level of defense of organism homeostasis against environmental stress and therefore represents the potential to deal with rapid environmental changes. Transitions between low complexity, artificial environments and complex, natural habitats can promote phenotypic plasticity. Here, we conducted an experimental introduction with juvenile brown trout to evaluate the plasticity of shape in response to a transition between contrasting environments. We released 202 juvenile trout reared under hatchery conditions in a natural stream and analyzed changes in shape and morphological variability after 5 months. A geometric morphometrics approach based on 14 landmarks was used to compare changes in body shape for 37 fish recaptured at the end of the experiment. A similar number of hatchery and wild fish caught at the receptor stream were used as controls for shape in the two environments. After 5‐months, fish showed significant change in shape, shifting from elongated to robust shapes, and affecting to the relative position of the caudal peduncle. These new shapes were closer to wild than to the hatchery shapes, suggesting a process of rapid phenotype change. Moreover, these changes were concomitant with a marked increase in morphological variability. Our results support the hypothesis that phenotypic plasticity is a major potential for adjustment to environmental change but not the idea that shape can be constrained by initial shapes. We confirmed the “increased” variance hypothesis and phenotype convergence with wild morphs. This has important implications because stresses the role of phenotypic plasticity as a buffer that allows organisms to cope with important environmental discontinuities at time scales that preclude the onset of adaptive adjustments. We suggest that environmental conditioning and shape plasticity can overcome both reduced morphological diversity and phenotype uncoupling with habitat characteristics resulting from initial rearing in low complexity artificial environments.     

Biomechanical study on the edge shapes for penetrating keratoplasty

A parametric study to investigate the compressive and the shear stress distributions for various edge shapes created during penetrating keratoplasty (PK) using femtosecond laser is reported. The finite element analysis has been implemented using ABAQUS to study the cornea with various edge shapes, namely the standard edge shape, the zigzag edge shape, the top hat edge shape and the mushroom edge shape for PK. The ratio of maximum compressive stress to maximum shear stress is used as the main factor to assess the relative merits of wound healing rate for different edge shapes. For the typical values of tissue mechanical properties, the zigzag edge shape has the highest ratio of maximum compressive stress to maximum shear stress (11.1 in the xy-direction and 3.7 in the yz-direction), followed by the mushroom edge shape (7.7 in the xy-direction and 3.2 in the yz-direction). The ratios for the top hat and the standard edge shapes are even lower in both directions. A sensitivity analysis of the model has been done to demonstrate that the zigzag edge shape always results in the highest ratios of stresses regardless of the difference in the tissue mechanical properties. The zigzag edge shape also gives the lowest dioptric power D?=?45.4. The present results imply that the zigzag edge shape provides the best wound healing rate and optical outcome among the four edge shapes models for PK.     

Biomechanical study on the edge shapes for penetrating keratoplasty

A parametric study to investigate the compressive and the shear stress distributions for various edge shapes created during penetrating keratoplasty (PK) using femtosecond laser is reported. The finite element analysis has been implemented using ABAQUS to study the cornea with various edge shapes, namely the standard edge shape, the zigzag edge shape, the top hat edge shape and the mushroom edge shape for PK. The ratio of maximum compressive stress to maximum shear stress is used as the main factor to assess the relative merits of wound healing rate for different edge shapes. For the typical values of tissue mechanical properties, the zigzag edge shape has the highest ratio of maximum compressive stress to maximum shear stress (11.1 in the xy-direction and 3.7 in the yz-direction), followed by the mushroom edge shape (7.7 in the xy-direction and 3.2 in the yz-direction). The ratios for the top hat and the standard edge shapes are even lower in both directions. A sensitivity analysis of the model has been done to demonstrate that the zigzag edge shape always results in the highest ratios of stresses regardless of the difference in the tissue mechanical properties. The zigzag edge shape also gives the lowest dioptric power D = 45.4. The present results imply that the zigzag edge shape provides the best wound healing rate and optical outcome among the four edge shapes models for PK.     

Cross-talk between Rho and Rac GTPases drives deterministic exploration of cellular shape space and morphological heterogeneity

One goal of cell biology is to understand how cells adopt different shapes in response to varying environmental and cellular conditions. Achieving a comprehensive understanding of the relationship between cell shape and environment requires a systems-level understanding of the signalling networks that respond to external cues and regulate the cytoskeleton. Classical biochemical and genetic approaches have identified thousands of individual components that contribute to cell shape, but it remains difficult to predict how cell shape is generated by the activity of these components using bottom-up approaches because of the complex nature of their interactions in space and time. Here, we describe the regulation of cellular shape by signalling systems using a top-down approach. We first exploit the shape diversity generated by systematic RNAi screening and comprehensively define the shape space a migratory cell explores. We suggest a simple Boolean model involving the activation of Rac and Rho GTPases in two compartments to explain the basis for all cell shapes in the dataset. Critically, we also generate a probabilistic graphical model to show how cells explore this space in a deterministic, rather than a stochastic, fashion. We validate the predictions made by our model using live-cell imaging. Our work explains how cross-talk between Rho and Rac can generate different cell shapes, and thus morphological heterogeneity, in genetically identical populations.     

Shapes of discoid intracellular compartments with small relative volumes

A prominent feature of many intracellular compartments is a large membrane surface area relative to their luminal volume, i.e., the small relative volume. In this study we present a theoretical analysis of discoid membrane compartments with a small relative volume and then compare the theoretical results to quantitative morphological assessment of fusiform vesicles in urinary bladder umbrella cells. Specifically, we employ three established extensions of the standard approach to lipid membrane shape calculation and determine the shapes that could be expected according to three scenarios of membrane shaping: membrane adhesion in the central discoid part, curvature driven lateral segregation of membrane constituents, and existence of stiffer membrane regions, e.g., support by protein scaffolds. The main characteristics of each scenario are analyzed. The results indicate that even though all three scenarios can lead to similar shapes, there are values of model parameters that yield qualitatively distinctive shapes. Consequently, a distinctive shape of an intracellular compartment may reveal its membrane shaping mechanism and the membrane structure. The observed shapes of fusiform vesicles fall into two qualitatively different classes, yet they are all consistent with the theoretical results and the current understanding of their structure and function.     

Model-based inverse estimation for active contraction stresses of tongue muscles using 3D surface shape in speech production

This paper presents a novel inverse estimation approach for the active contraction stresses of tongue muscles during speech. The proposed method is based on variational data assimilation using a mechanical tongue model and 3D tongue surface shapes for speech production. The mechanical tongue model considers nonlinear hyperelasticity, finite deformation, actual geometry from computed tomography (CT) images, and anisotropic active contraction by muscle fibers, the orientations of which are ideally determined using anatomical drawings. The tongue deformation is obtained by solving a stationary force-equilibrium equation using a finite element method. An inverse problem is established to find the combination of muscle contraction stresses that minimizes the Euclidean distance of the tongue surfaces between the mechanical analysis and CT results of speech production, where a signed-distance function represents the tongue surface. Our approach is validated through an ideal numerical example and extended to the real-world case of two Japanese vowels, /ʉ/ and /ɯ/. The results capture the target shape completely and provide an excellent estimation of the active contraction stresses in the ideal case, and exhibit similar tendencies as in previous observations and simulations for the actual vowel cases. The present approach can reveal the relative relationship among the muscle contraction stresses in similar utterances with different tongue shapes, and enables the investigation of the coordination of tongue muscles during speech using only the deformed tongue shape obtained from medical images. This will enhance our understanding of speech motor control.     

Context shapes: Efficient complementary shape matching for protein-protein docking

We describe an efficient method for partial complementary shape matching for use in rigid protein-protein docking. The local shape features of a protein are represented using boolean data structures called Context Shapes. The relative orientations of the receptor and ligand surfaces are searched using precalculated lookup tables. Energetic quantities are derived from shape complementarity and buried surface area computations, using efficient boolean operations. Preliminary results indicate that our context shapes approach outperforms state-of-the-art geometric shape-based rigid-docking algorithms.     

Imitation,Genetic Lineages,and Time Influenced the Morphological Evolution of the Violin

Violin design has been in flux since the production of the first instruments in 16^th century Italy. Numerous innovations have improved the acoustical properties and playability of violins. Yet, other attributes of the violin affect its performance less, and with fewer constraints, are potentially more sensitive to historical vagaries unrelated to quality. Although the coarse shape of violins is integral to their design, details of the body outline can vary without significantly compromising sound quality. What can violin shapes tell us about their makers and history, including the degree that luthiers have influenced each other and the evolution of complex morphologies over time? Here, I provide an analysis of morphological evolution in the violin family, sampling the body shapes of over 9,000 instruments over 400 years of history. Specific shape attributes, which discriminate instruments produced by different luthiers, strongly correlate with historical time. Linear discriminant analysis reveals luthiers who likely copied the outlines of their instruments from others, which historical accounts corroborate. Clustering of averaged violin shapes places luthiers into four major groups, demonstrating a handful of discrete shapes predominate in most instruments. Violin shapes originating from multi-generational luthier families tend to cluster together, and familial origin is a significant explanatory factor of violin shape. Together, the analysis of four centuries of violin shapes demonstrates not only the influence of history and time leading to the modern violin, but widespread imitation and the transmission of design by human relatedness.