Testing different 3D techniques using geometric morphometrics: Implications for cranial fluctuating asymmetry in humans

This study aimed to test the performance of 3D digitizer, CT scanner, and surface scanner in detecting cranial fluctuating asymmetry. Sets of 32 landmarks (6 in the midline and 13 bilateral) were acquired from 14 archeological crania using a 3D digitizer, and from 3D models generated from a CT scanner and surface scanner using Viewbox 4. Levels of shape variation were analyzed in MorphoJ using Procrustes analysis of variance and Principal component analysis. Intra-observer error accounted for 1.7%, 1.8%, and 4.5% of total shape variation for 3D digitizer, CT scanner, and surface scanner respectively. Fluctuating asymmetry accounted for 15%–16% of total shape variation. Variation between techniques accounted for 18% of total shape variation. We found a higher level of missing landmarks in our surface scan data than for both 3D digitizer and CT scanner data, and both 3D model-based techniques sometimes obscured taphonomic damage. All three 3D techniques are appropriate for measuring cranial fluctuating asymmetry. We advise against combining data collected with different techniques.     

Dealing with allometry in linear and geometric morphometrics: a taxonomic case study in the Leporinus cylindriformis group (Characiformes: Anostomidae) with description of a new species from Suriname

To achieve maximum efficacy, taxonomic studies that seek to distinguish amongst species must first account for allometric shape variation within species. Two recently developed software packages (SMATR and MorphoJ) offer regression‐based allometric approaches that are notable for their statistical power and ease of use and that may prove highly useful to taxonomists working with linear or geometric morphometric data. We investigate species delimitation of the slender‐bodied fishes in the Leporinus cylindriformis group using these programs and demonstrate the utility of the allometric corrections that they provide. Without allometric correction, many pairs of species are difficult to distinguish on the basis of morphometrics, but once regressions are used to account for marked allometric variation within species, most of the recognized species in this group can be readily distinguished with linear or geometric morphometrics, particularly using variation in the depth of the body. Both approaches returned congruent patterns of separation amongst putative species, but the geometric approach in MorphoJ distinguished amongst four more pairs of species than did the linear approach in SMATR and appears to provide slightly more statistical power. Based on distinctive morphometrics, meristics, and coloration, a highly elongate species of Leporinus from the Suriname, Corantijn, and Coppename rivers of Suriname is described herein as a new species, Leporinus apollo sp. nov. The unique L. cylindriformis holotype from Porto de Moz, Brazil differs in morphology, meristics, and pigmentation from specimens commonly referred to that species from the main basin of the Amazon; the latter specimens may represent an additional undescribed species. The L. cylindriformis holotype itself may represent a rare species or a specimen collected at the edge of its native range. Measurements of the holotype and paratype of Leporinus niceforoi, which were collected in the Amazonian slope of Colombia, differ substantially from similarly pigmented and putatively conspecific specimens from Amazonian portions of Ecuador and Peru. Recently collected specimens from Colombia are needed to determine whether the observed morphometric variation encompassed by the current concept of L. niceforoi indicates a morphocline within a single species, suggests the presence of multiple cryptic species, or results from shrinkage of the types. In all these cases, linear or geometric morphometric data can reliably differentiate amongst species, but only after one accounts for allometric shape variation. The new SMATR and MorphoJ software packages both offer easy and effective approaches to such allometrically informed taxonomy, and may prove useful to any systematist working on taxa that change shape as they grow. © 2011 The Linnean Society of London, Zoological Journal of the Linnean Society, 2011, 162 , 103–130.     

The Gavialis-Tomistoma debate: the contribution of skull ontogenetic allometry and growth trajectories to the study of crocodylian relationships

The phylogenetic placement of Tomistoma and Gavialis crocodiles depends largely upon whether molecular or morphological data are utilized. Molecular analyses consider them as sister taxa, whereas morphological/paleontological analyses set Gavialis apart from Tomistoma and other crocodylian species. Here skull allometric trajectories of Tomistoma and Gavialis were contrasted with those of two longirostral crocodylian taxa, Crocodylus acutus and Mecistops cataphractus, to examine similarities in growth trajectories in light of this phylogenetic controversy. Entire skull shape and its two main modules, rostrum and postrostrum, were analyzed separately. We tested differences for both multivariate angles between trajectories and for shape differences at early and late stages of development. Based on a multivariate regression of shape data and size, Tomistoma seems to possess a peculiar rate of growth in comparison to the remaining taxa. However, its morphology at both juvenile and adult sizes is always closer to those of Brevirostres crocodylians, for the entire head shape, as well as the shape of the postrostrum and rostrum. By contrast, the allometric trajectory of Gavialis always begins and ends in a unique region of the multidimensional morphospace. These findings concur with a morphological hypothesis that places Gavialis separate from Brevirostres, and Tomistoma closer to other crocodylids, and provides an additional, and independent, data set to inform on this ongoing phylogenetic discussion.     

Multivariate analyses of shape variation for genetically distinct groups

Many multivariate techniques have been proprosed for the analysis of shape variation. This article discusses several approaches in the context of examining shape similarities and differences for landmark data from two genetically distinct groups. Describing and understanding these variations will help develop insight into how genetically determined differences arise and are maintained. We discuss techniques based on principal component analyses including the use of a «sheared» component as the shape component and the use of a holistic size measure for adjustment of the original log-transformed measurements. Finally we examine a recently developed morphometric technique of analysis of triangles defined by sets of three appropriate landmarks.     

mvmapper: Interactive spatial mapping of genetic structures

Characterizing genetic structure across geographic space is a fundamental challenge in population genetics. Multivariate statistical analyses are powerful tools for summarizing genetic variability, but geographic information and accompanying metadata are not always easily integrated into these methods in a user‐friendly fashion. Here, we present a deployable Python‐based web‐tool, mvmapper , for visualizing and exploring results of multivariate analyses in geographic space. This tool can be used to map results of virtually any multivariate analysis of georeferenced data, and routines for exporting results from a number of standard methods have been integrated in the R package adegenet , including principal components analysis (PCA), spatial PCA, discriminant analysis of principal components, principal coordinates analysis, nonmetric dimensional scaling and correspondence analysis. mvmapper 's greatest strength is facilitating dynamic and interactive exploration of the statistical and geographic frameworks side by side, a task that is difficult and time‐consuming with currently available tools. Source code and deployment instructions, as well as a link to a hosted instance of mvmapper , can be found at https://popphylotools.github.io/mvMapper/ .     

Sexual dimorphism in the skull of minks Mustela vison, badgers Meles meles and otters Lutra lutra

Multiple-group principal component analysis and discriminant analysis were used to investigate the morphological differences between adult skulls of male and female minks, badgers and otters from Norway. The first principal component axis, calculated from the variance-covariance matrix of log-transformed data, was interpreted as a growth-free size axis in all three species, while the other components were interpreted as representing shape. Having largely separated size and shape variation, these two aspects of sexual dimorphism could be studied. The standardized component scores were subjected to an analysis of variance and discriminant analyses were performed on size-in and size-out data. Sexual dimorphism was disclosed on eight of the 12 components in minks and on seven of the 12 components in badgers and otters. In mink the multivariate differences were more due to size than to shape, whereas in badgers and otters most of the multivariate differences were due to shape, but the differences in size were also significant. The shape dimorphism was shown to be functionally related to jaw and neck muscles. The results were discussed in relation to recent theories to explain the evolutionary significance of sexual dimorphism in body size of mustelids. It was concluded that these theories do not fully explain the dimorphism found in the skulls of the moderately dimorphic badger and otter.     

Ontogenetic and environmental effects on otolith shape variability in three Mediterranean European eel (Anguilla anguilla, L.) local stocks

Otolith morphology is an efficient tool for the discrimination of fish stocks, populations and species when comparative genetic data are not available. Currently, the relationship between environmental factors and otolith shape is poorly characterized for the European eel (Anguilla anguilla), a highly migratory catadromous species constituting a single, randomly mating stock. The present study analyses the differences in otolith morphology between three Mediterranean eel local stocks from different environmental contexts (i.e. two brackish lagoons and one river). The relationship between otolith shape and otolith size was studied by means of Elliptic Fourier analysis and multivariate statistics. Otolith profile was digitally acquired and Cartesian coordinates were extracted. Partial Least Square (PLS) analysis pointed to continuous allometric growth in size and shape in otoliths from all three sites. In the three environments, shape variations occurred during growth as indicated by the presence of a significant and positive relationship between otolith size and the first PLS latent vector (i.e. which bears most of the information regarding otolith outline). Differences between smaller and larger sized otoliths were investigated using PLS Discriminant Analysis (PLSDA) and cluster analysis. Results indicate that otolith shape is highly uniform at smaller than at larger sizes. These shape differences apparently overlap the initial differentiation of the small otolith outlines acquired by eels during the growing phase as elvers in the marine environment. Data were discussed considering that the physical and chemical habitat variability in brackish lagoons and river could underlie a marked change in otolith shape during the animals' growth.     

Elliptical fourier analysis of symphyseal shape in great ape mandibles

The midsagittal profile of the mandibular symphysis has served as both a taxonomic marker and a phylogenetically salient character in debates over hominoid evolution. Nevertheless, the utility of symphyseal shape as an informative attribute for paleobiological reconstructions is suspect. Quantification of shape variation has proven to be particularly problematic; it has long been recognized that conventional linear measurements (and the indices derived from them), while replicable, summarize aspects of shape very poorly because of the vast amount of contour information that is lost in the process.In this study, a type of Fourier analysis is applied to cross-sectional contours of ape mandibles in order to provide a mathematical accounting of shape variation in a "global" sense; that is, by applying the "totality" of contour information in a comparative analysis. Shape variation in the mandibular symphysis is explored through the decomposition of coordinate data into elliptical Fourier coefficients. These coefficients are used to compute average taxonomic distances (ATD) among individuals of chimpanzees, gorillas, and orang-utans. The resulting shape-based distances are summarized via clustering (UPGMA) and ordination (principal coordinates analysis-PCO). Principal coordinate scores are subjected to analysis of variance in univariate and multivariate designs; these data are also applied to discriminant function analyses.Species and sex effects on morphology are statistically significant; however, no significant interaction of these factors is indicated. This would seem to imply that patterns of sexual dimorphism are not distinct among great apes; to the contrary, within-species sex comparisons reveal that significant size and shape dimorphism is present only in Gorilla. Despite significant size dimorphism in Pan and Pongo, significant shape differences between males and females are not apparent in these taxa.These results suggest that it is theoretically possible to sort taxa by a symphyseal shape criterion, but the discriminant function results suggest that there still exists a large potential for error in assigning particular shapes to a given species or sex. Thus, despite real shape differences among these species, the use of symphyseal shape as a character in species identification or in systematic arguments remains limited and problematic.     

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.     

EviCor: Interactive Web Platform for Exploration of Molecular Features and Response to Anti-cancer Drugs

Experimental biologists are often left alone with the task to download, process, and analyze big datasets in order to perform correlation or other simpler analyses. To address these issues, we introduce EviCor, a handy toolbox for exploration of data from large public resources such as The Cancer Genome Atlas and The Cancer Cell Line Encyclopedia, complemented with follow-up information on same samples, which couples omics datasets with drug response profiles (https://www.evicor.org/). The data was processed for easy retrieval from the server-side database and includes pre-computed drug-feature correlation tables. Using information from multiple independent sources, the task-oriented web interface presents relations between phenotype, single-molecule, and pathway variables with graphical, statistical, and network analysis tools. Building custom multivariate models is enabled via user-friendly web interface and programmatic access via RESTinterface. Project code is available at https://github.com/aveviort/HyperSet.     

Avian wing proportions and flight styles: first step towards predicting the flight modes of mesozoic birds

We investigated the relationship between wing element proportions and flight mode in a dataset of living avian species to provide a framework for making basic estimates of the range of flight styles evolved by Mesozoic birds. Our results show that feather length (f(prim)) and total arm length (ta) (sum of the humerus, ulna and manus length) ratios differ significantly between four flight style groups defined and widely used for living birds and as a result are predictive for fossils. This was confirmed using multivariate ordination analyses, with four wing elements (humerus, ulna/radius, manus, primary feathers), that discriminate the four broad flight styles within living birds. Among the variables tested, manus length is closely correlated with wing size, yet is the poorest predictor for flight style, suggesting that the shape of the bones in the hand wing is most important in determining flight style. Wing bone thickness (shape) must vary with wing beat strength, with weaker forces requiring less bone. Finally, we show that by incorporating data from Mesozoic birds, multivariate ordination analyses can be used to predict the flight styles of fossils.     

Application of method of moments analysis to fluorescence decay lifetime distributions

In fluorescence decay work, distributions of exponential decay lifetimes are anticipated where complex systems are examined. We describe here methods of gaining information on such distributions using the method of moments analysis approach. The information obtained may be as simple as the average and deviation of the lifetime distribution, quantities which we show may be estimated directly from the results of a multiexponential analysis. An approximation to the actual distribution shape may also be obtained using a procedure we call the variable filter analysis (VFA) method without making any assumptions about the shape of the distribution. Tests of VFA using both simulated and experimental data are described. Limitations of this method and of distribution analysis methods in general are discussed. Results of analyses on experimental decays for ethidium intercalated in core particles and in free DNA are reported.     

Bioanthropological analysis of human occipital condyles using geometric morphometric method

Sex differences are present in all parts of the body, including the skeletal system. Several methods are used to analyze the sex differences of skeleton, while more recently, a new method called geometric morphometry has been used. The aim of this study was to examine the sexual dimorphism of occipital condyles on human skulls originating from the population of Bosnia and Herzegovina using the geometric morphometric method.Material and methodsThe study was conducted on 214 human skulls of known gender from Bosnian population. For analysis of sexual dimorphism of occipital condyles, we used geometric morphometry, where all the skulls were scanned to obtain three-dimensional skull models. On the obtained models, we marked anthropometric points on occipital condyles in a Landmark Editor program from which we exported data in the form NTSYS file and analyzed it in MorphoJ program.ResultsFirst principal component PC1 describes 26.917% of total variability, the second principal component PC2 describes 20.992% of total variability, while the first eight principal components together describe 100% of total variability. The greatest variability between the male skulls and female skulls was present in the anterior-posterior diameter (length of occipital condyles). Discriminant functional analysis of the shape and size of the occipital condyles was possible with 69.50% accuracy for male skulls and with 60.27% accuracy for female skulls. The size of the occipital condyles showed a statistically significant effect on sexual determination. Discriminant functional analysis of the shape of the occipital condyles without affecting size enabled the determination of gender with with 65.96% accuracy for male skulls and with 63.01% accuracy for female skulls.ConclusionAnalysis of sexual dimorphism of occipital condyles using geometric morphometry showed statistically significant differences in the shape and size of occipital condyles between the sexes. The accuracy of sex determination based on occipital condyles was higher for male gender.     

Hypothesis testing in comparative and experimental studies of function-valued traits

Many traits of evolutionary interest, when placed in their developmental, physiological, or environmental contexts, are function-valued. For instance, gene expression during development is typically a function of the age of an organism and physiological processes are often a function of environment. In comparative and experimental studies, a fundamental question is whether the function-valued trait of one group is different from another. To address this question, evolutionary biologists have several statistical methods available. These methods can be classified into one of two types: multivariate and functional. Multivariate methods, including univariate repeated-measures analysis of variance (ANOVA), treat each trait as a finite list of data. Functional methods, such as repeated-measures regression, view the data as a sample of points drawn from an underlying function. A key difference between multivariate and functional methods is that functional methods retain information about the ordering and spacing of a set of data values, information that is discarded by multivariate methods. In this study, we evaluated the importance of that discarded information in statistical analyses of function-valued traits. Our results indicate that functional methods tend to have substantially greater statistical power than multivariate approaches to detect differences in a function-valued trait between groups.     

The copula approach to characterizing dependence structure in neural populations

The question as to the role that correlated activity plays in the coding of information in the brain continues to be one of the most important in neuroscience. One approach to understanding this role is to formally model the ensemble responses as multivariate probability distributions. We have previously introduced alternatives to linear assumptions of multivariate Gaussian dependence for spike timing in neural ensembles using the probabilistic copula approach. In probability theory the copula "couples" marginal distributions to form flexible multivariate distribution functions for characterizing ensemble behavior. The parametric copula can be factored out of the joint probability density, and as such is independent and isolated from the marginal densities. This greatly simplifies the analysis, and allows a direct examination of the shape of the dependence independent of the marginals. The shape of the copula function goes beyond describing the dependence with a single summarizing statistic. In this review, we illustrate the construction of the copula, and how it contributes to the analysis of information conveyed by populations of neurons.     

A simulation program examining the use of ratios as raw variables in analyses of variance

An interactive, BASIC-PLUS, simulation program is described for performing a large number of multivariate analyses in accord with, or in violation of, known underlying models. Using a PDP 11/40 computer, random numbers are generated and converted into bivariate normal observations X and Y. These data are then analyzed according to three models. The three analyses are: (1) a standard analysis of variance ignoring the concomitant variable; (2) an analysis of covariance; (3) an analysis of variance on the ratio Y/X. The program can be used to examine the effect of performing multivariate analyses on data transformed into ratios. The utility of the program is the simplicity with which one can alter the underlying models and/or the mathematical relationships between X and Y. Output provides comparisons between models by accumulating rejections and other statistics on critical F-values for each model.     

Enhanced Understanding of Pharmaceutical Materials Through Advanced Characterisation and Analysis

The impact of pharmaceutical materials properties on drug product quality and manufacturability is well recognised by the industry. An ongoing effort across industry and academia, the Manufacturing Classification System consortium, aims to gather the existing body of knowledge in a common framework to provide guidance on selection of appropriate manufacturing technologies for a given drug and/or guide optimization of the physical properties of the drug to facilitate manufacturing requirements for a given processing route. Simultaneously, material scientists endeavour to develop characterisation methods such as size, shape, surface area, density, flow and compactibility that enable a stronger understanding of materials powder properties. These properties are routinely tested drug product development and advances in instrumentation and computing power have enabled novel characterisation methods which generate larger, more complex data sets leading to a better understanding of the materials. These methods have specific requirements in terms of data management and analysis. An appropriate data management strategy eliminates time-consuming data collation steps and enables access to data collected for multiple methods and materials simultaneously. Methods ideally suited to extract information from large, complex data sets such as multivariate projection methods allow simpler representation of the variability contained within the data and easier interpretation of the key information it contains. In this review, an overview of the current knowledge and challenges introduced by modern pharmaceutical material characterisation methods is provided. Two case studies illustrate how the incorporation of multivariate analysis into the material sciences workflow facilitates a better understanding of materials.     

Multivariate analysis in biological anthropology: Some considerations

The relation between modern multivariate statistical analysis and common objectives in biological anthropology is discussed. Many formal statistical assumptions should be satisfied to fully justify multi-variate analysis, but rarely are. Their failure does not have as adverse an effect upon scientific research as some procedural errors in research design. These include the treatment of single specimens as if they are samples, and the failure to separate considerations of size and shape. The superiority of elaborate multivariate distances over simpler quantitative techniques, inferred from the former's consideration of trait intercorrelations, is unwarranted from both theoretical and practical aspects. Based on these points and several comparative examples of analyses, it is argued that simpler, non-statistical approaches such as those of the school of numerical taxonomy have much to offer primato-logical studies. Classic multivariate statistics, while useful for studying closely similar living populations, are considerably more limited in usefulness and significance for paleoanthropological studies.