Sharing is caring? Measurement error and the issues arising from combining 3D morphometric datasets

Geometric morphometrics is routinely used in ecology and evolution and morphometric datasets are increasingly shared among researchers, allowing for more comprehensive studies and higher statistical power (as a consequence of increased sample size). However, sharing of morphometric data opens up the question of how much nonbiologically relevant variation (i.e., measurement error) is introduced in the resulting datasets and how this variation affects analyses. We perform a set of analyses based on an empirical 3D geometric morphometric dataset. In particular, we quantify the amount of error associated with combining data from multiple devices and digitized by multiple operators and test for the presence of bias. We also extend these analyses to a dataset obtained with a recently developed automated method, which does not require human‐digitized landmarks. Further, we analyze how measurement error affects estimates of phylogenetic signal and how its effect compares with the effect of phylogenetic uncertainty. We show that measurement error can be substantial when combining surface models produced by different devices and even more among landmarks digitized by different operators. We also document the presence of small, but significant, amounts of nonrandom error (i.e., bias). Measurement error is heavily reduced by excluding landmarks that are difficult to digitize. The automated method we tested had low levels of error, if used in combination with a procedure for dimensionality reduction. Estimates of phylogenetic signal can be more affected by measurement error than by phylogenetic uncertainty. Our results generally highlight the importance of landmark choice and the usefulness of estimating measurement error. Further, measurement error may limit comparisons of estimates of phylogenetic signal across studies if these have been performed using different devices or by different operators. Finally, we also show how widely held assumptions do not always hold true, particularly that measurement error affects inference more at a shallower phylogenetic scale and that automated methods perform worse than human digitization.     

The problem of assessing landmark error in geometric morphometrics: theory, methods, and modifications

Geometric morphometric methods rely on the accurate identification and quantification of landmarks on biological specimens. As in any empirical analysis, the assessment of inter- and intra-observer error is desirable. A review of methods currently being employed to assess measurement error in geometric morphometrics was conducted and three general approaches to the problem were identified. One such approach employs Generalized Procrustes Analysis to superimpose repeatedly digitized landmark configurations, thereby establishing whether repeat measures fall within an acceptable range of variation. The potential problem of this error assessment method (the "Pinocchio effect") is demonstrated and its effect on error studies discussed. An alternative approach involves employing Euclidean distances between the configuration centroid and repeat measures of a landmark to assess the relative repeatability of individual landmarks. This method is also potentially problematic as the inherent geometric properties of the specimen can result in misleading estimates of measurement error. A third approach involved the repeated digitization of landmarks with the specimen held in a constant orientation to assess individual landmark precision. This latter approach is an ideal method for assessing individual landmark precision, but is restrictive in that it does not allow for the incorporation of instrumentally defined or Type III landmarks. Hence, a revised method for assessing landmark error is proposed and described with the aid of worked empirical examples.     

Inferring the Nature of Allometry from Geometric Data

The form of an organism is the combination of its size and its shape. For a sample of forms, biologists wish to characterize both mean form and the variation in form. For geometric data, where form is characterized as the spatial locations of homologous points, the first step in analysis superimposes the forms, which requires an assumption about what measure of size is appropriate. Geometric morphometrics adopts centroid size as the natural measure of size, and assumes that variation around the mean form is isometric with size. These assumptions limit the interpretation of the resulting estimates of mean and variance in form. We illustrate these problems using allometric variation in shape. We show that superimposition based on subsets of relatively isometric points can yield superior inferences about the overall pattern of variation. We propose and demonstrate two superimposition techniques based on this idea. In subset superimposition, landmarks are progressively discarded from the data used for superimposition if they result in significant decreases in the variation among the remaining landmarks. In outline superimposition, regularly distributed pseudolandmarks on the continuous outline of a form are used as the basis for superimposition of the landmarks contained within it. Simulations show that these techniques can result in dramatic improvements in the accuracy of estimated variance-covariance matrices among landmarks when our assumptions are roughly satisfied. The pattern of variation inferred by means of our superimposition techniques can be quite different from that recovered from full generalized Procrustes superimposition. The pattern of shape variation in the wings of drosophilid flies appears to meet these assumptions. Adoption of superimposition procedures that incorporate biological assumptions about the nature of size and of the variation in shape can dramatically improve the ability to infer the pattern of variation in geometric morphometric data.     

Getting into Shape: An Empirical Comparison of Traditional Truss-Based Morphometric Methods with a Newer Geometric Method Applied to New World Cichlids

Body shape is a difficult, but important, trait to quantify. Researchers have traditionally used multivariate analysis of several linear measures ('trusses') across the body form to quantify shape. Newer geometric morphometric methods claim to better estimate shape because they analyze the geometry among the locations of all landmarks simultaneously rather than the linear distances between pairs of landmarks. We tested this claim by comparing the results of several traditional morphometric analyses against a newer geometric analysis involving thin-plate splines (TPS), all applied to a common data set of morphologically variable new world cichlids Amphilophus citrinellus and A. zaliosus. The TPS method yielded slightly stronger evidence of morphological differences among forms, although traditional methods also distinguished the two species. Perhaps our most important result was the idiosyncratic interpretation of shape variation among the traditional truss-based methods, whereas the generation of deformation grids using the TPS approach yielded clear and visually interpretable figures. Our results indicate that geometric morphometrics can be a more effective way to analyze and interpret body form, but also that traditional methods can be relied upon to provide statistical evidence of shape differences, although not necessarily accurate information about the nature of variation in shape.     

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.     

GEOMETRIC MORPHOMETRICS OF DEVELOPMENTAL INSTABILITY: ANALYZING PATTERNS OF FLUCTUATING ASYMMETRY WITH PROCRUSTES METHODS

Although fluctuating asymmetry has become popular as a measure of developmental instability, few studies have examined its developmental basis. We propose an approach to investigate the role of development for morphological asymmetry by means of morphometric methods. Our approach combines geometric morphometrics with the two-way ANOVA customary for conventional analyses of fluctuating asymmetry and can discover localized features of shape variation by examining the patterns of covariance among landmarks. This approach extends the notion of form used in studies of fluctuating asymmetry from collections of distances between morphological landmarks to an explicitly geometric concept of shape characterized by the configuration of landmarks. We demonstrate this approach with a study of asymmetry in the wings of tsetse flies (Glossina palpalis gambiensis). The analysis revealed significant fluctuating and directional asymmetry for shape as well as ample shape variation among individuals and between the offspring of young and old females. The morphological landmarks differed markedly in their degree of variability but multivariate patterns of landmark covariation identified by principal component analysis were generally similar between fluctuating asymmetry (within-individual variability) and variation among individuals. Therefore there is no evidence that special developmental processes control fluctuating asymmetry. We relate some of the morphometric patterns to processes known to be involved in the development of fly wings.     

Craniofacial variation of the Chinese macaques explored with Morphologika

In order to analyze, separately and dynamically, the variation in cranial size and shape of Chinese macaques, a new method, Morphologika, was used to illustrate 3D profiles based on the coordinates of 26 landmarks on the skull. Striking image variation between the two sexes was detected on the facial region: males exhibited a larger and more protrusive facial structure. Males also displayed a bigger cranium than females. The two sexes also showed quite different images in skull shape. However, they expressed the same allometric pattern with regard to the relationship between size and shape, which was significantly positively associated with each other along the first axis. The same relationship was negatively displayed along the second axis when the two sexes were analyzed together. However, only the relationship for females reached a significant level when the two sexes were studied separately. This was considered to be related to their differentiation in growth trajectory. This study also tested the concept of size revealed by the second axis of principal components analysis based on traditional morphometric methods on the same taxa.     

Allometric and nonallometric components of Drosophila wing shape respond differently to developmental temperature

Phenotypic plasticity of wing size and shape of Drosophila simulans was analyzed across the entire range of viable developmental temperatures with Procrustes geometric morphometric method. In agreement with previous studies, size clearly decreases when temperature increases. Wing shape variation was decomposed into its allometric (24%) and nonallometric (76%) components, and both were shown to involve landmarks located throughout the entire wing blade. The allometric component basically revealed a progressive, monotonous variation along the temperature. Surprisingly, nonallometric shape changes were highly similar at both extremes of the thermal range, suggesting that stress, rather than temperature per se, is the key developmental factor affecting wing shape.     

Cranial morphological variation of Dromiciops gliroides (Microbiotheria) along its geographical distribution in south-central Chile: A three-dimensional analysis

We analyzed the variation in cranial morphology of the marsupial Dromiciops gliroides along its distribution in south-central Chile. We evaluated whether the cranial morphological variation is congruent with the phylogeographic structure previously observed in this species. We built three-dimensional models of 69 crania on which we digitized 30 landmarks. We used standard geometric morphometric methods to extract and analyze the shape and size components of the crania. Our data showed a subtle but consistent cranial size and shape variation along the studied distributional range, suggesting a geographic variation pattern rather than a phylogeographic structuring. Indeed, our multivariate analyses recovered a subtle morphological differentiation between island and mainland populations, contrary to what is suggested by a former phylogeographic study. We detected that either the cranial size variation, as well as the insularity and the latitude could be important factors underlying the cranial shape changes. We suggest that an interplay of historical and contemporary processes could be shaping the morphological pattern observed in this marsupial.     

Geographical variation in shell shape of the pod razor shell Ensis siliqua (Bivalvia: Pharidae)

The present study assessed the existence of variation in the shell shape of the pod razor shell (Ensis siliqua) throughout its distributional range in the north-eastern Atlantic. Shells of E. siliqua caught at seven collecting sites (three in Portugal, three in Spain and one in Ireland) were studied by geometric morphometric methods, using both landmark- and contour-based methods. Both approaches (landmarks inside the valves and shell outline) discriminated the shells from Aveiro (centre of Portugal) and Strangford Lough (Ireland) from those caught in the nearby localities (remaining Portuguese and Spanish sites, maximum distance of 550 km by sea). Landmark analysis revealed that shells from Aveiro were more similar to shells from Ireland (~1,500 km far away). Contour analysis revealed that shells from Aveiro had a shape with a comparatively larger height-to-width ratio, whereas shells from Ireland showed a slightly more curved outline than in the remaining sites. Landmark- and contour-based methods provided coherent complementary information, confirming the usefulness of geometric morphometric analyses for discerning differences in shell shape among populations of E. siliqua. A brief review of previous applications of geometric morphometric methods to modern bivalve species is also provided.     

Advances in Geometric Morphometrics

Geometric morphometrics is the statistical analysis of form based on Cartesian landmark coordinates. After separating shape from overall size, position, and orientation of the landmark configurations, the resulting Procrustes shape coordinates can be used for statistical analysis. Kendall shape space, the mathematical space induced by the shape coordinates, is a metric space that can be approximated locally by a Euclidean tangent space. Thus, notions of distance (similarity) between shapes or of the length and direction of developmental and evolutionary trajectories can be meaningfully assessed in this space. Results of statistical techniques that preserve these convenient properties—such as principal component analysis, multivariate regression, or partial least squares analysis—can be visualized as actual shapes or shape deformations. The Procrustes distance between a shape and its relabeled reflection is a measure of bilateral asymmetry. Shape space can be extended to form space by augmenting the shape coordinates with the natural logarithm of Centroid Size, a measure of size in geometric morphometrics that is uncorrelated with shape for small isotropic landmark variation. The thin-plate spline interpolation function is the standard tool to compute deformation grids and 3D visualizations. It is also central to the estimation of missing landmarks and to the semilandmark algorithm, which permits to include outlines and surfaces in geometric morphometric analysis. The powerful visualization tools of geometric morphometrics and the typically large amount of shape variables give rise to a specific exploratory style of analysis, allowing the identification and quantification of previously unknown shape features.     

Technical note: Quantification of neurocranial shape variation using the shortest paths connecting pairs of anatomical landmarks

Three‐dimensional geometric morphometric techniques have been widely used in quantitative comparisons of craniofacial morphology in humans and nonhuman primates. However, few anatomical landmarks can actually be defined on the neurocranium. In this study, an alternative method is proposed for defining semi‐landmarks on neurocranial surfaces for use in detailed analysis of cranial shape. Specifically, midsagittal, nuchal, and temporal lines were approximated using Bezier curves and equally spaced points along each of the curves were defined as semi‐landmarks. The shortest paths connecting pairs of anatomical landmarks as well as semi‐landmarks were then calculated in order to represent the surface morphology between landmarks using equally spaced points along the paths. To evaluate the efficacy of this method, the previously outlined technique was used in morphological analysis of sexual dimorphism in modern Japanese crania. The study sample comprised 22 specimens that were used to generate 110 anatomical semi‐landmarks, which were used in geometric morphometric analysis. Although variations due to sexual dimorphism in human crania are very small, differences could be identified using the proposed landmark placement, which demonstrated the efficacy of the proposed method. Am J Phys Anthropol 151:658–666, 2013. © 2013 Wiley Periodicals, Inc.     

Morphological disparity in theropod jaws: comparing discrete characters and geometric morphometrics

Disparity, the diversity of form and function of organisms, can be assessed from cladistic or phenetic characters, and from discrete characters or continuous characters such as landmarks, outlines, or ratios. But do these different methods of assessing disparity provide comparable results? Here we provide evidence that all metrics correlate significantly with each other and capture similar patterns of morphological variation. We compare three methods of capturing morphological disparity (discrete characters, geometric morphometric outlines and geometric morphometric landmarks) in coelurosaurian dinosaurs. We standardize our study by focusing all our metrics on the mandible, so avoiding the risk of confounding disparity methods with anatomical coverage of the taxa. The correlation is strongest between the two geometric morphometric methods, and weaker between the morphometric methods and the discrete characters. By using phylogenetic simulations of discrete character and geometric morphometric data sets, we show that the strength of these correlations is significantly greater than expected from the evolution of random data under Brownian motion. All disparity metrics confirm that Maniraptoriformes had the highest disparity of all coelurosaurians, and omnivores and herbivores had higher disparity than carnivores.     

Statistical power comparisons among alternative morphometric methods

This paper compares the statistical power of various tests that have been proposed to test for equality of shape in two populations. Power surfaces are computed with emphasis on the simplest case of three points in the plane (i.e., landmarks at the vertices of a triangle). Goodall's ([1991] J Roy Stat Soc Serb 53:285-339) F-test was found to have the highest power followed by T(2)-tests using Kendall tangent space coordinates. Power for T(2)-tests using Bookstein shape coordinates was good if the baseline was not the shortest side of the triangle. The Rao and Suryawanshi ([1996] Proc Natl Acad Sci 93:12132-12136 and Rao and Suryawanshi [1998] Proc Natl Acad Sci 95:4121-4125) shape variables had much lower power when triangles were not close to being equilateral. Power surfaces for the EDMA-I T statistic revealed very low power for many shape comparisons including those between very different shapes. Power surface for the EDMA-II Z statistic were also complicated and depended strongly on the choice of baseline used for size scaling. The type I error rate was also often not correct for this method. Results for more than three landmarks are also presented. The implications of the results for practical applications of morphometrics are discussed.     

Geometric morphometries and the analysis of higher taxa: a case study based on the metendosternite of the Scarabaeoidea (Coleoptera)

A geometric morphometric analysis of families belonging to the Scarabaeoidea, using landmarks from three two-dimensional views (frontal, dorsal and lateral) of an internally situated rigid structure, the metendosternite, was carried out. Procrustes distances matrices were obtained to produce phenograms from the three analyses. Relative warp analyses were also performed and the first two relative warps for the three data sets plotted against each other. The metendosternite is an internally situated anatomical structure that has largely been neglected in past studies. However, it proved to be useful in geometric morphometric studies, because it is rigid and landmarks can be easily identified. Geometric morphometries is shown to be a powerful tool to identify phenetic relationships between higher level taxa, and the metendosternite is a new structure available for beetle systematisists.     

Geometric morphometric analysis of Eysarcoris guttiger,E.annamita and E.ventralis (Hemiptera: Pentatomidae)

The genus Eysarcoris can be easily distinguished from other genera through the two spots in the basal angle of the scutellum.Nevertheless,Eysarcoris species show complex variances.Geometric morphometric methods have been increasingly applied to distinguish species and to define the boundary of genera among insects.In the present study,geometric morphometric approach was firstly employed to evaluate the shape variation of three characters (fore wing,hind wing and pygophore) of E.guttiger,E.annamita and E.ventralis using E.aeneus as outgroup to ascertain whether this approach is a reliable method for the taxonomy of Eysarcoris.Analysis was conducted on the landmarks of the three characters of these species.Multivariate regression of procrustes coordinates against centroid size was conducted to test the presence of allometry.Principal component analysis (PCA),canonical variate analysis (CVA)and cluster analysis were utilized to describe variations in shapes among the studied species.For all of the three characters,though PCA analysis showed some overlap among species,p-values for procrustes distance and mahalanobis distance were all less than 0.0001.The distribution of the three studied species corresponds with their species status.This study demonstrates that the geometric morphometrics of both the fore wing and the hind wing might represent a possible tool for the identification of species within this genus.