Landmarking the Brain for Geometric Morphometric Analysis: An Error Study

Neuroanatomic phenotypes are often assessed using volumetric analysis. Although powerful and versatile, this approach is limited in that it is unable to quantify changes in shape, to describe how regions are interrelated, or to determine whether changes in size are global or local. Statistical shape analysis using coordinate data from biologically relevant landmarks is the preferred method for testing these aspects of phenotype. To date, approximately fifty landmarks have been used to study brain shape. Of the studies that have used landmark-based statistical shape analysis of the brain, most have not published protocols for landmark identification or the results of reliability studies on these landmarks. The primary aims of this study were two-fold: (1) to collaboratively develop detailed data collection protocols for a set of brain landmarks, and (2) to complete an intra- and inter-observer validation study of the set of landmarks. Detailed protocols were developed for 29 cortical and subcortical landmarks using a sample of 10 boys aged 12 years old. Average intra-observer error for the final set of landmarks was 1.9 mm with a range of 0.72 mm–5.6 mm. Average inter-observer error was 1.1 mm with a range of 0.40 mm–3.4 mm. This study successfully establishes landmark protocols with a minimal level of error that can be used by other researchers in the assessment of neuroanatomic phenotypes.     

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.     

Are geometric morphometric analyses replicable? Evaluating landmark measurement error and its impact on extant and fossil Microtus classification

Geometric morphometric analyses are frequently employed to quantify biological shape and shape variation. Despite the popularity of this technique, quantification of measurement error in geometric morphometric datasets and its impact on statistical results is seldom assessed in the literature. Here, we evaluate error on 2D landmark coordinate configurations of the lower first molar of five North American Microtus (vole) species. We acquired data from the same specimens several times to quantify error from four data acquisition sources: specimen presentation, imaging devices, interobserver variation, and intraobserver variation. We then evaluated the impact of those errors on linear discriminant analysis‐based classifications of the five species using recent specimens of known species affinity and fossil specimens of unknown species affinity. Results indicate that data acquisition error can be substantial, sometimes explaining >30% of the total variation among datasets. Comparisons of datasets digitized by different individuals exhibit the greatest discrepancies in landmark precision, and comparison of datasets photographed from different presentation angles yields the greatest discrepancies in species classification results. All error sources impact statistical classification to some extent. For example, no two landmark dataset replicates exhibit the same predicted group memberships of recent or fossil specimens. Our findings emphasize the need to mitigate error as much as possible during geometric morphometric data collection. Though the impact of measurement error on statistical fidelity is likely analysis‐specific, we recommend that all geometric morphometric studies standardize specimen imaging equipment, specimen presentations (if analyses are 2D), and landmark digitizers to reduce error and subsequent analytical misinterpretations.     

Applications of finite-element scaling analysis in primatology

The study of biological shape in three dimensions using landmark data can now be accomplished using several alternative methods. This report focuses on the use of finite-element scaling analysis in primate craniofacial morphology. The method is particularly useful in its ability to localize the differences between forms, thereby indicating those loci that differ most between specimens. Several examples of this feature are provided from primatological research. Particulars of the methods are also discussed in an attempt to provide the reader with cautionary knowledge for prudent application of the method in future research.     

A simple method for visualization of influential landmarks when using euclidean distance matrix analysis

Euclidean distance matrix analysis (EDMA) differs from most other morphometric methods for the analysis of landmark coordinate data in that it is coordinate-system invariant. However, strict adherence to coordinate-system invariance (for both biological and statistical reasons) introduces some difficulty in using graphic aids for the analysis and interpretation of EDMA results. We present a simple and effective graphic method to help localize important differences in form, growth, or shape by identifying “influential” landmarks. Examples are presented using simulated data and real data involving both children with craniofacial dysmorphologies and sexual dimorphism in adult Macaca fascicularis. Am J Phys Anthropol 107:273–283, 1998. © 1998 Wiley-Liss, Inc.     

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.     

The nature and basis of sexual dimorphism in the primate skeleton

This study sets out to document and analyse sexual dimorphism in the teeth and bones of five primate groups, including man. Specimens were only included in the analysis if their sexual attribution was reliable and was based on non-osteological criteria. Ninety raw measurements, both cranial and post-cranial, were used and 11 indices were computed from them.
The parameters of each sample were computed in order to compare these results with previous estimates of dimorphism which have not always been based on reliably sexed samples. Correlation matrices were computed.
The overall sex differences were subdivided into "shape" and "size" components using Penrose's size and shape distances and by computing the principal components of each data set. The visually apparent shape differences were confirmed metrically and then examined to see whether they could be explained by allometric effects or whether there was evidence for sexual differences in growth patterns.
Using femur length as the independent variable, because of its correlation with overall size, allometric coefficients were computed for the logarithmically transformed data. The coefficients were in some cases very different between sexes but the majority did not achieve statistical significance. Of those that were significantly different only in Homo did such differences narrowly exceed the number that would be expected by chance alone.
As the vast majority of allometric coefficients for the pooled male and female data differed from unity, the hypothesis that most of the considerable shape differences that exist between some male and female primates are due to underlying growth differences must be rejected. It is suggested that such differences are simply the result of disproportionate change in size.     

Quantification of Orofacial Phenotypes in Xenopus

Xenopus has become an important tool for dissecting the mechanisms governing craniofacial development and defects. A method to quantify orofacial development will allow for more rigorous analysis of orofacial phenotypes upon abrogation with substances that can genetically or molecularly manipulate gene expression or protein function. Using two dimensional images of the embryonic heads, traditional size dimensions-such as orofacial width, height and area- are measured. In addition, a roundness measure of the embryonic mouth opening is used to describe the shape of the mouth. Geometric morphometrics of these two dimensional images is also performed to provide a more sophisticated view of changes in the shape of the orofacial region. Landmarks are assigned to specific points in the orofacial region and coordinates are created. A principle component analysis is used to reduce landmark coordinates to principle components that then discriminate the treatment groups. These results are displayed as a scatter plot in which individuals with similar orofacial shapes cluster together. It is also useful to perform a discriminant function analysis, which statistically compares the positions of the landmarks between two treatment groups. This analysis is displayed on a transformation grid where changes in landmark position are viewed as vectors. A grid is superimposed on these vectors so that a warping pattern is displayed to show where significant landmark positions have changed. Shape changes in the discriminant function analysis are based on a statistical measure, and therefore can be evaluated by a p-value. This analysis is simple and accessible, requiring only a stereoscope and freeware software, and thus will be a valuable research and teaching resource.     

Euclidean distance matrix analysis: a coordinate-free approach for comparing biological shapes using landmark data.

For problems of classification and comparison in biological research, the primary focus is on the similarity of forms. A biological form can be conveniently defined as consisting of size and shape. Several approaches for comparing biological shapes using landmark data are available. Lele (1991a) critically discusses these approaches and proposes a new method based on the Euclidean distance matrix representation of the form of an object. The purpose of this paper is to extend this new methodology to the comparison of groups of objects. We develop the statistical versions of various concepts introduced by Lele (1991a) and use them for developing statistical procedures for testing the hypothesis of shape difference between biological forms. We illustrate the use of this method by studying morphological differences between normal children and those affected with Crouzon and Apert syndromes and craniofacial sexual dimorphism in Cebus apella.     

Left,right or both? Estimating and improving accuracy of one‐side‐only geometric morphometric analyses of cranial variation

Procrustes‐based geometric morphometric analyses of bilaterally symmetric structures are often performed using only one side. This is particularly common in studies of cranial variation in mammals and other vertebrates. When one is not interested in quantifying asymmetry, landmarking one side, instead of both, reduces the number of variables as well as the time and costs of data collection. It is assumed that the loss of information in the other half, on which landmarks are not digitized, is negligible, but this has seldom been tested. Using 10 samples of mammalian crania and a total of more than 500 specimens, and five different landmark configurations, I demonstrate that this assumption is indeed easily met for size. For shape, in contrast, one‐side landmarking has potentially more severe consequences on the estimates of similarity relationships in a sample. In this respect, microevolutionary analyses of small differences are particularly affected, whereas macroevolutionary studies are fairly robust. In almost all instances, however, a simple preliminary operation improves accuracy by making one‐side‐only shape data more similar to those obtained by landmarking both sides. The same operation also makes estimates of allometry more accurate and improves the visualization. This operation consists in estimating the missing side by a mirror reflection of bilateral landmarks. In the Supporting Information, I exemplify how this can be easily done using free user‐friendly software. I also provide an example data set for readers to repeat and learn the steps of this simple procedure.     

Integration and modularity of quantitative trait locus effects on geometric shape in the mouse mandible

The mouse mandible has long served as a model system for complex morphological structures. Here we use new methodology based on geometric morphometrics to test the hypothesis that the mandible consists of two main modules, the alveolar region and the ascending ramus, and that this modularity is reflected in the effects of quantitative trait loci (QTL). The shape of each mandible was analyzed by the positions of 16 morphological landmarks and these data were analyzed using Procrustes analysis. Interval mapping in the F(2) generation from intercrosses of the LG/J and SM/J strains revealed 33 QTL affecting mandible shape. The QTL effects corresponded to a variety of shape changes, but ordination or a parametric bootstrap test of clustering did not reveal any distinct groups of QTL that would affect primarily one module or the other. The correlations of landmark positions between the two modules tended to be lower than the correlations between arbitrary subsets of landmarks, indicating that the modules were relatively independent of each other and confirming the hypothesized location of the boundary between them. While these results are in agreement with the hypothesis of modularity, they also underscore that modularity is a question of the relative degrees to which QTL contribute to different traits, rather than a question of discrete sets of QTL contributing to discrete sets of traits.     

Do dung beetles show interrelated evolutionary trends in wing morphology,flight biomechanics and habitat preference?

In flying organisms, wing shape and biomechanical properties are recognized as key traits related to dispersal, foraging behavior, sexual selection and habitat preferences. To determine if differences in dung beetle wing shape and flight biomechanics are consistent with habitat preferences in a phylogenetic context, we examined how wing morphology varied in a set of 18 Mozambique forest and grassland dung beetle (Scarabaeinae) species, representing nine genera and six tribes. Geometric morphometric measurements were taken of entire wings, as well as two additional shape characters comprising the RA4 and CuA to J regions of veins. Ordination (Principal Components Analysis and Canonical Variate Analysis) of landmark data revealed three different trends in wing shape related to expansion or contraction in external wing margins. These trends were consistent with published dung beetle phylogenies and a phylogenetic reconstruction of ancestral morphological changes using parsimony analysis of wing landmark configurations. Analysis of variance showed that the Procrustes distances between wing shapes were significantly correlated to species identity (~?48% of variance), wing size (~?27%), habitat (~?11%) and two of the three, tested, biomechanical variables (wing loading, wing aspect ratio: ~?1%). However, while a phylogenetic generalized least squares analysis confirmed a strongly significant phylogenetic signal for wing shape, it found no significant effect of any other variable. Therefore, wing shape evolution in dung beetles appears to have been phylogenetically constrained and habitat may constitute only a weak selective pressure for changes in wing shape.     

Influence of visual targets and landmarks on honey bee foraging and waggle dancing

Animals use diverse sensory stimuli to navigate their environment and to recognize rewarding food sources.Honey bees use visual atributes of the targeted food source,such as its color,shape,size,direction and distance from the hive,and the landmarks around it to navigate during foraging.They transmit the location information of the food source to other bees if it is highly rewarding.To investigate the relative importance of these attributes,we trained bees to feeders in two different experiments.In the first experiment,we asked whether bees prefer to land on(a)a similar feeder at a different distance on the same heading or on(b)a visually distinct feeder located at the exact same location.We found that,within a short foraging range,bees relied heavily on the color and the shape of the food source and to a lesser extent on its distance from the hive.In the second experiment,we asked if moving the main landmark or the feeder(visual target)influenced recruitment dancing for the feeder.We found that foragers took longer to land and danced fewer circuits when the location of the food source,or a major landmark associated with it,changed.These results demonstrate that prominent visual atributes of food sources and landmarks are evidently more reliable than distance information and that foraging bees heavily utilize these visual cues at the later stages of their journey.     

Heat stress and age induced maternal effects on wing size and shape in parthenogenetic Drosophila mercatorum

Maternal effects on progeny wing size and shape in a homozygous parthenogenetic strain of Drosophila mercatorum were investigated. The impact of external maternal factors (heat stress) and the impact of internal maternal factors (different maternal and grand maternal age) were studied. The offspring developed under identical environmental conditions, and due to lack of genetic variation any phenotypic difference among offspring could be ascribed to maternal effects. Wing size was estimated by centroid size, shape was analysed with the Procrustes geometric morphometric method and variation in landmark displacement was visualized by principal component analysis. Both kinds of maternal effects had a significant impact on progeny wing size and shape. Maternal heat stress led to the same pattern of response in size and shape among the progeny, with increased difference between the control group and progeny from heat stressed flies in both size and shape with increased maternal heat stress temperature. The effects of maternal age, however, led to different responses in size and shape between the different progeny groups. The observed variation in landmark displacements was similar, and in both cases mainly associated with shape differences of the posterior part of the wing. Finally, our results suggest that maternal effect has some evolutionary implications by altering the genetic correlations among traits, which can affect the response to selective pressures.