Technical note: Performance of semi and fully automated approaches for registration of 3D surface coordinates in geometric morphometric studies

A landmarking protocol for geometric morphometric analysis of squamate endocasts

Landmark-based geometric morphometrics is widely used to study the morphology of the endocast, or internal mold of the braincase, and the diversity associated with this structure across vertebrates. Landmarks, as the basic unit of such methods, are intended to be points of correspondence, selected depending on the question at hand, whose proper definition is essential to guarantee robustness and reproducibility of results. In this study, 20 landmarks are defined to provide a framework to analyze the morphological variability in squamate endocasts. Ten species representing a cross-section of the diversity of Squamata from both phylogenetic and ecological (i.e., habitat) perspectives were considered, to select landmarks replicable throughout the entire clade, regardless of the degree of neuroanatomical resolution of the endocast. To assess the precision, accuracy, and repeatability of these newly defined landmarks, both intraobserver and interobserver error were investigated. Estimates of measurement error show that most of the landmarks established here are highly replicable, and preliminary results suggest that they capture aspects of endocast shape related to both phylogenetic and ecologic signals. This study provides a basis for further examinations of squamate endocast disparity using landmark-based geometric morphometrics.

A landmark-free analysis of the pelvic girdle in Sulawesi ricefishes (Adrianichthyidae): How 2D and 3D geometric morphometrics can complement each other in the analysis of a complex structure

Geometric morphometrics (GM) enable the quantification of morphological variation on various scales. Recent technical advances allow analyzing complex three-dimensional shapes also in cases where landmark-based approaches are not appropriate. Pelvic girdle bones (basipterygia) of Sulawesi ricefishes are 3D structures that challenge traditional morphometrics. We hypothesize that the pelvic girdle of ricefishes experienced sex-biased selection pressures in species where females provide brood care by carrying fertilized eggs supported by elongated pelvic fins ("pelvic brooding"). We test this by comparing pelvic bone shapes of both sexes in species exhibiting pelvic brooding and the more common reproductive strategy "transfer brooding," by using landmark-free 2D and 3D GM, as well as qualitative shape descriptions. Both landmark-free approaches revealed significant interspecific pelvic bone variation in the lateral process, medial facing side of the pelvic bone, and overall external and internal wing shape. Within pelvic brooders, the three analyzed species are clearly distinct, while pelvic bones of the genus Adrianichthys are more similar to transfer brooding Oryzias. Female pelvic brooding Oryzias exhibit prominent, medially pointing tips extending from the internal wing and basipterygial plate that are reduced or absent in conspecific males, Adrianichthys and transfer brooding Oryzias, supporting our hypothesis that selection pressures affecting pelvic girdle shape are sex-biased in Sulawesi ricefishes. Furthermore, both sexes of pelvic brooding Oryzias have overall larger pelvic bones than other investigated ricefishes. Based on these differences, we characterized two reproductive strategy- and sex-dependent pelvic girdle types for Sulawesi ricefishes. Morphological differences between the investigated pelvic brooding genera Adrianichthys and Oryzias provide additional evidence for two independent origins of pelvic brooding. Overall, our findings add to a better understanding on traits related to pelvic brooding in ricefishes and provide a basis for upcoming studies on pelvic girdle function and morphology.

3D pollination biology using micro-computed tomography and geometric morphometrics in Theobroma cacao

Premise

Imaging technologies that capture three-dimensional (3D) variation in floral morphology at micro- and nano-resolutions are increasingly accessible. In herkogamous flowers, such as those of Theobroma cacao, structural barriers between anthers and stigmas represent bottlenecks that restrict pollinator size and access to reproductive organs. To study the unresolved pollination biology of cacao, we present a novel application of micro-computed tomography (micro-CT) using floral dimensions to quantify pollinator functional size limits.

Methods

We generated micro-CT data sets from field-collected flowers and museum specimens of potential pollinators. To compare floral variation, we used 3D Slicer to place landmarks on the surface models and performed a geometric morphometric (GMM) analysis using geomorph R. We identified the petal side door (an opening between the petal hoods and filament) as the main bottleneck for pollinator access. We compared its mean dimensions with proposed pollinators to identify viable candidates.

Results

We identified three levels of likelihood for putative pollinators based on the number of morphological (body) dimensions that fit through the petal side door. We also found floral reward microstructures whose presence and location were previously unclear.

Discussion

Using micro-CT and GMM to study the 3D pollination biology of cacao provides new evidence for predicting unknown pollinators. Incorporating geometry and floral rewards will strengthen plant-pollinator trait matching models for cacao and other species.

A Comparison of Semilandmarking Approaches in the Analysis of Size and Shape

Often, few landmarks can be reliably identified in analyses of form variation and covariation. Thus, ‘semilandmarking’ algorithms have increasingly been applied to surfaces and curves. However, the locations of semilandmarks depend on the investigator’s choice of algorithm and their density. In consequence, to the extent that different semilandmarking approaches and densities result in different locations of semilandmarks, they can be expected to yield different results concerning patterns of variation and co-variation. The extent of such differences due to methodology is, as yet, unclear and often ignored. In this study, the performance of three landmark-driven semilandmarking approaches is assessed, using two different surface mesh datasets (ape crania and human heads) with different degrees of variation and complexity, by comparing the results of morphometric analyses. These approaches produce different semilandmark locations, which, in turn, lead to differences in statistical results, although the non-rigid semilandmarking approaches are consistent. Morphometric analyses using semilandmarks must be interpreted with due caution, recognising that error is inevitable and that results are approximations. Further work is needed to investigate the effects of using different landmark and semilandmark templates and to understand the limitations and advantages of different semilandmarking approaches.

A Comparison of Semilandmarking Approaches in the Visualisation of Shape Differences

In landmark-based analyses of size and shape variation and covariation among biological structures, regions lacking clearly identifiable homologous landmarks are commonly described by semilandmarks. Different algorithms may be used to apply semilandmarks, but little is known about the consequences of analytical results. Here, we assess how different approaches and semilandmarking densities affect the estimates and visualisations of mean and allometrically scaled surfaces. The performance of three landmark-driven semilandmarking approaches is assessed using two different surface mesh datasets with different degrees of variation and complexity: adult human head and ape cranial surfaces. Surfaces fitted to estimates of the mean and allometrically scaled landmark and semilandmark configurations arising from geometric morphometric analyses of these datasets are compared between semilandmarking approaches and different densities, as well as with those from warping to landmarks alone. We find that estimates of surface mesh shape (i.e., after re-semilandmarking and then re-warping) made with varying numbers of semilandmarks are generally consistent, while the warping of surfaces using landmarks alone yields surfaces that can be quite different to those based on semilandmarks, depending on landmark coverage and choice of template surface for warping. The extent to which these differences are important depends on the particular study context and aims.

Thirty years of geometric morphometrics: Achievements, challenges, and the ongoing quest for biological meaningfulness

The foundations of geometric morphometrics were worked out about 30 years ago and have continually been refined and extended. What has remained as a central thrust and source of debate in the morphometrics community is the shared goal of meaningful biological inference through a tight connection between biological theory, measurement, multivariate biostatistics, and geometry. Here we review the building blocks of modern geometric morphometrics: the representation of organismal geometry by landmarks and semilandmarks, the computation of shape or form variables via superimposition, the visualization of statistical results as actual shapes or forms, the decomposition of shape variation into symmetric and asymmetric components and into different spatial scales, the interpretation of various geometries in shape or form space, and models of the association between shape or form and other variables, such as environmental, genetic, or behavioral data. We focus on recent developments and current methodological challenges, especially those arising from the increasing number of landmarks and semilandmarks, and emphasize the importance of thorough exploratory multivariate analyses rather than single scalar summary statistics. We outline promising directions for further research and for the evaluation of new developments, such as "landmark-free" approaches. To illustrate these methods, we analyze three-dimensional human face shape based on data from the Avon Longitudinal Study of Parents and Children (ALSPAC).

A feature-based statistical shape model for geometric analysis of the human talus and development of universal talar prostheses

Statistical data pertaining to anatomic variations of the human talus contain valuable information for advances in biological anthropology, diagnosis of the talar pathologies, and designing talar prostheses. A statistical shape model (SSM) can be a powerful data analysis tool for the anatomic variations of the talus. The main concern in constructing an SSM for the talus is establishing the true geometric correspondence between the talar geometries. The true correspondence complies with biological and/or mathematical homologies on the talar surfaces. In this study, we proposed a semi-automatic approach to establish a dense correspondence between talar surfaces discretized by triangular meshes. Through our approach, homologous salient surface features in the form of crest lines were detected on 49 talar surfaces. Then, the point-wise correspondence information of the crest lines was recruited to create posterior Gaussian process morphable models that non-rigidly registered the talar meshes and consequently established inter-mesh dense correspondence. The resultant correspondence perceptually represented the true correspondence as per our visual assessments. Having established the correspondence, we computed the mean shape using full generalized Procrustes analysis and constructed an SSM by means of principal component analysis. Anatomical variations and the mean shape of the talus were predicted by the SSM. As a clinically related application, we considered the mean shape and investigated the feasibility of designing universal talar prostheses. Our results suggest that the mean shape of (the shapes of) tali can be used as a scalable shape template for designing universal talar prostheses.

Comparing semi-landmarking approaches for analyzing three-dimensional cranial morphology

OBJECTIVES

Increased use of three-dimensional (3D) imaging data has led to a need for methods capable of capturing rich shape descriptions. Semi-landmarks have been demonstrated to increase shape information but placement in 3D can be time consuming, computationally expensive, or may introduce artifacts. This study implements and compares three strategies to more densely sample a 3D image surface.

MATERIALS AND METHODS

Three dense sampling strategies: patch, patch-thin-plate spline (TPS), and pseudo-landmark sampling, are implemented to analyze skulls from three species of great apes. To evaluate the shape information added by each strategy, the semi or pseudo-landmarks are used to estimate a transform between an individual and the population average template. The average mean root squared error between the transformed mesh and the template is used to quantify the success of the transform.

RESULTS

The landmark sets generated by each method result in estimates of the template that on average were comparable or exceeded the accuracy of using manual landmarks alone. The patch method demonstrates the most sensitivity to noise and missing data, resulting in outliers with large deviations in the mean shape estimates. Patch-TPS and pseudo-landmarking provide more robust performance in the presence of noise and variability in the dataset.

CONCLUSIONS

Each landmarking strategy was capable of producing shape estimations of the population average templates that were generally comparable to manual landmarks alone while greatly increasing the density of the shape information. This study highlights the potential trade-offs between correspondence of the semi-landmark points, consistent point spacing, sample coverage, repeatability, and computational time.

High-Density Morphometric Analysis of Shape and Integration: The Good, the Bad, and the Not-Really-a-Problem

The field of comparative morphology has entered a new phase with the rapid generation of high-resolution three-dimensional (3D) data. With freely available 3D data of thousands of species, methods for quantifying morphology that harness this rich phenotypic information are quickly emerging. Among these techniques, high-density geometric morphometric approaches provide a powerful and versatile framework to robustly characterize shape and phenotypic integration, the covariances among morphological traits. These methods are particularly useful for analyses of complex structures and across disparate taxa, which may share few landmarks of unambiguous homology. However, high-density geometric morphometrics also brings challenges, for example, with statistical, but not biological, covariances imposed by placement and sliding of semilandmarks and registration methods such as Procrustes superimposition. Here, we present simulations and case studies of high-density datasets for squamates, birds, and caecilians that exemplify the promise and challenges of high-dimensional analyses of phenotypic integration and modularity. We assess: (1) the relative merits of "big" high-density geometric morphometrics data over traditional shape data; (2) the impact of Procrustes superimposition on analyses of integration and modularity; and (3) differences in patterns of integration between analyses using high-density geometric morphometrics and those using discrete landmarks. We demonstrate that for many skull regions, 20-30 landmarks and/or semilandmarks are needed to accurately characterize their shape variation, and landmark-only analyses do a particularly poor job of capturing shape variation in vault and rostrum bones. Procrustes superimposition can mask modularity, especially when landmarks covary in parallel directions, but this effect decreases with more biologically complex covariance patterns. The directional effect of landmark variation on the position of the centroid affects recovery of covariance patterns more than landmark number does. Landmark-only and landmark-plus-sliding-semilandmark analyses of integration are generally congruent in overall pattern of integration, but landmark-only analyses tend to show higher integration between adjacent bones, especially when landmarks placed on the sutures between bones introduces a boundary bias. Allometry may be a stronger influence on patterns of integration in landmark-only analyses, which show stronger integration prior to removal of allometric effects compared to analyses including semilandmarks. High-density geometric morphometrics has its challenges and drawbacks, but our analyses of simulated and empirical datasets demonstrate that these potential issues are unlikely to obscure genuine biological signal. Rather, high-density geometric morphometric data exceed traditional landmark-based methods in characterization of morphology and allow more nuanced comparisons across disparate taxa. Combined with the rapid increases in 3D data availability, high-density morphometric approaches have immense potential to propel a new class of studies of comparative morphology and phenotypic integration.

A Practical Guide to Sliding and Surface Semilandmarks in Morphometric Analyses

Advances in imaging technologies, such as computed tomography (CT) and surface scanning, have facilitated the rapid generation of large datasets of high-resolution three-dimensional (3D) specimen reconstructions in recent years. The wealth of phenotypic information available from these datasets has the potential to inform our understanding of morphological variation and evolution. However, the ever-increasing ease of compiling 3D datasets has created an urgent need for sophisticated methods of capturing high-density shape data that reflect the biological complexity in form. Landmarks often do not take full advantage of the rich shape information available from high-resolution 3D specimen reconstructions, as they are typically restricted to sutures or processes that can be reliably identified across specimens and exclude most of the surface morphology. The development of sliding and surface semilandmark techniques has greatly enhanced the quantification of shape, but their application to diverse datasets can be challenging, especially when dealing with the variable absence of some regions within a structure. Using comprehensive 3D datasets of crania that span the entire clades of birds, squamates and caecilians, we demonstrate methods for capturing morphology across incredibly diverse shapes. We detail many of the difficulties associated with applying semilandmarks to comparable regions across highly disparate structures, and provide solutions to some of these challenges, while considering the consequences of decisions one makes in applying these approaches. Finally, we analyze the benefits of high-density sliding semilandmark approaches over landmark-only studies for capturing shape across diverse organisms and discuss the promise of these approaches for the study of organismal form.

Development and Assessment of Fully Automated and Globally Transitive Geometric Morphometric Methods, With Application to a Biological Comparative Dataset With High Interspecific Variation

Automated geometric morphometric methods are promising tools for shape analysis in comparative biology, improving researchers' abilities to quantify variation extensively (by permitting more specimens to be analyzed) and intensively (by characterizing shapes with greater fidelity). Although use of these methods has increased, published automated methods have some notable limitations: pairwise correspondences are frequently inaccurate and pairwise mappings are not globally consistent (i.e., they lack transitivity across the full sample). Here, we reassess the accuracy of published automated methods-cPDist (Boyer et al. Proc Nat Acad Sci 108 () 18221-18226) and auto3Dgm (Boyer et al.: Anat Rec 298 () 249-276)-and evaluate several modifications to these methods. We show that a substantial percentage of alignments and pairwise maps between specimens of dissimilar geometries were inaccurate in the study of Boyer et al. (Proc Nat Acad Sci 108 () 18221-18226), despite a taxonomically partitioned variance structure of continuous Procrustes distances. We show these inaccuracies are remedied using a globally informed methodology within a collection of shapes, rather than relying on pairwise comparisons (c.f. Boyer et al.: Anat Rec 298 () 249-276). Unfortunately, while global information generally enhances maps between dissimilar objects, it can degrade the quality of correspondences between similar objects due to the accumulation of numerical error. We explore a number of approaches to mitigate this degradation, quantify their performance, and compare the generated pairwise maps (and the shape space characterized by these maps) to a "ground truth" obtained from landmarks manually collected by geometric morphometricians. Novel methods both improve the quality of the pairwise correspondences relative to cPDist and achieve a taxonomic distinctiveness comparable to auto3Dgm. Anat Rec, 301:636-658, 2018. © 2017 Wiley Periodicals, Inc.

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.

Semi-supervised determination of pseudocryptic morphotypes using observer-free characterizations of anatomical alignment and shape

Accurate, quantitative characterization of complex shapes is recognized as a key methodological challenge in biology. Recent development of automated three‐dimensional geometric morphometric protocols (auto3dgm) provides a promising set of tools to help address this challenge. While auto3dgm has been shown to be useful in characterizing variation across clades of morphologically very distinct mammals, it has not been adequately tested in more problematic cases where pseudolandmark placement error potentially confounds interpretation of true shape variation. Here, we tested the sensitivity of auto3dgm to the degree of variation and various parameterization settings using a simulation and three microCT datasets that characterize mammal tooth crown morphology as biological examples. The microCT datasets vary in degree of apparent morphological differentiation, with two that include grossly similar morphospecies and one that includes two laboratory strains of a single species. Resulting alignments are highly sensitive to the number of pseudolandmarks used to quantify shapes. The degree to which the surfaces were downsampled and the apparent degree of morphological differentiation across the dataset also influenced alignment repeatability. We show that previous critiques of auto3dgm were based on poorly parameterized alignments and suggest that sample‐specific sensitivity analyses should be added to any research protocol including auto3dgm. Auto3dgm is a useful tool for studying samples when pseudolandmark placement error is small relative to the true differences between specimens. This method therefore represents a promising avenue forward in morphometric studies at a wide range of scales, from samples that differ by a single genetic locus to samples that represent multiple phylogenetically diverse clades.

Towards a morphological metric of assemblage dynamics in the fossil record: a test case using planktonic foraminifera

With a glance, even the novice naturalist can tell you something about the ecology of a given ecosystem. This is because the morphology of individuals reflects their evolutionary history and ecology, and imparts a distinct ‘look’ to communities—making it possible to immediately discern between deserts and forests, or coral reefs and abyssal plains. Once quantified, morphology can provide a common metric for characterizing communities across space and time and, if measured rapidly, serve as a powerful tool for quantifying biotic dynamics. Here, we present and test a new high-throughput approach for analysing community shape in the fossil record using semi-three-dimensional (3D) morphometrics from vertically stacked images (light microscopic or photogrammetric). We assess the potential informativeness of community morphology in a first analysis of the relationship between 3D morphology, ecology and phylogeny in 16 extant species of planktonic foraminifera—an abundant group in the marine fossil record—and in a preliminary comparison of four assemblages from the North Atlantic. In the species examined, phylogenetic relatedness was most closely correlated with ecology, with all three ecological traits examined (depth habitat, symbiont ecology and biogeography) showing significant phylogenetic signal. By contrast, morphological trees (based on 3D shape similarity) were relatively distantly related to both ecology and phylogeny. Although improvements are needed to realize the full utility of community morphometrics, our approach already provides robust volumetric measurements of assemblage size, a key ecological characteristic.