Quantifying morphological variation is critical for conducting anatomical research. Three‐dimensional geometric morphometric (3D GM) landmark analyses quantify shape using homologous Cartesian coordinates (landmarks). Setting up a high‐density landmark set and placing it on all specimens, however, can be a time‐consuming task. Weighted spherical harmonics (SPHARM) provides an alternative method for analyzing the shape of such objects. Here we compare sliding semilandmark and SPHARM analyses of the calcaneus of
High-Density Morphometric Analysis of Shape and Integration: The Good, the Bad, and the Not-Really-a-Problem
Abstract 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.
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- Award ID(s):
- 1839250
- NSF-PAR ID:
- 10170993
- Date Published:
- Journal Name:
- Integrative and Comparative Biology
- Volume:
- 59
- Issue:
- 3
- ISSN:
- 1540-7063
- Page Range / eLocation ID:
- 669 to 683
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract Gorilla gorilla gorilla (n = 20),Pan troglodytes troglodytes (n = 20), andHomo sapiens (n = 20) to determine whether the SPHARM and sliding semilandmark analyses capture comparable levels of shape variation. We also compare both the sliding semilandmark and SPHARM analyses to a novel combination of the two methods, here termed SPHARM–sliding. In SPHARM–sliding, the vertices of the surface models produced from the SPHARM analysis (that are the same in number and relative location) are used as the starting landmark positions for a sliding semilandmark analysis. Calcaneal shape variation quantified by all three analyses was summarized using separate principal components analyses. Results were compared using the root mean square (RMS) and maximum distance between surface models of species averages scaled (up) to centroid size created from each analysis. The average RMS was 0.23 mm between sliding semilandmark and SPHARM average surface models, 0.19 mm between SPHARM and SPHARM sliding average surface models, and 0.22 mm between sliding semilandmark and SPHARM sliding average surface models. Although results indicate that all three analyses are comparable methods for 3D shape analysis, there are advantages and disadvantages to each. While the SPHARM analysis is less time‐intensive, it is unable to capture the same level of detail around the sharp edges of articular facets on average surface models as the sliding semilandmark analysis. The SPHARM analysis also does not allow for individual articular facets to be analyzed in isolation. SPHARM–sliding, however, captures the same level of detail as the sliding semilandmark analysis, and (as in the sliding semilandmark analysis) allows for the evaluation of individual portions of bone. SPHARM is a comparable method to a 3D GM analysis for small, irregularly shaped bones, such as the calcaneus, and SPHARM–sliding allows for an expedited set up process for a sliding semilandmark analysis. -
Esposito, Lauren (Ed.)Abstract This article investigates a form of rank deficiency in phenotypic covariance matrices derived from geometric morphometric data, and its impact on measures of phenotypic integration. We first define a type of rank deficiency based on information theory then demonstrate that this deficiency impairs the performance of phenotypic integration metrics in a model system. Lastly, we propose methods to treat for this information rank deficiency. Our first goal is to establish how the rank of a typical geometric morphometric covariance matrix relates to the information entropy of its eigenvalue spectrum. This requires clear definitions of matrix rank, of which we define three: the full matrix rank (equal to the number of input variables), the mathematical rank (the number of nonzero eigenvalues), and the information rank or “effective rank” (equal to the number of nonredundant eigenvalues). We demonstrate that effective rank deficiency arises from a combination of methodological factors—Generalized Procrustes analysis, use of the correlation matrix, and insufficient sample size—as well as phenotypic covariance. Secondly, we use dire wolf jaws to document how differences in effective rank deficiency bias two metrics used to measure phenotypic integration. The eigenvalue variance characterizes the integration change incorrectly, and the standardized generalized variance lacks the sensitivity needed to detect subtle changes in integration. Both metrics are impacted by the inclusion of many small, but nonzero, eigenvalues arising from a lack of information in the covariance matrix, a problem that usually becomes more pronounced as the number of landmarks increases. We propose a new metric for phenotypic integration that combines the standardized generalized variance with information entropy. This metric is equivalent to the standardized generalized variance but calculated only from those eigenvalues that carry nonredundant information. It is the standardized generalized variance scaled to the effective rank of the eigenvalue spectrum. We demonstrate that this metric successfully detects the shift of integration in our dire wolf sample. Our third goal is to generalize the new metric to compare data sets with different sample sizes and numbers of variables. We develop a standardization for matrix information based on data permutation then demonstrate that Smilodon jaws are more integrated than dire wolf jaws. Finally, we describe how our information entropy-based measure allows phenotypic integration to be compared in dense semilandmark data sets without bias, allowing characterization of the information content of any given shape, a quantity we term “latent dispersion”. [Canis dirus; Dire wolf; effective dispersion; effective rank; geometric morphometrics; information entropy; latent dispersion; modularity and integration; phenotypic integration; relative dispersion.]more » « less
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Background Comparative morphology fundamentally relies on the orientation and alignment of specimens. In the era of geometric morphometrics, point-based homologies are commonly deployed to register specimens and their landmarks in a shared coordinate system. However, the number of point-based homologies commonly diminishes with increasing phylogenetic breadth. These situations invite alternative, often conflicting, approaches to alignment. The bivalve shell (Mollusca: Bivalvia) exemplifies a homologous structure with few universally homologous points—only one can be identified across the Class, the shell ‘beak’. Here, we develop an axis-based framework, grounded in the homology of shell features, to orient shells for landmark-based, comparative morphology. Methods Using 3D scans of species that span the disparity of shell morphology across the Class, multiple modes of scaling, translation, and rotation were applied to test for differences in shell shape. Point-based homologies were used to define body axes, which were then standardized to facilitate specimen alignment via rotation. Resulting alignments were compared using pairwise distances between specimen shapes as defined by surface semilandmarks. Results Analysis of 45 possible alignment schemes finds general conformity among the shape differences of ‘typical’ equilateral shells, but the shape differences among atypical shells can change considerably, particularly those with distinctive modes of growth. Each alignment corresponds to a hypothesis about the ecological, developmental, or evolutionary basis of morphological differences, but we suggest orientation via the hinge line for many analyses of shell shape across the Class, a formalization of the most common approach to morphometrics of shell form. This axis-based approach to aligning specimens facilitates the comparison of approximately continuous differences in shape among phylogenetically broad and morphologically disparate samples, not only within bivalves but across many other clades.more » « less
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Abstract Landmark‐based geometric morphometrics has emerged as an essential discipline for the quantitative analysis of size and shape in ecology and evolution. With the ever‐increasing density of digitized landmarks, the possible development of a fully automated method of landmark placement has attracted considerable attention. Despite the recent progress in image registration techniques, which could provide a pathway to automation, three‐dimensional (3D) morphometric data are still mainly gathered by trained experts. For the most part, the large infrastructure requirements necessary to perform image‐based registration, together with its system specificity and its overall speed, have prevented its wide dissemination.
Here, we propose and implement a general and lightweight point cloud‐based approach to automatically collect high‐dimensional landmark data in 3D surfaces (Automated Landmarking through Point cloud Alignment and Correspondence Analysis). Our framework possesses several advantages compared with image‐based approaches. First, it presents comparable landmarking accuracy, despite relying on a single, random reference specimen and much sparser sampling of the structure's surface. Second, it can be efficiently run on consumer‐grade personal computers. Finally, it is general and can be applied at the intraspecific level to any biological structure of interest, regardless of whether anatomical atlases are available.
Our validation procedures indicate that the method can recover intraspecific patterns of morphological variation that are largely comparable to those obtained by manual digitization, indicating that the use of an automated landmarking approach should not result in different conclusions regarding the nature of multivariate patterns of morphological variation.
The proposed point cloud‐based approach has the potential to increase the scale and reproducibility of morphometrics research. To allow ALPACA to be used out‐of‐the‐box by users with no prior programming experience, we implemented it as a SlicerMorph module. SlicerMorph is an extension that enables geometric morphometrics data collection and 3D specimen analysis within the open‐source 3D Slicer biomedical visualization ecosystem. We expect that convenient access to this platform will make ALPACA broadly applicable within ecology and evolution.
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The foot plays a prominent role in weight-bearing suggesting it may reflect locomotor variation. Despite the immense amount of foot research, the calcaneus has been relatively understudied. Here we analyzed the entire calcaneal shape of Gorilla gorilla gorilla (n=41), Gorilla beringei graueri (n=17) and Gorilla beringei beringei (n=8) to understand how morphology relates to locomotor behavior. Calcanei were surface scanned and external shape analyzed using a three-dimensional geometric morphometric sliding semilandmark analysis. Semilandmarks were slid to minimize the bending energy of the thin plate spline interpolation function relative to the updated Procrustes average. Generalized Procrustes Analysis was used to align landmark configurations and shape variation was summarized using a principal components analysis. Procrustes distances between species were calculated and resampling statistics were run to test for group differences. All subspecies demonstrate statistically different morphologies (p<0.005 for pairwise comparisons). G. b. graueri separates from other subspecies based on posterolateral morphology, with G. b. graueri demonstrating an elongated peroneal trochlea, and thus more bone superiorly than G. g. gorilla. Compared to G. b. beringei, G. b. graueri has less bone inferiorly near the tuberosity. Cuboid and posterior talar facet shapes correlate with arboreality. G. b. beringei (most terrestrial) has a flatter cuboid facet and a more transversely oriented/relatively smaller posterior talar facet than G. g. gorilla (most arboreal) and G. b. graueri represents an intermediate morphology. These differences demonstrate a relationship between calcaneal shape and locomotor behavior and suggest that G. b. graueri may load its foot differently from the other subspecies. This project was supported by NSF grant # BCS - 1824630.more » « less
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1093/icb/icz120
