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
Recent methodological advances have led to a rapid expansion of evolutionary studies employing three‐dimensional landmark‐based geometric morphometrics (GM). GM methods generally enable researchers to capture and compare complex shape phenotypes, and to quantify their relationship to environmental gradients. However, some recent studies have shown that the common, inexpensive, and relatively rapid two‐dimensional GM methods can distort important information and produce misleading results because they cannot capture variation in the depth (
- NSF-PAR ID:
- 10455725
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Ecology and Evolution
- Volume:
- 10
- Issue:
- 23
- ISSN:
- 2045-7758
- Page Range / eLocation ID:
- p. 13297-13311
- 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. -
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Abstract Whether it is swimming, walking, eating, or jumping, motions are a fundamental way in which organisms interact with their environment. Understanding how morphology contributes to motion is a primary focus of kinematic research and is necessary for gaining insights into the evolution of functional systems. However, an element that is largely missing from traditional analyses of motion is the spatial context in which they occur. We explore an application of geometric morphometrics (GM) for analyzing and comparing motions to evaluate the outputs of biomechanical linkage models. We focus on a common model for oral jaw mechanics of perciform fishes, the fourbar linkage, using GM to summarize motion as a trajectory of shape change. Two traits derived from trajectories capture the total kinesis generated by a linkage (trajectory length) and the kinematic asynchrony (KA) of its mobile components (trajectory nonlinearity). Oral jaw fourbar data from two subfamilies of Malagasy cichlids were used to generate form–function landscapes, describing broad features of kinematic diversity. Our results suggest that kinesis and KA have complex relationships with fourbar morphology, each displaying a pattern in which different shapes possess equivalent kinematic trait values, known as many-to-one mapping of form-to-function. Additionally, we highlight the observation that KA captures temporal differences in the activation of motion components, a feature of kinesis that has long been appreciated but was difficult to measure. The methods used here to study fourbar linkages can also be applied to more complex biomechanical models and broadly to motions of live organisms. We suggest that they provide a suitable alternative to traditional approaches for evaluating linkage function and kinematics.more » « less
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Abstract Motivation Cell shape provides both geometry for, and a reflection of, cell function. Numerous methods for describing and modeling cell shape have been described, but previous evaluation of these methods in terms of the accuracy of generative models has been limited.
Results Here we compare traditional methods and deep autoencoders to build generative models for cell shapes in terms of the accuracy with which shapes can be reconstructed from models. We evaluated the methods on different collections of 2D and 3D cell images, and found that none of the methods gave accurate reconstructions using low dimensional encodings. As expected, much higher accuracies were observed using high dimensional encodings, with outline-based methods significantly outperforming image-based autoencoders. The latter tended to encode all cells as having smooth shapes, even for high dimensions. For complex 3D cell shapes, we developed a significant improvement of a method based on the spherical harmonic transform that performs significantly better than other methods. We obtained similar results for the joint modeling of cell and nuclear shape. Finally, we evaluated the modeling of shape dynamics by interpolation in the shape space. We found that our modified method provided lower deformation energies along linear interpolation paths than other methods. This allows practical shape evolution in high dimensional shape spaces. We conclude that our improved spherical harmonic based methods are preferable for cell and nuclear shape modeling, providing better representations, higher computational efficiency and requiring fewer training images than deep learning methods.
Availability and implementation All software and data is available at http://murphylab.cbd.cmu.edu/software.
Supplementary information Supplementary data are available at Bioinformatics online.
