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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Use of scalation landmarks in geometric morphometrics of squamate reptiles: a comment on homology
Geometric morphometrics (GM) is a powerful analytical approach for evaluating phenotypic variation relevant to taxonomy and systematics, and as with any statistical methodology, requires adherence to fundamental assumptions for inferences to be strictly valid. An important consideration for GM is how landmark configurations, which represent sets of anatomical loci for evaluating shape variation through Cartesian coordinates, relate to underlying homology (Zelditch et al. 1995; Polly 2008). Perhaps more so than with traditional morphometrics, anatomical homology is a crucial assumption for GM because of the mathematical and biological interpretations associated with shape change depicted by deformation grids, such as the thin plate spline (Klingenberg 2008; Zelditch et al. 2012). GM approaches are often used to analyze shapes or outlines of structures, which are not necessarily related to common ancestry, and in this respect GM approaches that use linear semi-landmarks and related methods are particularly amenable to evaluating primary homology, or raw similarity between structures (De Pinna 1991; Palci & Lee 2019). This relaxed interpretation of homology that focuses more on recognizable and repeatable landmarks is defensible so long as authors are clear regarding the purpose of the analyses and in defining their landmark configurations (Palci & Lee 2019). Secondary homology, or similarity due to common ancestry, can also be represented with GM methods and is often assumed to be reflected in fixed Type 1 (juxtaposition of tissues) or Type 2 (self-evident geometry) landmarks (Bookstein 1991).
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- Award ID(s):
- 1655571
- NSF-PAR ID:
- 10225729
- Date Published:
- Journal Name:
- Zootaxa
- Volume:
- 4816
- Issue:
- 3
- ISSN:
- 1175-5326
- Page Range / eLocation ID:
- 397 to 400
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract 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 (
Z ) dimension. We use micro‐CT scanned threespine stickleback (Gasterosteus aculeatus Linnaeus, 1758) from six parapatric lake‐stream populations on Vancouver Island, British Columbia, to test whether the loss of the depth dimension in 2D GM studies results in misleading interpretations of parallel evolution. Using joint locations described with 2D or 3D landmarks, we compare results from separate 2D and 3D shape spaces, from a combined 2D‐3D shape space, and from estimates of biomechanical function. We show that, although shape is distorted enough in 2D projections to strongly influence the interpretation of morphological parallelism, estimates of biomechanical function are relatively robust to the loss of the Z dimension. -
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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.
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Abstract Current approaches to quantify phalangeal curvature assume that the long axis of the bone's diaphysis approximates the shape of a portion of a circle (included angle method) or a parabola (second‐degree polynomial method). Here we developed, tested, and employed an alternative geometric morphometrics‐based (GM) approach to quantify diaphysis shape of proximal phalanges in humans, apes and monkeys with diverse locomotor behaviors. One hundred landmarks of the central longitudinal axis were extracted from 3D surface models and analyzed using 2DGM methods, including generalized Procrustes analyses. Principal components analyses were performed and PC1 scores (>80% of variation) represented the dorsopalmar shape of the bone's central longitudinal axis and separated taxa consistently and in accord with known locomotor behavioral profiles. The most suspensory taxa, including orangutans, hylobatids and spider monkeys, had significantly lower PC1 scores reflecting the greatest amounts of phalangeal curvature. In contrast, bipedal humans and the quadrupedal cercopithecoid monkeys sampled (baboons, proboscis monkeys) exhibited significantly higher PC1 scores reflecting flatter phalanges. African ape (gorillas, chimpanzees and bonobos) phalanges fell between these two extremes and were not significantly different from each other. PC1 scores were significantly correlated with both included angle and the
a coefficient of a second‐degree polynomial calculated from the same landmark dataset, but had a significantly higher correlation with included angles. Our alternative approach for quantifying diaphysis shape of proximal phalanges to investigate dorsopalmar curvature is replicable and does not assume a priori either a circle or parabola model of shape, making it an attractive alternative compared with existing methodologies. -
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
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.11646/zootaxa.4816.3.12
