SHAPE ANALYSIS OF SYMMETRIC STRUCTURES: QUANTIFYING VARIATION AMONG INDIVIDUALS AND ASYMMETRY

By C. Klingenberg, M. Barluenga, Axel Meyer. Evolution; international journal of organic evolution, 2002

1,101 citations recorded by the source corpus.

Abstract Morphometric studies often consider parts with internal left-right symmetry, for instance, the vertebrate skull. This type of symmetry is called object symmetry and is distinguished from matching symmetry, in which two separate structures exist as mirror images of each other, one on each body side. We explain a method for partitioning the total shape variation of landmark configurations with object symmetry into components of symmetric variation among individuals and asymmetry. This method is based on the Procrustes superimposition of the original and a reflected copy of each landmark configuration and is compatible with the two-factor ANOVA model customary in studies of fluctuating asymmetry. We show a fully multivariate framework for testing the effects in the two-factor model with MANOVA statistics, which also applies to shapes with matching symmetry. We apply the new methods in a small case study of pharyngeal jaws of the Neotropical cichlid fish Amphilophus citrinellus. The analysis revealed that the symmetric component of variation in the pharyngeal jaws is dominated by the contrast between two alternative trophic morphs in this species and that there is subtle but statistically significant directional asymmetry. Finally, we provide some general recommendations for morphometric studies of symmetric shapes.

Subfields: Geometry and Topology, Paleontology

View Paper: https://www.semanticscholar.org/paper/e0e0a401ac3aa764cbaba0b2d933815dc29507cb

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Citations in the corpus

Fluctuating asymmetry and exogenous stress in fishes: a review (2011, methodology): “Klingenberg et al. (2002) detail a method of symmetrical structure shape analysis that combines earlier work that partitioned shape variation into components of symmetric shape and of asymmetry (Bookstein 1996; Auffray et al. 1999) with a formal test for directional asymmetry (Mardia et al. 2000;…”
Non-commercial Research and Educational Use including without Limitation Use in Instruction at Your Institution, Sending It to Specific Colleagues That You Know, and Providing a Copy to Your Institution's Administrator. All Other Uses, Reproduction and Distribution, including without Limitation Comm (2005, neutral): “(1) in which all the dipole–dipole couplings and chemical shielding parameters are varied.”
Building Developmental Integration into Functional Systems: Function-Induced Integration of Mandibular Shape (2009, methodology): “This approach has been adapted to analysis of shape using Procrustes-based methods (Auffray et al. 1996; Klingenberg and McIntyre 1998; Klingenberg et al. 2002 ).”
Analyzing Fluctuating Asymmetry with Geometric Morphometrics: Concepts, Methods, and Applications (2015, methodology): “It is also at the core of methods for analyzing asymmetry of shape [11,13].”
A field comes of age: geometric morphometrics in the 21 st century (2013, methodology): “For instance, shape variation due to directional and fluctuating asymmetry can be quantified and analysed to test hypotheses of symmetry in a sample (Klingenberg and McIntyre, 1998; Mardia et al., 2000; Kent and Mardia, 2001; Klingenberg et al., 2002; Schaefer et al., 2006).”
MORPHOLOGICAL AND ECOLOGICAL VARIATION WITHIN THE ACHNANTHIDIUM MINUTISSIMUM (BACILLARIOPHYCEAE) SPECIES COMPLEX 1 (2007, background): “…image three 564 MARINA POTAPOVA AND PAUL B. HAMILTON times along its vertical and horizontal axes by changing the signs of x- or y-coordinates and renumbering them, and then by averaging the coordinates among four resulting sets of landmark coordinates (Mardia et al. 2000, Klingenberg et al. 2002).”
Fluctuating Asymmetry: Methods, Theory, and Applications (2010, methodology): “The methods of geometric morphometrics [21, 39] are suitable for quantifying asymmetry of consistent objects.”
geomorph: an r package for the collection and analysis of geometric morphometric shape data (2013, methodology): “The resulting data are then stored in R as a three-dimensional array for subsequent morphometric analyses ( p landmarks 9 k dimensions 9 N specimens).”
MorphoJ: an integrated software package for geometric morphometrics (2011, methodology): “Symmetric structures, such as vertebrate skulls, are frequently used in morphometric studies and pose some special challenges (Mardia et al. 2000; Klingenberg et al. 2002).”