Shape analysis of symmetric structures: quantifying variation among individuals and asymmetry
Open accessAbstract
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.
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Human skulls exhibit object symmetry (the axis of symmetry passes through mid-plane, and the left and right halves are mirror images of each other).
“Human skulls exhibit object symmetry (i.e. the axis of symmetry passes through mid-plane, and hence the left and right halves are mirror images of each other), therefore the recommendations of [100,101] were followed.”
From Morphological consequences of artificial cranial deformation: Modularity and integration (2020) · cites this paper as [101]
In “Matching Symmetry and Object Symmetry,” the paper identifies the vertebrate skull as having an internal plane of symmetry. The Figure 1 caption says the left and right halves are mirror images **with the exception of asymmetries**, and the same section notes that real organisms are hardly ever perfectly symmetric. The claim omits that qualification. (LLM, conf=0.84)
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Cites
Biometry: The Principles and Practice of Statistics in Biological Research
Sokal, R. R., & Rohlf, F. J. (1969) · Cited by 20,963 · see citing works
Biometry. The Principles and Practice of Statistics in Biological Research
Fienberg, S. E., Sokal, R. R., Rohlf, F. J., Rohlf, F. J., & Sokal, R. R. (1970) · Biometrics · doi:10.2307/2529087 · Cited by 9,363 · see citing works
Morphometric Tools for Landmark Data
Bookstein, F. L. (1992) · Cambridge University Press eBooks · doi:10.1017/cbo9780511573064 · Cited by 4,395 · see citing works
Extensions of the procrustes method for the optimal superimposition of landmarks
Rohlf, F. J., & Slice, D. (1990) · Systematic Zoology · doi:10.2307/2992207 · Cited by 4,289 · see citing works
Morphometric Tools for Landmark Data: Geometry and Biology.
Reyment, R. A., & Bookstein, F. L. (1992) · Biometrics · doi:10.2307/2532725 · Cited by 2,792 · see citing works
FLUCTUATING ASYMMETRY: Measurement, Analysis, Patterns
Palmer, A. R., & Strobeck, C. (1986) · Annual Review of Ecology and Systematics · doi:10.1146/annurev.es.17.110186.002135 · Cited by 2,131 · see citing works
Edgington, E. S., Edgington, E., & Onghena, P. (1964) · Encyclopedia of Statistical Sciences · doi:10.1002/0471667196.ess2169 · Cited by 2,034 · see citing works
Procrustes Methods in the Statistical Analysis of Shape
Goodall, C. R. (1991) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.2517-6161.1991.tb01825.x · Cited by 2,032 · see citing works
Permutation Tests: A Practical Guide to Resampling Methods for Testing Hypotheses
Niknian, M., & Good, P. (1995) · Technometrics · doi:10.2307/1269919 · Cited by 1,406 · see citing works
Asymmetry, Developmental Stability, and Evolution
Møller, A. P., & Swaddle, J. P. (1997) · doi:10.1093/oso/9780198548959.001.0001 · Cited by 1,284 · see citing works
Seber, G. A. F. (1984) · Wiley series in probability and statistics · doi:10.1002/9780470316641 · Cited by 1,254 · see citing works
Fluctuating asymmetry analyses: a primer
Palmer, A. R. (1994) · Contemporary issues in genetics and evolution · doi:10.1007/978-94-011-0830-0_26 · Cited by 998 · see citing works
Klingenberg, C. P., & McIntyre, G. S. (1998) · Evolution · doi:10.1111/j.1558-5646.1998.tb02018.x · Cited by 945 · see citing works
Self-citationShape Statistics: Procrustes Superimpositions and Tangent Spaces
Rohlf, F. J. (1999) · Journal of Classification · doi:10.1007/s003579900054 · Cited by 904 · see citing works
Marcus, L. F., Corti, M., Loy, A., Naylor, G. J. P., & Slice, D. E. (1996) · Springer eBooks · doi:10.1007/978-1-4757-9083-2 · Cited by 855 · see citing works
Evolutionary Strategies and Morphological Innovations: Cichlid Pharyngeal Jaws
Liem, K. (1973) · Systematic Zoology · doi:10.2307/2412950 · Cited by 684 · see citing works
Klingenberg, C. P., & McIntyre, G. S. (1998) · Evolution · doi:10.2307/2411306 · Cited by 458 · see citing works
Self-citationBiometrics, biomathematics and the morphometric synthesis
Bookstein, F. L. (1996) · Bulletin of Mathematical Biology · doi:10.1007/bf02458311 · Cited by 456 · see citing works
Combining the Tools of Geometric Morphometrics
Bookstein, F. L. (1996) · Springer eBooks · doi:10.1007/978-1-4757-9083-2_12 · Cited by 447 · see citing works
Statistical assessment of bilateral symmetry of shapes
Mardia, K. (2000) · Biometrika · doi:10.1093/biomet/87.2.285 · Cited by 405 · see citing works
O’Higgins, P., & Jones, N. (1998) · Journal of Anatomy · doi:10.1046/j.1469-7580.1998.19320251.x · Cited by 391 · see citing works
Good, P. (1994) · Springer series in statistics · doi:10.1007/978-1-4757-2346-5 · Cited by 391 · see citing works
Morphometric Tools for Landmark Data: Geometry and Biology
Lele, S. R., & Bookstein, F. L. (1999) · Journal of the American Statistical Association · doi:10.2307/2669711 · Cited by 377 · see citing works
Neanderthal cranial ontogeny and its implications for late hominid diversity
de León, M. S. P., & Zollikofer, C. P. E. (2001) · Nature · doi:10.1038/35087573 · Cited by 321 · see citing works
Developmental instability: Causes and consequences
Lalumière, M. L. (2004) · American Journal of Human Biology · doi:10.1002/ajhb.20050 · Cited by 320 · see citing works
Mechanisms of Left–Right Determination in Vertebrates
Capdevila, J., Vogan, K. J., Tabin, C. J., et al. (2000) · Cell · doi:10.1016/s0092-8674(00)80619-4 · Cited by 313 · see citing works
Methods for the Comparative Analysis of Variation Patterns
Cheverud, J. M., Wagner, G. P., & Dow, M. M. (1989) · Systematic Zoology · doi:10.2307/2992282 · Cited by 296 · see citing works
Klingenberg, C. P., Badyaev, A. V., Sowry, S. M., & Beckwith, N. J. (2001) · The American Naturalist · doi:10.1086/317002 · Cited by 257 · see citing works
Self-citationKlingenberg, C. P., Leamy, L. J., Routman, E. J., & Cheverud, J. M. (2001) · Genetics · doi:10.1093/genetics/157.2.785 · Cited by 239 · see citing works
Self-citationMORPHOLOGICAL INTEGRATION BETWEEN DEVELOPMENTAL COMPARTMENTS IN THE DROSOPHILA WING
Klingenberg, C. P., & Zaklan, S. D. (2000) · Evolution · doi:10.1554/0014-3820(2000)054[1273:mibdci]2.0.co;2 · Cited by 237 · see citing works
Self-citationQUANTITATIVE GENETICS OF GEOMETRIC SHAPE IN THE MOUSE MANDIBLE
Klingenberg, C., & Leamy, L. (2001) · Evolution; international journal of organic evolution · doi:10.1554/0014-3820(2001)055[2342:qgogsi]2.0.co;2 · Cited by 237 · see citing works
Self-citationQUANTITATIVE GENETICS OF GEOMETRIC SHAPE IN THE MOUSE MANDIBLE
Klingenberg, C. P., & Leamy, L. J. (2001) · Evolution · doi:10.1111/j.0014-3820.2001.tb00747.x · Cited by 228 · see citing works
Self-citationMorphometric Studies in Inbred and Hybrid House Mice. V. Directional and Fluctuating Asymmetry
Leamy, L. J. (1984) · The American Naturalist · doi:10.1086/284225 · Cited by 225 · see citing works
Fluctuating Asymmetry: Measurement, Analysis, Patterns
Palmer, A. (1986) · Annual Review of Ecology and Systematics · doi:10.1146/annurev.ecolsys.17.1.391 · Cited by 211 · see citing works
Meyer, A. (1990) · Biological Journal of the Linnean Society · doi:10.1111/j.1095-8312.1990.tb00517.x · Cited by 192 · see citing works
Self-citationBeyond heterochrony : the evolution of development
Zelditch, M. L. (2001) · Cited by 171 · see citing works
Independence between developmental stability and canalization in the skull of the house mouse
Debat, V., Alibert, P., David, P., Paradis, E., & Auffray, J. (2000) · Proceedings of the Royal Society B Biological Sciences · doi:10.1098/rspb.2000.1017 · Cited by 162 · see citing works
Demidenko, E. (1987) · Wiley series in probability and statistics · doi:10.1002/9781118651537.ch11 · Cited by 158 · see citing works
Left–right asymmetry of fly wings and the evolution of body axes
Klingenberg, C. P., McIntyre, G. S., & Zaklan, S. D. (1998) · Proceedings of the Royal Society B Biological Sciences · doi:10.1098/rspb.1998.0427 · Cited by 144 · see citing works
Self-citationOn Growth and Form: Spatio-temporal Pattern Formation in Biology
Chaplain, M. A. J., McLachlan, J. C., & Singh, G. D. (2000) · Medical Entomology and Zoology · Cited by 140 · see citing works
Meyer, A. (1989) · Oecologia · doi:10.1007/bf00379047 · Cited by 137 · see citing works
Self-citationKlingenberg, C. P. (2003) · doi:10.1093/oso/9780195143454.003.0024 · Cited by 133 · see citing works
Self-citationFluctuating asymmetry in the honey bee,
Smith, D. R., Crespi, B. J., & Bookstein, F. L. (1997) · Journal of Evolutionary Biology · doi:10.1007/s000360050041 · Cited by 132 · see citing works
Geometric morphometric study of the regional variation of modern human craniofacial form
Hennessy, R. J., & Stringer, C. B. (2001) · American Journal of Physical Anthropology · doi:10.1002/ajpa.10005 · Cited by 124 · see citing works
Meyer, A. (1990) · Journal of Zoology · doi:10.1111/j.1469-7998.1990.tb03994.x · Cited by 124 · see citing works
Self-citationFluctuating asymmetry in the honey bee, Apis mellifera: effects of ploidy and hybridization
Smith, D. R., Crespi, B. J., & Bookstein, F. L. (1997) · Journal of Evolutionary Biology · doi:10.1046/j.1420-9101.1997.10040551.x · Cited by 119 · see citing works
Demidenko, E. (2004) · Wiley series in probability and statistics · doi:10.1002/0471728438.ch11 · Cited by 118 · see citing works
Badyaev, A. V., & Foresman, K. R. (2000) · Proceedings of the Royal Society B Biological Sciences · doi:10.1098/rspb.2000.1011 · Cited by 113 · see citing works
Morphological integration of fluctuating asymmetry in the mouse mandible
Leamy, L. J. (1994) · Contemporary issues in genetics and evolution · doi:10.1007/978-94-011-0830-0_11 · Cited by 102 · see citing works
Shape, Procrustes tangent projections and bilateral symmetry
Kent, J. T. (2001) · Biometrika · doi:10.1093/biomet/88.2.469 · Cited by 99 · see citing works
Morphological integration of fluctuating asymmetry in the mouse mandible
Leamy, L. J. (1993) · Genetica · doi:10.1007/bf02424510 · Cited by 96 · see citing works
Galis, F. F., & Drucker, E. G. (1996) · Journal of Evolutionary Biology · doi:10.1046/j.1420-9101.1996.9050641.x · Cited by 91 · see citing works
Huysseune, A., Sire, J., & Meunier, F. J. (1994) · Journal of Morphology · doi:10.1002/jmor.1052210103 · Cited by 74 · see citing works
Biometrics, biomathematics and the morphometric synthesis
Bookstein, F. (1996) · Bulletin of Mathematical Biology · doi:10.1016/0092-8240(95)00329-0 · Cited by 60 · see citing works
Smits, J. D., Witte, F., & Veen, F. G. V. (1996) · Biological Journal of the Linnean Society · doi:10.1111/j.1095-8312.1996.tb01473.x · Cited by 57 · see citing works
Klingenberg, Badyaev, Sowry, & Beckwith (2001) · The American Naturalist · doi:10.2307/3079085 · Cited by 56 · see citing works
Fluctuating Asymmetry in Mus musculus Subspecific Hybridization
Auffray, J., Alibert, P., Renaud, S., Orth, A., & Bonhomme, F. (1996) · Springer eBooks · doi:10.1007/978-1-4757-9083-2_23 · Cited by 50 · see citing works
Specification of left-right asymmetry in the embryonic gut of Drosophila
Ligoxygakis, P., Strigini, M., & Averof, M. (2001) · Development · doi:10.1242/dev.128.7.1171 · Cited by 44 · see citing works
Leamy, L. J., Meagher, S., Taylor, S., Carroll, L. S., & Potts, W. K. (2001) · Evolution · doi:10.1111/j.0014-3820.2001.tb00746.x · Cited by 33 · see citing works
Corti, M., Aguilera, M., & Capanna, E. (2001) · Journal of Zoology · doi:10.1017/s0952836901000498 · Cited by 33 · see citing works
Molecular basis of left–right asymmetry
Tamura, K. (1999) · Development Growth & Differentiation · doi:10.1046/j.1440-169x.1999.00465.x · Cited by 32 · see citing works
Smits, J. D., Witte, F., & Povel, G. D. E. (1996) · Biological Journal of the Linnean Society · doi:10.1111/j.1095-8312.1996.tb01472.x · Cited by 26 · see citing works
Comparing Ontogenetic Trajectories Using Growth Process Data
Magwene, P. M. (2001) · Systematic Biology · doi:10.1080/106351501753328785 · Cited by 21 · see citing works
Dalapicolla, J., do Prado, J. R., Percequillo, A. R., & Knowles, L. L. (2021) · Journal of Biogeography · doi:10.1111/jbi.14281 · Cited by 12 · see citing works
Leamy, L. J., Meagher, S., Taylor, S., et al. (2001) · Evolution · doi:10.1554/0014-3820(2001)055[2333:safaom]2.0.co;2 · Cited by 5 · see citing works
Smits, J. R. (1996) · Biological Journal of the Linnean Society · doi:10.1006/bijl.1996.0070 · Cited by 4 · see citing works
SMITS, J. (1996) · Biological Journal of the Linnean Society · doi:10.1006/bijl.1996.0071 · Cited by 3 · see citing works
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Singh, N., Harvati, K., Hublin, J.-J., & Klingenberg, C. P. (2012) · Journal of Human Evolution · doi:10.1016/j.jhevol.2011.11.006 · Cited by 129 · see citing works
Self-citationCardini, A. (2017) · Journal of Zoological Systematics and Evolutionary Research · doi:10.1111/jzs.12144 · Cited by 64 · see citing works
Claes, P., Reijniers, J., Shriver, M. D., Snyders, J., Suetens, P., Nielandt, J., De Tré, G., & Vandermeulen, D. (2015) · Journal of Anatomy · doi:10.1111/joa.12252 · Cited by 32 · see citing works
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- Authors
- Klingenberg, C. P., Barluenga, M., & Meyer, A.
- Affiliations
- University of Konstanz (DE)
- Venue
- Evolution
- Publisher
- Oxford University Press (OUP)
- Published
- 2002-10
- Volume
- 56
- Issue
- 10
- Pages
- 1909-1920
- ISSN
- 0014-3820 (ISSN-L)
- 1558-5646
- OpenAlex
- W2114574345
- Cited by
- 1,109
- References
- 67
- Citations by year
- 2026: 44 · 2025: 54 · 2024: 59 · 2023: 55 · 2022: 62 · 2021: 69 · 2020: 97 · 2019: 82 · 2018: 87 · 2017: 64 · 2016: 74 · 2015: 44 · 2014: 76 · 2013: 50 · 2012: 39
- FWCI
- 11.89
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Evolution (publishedVersion)
- PubMed (publishedVersion)
- Research Explorer (The University of Manchester) (publishedVersion)
- KOPS (University of Konstanz) (submittedVersion, cc-by-nc-nd)
- BioOne Complete (BioOne) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Geometry and Topology › Morphological variations and asymmetry
- Life Sciences › Agricultural and Biological Sciences › Ecology, Evolution, Behavior and Systematics › Animal Behavior and Reproduction
- Health Sciences › Medicine › Urology › Comparative Animal Anatomy Studies
- Keywords
- object symmetry, fluctuating asymmetry, Procrustes superimposition, two-factor ANOVA, directional asymmetry, pharyngeal jaw, Amphilophus citrinellus, cichlid fish
- MeSH terms
- Analysis of Variance, Animals, Biometry, Humans, Mathematics, Models, Anatomic, Software, Body Patterning, Cichlids
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