Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-21T18:51:36.590Z Has data issue: false hasContentIssue false
  • English
  • Français

A Practical Introduction to Landmark-Based Geometric Morphometrics

Published online by Cambridge University Press:  21 July 2017

Mark Webster  and
H. David Sheets
Mark Webster
Affiliation:
Department of the Geophysical Sciences, University of Chicago, 5734 South Ellis Avenue, Chicago, IL 60637
H. David Sheets
Affiliation:
Department of Physics, Canisius College, 2001 Main Street, Buffalo, NY 14208
Get access

Abstract

Landmark-based geometric morphometrics is a powerful approach to quantifying biological shape, shape variation, and covariation of shape with other biotic or abiotic variables or factors. The resulting graphical representations of shape differences are visually appealing and intuitive. This paper serves as an introduction to common exploratory and confirmatory techniques in landmark-based geometric morphometrics. The issues most frequently faced by (paleo)biologists conducting studies of comparative morphology are covered. Acquisition of landmark and semilandmark data is discussed. There are several methods for superimposing landmark configurations, differing in how and in the degree to which among-configuration differences in location, scale, and size are removed. Partial Procrustes superimposition is the most widely used superimposition method and forms the basis for many subsequent operations in geometric morphometrics. Shape variation among superimposed configurations can be visualized as a scatter plot of landmark coordinates, as vectors of landmark displacement, as a thin-plate spline deformation grid, or through a principal components analysis of landmark coordinates or warp scores. The amount of difference in shape between two configurations can be quantified as the partial Procrustes distance; and shape variation within a sample can be quantified as the average partial Procrustes distance from the sample mean. Statistical testing of difference in mean shape between samples using warp scores as variables can be achieved through a standard Hotelling's T2 test, MANOVA, or canonical variates analysis (CVA). A nonparametric equivalent to MANOVA or Goodall's F-test can be used in analysis of Procrustes coordinates or Procrustes distance, respectively. CVA can also be used to determine the confidence with which a priori specimen classification is supported by shape data, and to assign unclassified specimens to pre-defined groups (assuming that the specimen actually belongs in one of the pre-defined groups).

Examples involving Cambrian olenelloid trilobites are used to illustrate how the various techniques work and their practical application to data. Mathematical details of the techniques are provided as supplemental online material. A guide to conducting the analyses in the free Integrated Morphometrics Package software is provided in the appendix.

Type
Morphological Data
Information
The Paleontological Society Papers , Volume 16: Quantitative Methods in Paleobiology , October 2010 , pp. 163 - 188
Copyright
Copyright © 2010 by the Paleontological Society 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Adams, D. C., Rohlf, F. J., and Slice, D. E. 2004. Geometric morphometrics: ten years of progress following the ‘revolution’. Italian Journal of Zoology, 71:5–16.Google Scholar
Anderson, M. J. 2001. A new method for non-parametric multivariate analysis of variance. Austral Ecology, 26:32–46.Google Scholar
Andresen, P. R., Bookstein, F. L., Conradsen, K., Ersbøll, B., Marsh, J., and Kreiborg, S. 2000. Surface-bounded growth modeling applied to human mandibles. IEEE Transactions in Medical Imaging, 19:1053–1063.Google Scholar
Bookstein, F. L. 1986. Size and shape spaces for landmark data in two dimensions. Statistical Science, 1:181–242.Google Scholar
Bookstein, F. L. 1989. Principal warps: Thin-plate splines and the decomposition of deformations. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11:567–585.Google Scholar
Bookstein, F. L. 1991. Morphometric Tools for Landmark Data: Geometry and Biology. Cambridge Univeristy Press, 435 p.Google Scholar
Bookstein, F. L. 1996A. Biometrics, biomathematics and the morphometric synthesis. Bulletin of Mathematical Biology, 58:313–365.Google Scholar
Bookstein, F. L. 1996B. Standard formula for the uniform shape component in landmark data, p. 153–168. In Marcus, L. F., Corti, M., Loy, A., Naylor, G. J. P., and Slice, D. E. (eds.), Advances in Morphometrics. NATO ASI Series A: Life Sciences Volume 284. Plenum Press, New York.Google Scholar
Bookstein, F. L. 1997. Landmark methods for forms without landmarks: morphometrics of group differences in outline shape. Medical Image Analysis, 1:97–118.Google Scholar
Bookstein, F. L., Streissguth, A. P., Ssampson, P. D., Connor, P. D., and Barr, H. M. 2002. Corpus callosum shape and neuropsychological deficits in adult males with heavy fetal alcohol exposure. Neuroimage, 15:233–251.CrossRefGoogle ScholarPubMed
Chatfield, C., and Collins, A. J. 1980. Introduction to Multivariate Analysis. Chapman and Hall/CRC, Boca Raton, Florida, 246 p.Google Scholar
Claude, J. 2008. Morphometrics With R. Springer, New York, 316 p.Google Scholar
Dryden, I. L., and Mardia, K. V. 1998. Statistical Shape Analysis. John Wiley and Sons, Chichester, England, 347 p.Google Scholar
Efron, B. and Tibshirani, R. J. 1998. An Introduction to the Bootstrap. Chapman and Hall, London, 436 p.Google Scholar
Eelewa, A. M. T. (ED.). 2004. Morphometrics: Applications in Biology and Paleontology. Springer-Verlag, Berlin, 263 p.Google Scholar
Feldmanm, R. M., Chapman, R. E., and Hannibal, J. T. (EDS.). 1989. Paleotechniques. Paleontological Society Special Publication Number 4, 358 p.Google Scholar
Foote, M. 1993. Contributions of individual taxa to overall morphological disparity. Paleobiology, 19:403–419.Google Scholar
Good, P. 2000. Permutation Tests. Second Edition. Springer, New York, 270 p.Google Scholar
Goodall, C. 1991. Procrustes methods in the statistical analysis of shape. Journal of the Royal Statistical Society, Series B (Methodological), 53:285–339.CrossRefGoogle Scholar
Gower, J. C. 1975. Generalized Procrustes analysis. Psychometrika, 40:33–50.CrossRefGoogle Scholar
Green, W. D. K. 1996. The thin-plate spline and images with curving features, p. 79–87. In Mardia, K. V., Gill, C. A. and Dryden, I. L. (eds.), Image Fusion and Shape Variability. University of Leeds Press, Leeds.Google Scholar
Gunz, P., Mitteroecker, P., and Bookstein, F. L. 2005. Semilandmarks in three dimensions, p. 73–98. In Slice, D. E. (ed.), Modern Morphometrics In Physical Anthropology. Kluwer Academic Publishers/Plenum, New York.Google Scholar
Kendall, D. G. 1977. The diffusion of shape. Advances in Applied Probability, 9:428–430.CrossRefGoogle Scholar
Kendall, D. G. 1984. Shape manifolds, Procrustean metrics, and complex projective spaces. Bulletin of the London Mathematical Society, 16:81–121.CrossRefGoogle Scholar
Lawing, A. M., and Polly, P. D. 2010. Geometric morphometrics: recent applications to the study of evolution and development. Journal of Zoology, 280:1–7.Google Scholar
Macleod, N. 2002. Geometric morphometrics and geological shape-classification systems. Earth-Science Reviews, 59:27–47.Google Scholar
Manly, B. F. J. 1997. Randomization, Bootstrap and Monte Carlo Methods in Biology. Second Edition. Chapman and Hall, London, 399 p.Google Scholar
Marcus, L. F., Corti, M., Loy, A., Naylor, G. J. P., and Slice, D. E. (EDS.). 1996. Advances in Morphometrics. NATO ASI Series A: Life Sciences Volume 284. Plenum Press, New York, 587 p.Google Scholar
O'Higgins, P. 2000. The study of morphological variation in the hominid fossil record: biology, landmarks and geometry. Journal of Anatomy, 197:103–120.Google Scholar
Palmer, A. R. 1998. Terminal Early Cambrian extinction of the Olenellina: Documentation from the Pioche Formation, Nevada. Journal of Paleontology, 72:650–672.Google Scholar
Perez, S. I., Bernal, V., and Gonzalez, P. N. 2006. Differences between sliding semi-landmark methods in geometric morphometrics, with an application to human craniofacial and dental variation. Journal of Anatomy, 208:769–784.Google Scholar
Richtsmeier, J. T., Deleon, V. B., and Lele, S. R. 2002. The promise of geometric morphometrics. Yearbook of Physical Anthropology, 45:63–91.CrossRefGoogle Scholar
Richtsmeier, J. T., Lele, S. R., and Cole, T. M. III. 2005. Landmark morphometrics and the analysis of variation, p. 49–69. In Hallgrímsson, B., and Hall, B. K. (eds.), Variation: A Central Concept in Biology. Elsevier Academic Press, Burlington, MA, 568 p.CrossRefGoogle Scholar
Rohlf, F. J. 1990. Morphometrics. Annual Review of Ecology and Systematics, 21:299–316.Google Scholar
Rohlf, F. J. 1998. On applications of geometric morphometrics to studies of ontogeny and phylogeny. Systematic Biology, 47:147–158.CrossRefGoogle ScholarPubMed
Rohlf, F. J. 1999. Shape statistics: Procrustes superimpositions and tangent spaces. Journal of Classification, 16:197–223.Google Scholar
Rohlf, F. J. 2000. Statistical power comparisons among alternative morphometric methods. American Journal of Physical Anthropology, 111:463–478.Google Scholar
Rohlf, F. J. 2003. Bias and error in estimates of mean shape in geometric morphometrics. Journal of Human Evolution, 44:665–683.CrossRefGoogle ScholarPubMed
Rohlf, F. J. 2008. TPSUTIL. Version 1.40. Department of Ecology and Evolution, State University of New York. Available at <http://life.bio.sunysb.edu.morph/>.Google Scholar
Rohlf, F. J. 2009A. tpsDig. Version 2.14. Department of Ecology and Evolution, State University of New York. Available at <http://life.bio.sunysb.edu.morph/>.Google Scholar
Rohlf, F. J. 2009B. tpsRegr. Version 1.37. Department of Ecology and Evolution, State University of New York. Available at <http://life.bio.sunysb.edu.morph/>.Google Scholar
Rohlf, F. J., and Bookstein, F. L. (EDS.). 1990. Proceedings of the Michigan Morphometrics Workshop. University of Michigan Museum of Zoology Special Publication Number 2, Ann Arbor, Michigan, 380 p.Google Scholar
Rohlf, F. J., and Marcus, L. F. 1993. A revolution in morphometrics. Trends in Ecology and Evolution, 8:129–132.Google Scholar
Rohlf, F. J., and Slice, D. 1990. Extensions of the Procrustes method for the optimal superimposition of landmarks. Systematic Zoology, 39:40–59.Google Scholar
Roth, V. L., and Mercer, J. M. 2000. Morphometrics in development and evolution. American Zoologist, 40:801–810.Google Scholar
Sampson, P. D., Bookstein, F. L., Sheehan, H., and Bolson, E. L. 1996. Eigenshape analysis of left ventricular outlines from contrast ventriculograms, p. 131–152. In Marcus, L. F., Corti, M., Loy, A., Naylor, G. J. P. and Slice, D. E. (eds.), Advances in Morphometrics. Nato ASI Series, Series A: Life Science, New York.Google Scholar
Shaw, A. B. 1956. Quantitative trilobite studies I. The statistical description of trilobites. Journal of Paleontology, 30:1209–1224.Google Scholar
Shaw, A. B. 1957. Quantitative trilobite studies II. Measurement of the dorsal shell of non-agnostidean trilobites. Journal of Paleontology, 31:193–207.Google Scholar
Sheets, H. D., Kim, K., and Mitchell, C. E. 2004. A combined landmark and outline-based approach to ontogenetic shape change in the Ordovician trilobite Triarthrus becki, p. 67–82. In Elewa, A. M. T. (ed.), Morphometrics: Applications in Biology and Paleontology. Springer-Verlag, Berlin.Google Scholar
Slice, D. E. 2007. Geometric morphometrics. Annual Review of Anthropology, 36:261–281.CrossRefGoogle Scholar
Small, C. G. 1996. The Statistical Theory of Shape. Springer Series in Statistics. Springer, New York, 227 p.Google Scholar
Thompson, D. W. 1917. On Growth and Form. Cambridge University Press.Google Scholar
Thompson, D. W. 1942. On Growth and Form. A New Edition. Cambridge University Press, 1116 p.Google Scholar
Webster, M. 2007. Ontogeny and evolution of the Early Cambrian trilobite genus Nephrolenellus (Olenelloidea). Journal of Paleontology, 81:1168–1193.CrossRefGoogle Scholar
Webster, M., and Hughes, N. C. 1999. Compaction-related deformation in Cambrian olenelloid trilobites and its implications for fossil morphometry. Journal of Paleontology, 73:355–371.Google Scholar
Webster, M., and Zelditch, M. L. 2005. Evolutionary modifications of ontogeny: heterochrony and beyond. Paleobiology, 31:354–372.Google Scholar
Webster, M., and Zelditch, M. L. 2008. Integration and regulation of developmental systems in trilobites, p. 427–433. In Rábano, I., Gozalo, R., and García-Bellido, D (eds.), Advances In Trilobite Research. Cuadernos del Museo Geominero 9. Instituto Geológico y Minero de España, Madrid.Google Scholar
Webster, M., Sheets, H. D., and Hughes, N. C. 2001. Allometric patterning in trilobite ontogeny: testing for heterochrony in Nephrolenellus, p. 105–144. In Zelditch, M. L. (ed.), Beyond Heterochrony: The Evolution of Development. Wiley and Sons, New York.Google Scholar
Webster, M., Gaines, R. R., and Hughes, N. C. 2008. Microstratigraphy, trilobite biostratinomy, and depositional environment of the “Lower Cambrian” Ruin Wash Lagerstätte, Pioche Formation, Nevada. Palaeogeography, Palaeoclimatology, Palaeoecology, 264:100–122.CrossRefGoogle Scholar
White, C. A. 1874. Preliminary report upon invertebrate fossils collected by the expeditions of 1871, 1872, and 1873, with descriptions of new species. U. S. Geographic and Geologic Surveys West of the 100th Meridian Report. Pp. 5–27.Google Scholar
Zelditch, M. L., Swiderski, D. L., Sheets, H. D., and Fink, W. L. 2004. Geometric Morphometrics of Biologists: A Primer. Elsevier Academic Press, San Diego, 443 p.Google Scholar