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Generalizing and extending the eigenshape method of shape space visualization and analysis

Published online by Cambridge University Press:  20 May 2016

Norman MacLeod
Norman MacLeod*
Affiliation:
Department of Palaeontology, The Natural History Museum, Cromwell Road, London, SW7 5BD United Kingdom. E-mail: [email protected]
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Abstract

Outline-based morphometric methods have been more or less restricted to the consideration of closed curves and plagued by problems related to the maintenance of close biological correspondence across all forms within a sample. Methods developed herein generalize and extend the eigenshape method of outline analysis along the following lines: (1) consideration of open curves, (2) improvement of interobject correspondence via incorporation of information provided by landmarks, and (3) extension to the analysis of three-dimensional (open and closed) curves. In addition, techniques for using eigenshape results to create models of shape variation and for more consistently assessing the digital resolution necessary to represent an object are discussed and illustrated. These improvements are then placed in context via discussions of previous attempts to extend morphometric outline analysis methods, the relation between landmark and outline-based morphometric methods, the use of morphometric analyses to test biological hypotheses, and the nature of morphometric shape spaces (with special reference to studies of morphological disparity).

Type
Articles
Information
Paleobiology , Volume 25 , Issue 1 , Winter 1999 , pp. 107 - 138
Copyright
Copyright © The Paleontological Society 

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References

Literature Cited

Attneave, F. 1954. Some informational aspects of visual perception. Psychological Review 61: 183–193.Google Scholar
Blackith, R. E. and Reyment, R. A. 1971. Multivariate morphometrics. Academic Press, London.Google Scholar
Bookstein, F. L. 1978. The measurement of biological shape and shape change. Springer, Berlin.Google Scholar
Bookstein, F. L. 1980. When one form is between two others: an application of biorthogonal analysis. American Zoologist 20: 627–641.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. 1990. Analytic methods: introduction and overview. pp. 61–74in Rohlf and Bookstein 1990.Google Scholar
Bookstein, F. L. 1991. Morphometric tools for landmark data: geometry and biology. Cambridge University Press, Cambridge.Google Scholar
Bookstein, F. L. 1993. A brief history of the morphometric synthesis. pp. 18–40in Marcus et al. 1993.Google Scholar
Bookstein, F. L. 1994. Can biometrical shape be a homologous character? Pp. 197–227in Hall, B. K. ed. Homology: the hierarchical basis of comparative biology. Academic Press, San Diego.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. Landmark methods for forms without landmarks: localizing group differences in outline shape. pp. 279–289in Amini, A., Bookstein, F. L., Wilson, D. eds. Proceedings of the workshop on mathematical methods in biomedical image analysis. IEEE Computer Society, San Francisco.Google Scholar
Bookstein, F. L. and Green, W.D.K. 1993. A feature space for edgels in images with landmarks. Journal of Mathematical Imaging and Vision 3: 213–261.Google Scholar
Bookstein, F. L., Strauss, R. E., Humphries, J. M., Chernoff, B., Elder, R. L., and Smith, G. R. 1982. A comment on the uses of Fourier methods in systematics. Systematic Zoology 31: 85–92.Google Scholar
Bookstein, F., Chernoff, B., Elder, R., Humphries, J., Smith, G., and Strauss, R. 1985. Morphometrics in evolutionary biology. Academy of Natural Sciences of Philadelphia, Philadelphia.Google Scholar
Christopher, R. A. and Waters, J. A. 1974. Fourier analysis as a quantitative descriptor of miosphere shape. Journal of Paleontology 48: 697–709.Google Scholar
Clark, M. W. 1981. Quantitative shape analysis: a review. Mathematical Geology 13: 303–320.Google Scholar
Davis, J. C. 1973. Statistics and data analysis in geology. Wiley, New York.Google Scholar
Davis, J. C. 1986. Statistics and data analysis in geology, 2d ed. Wiley, New York.Google Scholar
Ehrlich, R., Pharr, R. B. Jr., and Williams, N. Healy 1983. Comments on the validity of Fourier descriptors in systematics: a reply to Bookstein et al. Systematic Zoology 31: 85–92.Google Scholar
Eldredge, N. and Cracraft, J. 1980. Phylogenetic patterns and the evolutionary process. Columbia University Press, New York.Google Scholar
Ferson, S., Rohlf, F. J., and Koehn, R. K. 1985. Measuring shape variation in two dimensional outlines. Systematic Zoology 34: 59–68.CrossRefGoogle Scholar
Foote, M. 1989. Perimeter-based Fourier analysis: a new morphometric method applied to the trilobite cranidium. Journal of Paleontology 63: 880–885.Google Scholar
Foote, M. 1991a. Analysis of morphological data. In Gilinsky, N. L., Signor, P. W. eds. Analytical paleobiology. Short Courses in Paleontology 4: 59–86. Paleontological Society, Knoxville, Tenn.Google Scholar
Foote, M. 1991b. Morphologic patterns of diversification: examples from trilobites. Palaeontology 34: 461–485.Google Scholar
Foote, M. 1993. Discordance and concordance between morphological and taxonomic diversity. Paleobiology 19: 185–204.Google Scholar
Foote, M. 1996. Models of morphological diversification. pp. 63–86in Jablonski, D., Erwin, D. H., Lipps, J. eds. Evolutionary paleobiology. University of Chicago Press, Chicago.Google Scholar
Foote, M. 1997. Sampling, taxonomic description, and our evolving knowledge of morphological disparity. Paleobiology 23: 181–206.Google Scholar
Goodall, C. R. 1991. Procrustes methods in the statistical analysis of shape. Journal of the Royal Statistical Society B 53: 285–339.Google Scholar
Hughes, N. and Chapman, R. E. 1992. Growth and variation in the Silurian proetid trilobite Aulacopleura konincki and its implications for trilobite palaeobiology. Lethaia 28: 333–353.CrossRefGoogle Scholar
Jöreskog, K. G., Klovan, J. E., and Reyment, R. A. 1976. Geological factor analysis. Elsevier, Amsterdam.Google Scholar
Kendall, D. G. 1984. Shape manifolds, procrustean metrics and complex projective spaces. Bulletin of the London Mathematical Society 16: 81–121.Google Scholar
Klapper, G. and Foster, C. T. Jr. 1986. Quantification of outlines in Frasnian (Upper Devonian) platform conodonts. Canadian Journal of Earth Sciences 23: 1214–1222.Google Scholar
Koffka, K. 1935. Principles of gestalt psychology. Routledge and Kegan Paul, London.Google Scholar
Kucera, M. and Malmgren, B. A. 1996. Latitudinal variation in the planktic foraminifera Contusatruncana contusa in the terminal Cretaceous ocean. Marine Micropaleontology 28: 31–52.Google Scholar
Labandiera, C. C. and Hughes, N. C. 1994. Biometry of the late Cambrian trilobite genus Dikelocephalus and its implications for trilobite systematics. Journal of Paleontology 68: 492–517.Google Scholar
Lele, S. and Cole, T. 1995. Euclidean distance matrix analysis: a statistical review. pp. 21–32in Mardia, K. V. ed. Proceedings of the international conference on current issues in statistical shape analysis University of Leeds, Leeds, England.Google Scholar
Lele, S. and Cole, T. 1996. Testing for shape differences when the covariance matrices are unequal. Journal of Human Evolution 31: 193–212.Google Scholar
Lestrel, P. E. 1997a. Introduction. pp. 3–21in Lestrel, P. E. ed. Fourier descriptors and their applications in biology. Cambridge University Press, Cambridge.Google Scholar
Lestrel, P. E. 1997b. Introduction and overview of Fourier descriptors. pp. 22–44in Lestrel, P. E. ed. Fourier descriptors and their applications in biology. Cambridge University Press, Cambridge.Google Scholar
Lohmann, G. P. 1983. Eigenshape analysis of microfossils: a general morphometric method for describing changes in shape. Mathematical Geology 15: 659–672.Google Scholar
Lohmann, G. P. and Malmgren, B. A. 1983. Equatorward migration of Globorotalia truncatulinoides ecophenotypes through the Late Pleistocene: gradual evolution or ocean change? Paleobiology 9: 414–421.Google Scholar
Lohmann, G. P. and Schweitzer, P. N. 1990a. On eigenshape analysis. pp. 145–166in Rohlf and Bookstein 1990.Google Scholar
Lohmann, G. P. and Schweitzer, P. N. 1990b. Globorotalia truncatulinoides' growth and chemistry as probes of the past thermocline: 1: shell size. Paleoceanography 5: 55–75.Google Scholar
MacLeod, N. and Carr, T. R. 1987. Morphometrics and the analysis of shape in conodonts. pp. 168–187in Austin, R. L. ed. Conodonts: investigative techniques and applications. Ellis Horwood, Chichester, England.Google Scholar
MacLeod, N. and Rose, K. D. 1993. Inferring locomotor behavior in Paleogene mammals via eigenshape analysis. American Journal of Science 293-A: 300–355.Google Scholar
MacLeod, N. and Rose, K. D. 1997. 3D morphometric-functional analysis of modern and Paleogene mammalian radial heads. Journal of Vertebrate Paleontology Abstracts of Papers 17: 61A.Google Scholar
Malmgren, B. A., Berggren, W. A., and Lohmann, G. P. 1983. Evidence for punctuated gradualism in the late Neogene Globorotalia tumida lineage of planktonic foraminifera. Paleobiology 9: 377–389.Google Scholar
Marcus, L. F., Bello, E., and García-Valdecasas, A. 1993. Contributions to morphometrics. Museo Nacional de Ciencias Naturales 8, Madrid.Google Scholar
Marcus, L. F., Corti, M., Loy, A., Naylor, G.J.P., and Slice, D. E. 1996. Advances in morphometrics. Plenum, New York.Google Scholar
Mardia, K. V. 1995. In. Proceedings of the international conference on current issues in statistical shape analysis. University of Leeds, Leeds, England.Google Scholar
Mardia, K. V. and Dryden, I. 1989. The statistical analysis of shape data. Biometrika 76: 271–282.Google Scholar
Marr, D. 1976. Early processing of visual information. Philosophical Transactions of the Royal Society of London B 275: 483–524.Google Scholar
Neff, N. A. and Marcus, L. F. 1980. A survey of multivariate methods for systematists. Privately published, New York.Google Scholar
Norris, R. D., Corfield, R. M., and Cartlidge, J. 1996. What is gradualism?Cryptic speciation in globorotalid foraminifera. Paleobiology 22: 386–405.Google Scholar
Pimentel, R. A. 1979. Morphometrics: the multivariate analysis of biological data. Kendall/Hunt, Dubuque, Iowa.Google Scholar
Ray, T. S. 1990. Application of eigenshape analysis to second order leaf shape ontogeny in Syngonium podophyllum (Araceae). pp. 201–213in Rohlf and Bookstein 1990.Google Scholar
Ray, T. S. 1992. Landmark eigenshape analysis: homologous contours: leaf shape in Syngonium (Araceae). American Journal of Botany 79: 69–76.CrossRefGoogle Scholar
Read, D. W. and Lestrel, P. E. 1986. Comment on the uses of homologous point measures in systematics: a reply to Bookstein et al. Systematic Zoology 35: 241–253.Google Scholar
Remane, A. 1956. Die Grundlagen des naturlichen Systems der verleichenden Anatomie und Phylogenetik 2. Geest and Portig, K.-G., Leipzig.Google Scholar
Reyment, R. A. 1991. Multidimensional paleobiology. Pergammon, Oxford.Google Scholar
Reyment, R. A. 1996. Some applications of geometric morphometrics to Ostracoda. pp. 387–398in Marcus et al. 1996.Google Scholar
Reyment, R. A., Blackith, R. E., and Campbell, N. A. 1984. Multivariate morphometrics, 2d ed. Academic Press, London.Google Scholar
Riedel, R. and Jefferies, R.P.S. 1978. Order in living organisms: a systems analysis of evolution. Wiley, Chichester, England.Google Scholar
Rohlf, F. J. 1986. Relationships among eigenshape analysis, Fourier analysis, and analysis of coordinates. Mathematical Geology 18: 845–857.Google Scholar
Rohlf, F. J. 1993. Relative warp analysis and an example of its application to mosquito wings. pp. 131–160in Marcus et al. 1993.Google Scholar
Rohlf, F. J. 1996. Introduction to outlines. pp. 209–210in Marcus et al. 1996.Google Scholar
Rohlf, F. J. and Bookstein, F. L. 1990. Proceedings of the Michigan morphometrics workshop. University of Michigan Museum of Zoology Special Publication No. 2. Ann Arbor.Google Scholar
Romer, A. S. 1956. Osteology of the reptiles. University of Chicago Press, Chicago.Google Scholar
Sampson, P. D., Bookstein, F. L., Sheehan, F. H., and Bolson, E. L. 1996. Eigenshape analysis of left ventricular outlines from contrast ventriculograms. pp. 211–234in Marcus et al. 1996.Google Scholar
Sarà, M. 1996. A landmark-based morphometrics approach to the systematics of Crocidurinare: a case study on endemic shrews Crocidura sicula and C. canariensis (Soricidae, Mammalia). pp. 335–344in Marcus et al. 1996.Google Scholar
Schweitzer, P. N. and Lohmann, G. P. 1990. Life-history and the evolution of ontogeny in the ostracode genus Cyprideis. Paleobiology 16: 107–125.Google Scholar
Scott, G. H. 1980. The value of outline processing in the biometry and systematics of fossils. Palaeontology 23: 757–768.Google Scholar
Smith, A. B. 1994. Systematics and the fossil record: documenting evolutionary patterns. Blackwell Scientific, London.Google Scholar
Smith, L. H. 1998. Species level phenotypic variation in lower Paleozoic trilobites. Paleobiology 24: 17–36.CrossRefGoogle Scholar
Sneath, P.H.A. 1967. Trend surface analysis of transformation grids. Journal of Zoology 151: 65–122.Google Scholar
Sneath, P.H.A. and Sokal, R. R. 1973. Numerical taxonomy: the principles and practice of numerical classification. W. H. Freeman, San Francisco.Google Scholar
Temple, J. T. 1975a. Early Llandovery trilobites from Wales with notes on British Llandovery calymednids. Palaeontology 18: 137–159.Google Scholar
Temple, J. T. 1975b. Standardisation of trilobite orientation and measurement. Fossils and Strata 4: 461–467.Google Scholar
Thompson, D. W. 1917. On growth and form. Cambridge University Press, Cambridge.Google Scholar
van Dam, J. 1996. Stephanodonty in fossil murids: a landmark-based morphometric approach. pp. 449–462in Marcus et al. 1996.Google Scholar
Walker, J. A. 1993. Ontogenetic allometry of threespine stickleback body form using landmark based morphometrics. pp. 193–214in Marcus et al. 1993.Google Scholar
Wills, M. A., Briggs, D.E.G., and Fortey, R. A. 1994. Disparity as an evolutionary index: a comparison of Cambrian and Recent arthropods. Paleobiology 20: 93–130.Google Scholar
Zahn, C. T. and Roskies, R. Z. 1972. Fourier descriptors for plane closed curves. IEEE Transactions, Computers C-21: 269–281.Google Scholar
Zelditch, M. L., Fink, W. L., and Swiderski, D. L. 1995. Morphometrics, homology, and phylogenetics: quantified characters as synapomorphies. Systematic Biology 44: 179–189.Google Scholar