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Landmark-based morphometrics of spiral accretionary growth

Published online by Cambridge University Press:  08 February 2016

Mark R. Johnston
Museum of Paleontology and Department of Geological Sciences, University of Michigan, Ann Arbor, Michigan 48109
R. Elena Tabachnick
Museum of Paleontology and Department of Geological Sciences, University of Michigan, Ann Arbor, Michigan 48109
Fred L. Bookstein
Center for Human Growth and Development, University of Michigan, Ann Arbor, Michigan 48109


Many organisms continue to grow their skeletons throughout ontogeny. In the shells of molluscs, protists, and brachiopods and in bovid horns, accretionary spiral growth provides a detailed and continuous growth history. Although a shell may be described as a single static form, the overall morphology is a summation of the ongoing accretionary process. For this reason, an explicitly ontogenetic characterization of form provides insight into the final form achieved. Analysis of landmark transformations offers direct access to major components of morphological variation, both among adult individuals and through an individual's ontogeny. Parameters of preconceived, abstract geometric models can also be used to characterize morphological variation, but there is no guarantee that these parameters will coincide with the major features of shape variation.

In order to locate landmarks at equivalent ontogenetic stages, features that indicate ontogenetic stage of coiled forms must be identified (e.g., growth increments, age, size, whorls). The gastropod Epitonium (Nitidiscala) tinctum exhibits prominent varices that provide landmark locations throughout ontogeny. Recent specimens of this species were obtained from three localities in Baja, Mexico. The morphological variation among individuals, treated as whole shells and within individual ontogenies, was analyzed using shape coordinates of landmark configurations. Deformation of shape is expressed in the uniform and nonuniform shape subspaces. The empirical components of shape variation found are similar to those generated by two parameters of an equiangular spiral: θ, the angle between consecutive varices, and W, the whorl expansion rate. The distribution of individuals is examined within morphospaces constructed from these shape features.

Three scales of analysis are necessary to characterize adequately the shape variation within and among specimens. The smallest scale is equivalent to increment-by-increment changes in θ and W. The middle scale comprises variation equivalent to whorls resulting from systematic changes in θ and W during an individual's ontogeny. Finally, there is the overall ontogenetic trajectory. Mean shape must be a function of initial shape and ontogenetic trajectory in shape. Mean forms that are found to have similar shapes at the same arbitrary growth increment may achieve that shape in different ways.

Copyright © The Paleontological Society 

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Literature Cited

Ackerly, S. C. 1987. Using “local” coordinates to analyze shell form in molluscs. Geological Society of America Abstracts with Program 19:566.Google Scholar
Ackerly, S. C. 1989. The kinematics of accretionary shell growth, with examples from brachiopods and molluscs. Paleobiology 15:147164.CrossRefGoogle Scholar
Alberch, P., Gould, S. J., Oster, G. F., and Wake, D. B. 1979. Size and shape in ontogeny and phylogeny. Paleobiology 5:296317.CrossRefGoogle Scholar
Atchley, W. R. 1987. Developmental quantitative genetics and the evolution of ontogenies. Evolution 41:316330.CrossRefGoogle ScholarPubMed
Blackstone, N. W., and Yund, P. O. 1989. Morphological variation in a colonial marine hydroid: a comparison of size-based and age-based heterochrony. Paleobiology 15:110.CrossRefGoogle Scholar
Bookstein, F. L. 1986. Size and shape spaces for landmark data in two dimensions. Statistical Science 1:181242.Google Scholar
Bookstein, F. L. 1989. Principal warps: thin plate splines and the decomposition of deformations. IEEE Transactions on Pattern Analysis and Machine Intelligence 11:567585.CrossRefGoogle Scholar
Bookstein, F. L.In Press. Morphometric Tools for Landmark Data: Geometry and Biology. Cambridge University Press; Cambridge.CrossRefGoogle Scholar
Bookstein, F., Chernoff, B., Elder, R., Humphries, J., Smith, G., and Strauss, R. 1985. Morphometrics in Evolutionary Biology. Special Publication 15, Academy of Natural Science of Philadelphia; Philadelphia.Google Scholar
Creighton, G. K., and Strauss, R. E. 1986. Comparative patterns of growth and development in cricertine rodents and the evolution of ontogeny. Evolution 40:94106.CrossRefGoogle ScholarPubMed
DuShane, H. 1979. The family Epitoniidae (Mollusca: Gastropoda) in the Northeastern Pacific. Veliger 22:91134.Google Scholar
Ekaratne, S. U. K., and Crisp, D. J. 1982. Tidal microgrowth bands in intertidal gastropod shells with an evaluation of band-dating techniques. Proceedings of the Royal Society (B) 214:305323.Google Scholar
Ekaratne, S. U. K., and Crisp, D. J. 1983. A geometric analysis of growth in gastropod shells, with particular reference to turbinate forms. Bulletin of the Marine Biological Association of the United Kingdom 63:777797.CrossRefGoogle Scholar
Fink, W. L. 1982. The conceptual relationship between ontogeny and phylogeny. Paleobiology 8:254264.CrossRefGoogle Scholar
Foote, M., and Cowie, R. H. 1988. Developmental buffering as a mechanism for stasis: evidence from the pulmonate Theba pisana. Evolution 42:396399.Google ScholarPubMed
Fretter, V. 1967. The prosobranch veliger. Proceedings of The Malacological Society of London. 37:357366.Google Scholar
Gould, S. J., and Woodruff, D. S. 1986. Systematics of Cerion on New Providence Island: a radical revision. Bulletin of the Museum of Comparative Zoology, Harvard University 148:371415.Google Scholar
Jones, D. S. 1981. Annual growth increments in shells of Spisula solidissima record marine temperature variability. Science 211:165167.CrossRefGoogle ScholarPubMed
Kohn, A. J., and Riggs, A. C. 1975. Morphometry of the Conus shell. Systematic Zoology 24:346359.CrossRefGoogle Scholar
Lindberg, D. R. 1985. Shell sexual dimorphism of Margarites vorticigera: multivariant analysis and taxonomic implications. Malacological Review 18:18.Google Scholar
Linsley, R. M., and Javidpour, M. 1980. Episodic growth in Gastropoda. Malacologia 20(1):153160.Google Scholar
Løvtrup, S., and Løvtrup, M. 1988. The morphogenesis of molluscan shells: a mathematical account using biological parameters. Journal of Morphology 197:5362.CrossRefGoogle ScholarPubMed
McGhee, G. R. Jr. 1980. Shell form in the biconvex articulate brachiopoda: a geometric analysis. Paleobiology 6:5776.CrossRefGoogle Scholar
McLain, D. R., and Ingram, J. W. 1980. Pp. 1037. In Hayes, E. D. (ed.), Marine Environmental Conditions off the United States, January 1978–March 1979. NOAA Technical Memorandum NMFS-OF-5.Google Scholar
Moseley, H. 1838. On the geometric form of turbinate and discoid shells. Philosophical Transactions of the Royal Society, London 128:351370.Google Scholar
Moseley, H. 1842. On conchyliometry. London, Edinburgh and Dublin Philosophical Magazine and Journal of Science 21:300305.CrossRefGoogle Scholar
Newkirk, G. F., and Doyle, R. W. 1975. Genetic analysis of shell-shape variations in Littorina saxatilis on an environmental cline. Marine Biology 30:227237.CrossRefGoogle Scholar
Okamoto, T. 1988. Analysis of heteromorph ammonoids by differential geometry. Palaeontology 31:3552.Google Scholar
Raup, D. M. 1961. The geometry of coiling in gastropods. Proceedings of the National Academy of Sciences 47:602609.CrossRefGoogle ScholarPubMed
Raup, D. M. 1966. Geometric analyses of shell coiling: general problems. Journal of Paleontology 40:11781190.Google Scholar
Raup, D. M. 1972. Approaches to morphological analysis. Pp. 2844. In Schopf, T. J. M. (ed.), Models in Paleobiology. W. H. Freeman; San Francisco.Google Scholar
Reyment, R. A., Blackith, B. E., and Campbell, N. A. 1984. Multivariate Morphometrics. 2nd Ed.Academic Press; New York.Google Scholar
Robertson, R. 1983a. Extraordinarily rapid postlarval growth of a tropical wentletrap (Epitonium albidum). The Nautilus 97:6066.Google Scholar
Robertson, R. 1983b. Axial shell rib counts as systematic characters in Epitonium. The Nautilus 97:116118.Google Scholar
Robertson, R. 1983c. Observations on the life history of the wentletrap Epitonium albidum in the West Indies. American Malacological Bulletin 1:112.Google Scholar
Roth, V. L. 1984. On homology. Biological Journal of The Linnean Society 22:1329.CrossRefGoogle Scholar
Saunders, W. B., and Swan, A.R.H. 1984. Morphology and morphologic diversity of mid-Carboniferous (Namurian) ammonoids in time and space. Paleobiology 3:195228.CrossRefGoogle Scholar
Schindel, D. E. 1990. Architectural constraints on the coiled geometry of gastropod molluscs. In Ross, R. M., and Allmon, W. D. (eds.), Biotic and Abiotic Factors in Evolution: a Paleontological Perspective. University of Chicago Press; Chicago.Google Scholar
Schindel, D. E., and Gould, S. J. 1977. Biological interactions between fossil species: character displacement in Bermudian land snails. Paleobiology 3:259269.CrossRefGoogle Scholar
Smith, C. R., and Breyer, A. 1983. Comparisons of northern and southern populations of Epitonium tinctum (Carpenter, 1864) on the California coast. Veliger 26:3746.Google Scholar
Tabachnick, R. E., and Bookstein, F. L. 1990a. The structure of individual variation in Miocene Globorotalia. Evolution 44:416434.CrossRefGoogle ScholarPubMed
Tabachnick, R. E., and Bookstein, F. L. 1990b. Resolving factors of landmark deformation: Miocene Globorotalia, DSDP Site 593. Proceedings of the Michigan Morphometric Workshop. University of Michigan Press; Ann Arbor.Google Scholar
Thompson, D. W. 1943. On Growth and Form. Macmillan; New York.Google Scholar
Van Valen, L. 1982. Homology and causes. Journal of Morphology 173:305315.CrossRefGoogle ScholarPubMed
Verduin, A. 1982. How complete are diagnoses of coiled shells of regular build? A mathematical approach. Basteria 45:127142.Google Scholar
Vermeij, G. J. 1971. Gastropod evolution and morphological diversity in relation to shell geometry. Journal of Zoology, London 163:1523.CrossRefGoogle Scholar
Wefer, G., and Killingley, J.S. 1980. Growth histories of strombid snails from Bermuda recorded in their O-18 and C-13 profiles. Marine Biology 60:129135.CrossRefGoogle Scholar
Williamson, P. G. 1981. Paleontological documentation of speciation in Cenozoic molluscs from the Turkana Basin. Nature 293:427443.CrossRefGoogle Scholar