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Landmark-based morphometrics of spiral accretionary growth

Published online by Cambridge University Press:  08 February 2016

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

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.

Type
Articles
Information
Paleobiology , Volume 17 , Issue 1 , Winter 1991 , pp. 19 - 36
Copyright
Copyright © The Paleontological Society 

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