Abstract
AbstractA matrix manipulation new to the quantitative study of develomental stability reveals unexpected morphometric patterns in a classic data set of landmark-based calvarial growth. There are implications for evolutionary studies. Among organismal biology’s fundamental postulates is the assumption that most aspects of any higher animal’s growth trajectories are dynamically stable, resilient against the types of small but functionally pertinent transient perturbations that may have originated in genotype, morphogenesis, or ecophenotypy. We need an operationalization of this axiom for landmark data sets arising from longitudinal data designs. The present paper introduces a multivariate approach toward that goal: a method for identification and interpretation of patterns of dynamical stability in longitudinally collected landmark data. The new method is based in an application of eigenanalysis unfamiliar to most organismal biologists: analysis of a covariance matrix of Boas coordinates (Procrustes coordinates without the size standardization) against their changes over time. These eigenanalyses may yield complex eigenvalues and eigenvectors (terms involving $$i=\sqrt{-1}$$
i
=
-
1
); the paper carefully explains how these are to be scattered, gridded, and interpreted by their real and imaginary canonical vectors. For the Vilmann neurocranial octagons, the classic morphometric data set used as the running example here, there result new empirical findings that offer a pattern analysis of the ways perturbations of growth are attenuated or otherwise modified over the course of developmental time. The main finding, dominance of a generalized version of dynamical stability (negative autoregressions, as announced by the negative real parts of their eigenvalues, often combined with shearing and rotation in a helpful canonical plane), is surprising in its strength and consistency. A closing discussion explores some implications of this novel pattern analysis of growth regulation. It differs in many respects from the usual way covariance matrices are wielded in geometric morphometrics, differences relevant to a variety of study designs for comparisons of development across species.
Publisher
Springer Science and Business Media LLC
Subject
Ecology, Evolution, Behavior and Systematics
Reference43 articles.
1. Abarbanel, H. D. I., Brown, R., & Kennel, M. B. (1992). Local Lyapunov exponents computed from observed data. Journal of Nonlinear Science, 2, 343–365.
2. Boas, F. (1905). The horizontal plane of the skull and the general problem of the comparison of variable forms. Science, 21, 862–863.
3. Bookstein, F. L. (1983). The geometry of craniofacial growth invariants. American Journal of Orthodontics, 83, 221–234.
4. Bookstein, F. L. (1987). Describing a craniofacial anomaly: Finite elements and the biometrics of landmark locations. American Journal of Physical Anthropology, 74, 495–509.
5. Bookstein, F. L. (1991). Morphometric tools for landmark data: Geometry and biology. New York: Cambridge University Press.
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献