Quantitative studies in ovule development. III. An estimate of shape changes in Phyllostachys aurea

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Abstract
Multivariate analysis of ovule development data from Phyllostachys aurea determined that there are (i) changes in estimators of organization (eigenvectors of principal components axes, determinants of correlation, and variance-covariance matrices); (ii) differences of a shape component in each axis (angles between principal components axe and a vector of isometry); and (iii) an increase in variation in the parameters calculated. Angles between principal components axes are all significantly different from 0.degree. (zero), when calculated from jackknifed estimates, indicating that each axis represents different shape components. Because these vectors are derived from principal components axes, they are another manifestation of correlation structure, i.e., organization. Thus angular differences between vectors are a function of differences in organization. The relationship between organization and vectors implies that the concept of shape is another way of expressing the organization that is inherent in biological systems. The changing organization, including shape, and increasing variation with development are expressions of the increasing complexity concomitant with development. This increasing complexity would be predicted from the theory of Brooks and Wiley as a manifestation of the second law of thermodynamics as expressed in non-equilibrium systems.