QUANTIFYING THE DYNAMICS OF ORDER AND ORGANIZATION IN BIOLOGICAL-SYSTEMS

The concepts of "biological order" and "biological organization" have long proven elusive, to the point that biologists often have difficulty defining the order or organization that they intuit as basic properties of the living systems they study. Recent attempts to critically examine the definition of, and distinctions between, the concepts we recognize as the order and organization characteristic of biological systems have been primarily theoretical; we take a more data oriented approach and attempt to apply these ideas to biological systems and data that would be acquired in studies of development or comparative morphology. In this paper we (a) present protocols for quantifying order and organization in developing/evolving systems and demonstrate their application in two developing systems: ovule (immature seed) development in Nothofagus antarctica (southern beech), and mainstem and branch growth in Pseudotsuga menziesii (Douglas-fir); (b) relate our estimates to both formal measures of relative information and the notion of fractal dimension in nonlinear systems: (c) from the context of multivariate analysis, contrast the concepts of "order" and "organization"; relating the former to amount of dispersion, and the latter to shape of dispersion: and (d) suggest that such "shape" is information conveying, but requires an extension of the domain of classical information theory. An appropriate comparison for development may be found in dynamic systems of physical theory. Such a comparison allows a reorientation of thought on development and provides insight into some new analytical approaches to the study of development. © 1990 Academic Press Limited All rights reserved.