Satindranath Banerjee

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.

A Quantitative Genetic Analysis of Morphological Integration in Douglas Fir

We have investigated the contribution of specific parents and genotypes to morphological integration in needles of Douglas fir seedlings by diallel analysis. Integration was assessed by statistics that describe the strength and similarity of correlations within individual seedlings. These two statistics, assumed to assess order and organization, respectively, were the variables used in the diallel analysis. The greatest amount of variation was in the residual term of the analysis; neither general nor specific combining abilities were significant. This result seems not to reflect repeatability error but may be due to designimposed restrictions on the number of individuals, crosses, and genotypes. The high residual variation can be explained as the result of seedlings following different developmental trajectories due to diverse relationships among genotype-related growth rates. Diverging developmental trajectories could be the result of the accumulation of somatic mutations or changing gene expression in the face of continuously changing external and internal environments.

Studies into abstract properties of individuals. VI. The degree of emergence in individuals, populations, species and a three species lineage.

Emergent properties derived from the integration among descriptive variables were explored in three related grass species, Achnatherum lemmonii, Achnatherum hendersonii and Achnatherum wallowaensis. Different levels of organization were compared: individuals, populations, species, species-pairs and all three species combined. Emergence was seen at all levels with populations having the lowest degree followed by individuals, species and combinations of species. Because there were no variables unique to any level analyzed, emergence is more than the appearance of new structures. As the degree of emergence increases there is also an increase in variation in integration, the result of new growth rates. Time may explain the different degrees of emergence at the different levels. The trend populations-species-combination of species is easily related to time; the first are younger than the last. An individual develops over a greater period of time than a population. The greater time of existence of a species may account for a greater degree of emergence than an individual. In an individual the local time expressed during ontogeny establishes boundary conditions for an individual. As that local time becomes incorporated into global, or phylogenetic, time, the boundary conditions for taxa and lineages is established.

Studies into Abstract Properties of Individuals. VII. Emergence in Hesperostipa comata and Three Species of Achnatherum (Poaceae)

Emergence is examined in populations of Hesperostipa comata, and this grass is compared to individuals, populations, and three additional species of Achnatherum. The Achnatherum species are closely related and more distantly related to H. comata. Emergent properties are assessed through measurements of grass spikelets and the divergence from vectors of isometry as expressed in individuals, populations, species, and species groups. Our results demonstrate that the strongest degrees of emergence are expressed at the levels of individuals, species, and groups of species, with the strongest of all being seen when H. comata is compared with the trio of Achnatherum species; populations express the least emergence. This reflects evolutionary differentiation as expressed through the ontogenetic events that led to the formation of spikelets. It can be related to concepts of local and global time; the flow of energy, matter, and information; and the driving force of the expression of novelty (entropy) in organized and historically constrained biological systems.