Logistic Models for Simulating the Growth of Plants by Defining the Maximum Plant Size as the Limit of Information Flow

Abstract

Today, the Logistic equations are widely applied to simulate the population growth across a range of fields, chiefly, demography and ecology. Based on an assumption that growth-regulating factors within the Logistic model, namely, the rate of increase (r) and carrying capacity (K), can be considered as the functions reflecting the combination of the organism- and environment-specific parameters, here, we discussed the possible application of modified synthetic Logistic equations to the simulation of the changes in (1) population (density per volume) of photosynthetically growing free-living algae and (2) size (mass per individual) of higher plants, by newly composing r value as a function reflecting the photosynthetic activities. Since higher plants are multi-cellular organisms, a novel concept for the carrying capacity K must also be introduced. We brought the a priori assumption that information sharing amongst cells strongly influences the physiology of multi-cellular structures eventually defining the maximum size of plants, into view. A simplest form of ‘synthetic organism’ conformed to test this assumption is a linear chain of cells, and the first physiological phenomenon, modeled in this way, is growth. This combination of information flow along a chain, with exponential growth, produces a simple allotropic relationship. This relationship is compared with results for plants and is found to have excellent predictive power. This theory shows that fast-growing organisms, or multicellular structures, remain small, because of their inability to share information sufficiently quickly and, also, predicts determinate growth. The success of this simple model suggests, firstly, that the inclusion of information flows in theoretical physiology models, which have been, to date, dominated by energetic or metabolic assumptions, will be improved by incorporating information flows. Secondly, the application of more complex information theories, such as those of Shannon, to biological systems will offer deep insights into the mechanisms and control of intercellular communication.