Initial growth deceleration as an immanent property of plants

Abstract

A previously published sectional model of the system of tree branches (spruce) was expanded in the range (0,1) of the fractal model parameter μ, which links the value of green biomass of a “tree” to its size. The presence of branches in this range indicates the realization of green biomass in the form of photosynthe-sizing “points”, and is interpreted as endosymbiosis of cyanobacteria with protists. Using the method of box dimensionality, the parameter μ was estimated for the sets of points within an interval. The properties of the uniform and group distributions are shown to be different. For the group distribution, the trajectories of parameter μ are fundamentally different, depending on the method of point grouping, i.e., they decrease with an increase in the total number of points for a fixed number of points n_g in the groups and increase for a fixed number N_g groups. The initial endosymbiosis of cyanobacteria and “protists” is characterized by a lack of the necessary infrastructure in protists for feeding cyanobacteria and distributing their products and, thus, by a fixed number of “points” in the group. As the infrastructure of protists developed in the course of evolution, endosymbiosis tended to move towards an increased number of points in the group and, accordingly, increased μ. A special form of the dependence of parameter μ(N_g*n_g) provides the inherent nature of the initial growth deceleration and modularity of architecture, which are occasionally observed in extant plants.