[Evolutionary trajectories in the parameter space of the sectional model of green spruce crown biomass. The emergence of a "proto-plant"].

Abstract

The sectional model of system dynamics of regular branches of a tree together, with submodels for initial growth inhibition and inter-verticil branches, has been extended to the range (0, 3) of fractal parameter ц that connects green biomass and a spruce size, В ~ H µ . It is shown that spruce branches of first three orders appear in the subrange of µ (0, 1). Branches of the first order appear at µ ≈ 0.25. Inter-verticil branches appear at µ ≈ 1.4, which may be viewed as a means of spruce adaptation to unstable lighting conditions. The presence of green biomass at µ < 1.0 indicates that it can be represented as a set of photosynthesizing points (hypothetical cyanobacteria) placed in space. Therefore, the fractal properties of the set of points on the line segment have been considered as a model. It is shown that the condition µ < 1.0 can be fulfilled only if the points are arranged in groups. At that, µ is practically independent of groups alignment while depends on the number of groups and the number and type of points distribution within groups. Based on these fractal properties of points alignment within groups along the segment, and the hypothesis of trophic nature of organelles symbio-genesis in eukaryotic cells, an idea of a two-stage mechanism of proto-plants emergence was formulated. The mechanism is manifested through the motion along the trajectory of endosymbiosis, beginning with a fixed number of points in the group and then with an increase in the number of groups, until, in course of evolution, the host of endosymbiosis would create an infrastructure for the supply and inter-group interaction of cyanobacteria. At this stage, µ decreases from 1 to ≈ 0.25. When the infrastructure is created and it becomes possible to increase the number of points in the group, the motion along the trajectory occurs through doubling the number of cyanobacteria in a group. At this stage, µ value increases to 1. At the first stage, motion along such a composite trajectory results in slow growth of the photosynthetic system size, even with an exponential increase in the number of cyanobacteria groups. The size grows rapidly at the second stage, after the limitations on growth of cyanobacteria number within groups are taken off. It should be noted that such an initial growth inhibition occurs also in modern trees, and is reflected in the initial slow increase in the number of the orders of tree's branches.