Fractal model of the protoplant's appearance

V. V. Galitskii

Matematičeskaâ biologiâ i bioinformatika, Tome 11 (2016) no. 2, pp. 225-232.

Résumé

Sectional model of the tree's system branches, which was published earlier, was extended on the range $(0.1)$ of model's allometric parameter $\mu$, relating the magnitude of the green biomass of a tree and its size (for spruce $\mu\approx 1.83$). The model showed the presence of a green biomass in this range. According to the statements of fractal geometry this points out a possibility to interpret the placement of green biomass as a set of photosynthesis points. In turn according to contemporary notions about endosymbiotic character of appearance of organelles in eukaryotic cell this was interpreted as begin of endosymbiosis of cyanobacteria and a host (protist). This has been modeled by the groups’ placement of growing number of points on an interval under initial limitation of the number of points per group. The limitation is connected to the initial absence in protist an infrastructure which is need for the growing number of cyanobacteria. It was demonstrated that initially in course of increasing total points number the parameter $\mu$ decreases from $1.0$ to $0.25$ under the fixed number of points per group and then increases to $1.0$ under the fixed number of groups. This gives an initial braking (slowdown) of growth of protoplant's size (a characteristic geometrical dimension of set of points) and then exponential growth after deleting limitation of point number per group in evolution's course of host endosymbiosis similarly to higher plants. Morphological analogy of situations of begin of plant embryogenesis and begin of seed germination with the situation described by the model of protoplant appearance is discussed.

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