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.
Similar content being viewed by others
References
Borisov, N.M., Vorob’ev, F.Yu., Gilyarov, A.M, Eskov, K.Yu., Zhuravlev, A.Yu., Markov, A.V., Oskol’skii, A.A., Petrov, P.N., and Shipunov, A.B., Evidence of Evolution, Markova, A.V., Ed., 2010. http://evolbiol.ru/evidence.htm.
Eskov, K.Yu.,. Udivitel’naya paleontologiya. Istoriya zemli i zhizni na nei (Amazing Paleontology: History of the Earth and Life on It), Moscow: Nauchn. Tsentr ENAS, 2008.
Feder, J., Fractals, New York: Plenum Press, 1988.
Galitskii, V.V., On the dynamics of altitudinal distribution of the biomass of a freely growing tree: Model analysis, Dokl. Akad. Nauk Biol. Sci., 2006, vol. 407, no. 4, pp. 564–566.
Galitskii, V.V., Model analysis of the dynamics of distant transportation of assimilators of a freely growing tree, Electr. Zh. Matem. Biol. Bioinform, 2009, vol. 4, no. 1, pp. 1–19. http://www.matbio.org/downloads/Galitskii2009(4_1).pdf.
Galitskii, V.V., Sectional tree structure: Model analysis of vertical distribution of biomass, Zh. Obshch. Biol., 2010, vol. 71, no. 1, pp. 19–29.
Galitskii, V.V., Biomass dynamics of higher-order tree branches: An analysis of the model, Biol. Bull. Rev., 2013a, vol. 3, no. 5, pp. 412–421.
Galitskii, V.V., On the Evolution of the Tree Shape with Reference to the Fractal Parameters, 2013b. http://vixra.org/ abs/1311.0105.
Galitskii, V.V., Evolutionary trajectories in the space of the parameters of the sectional model of green biomass of the spruce crown, in Materialy Chetvertoi natsional’noi nauchnoi konferentsii s mezhdunarodnym uchastiem “Matematicheskoe modelirovanie v ekologii, Pushchino, 18–22 maya, 2015 (Materials of the Fourth National Scientific Conference with International Participation on the Mathematical Modeling in Ecology, Pushchino, May 18–22, 2015), Pushchino: Inst. Fiz.–Khim. Biol. Pochvoved. Ross. Akad. Nauk, 2015, pp. 39–40. http://ecomodelling.ru/emm2015/ files/EcolMod2015_Proceedings.pdf.
Gamalei, Yu.V., The origin and localization of plant organelles, Fiziol. Rast., 2009, vol. 44, no. 1, pp. 115–137.
Hanson, M.R. and Kohler, R.H., A novel view of chloroplast structure, in Plant Physiology Online, 2006. http://5e.plantphys.net/article.php?ch=&id=122.
Kazimirov, N.I., El’niki Karelii (Spruce Forests of Karelia), Leningrad: Nauka, 1971.
Kramer, P.J. and Kozlovski, T.T., Physiology of Trees, New York: Academic Press, 1979.
Kursanov, A.L., Transport assimilyatov v rastenii (Transportation of Assimilators in Plants), Moscow: Nauka, 1976.
Margulis, L., Symbiosis in Cell Evolution, San Francisco: Freeman, W.H. and Co., 1981.
Margulis, L., Serial endosymbiotic theory (SET) and composite individuality: Transition from bacterial to eukaryotic genomes, Microbiol. Today, 2004, vol. 31, pp. 172–174.
Niklas, K.J., Morphological evolution through complex domains of fitness, in Tempo and Mode in Evolution: Genetics and Paleontology, 50 years after Simpson, Fitch, W.M. and Ayala, F.J., Eds., Washington, DC: Nat. Acad. Press, 1995, pp. 145–165.
Nystedt, B., Street, N.R., Wetterbom, A., Zuccolo, A., Lin, Y.C., Scofield, D.G., Vezzi, F., Delhomme, N., Giacomello, S., Alexeyenko, A., et al., The Norway spruce genome sequence and conifer genome evolution, Nature, 2013, vol. 497, pp. 579–584.
Poletaev, I.A., On the mathematical models of elementary processes in biogeocoenoses, Probl. Kibernet., 1966, vol. 16, pp. 171–190.
Serebryakova, T.I., Voronin, N.S., Elenevskii, A.G, Batygina, T.B., Shorina, R.I., and Savinykh, N.P., Botanika s osnovami fitotsenologii: Anatomiya i morfologiya rastenii (Botany with the Foundation of Phytocoenology: Plant Anatomy and Morphology), Moscow: Akademkniga, 2006.
Smith, D.M., A Fortran Package for floating-point multiple-precision arithmetic, ACM Trans. Math. Softw., 1991, vol. 17, pp. 273–283.
Tomlinson, P.B. and Haggett, B.A., Partial shoot reiteration in Wollemia nobilis (Araucariaceae) does not arise from “axillary meristems,” Ann. Bot., 2011, vol. 107, pp. 909–916.
Treskin, P.P., Patterns of morphogenesis of the skeletal part of the crown of adult spruce trees, in Struktura i produktivnost’ elovykh lesov yuzhnoi taigi (Structure and Productivity of the Spruce Forests of Southern Taiga), Leningrad: Nauka, 1973, pp. 222–240.
Tsel’niker, Yu.L., Structure of the spruce tree crown, Lesovedenie, 1994, no. 4, pp. 35–44.
Zavarzin, G.A., Ombrophiles—inhabitants of plains, Priroda (Moscow, Russ. Fed.), 2009, no. 6, pp. 3–14.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Galitskii, V.V. Initial growth deceleration as an immanent property of plants. Paleontol. J. 50, 1549–1559 (2016). https://doi.org/10.1134/S0031030116130050
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0031030116130050