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Hierarchical Scale-Free Representation of Biological Realm—Its Origin and Evolution

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Biosphere Origin and Evolution

Abstract

In this work we develop the concept of biological referents to analyze the origin of complexity of biological systems. The concept, as we demonstrate, can be formalized by classes of the objects which constitute hierarchic scale-free patterning at different levels of biological complexity. By this reason, ultrametric relationships between these classes are assumed to be relevant to the referent representation. To explore this idea, we realize particular formalization of the referent concept including construction of objects and classes, construction of ultrametric space of classes, and description of the ultrametric space by a field of p-adic numbers. We discuss how a notation “evolution” can be introduced through ultrametric formalism. An example of ultrametric evolutionary equations is presented. Finally, we demonstrate that different aspects of the origin and evolution of the Biosphere (such as macroevolution and development) being verified in the frame of the referent concept acquire new contours and interpretations.

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Authors and Affiliations

  1. Far Eastern Branch, Institute of Biology and Soil Science Russian Academy of Sciences, Vladivostok, Russia

    Zhuravlev Yu.N. & Avetisov V.A.

Authors
  1. Zhuravlev Yu.N.
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  2. Avetisov V.A.
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Editor information

Editors and Affiliations

  1. Inst. Geology, Mineralogy and Geophysics, Institute of Geology and Mineralogy, 3 Pr.Koptyuga Novosibirsk, 630090 Novosibrisk, Russia

    Nikolay Dobretsov

  2. Institute of Cytology and Genetics, 17 Lavrenteva Prospekt Novosibirsk, 630090,Novosibirsk, Russia

    Nikolay Kolchanov

  3. Paleontological Institute of the Russian Academy of Sciences, 123 Profsoyuznaya, Moskva 117647, Moscow, Russia

    Alexey Rozanov

  4. Inst. Microbiology Winogradsky Institute of Microbiology of the Russian Academy of Sciences, 7/2 Prospekt 60 Let, Oktyabrya Moskva 117312, Moscow, Russia

    Georgy Zavarzin

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Yu.N., Z., V.A., A. (2008). Hierarchical Scale-Free Representation of Biological Realm—Its Origin and Evolution. In: Dobretsov, N., Kolchanov, N., Rozanov, A., Zavarzin, G. (eds) Biosphere Origin and Evolution. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-68656-1_5

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