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Within the framework of the active media concept, we develop a biophysical model of autowave self-organization which is treated as a hierarchy of active media in the evolution of the biosphere. We also propose a mathematical model of the autowave process of speciation in a flow of mutations for the three main taxonometric groups (prokaryotes, unicellular and multicellular eukaryotes) with a naturally determined lower boundary of living matter (the appearance of prokaryotes) and an open upper boundary for the formation of new species. It is shown that the fluctuation-bifurcation description of the evolution for the formation of new taxonometric groups as a trajectory of transformation of small fluctuations into giant ones adequately reflects the process of self-organization during the formation of taxa. The major concepts of biological evolution, conditions of hierarchy formation as a fundamental manifestation of self-organization and complexity in the evolution of biological systems are considered., (Copyright © 2020 Elsevier B.V. All rights reserved.)

A new approach has been proposed and developed: the selection of optimal variants in the evolutionary mutation flow is considered as an analogue of a percolation filter. Interaction of mutations in a series of generations and random processes of drift determine the collective behavior of nodes (individuals - carriers and converters of mutations) and bonds (mutations) in the space of percolation lattice. It is shown that the choice of the development trajectory at the population level depends on the spectrum of supporting and prohibiting mutations under the influence of conjugate deterministic and random factors. From the point of view of the fluctuation-bifurcation process, new concepts of the lower and upper thresholds of the percolation selection grid are defined in the hierarchical structure of speciation. The upper threshold determines the state of self-organized criticality, which, when overcome, leads to irreversible self-organization processes in the population caused by the accumulation of mutations., Competing Interests: Declaration of competing interest The authors declare no conflict of interest., (Copyright © 2020. Published by Elsevier B.V.)