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

  • Zhuravlev Yu.N.
  • Avetisov V.A.


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.


Species Concept Primary Element Biological Complexity Sign Carrier Ultrametric Space 
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  1. Alexander, S. (1920) Space, Time, and Deity, vol. 2. Macmillan, London (cited by Korn 2005).Google Scholar
  2. Andersson, S.G., Karlberg, O., Canback, B. and Kurland, C.G. (2003) On the origin of mitochondria: a genomics perspective. Phil. Trans. R. Soc. Lond. B 358, 165–177.CrossRefGoogle Scholar
  3. Arnold, M.L. (1997) Natural Hybridization and Evolution. Oxford University Press, New York.Google Scholar
  4. Avetisov, V.A. (2004) Origin of biological homochirality: in search of evolutional dynamics. In: G. Pályi, C. Zucchi and L. Calglioty (Eds), Progress in Biological Chirality. Elsevier, Amsterdam, pp. 3–12.Google Scholar
  5. Avetisov, V.A., Bikulov, A.H., Kozyrev S.V. and Osipov, V.A. (2002) p-Adic models of ultrametric diffusion constrained by hierarchical energy landscapes. J. Phys. A: Math. Gen. 35, 177–189.CrossRefGoogle Scholar
  6. Avetisov, V.A., Bikulov, A.H. and Osipov, V.A. (2003) p-Adic description of characteristic relaxation in complex systems. J. Phys. A: Math. Gen. 36, 4239–4246.CrossRefGoogle Scholar
  7. Avetisov, V.A. and Zhuravlev Yu.N. (2007) An evolutionary interpretation of the p-adic ultrametric diffusion equation. Doklady Math. 75, 453–455.CrossRefGoogle Scholar
  8. Ayala, F.J. (2000) Debating Darwin. Biol. Phil. 15, 559–573.CrossRefGoogle Scholar
  9. Ayala, F.J. and Coluzzi, M. (2005) Chromosome speciation: humans, Drosophila, and mosquitoes. Proc. Natl Acad. Sci. 102 (Suppl. 1), 6535–6542.PubMedCrossRefGoogle Scholar
  10. Carroll, R.L. (2002) Evolution of the capacity to evolve. J. Evol. Biol. 15, 911–921.CrossRefGoogle Scholar
  11. Cavalier-Smith, T. (2004) Only six kingdoms of life. Proc. Roy. Soc. Lond. B 271, 1251–1262.CrossRefGoogle Scholar
  12. Changizi, M.A., McDannald, M.A. and Widders, D. (2002) Scaling of differentiation in networks: nervous systems, organisms, ant colonies, ecosystems, businesses, universities, cities, electronic circuits, and Legos. J. Theor. Biol. 218, 215–237.PubMedCrossRefGoogle Scholar
  13. Claverie, J.-M. (2001) What if there are only 30 000 human genes? Science 291, 1255–1257.PubMedCrossRefGoogle Scholar
  14. Drake, L.A., Choi1, K.-H., Ruiz, G.M. and Dobbs, F.C. (2001) Global redistribution of bacterioplankton and virioplankton communities. Biol. Invasions 3, 193–199.CrossRefGoogle Scholar
  15. Dupre, J. (2002) Hidden treasure in the Linnean hierarchy. Biology and Philosophy 17, 423–433.CrossRefGoogle Scholar
  16. Dobzhansky, T. (1937) Genetics and the Origin of Species. Columbia University Press, New York.Google Scholar
  17. Eldredge, N. and Salthe, S.N. (1984) Hierarchy and evolution. Oxford Surv. Evol. Biol. 1, 184–208.Google Scholar
  18. Ereshefsky, M. (2001) The poverty of the Linnaean hierarchy: a phylosophical study of biological taxonomy. Cambridge University Press, New York.Google Scholar
  19. Erwin, D.H. (2000) Macroevolution is more than repeated rounds of microevolution. Evol. Dev. 2, 78–84.PubMedCrossRefGoogle Scholar
  20. Gould, S.J. (2002) The structure of evolutionary theory. Harvard University Press, Cambridge.Google Scholar
  21. Haken, H. (1988) Information and Self-organization. A macroscopic Approach to Complex Systems. Second enlarged edition. URSS, Moskwa, Russian translation, 2000.Google Scholar
  22. Harrison, R.G. (1990) Hybrid zones: windows on evolutionary process. Oxford Surv. Evol. Biol. 7, 69–128.Google Scholar
  23. Hatcher, B.G. (1997) Coral reef ecosystems: how much greater is the whole than the sum of the parts? Coral Reefs 16(Suppl.), S77–S91.CrossRefGoogle Scholar
  24. Hey, J. (2001) The mind of the species problem. Trends Ecol. Evol. 16, 326–329.PubMedCrossRefGoogle Scholar
  25. Honma, N., Abe, K., Sato, M. and Takeda, H. (1998) Adaptive evolution of holon networks by an autonomous decentralized method. Appl. Math. Comp.. 91, 43–61.CrossRefGoogle Scholar
  26. Hutchinson, C.A., Peterson, S.N., Gill, S.R., Cline, R.T., White, O., Fraser, C.M., Smith, H.O. and Venter, J.C. (1999) Global transposon mutagenesis and a minimal mycoplasma genome. Science 286, 2165–2169.CrossRefGoogle Scholar
  27. Koestler, A. (1967) The Ghost in the Machine. Arkana. The Penguin Group, London.Google Scholar
  28. Korn, R.W. (2002) Biological hierarchies, their birth, death and evolution by natural selection. Biol. Phil. 17, 199–221.CrossRefGoogle Scholar
  29. Korn, R.W. (2005) The Emergence Principle in Biological Hierarchies. Biol. Phil. 20, 137–151.CrossRefGoogle Scholar
  30. Kozo-Poljansky, B.M. (1925) New Principle in Biology. Studies on the Symbiogenetic Theory. Voronesh (in Russian).Google Scholar
  31. Kurland, C.G., Collins, L.J. and Penny, D. (2006) Genomics and the irreducible nature of eukaryote cells. Science 312, 1011–1014.PubMedCrossRefGoogle Scholar
  32. Mayden, R.L. (1997) A hierarchy of species concepts: the denouement in the saga of the species problem. In: M.F. Claridge et al. (Eds), Species: the Units of Biodiversity. Chapman & Hall, London, pp. 381–424.Google Scholar
  33. Mayr, E. (1982) The Growth of the Biological Thought. Harvard University Press, Belknap.Google Scholar
  34. Mayr, E. and Provine, W.B. (1980) The Evolutionary Synthesis. Harvard University Press, Cambridge.Google Scholar
  35. McShea, D.W. (2001) The minor transitions in hierarchical evolution and the question of a directional bias. J. Evol. Biol. 14, 502–518.CrossRefGoogle Scholar
  36. McShea, D.W. (2004) A Revised Darwinism. Biol. Phil. 19, 45–53.CrossRefGoogle Scholar
  37. McShea, D.W. and Changizi, M.A. (2003) Three puzzles in hierarchical evolution. Integr. Comp. Biol. 43, 74–81.CrossRefGoogle Scholar
  38. Michod, R.E. (1997) Cooperation and conflict in the evolution of individuality. 1. Multilevel selection of the organism. Am. Naturalist 149, 607–645.Google Scholar
  39. Michod, R.E. and Herron, M.D. (2006) Cooperation and conflict during evolutionary transitions in individuality. J. Evol. Biol. 19, 1406–1409.PubMedCrossRefGoogle Scholar
  40. Noda, T., Sagara, H., Yen, A., Takada, A., Kida, H., Cheng, R.H. and Kawaoka, Y. (2006) Architecture of ribonucleoprotein complexes in influenza A virus particles. Nature 439, 490–492.PubMedCrossRefGoogle Scholar
  41. Oltvai, Z.N. and Barabási, A.-L. (2002) Life's complexity pyramid. Science 298, 763–764.PubMedCrossRefGoogle Scholar
  42. Omelchenko, M.V., Makarova, K.S., Wolf, Y.I., Rogozin, I.B. and Koonin, E.V. (2003) Evolution of mosaic operons by horizontal gene transfer and gene displacement in situ. Genome Biol. 4, R55.PubMedCrossRefGoogle Scholar
  43. Pattee, H.H. (1970) The problem of biological hierarchy. In: C.H. Waddington (Ed.), Towards a Theoretical Biology, Edinburgh University Press, Edinburgh, Vol. 3, pp. 117–136.Google Scholar
  44. Pattee, H.H. (1995) Evolving self-reference: matter, symbols, and semantic closure. Comm. Cogn.-Artif. Intell. 12, 9–27.Google Scholar
  45. Poli, R. (2001) The basic problem of the theory of levels of reality. Axiomathes 12, 261–283.CrossRefGoogle Scholar
  46. Rivera, M.C. and Lake, J.A. (2004) The ring of life provides evidence for a genome fusion origin of eukaryotes. Nature 431, 152–155.PubMedCrossRefGoogle Scholar
  47. Rocha, L.M. (2001) Evolution with material symbol systems. Biosystems 60, 95–121.PubMedCrossRefGoogle Scholar
  48. Salthe, S.N. (2004) The spontaneous origin of new levels in a scalar hierarchy. Entropy 6, 327–324.CrossRefGoogle Scholar
  49. Santelices, B. (2004) Mosaicism and chimerism as components of intraorganismal genetic heterogeneity. J. Evol. Biol. 17, 1187–1188.PubMedCrossRefGoogle Scholar
  50. Schoof, H., Zaccaria, P., Gundlach, H., Lemcke, K., Rudd, S., Kolesov, G., Arnold, R., Mewes, H.W. and Mayer, K.F. (2002) MIPS Arabidopsis thaliana Database (MAtDB): an integrated biological knowledge resource based on the first complete plant genome. Nucl. Acids Res. 30, 91–93.PubMedCrossRefGoogle Scholar
  51. Schwendener, S. (1869) Die Algentypen der Flechtengonidien. Basel.Google Scholar
  52. Simon, H.A. (1962) The architecture of complexity: Hierarchic Systems. Proc. Am. Phil. Soc. 106, 467–482.Google Scholar
  53. Simonson, A.B., Servin, J.A., Skophammer, R.G., Herbold, C.W., Rivera, M.C. and Lake, J.A. (2005) Decoding the genomic tree of life. Proc. Natl Acad. Sci. 102(Suppl. 1), 6608–6613.PubMedCrossRefGoogle Scholar
  54. Sites, J.W. and Marshall, J.C. (2003) Delimiting species: a Renaissance issue in systematic biology. Trends Ecol. Evol. 18, 462–470.CrossRefGoogle Scholar
  55. Smith, J.M. and Szathmáry, E. (1995) The Major Transitions in Evolution. Oxford University Press, Oxford.Google Scholar
  56. Stebbins, G.L. (1950) Variation and Evolution in Plants. Columbia University Press, New York.Google Scholar
  57. Suhre, K., Audic, S. and Claverie, J.M. (2005) Mimivirus gene promoters exhibit an unprecedented conservation among all eukaryotes. Proc. Natl Acad. Sci. 102, 14689–14693.PubMedCrossRefGoogle Scholar
  58. Turchin, V. (1977) The Phenomenon of Science. A cybernetic approach to human evolution. Columbia University Press, New York. Russian translation, 1993.Google Scholar
  59. Valentine, J.W. (2000) Two genomic paths to the evolution of complexity in bodyplans. Paleobiology 26, 513–519.CrossRefGoogle Scholar
  60. Valentine, J.W. (2003) Architectures of biological complexity. Integr. Comp. Biol. 43, 99–103.CrossRefGoogle Scholar
  61. Valentine, J.W. and May, C.L. (1996) Hierarchies in biology and paleontology. Paleobiology 22, 23–33.Google Scholar
  62. Vorontsov, N.N. (1999) The Development of Evolution Idea in Biology. Progress-Traditsia-Press, Moscow.Google Scholar
  63. Woese, C. (1998) The universal ancestor. Proc. Natl Acad. Sci. 95, 6854–6859.PubMedCrossRefGoogle Scholar
  64. Woese, C.R. (2002) On the evolution of cells. Proc. Natl Acad. Sci. 99, 8742–8747.PubMedCrossRefGoogle Scholar
  65. Wommack, K.E. and Colwell, R.R. (2000) Virioplankton: viruses in aquatic ecosystems. Microbiol. Mol. Biol. Rev. 64, 69–114.PubMedCrossRefGoogle Scholar
  66. Wu, J. and David, J.L. (2002) A spatially explicit hierarchical approach to modeling complex ecological systems: theory and applications. Ecol. Modell. 153, 7–26.CrossRefGoogle Scholar
  67. Zimmer, C. (2006) Did DNA come from viruses? Science 312, 870.PubMedCrossRefGoogle Scholar
  68. Zhuravlev, Yu.N. (2002) Two rules of distribution of amino acids in the code table indicate chimeric nature of the genetic code. Dokl. Biochem. Biophys. 383, 85–87.PubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Zhuravlev Yu.N.
    • 1
  • Avetisov V.A.
    • 1
  1. 1.Far Eastern BranchInstitute of Biology and Soil Science Russian Academy of SciencesVladivostokRussia

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