Hierarchical scale-free representation of biological realm - Its 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. © Springer 2008.