[Scale invariance of biosystems: from embryo to community].

Abstract-Phenomena having the property of a scale invariance (that is, maintaining invariable structure in certain range of scales) are typical for biosystems of different levels. In this review, main manifestations of the scale-invariant phenomena at different levels of biological organization (including ontogenetic aspects) are stated, and the reasons of such wide distribution of fractal structures in biology are discussed. Almost all biological systems can be described in terms of synergetics as open nonequilibrium systems that exist due to substance and energy flow passing through them. The phenomenon of self-organization is typical for such dissipative systems; maintenance of energy flow requires the existence of complex structures that emerge spontaneously in the presence of the appropriate gradient. Critical systems, which form as a results of their activity scale-invariant structures (that are a kind of distribution channels), are optimal relative to the efficiency of substance and energy distribution. Thus, scale invariance of biological phenomena is a natural consequence of their dissipative nature.

[Multifractal analysis of the species structure of freshwater hydrobiocenoses].

The principles and methods of fractal analysis of the species structure of freshwater phytoplankton, zooplankton, and macrozoobenthos communities of plain water reservoirs and urban waterbodies are discussed. The theoretical foundation and experimental verification are provided for the authors' concept of self-similar (quasi-fractal) nature of the species structure of communities. According to this concept, the adequate mathematical image of species richness accumulation with growing sampling effort is quasi-monofractals, while the generalized geometric image of the species structure of the community is a multifractal spectrum.

[Fractal aspects of the taxic diversity].

Two approaches are suggested for describing taxic diversity as a fractal, or self-similar, object. One of them called "sampling approach" is based on necessity of taking into account the sampling process and on proceeding from the real ecological practice of exploration of the community structure. Verification of this approach is fulfilled using a multifractal analysis of the generic diversity of vascular plants of the National Park "Samarskaya Luka". The previously revealed regularities of multifractal spectrum of the species structure of communities are shown to be true to an extent for the generic structure, as well. The second approach called "topological" one is based on an abstract representation of the results of evolutionary process in form of phylogenetic tree characterized by a non-trivial topological structure. Approbations of this approach is fulfilled by analysis of topological structure of the taxonomic tree of the class Mammalia, our calculations indicating fractal properties of its graph. These results make it reasonable to suppose that the taxic diversity, as a replica of the real diversity of the fractally organized organic world, also possesses self-similar (fractal) structure.