[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.

Relay charge transport in thunderclouds and its role in lightning initiation.

A new mechanism of charge transport inside a thundercloud is suggested and numerically investigated. The considered mechanism can be called "relay" because it is provided by a dynamical network of a relatively small amount of continuously decaying and arising conducting plasma formations. It manifests itself in two consecutive modes corresponding to pre-streamer and streamer/leader stages of thundercloud development. The first one is provided by dynamics of conducting ionic spots recently described by Iudin et al.1 that prepare conditions for initiation of positive streamers. The second mode relies on dynamical network of streamer/leader discharges and finally results in the formation of a compact well-conducting structure that bridges an area of strong electric field inside a thundercloud and can be associated with a lightning "seed". The effectiveness of relay charge transport strongly depends on the relative proportion of conductive elements (plasma formations) and drastically increases in the field-dependent case.

From decimeter-scale elevated ionic conductivity regions in the cloud to lightning initiation.

In this work, we represent the lightning initiation scenario as a sequence of two transitions of discharge activity to progressively larger spatial scales: the first one is from small-scale avalanches to intermediate-scale streamers; and the second one is from streamers to the lightning seed. We postulate the existence of ion production centers in the cloud, whose occurrence is caused by electric field bursts accompanying hydrometeor collisions (or near collisions) in the turbulent thundercloud environment. When a new ion production center is created inside (fully or partially) the residual ion spot left behind by a previously established center, there is a cumulative effect in the increasing of ion concentration. As a result, the essentially non-conducting thundercloud becomes seeded by elevated ion-conductivity regions (EICRs) with spatial extent of 0.1-1 m and a lifetime of 1-10 s. The electric field on the surface of an EICR (due to its conductivity being at least 4 orders of magnitude higher than ambient) is a factor of 3 or more higher than ambient. For a maximum ambient electric field of 100 kV/m typically measured in thunderclouds, such field enhancement is sufficient for initiation of positive streamers and their propagation over distances of the order of decimeters, and this will be happening naturally, without any external agents (e.g., superenergetic cosmic ray particles) or extraordinary in-cloud conditions, such as very high potential differences or very large hydrometeors. Provided that each EICR generates at least one streamer during its lifetime, the streamers will form a 3D network, some parts of which will contain hot channel segments created via the cumulative heating and/or thermal-ionizational instability. These hot channel segments will polarize, interact with each other, and cluster, forming longer conducting structures in the cloud. When the ambient potential difference bridged by such a conducting structure exceeds 3 MV, we assume that the lightning seed, capable of self-sustained bidirectional extension, is formed.

[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.

[Power-law species richness accumulation as manifestation of the fractal community structure].

Applications of the fractal to describing the species structure of communities are discussed. Fundamental notions of fractal geometry are explained in the first part. The problem of applying the concept of fractal to describe the spatial allocation of particular species and of community as a whole is reviewed in the second part. In the final part, the usage of the selfsimirity principle for analyzing community organization is substantiated, and evidence of the fractal structure of biocenoses is presented according to Whittaker's concept of alpha diversity. It is shown that community is characterized, as a fractal object, by scale invariance, by power function relationship between the number of structural elements of the community (individuals, populations, species) and the scale (sampling effort), and, finally, by fractional value of the power (fractal dimension). Power function is the formula the takes into account the share of rare species, or species represented by a single individual. providing for no saturation of the function f(x). This formula also does not contradict the A.P. Levich's "rule of ecological non-additivity" and, lastly, allows the application of fractal formalism to characterize the species structure of a community. It is concluded that the mathematical image of species richness is a monofractal, i.e., a set characterised by only one parameter, fractal dimension. Thus, the species structure of a community (as well as the pattern of its spatial allocation) displays self-similarity and is a fractal.

Fractal dynamics of electric discharges in a thundercloud.

We have investigated the fractal dynamics of intracloud microdischarges responsible for the formation of a so-called drainage system of electric charge transport inside a cloud volume. Microdischarges are related to the nonlinear stage of multiflow instability development, which leads to the generation of a small-scale intracloud electric structure. The latter is modeled by using a two-dimensional lattice of finite-state automata. The results of numerical simulations show that the developed drainage system belongs to the percolation-cluster family. We then point out the parameter region relevant to the proposed model, in which the thundercloud exhibits behavior corresponding to a regime of self-organized criticality. The initial development and statistical properties of dynamic conductive clusters are investigated, and a kinetic equation is introduced, which permits us to find state probabilities of electric cells and to estimate macroscopic parameters of the system.

[Structural and bioindicative aspects of fluctuated asymmetry of bilateral organisms]. / Strukturnye i bioindikatsionnye aspekty fluktuiruiushchei asimmetrii bilateral'no-simmetrichnykh organizmov.

We have proposed and validated a method for quantitative assessment of phenotypic diversity of natural populations. Method is based on the fluctuated asymmetry (FA) indices of bilateral organisms, and it is applicable for biondicative investigations. Convolution of functions was proposed to estimate the mean (population) value of FA complex of features. This function could be written as finit sum [formula: see text] where eta is power of sample invariance (symmetry) for m individuals (i = 1, m). Eta is characterized by n asymmetric characteristics (j = 1, n) for the left (L) and the right (R) sides of the body. We have validated applicability of generalized function of desirability [formula: see text] (where di is partial desirability function [0,1]) for cumulative characterization of environment quality with results of bioindicative investigations. The value of function coincides with the value of symmetry of indicating species in this case.