Multifractal analysis of the species structure of small-mammal communities of the Volga-Ural paleobiocenosis

Abstract

The late Quaternary evolution of the Volga‐Ural paleobiocenosis has been used as an example to demonstrate the possibility of applying multifractal analysis to the species structure of fossil small-mammal communities. No logical contradictions have been found between the ecological specificities of small-mammal communities, as considered in temporal terms, determined by traditional methods and by means of multifractal formalism. The results have demonstrated that multifractal formalism methodologically based on the self-similarity principle may be regarded as an effective tool of paleoactualism in analysis of paleoecological data. Earlier, we demonstrated [3, 4, 7] that the species structure of biotic communities of modern organisms forming terrestrial and aquatic ecosystems, including zooplankton, zoobenthos, insects, and small mammals, may be satisfactorily described in terms of fractal geometry [9, 11]. The notion of self-similarity as an immanent characteristic of a biocenosis is the methodological basis of the fractal theory of community structure that we are developing. Indeed, biological systems are open, strongly nonequilibrium systems whose existence and evolution are determined by a flow of energy resources from the environment. The resultant systems exhibit spatiotemporal scaling (or self-similarity) within a wide range of parameters. This is one of fundamental types of symmetry of the physical world and a morphogenetic factor of the Universe. All of this applies to biotic communities as well. We have demonstrated that multifractal formalism can be adapted to describe the species structure of recent communities, and the multifractal singularity spectrum of the species structure of a community is an adequate generalize geometric image of the community, which cannot be