Multifractality in ecological monitoring

In this paper we introduce the concept of multifractality at the problem of ecological monitoring and species diversity estimation. Ecological communities can be considered as an open and strongly nonequilibrium systems, that experience an external driving. The process of resource consumption and resource allocation in communities reflects their complex internal structure. The structure is characterized by number of species, population, links between species and extent of domination. In experiment, we deal with relative frequencies or specific numbers of individuals in species that we find in a sample. We consider every species as a separate box that contain an arbitrary number of individuals and apply box-counting method for relative frequencies calculation. We find that box number or number of species as a function of sample population follows power law when population increases and, consequently, species distribution may be considered as a fractal set. To estimate species diversity one generally uses well-known diversity indexes, each of which simply enters a measure in space of relative frequencies. We tender multifractal generalization of this routine. An example from aquatic ecology is considered.