Modeling of population and ecosystem dynamics under reserve conditions

Several examples from the field of mathematical theory about biological populations and communities are used to illustrate the applicability of a mathematical statement of problems related to nature reserves. A description of the dynamics of an isolated population under impacts of random environmental fluctuations allows an assessment to be made of the probability of a population decrease below an established level depending upon the carrying capacity of the environment for a given species. The trophic chains theory permits a lower estimate for the size of an area necessary to sustain the stable existence of a community with several trophic levels. The criterion of a sign stability of a community matrix verified by a sign directed graph corresponding to the matrix provides a convenient instrument for a tentative analysis of a community pattern in terms of its stability properties. The need for developing sufficiently complex simulation models of a protected ecosystem as an instrument for making decisions on reserve management is noted. A conclusion is drawn on the close relationship between the functions of biosphere reserves and the development of mathematical methods in ecology. There is no doubt that technological civilization has become one of the factors determining evolution in the biosphere, and the impact of this factor is such that we many speak about an anthropogenic evolution of the biosphere. Although the biosphere equilibrium has been disturbed we do not know to what extent this has occurred. Has the homeostasis of the biosphere been disturbed or not? Is the biosphere moving to any other equilibrium (where biological species Homo sapiens may not find an ecological niche), or are we facing only fluctuations in the equilibrium that existed in the pre-industrial era? Until now we cannot give answers to these questions. For this reason it is necessary to conserve samples of the main functional subsystems of the biosphere: typical landscapes, biogeocenoses, communities, and populations, as well as their species and genotype structures. In other words, the problem is to create and run banks of ecological and genetic information which already exist in certain forms and are called biosphere reserves, wildlife refuges, national parks, etc.