Dimitri Abzianidze

The monograph is not a systematic guide to mathematical ecology, but its purpose is to present how mathematical methods should be used in solving practical problems of environmental protection. A wide range of materials and a variety of examples make the work useful for scholars in the field, as well as specialists in economics and other fields who are interested in environmental protection.

With the intensive development of industry and population growth, environmental protection and the correct use of natural resources are of great importance. For a proper assessment, monitoring and management of the environmental situation, it is necessary to possess cartographic, environmental and other information about all its components, analyze this information and make the right decisions. There are various ways to solve this problem. The article provides a brief description of the method that we applied to assess the ecological state in one of the sections of the Mtkvari (Kura), in particular, the content of heavy metals in the waters of the Mtkvari (Kura) River in the Zagesi – Red Bridge section. The degree of anthropogenic impact was assessed by methods of mathematical modeling and modern technologies of the geographic information system. In the mathematical processing of information, a whole range of mathematical modeling tools were used - starting with mathematical statistics and ending with a complex model. The main functions of the geographic information system were also used: information organization, its processing, analysis, verification, visualization, and etc. As a result, thematic maps were created, that clearly show the degree of pollution of the river section, as well as the dynamics of changes in the concentration of heavy metals. This method can be used for environmental assessment of various objects. With its help, it is possible to carry out environmental monitoring simply and at low cost.

The author of this article considered the question of the effectiveness of the application of mathematical methods in the analysis of ecological processes in the fourth issue of this journal in 2018. In the proposed article, the authors continue to develop this idea, considering this time the human interaction with the environment. The main focus of the authors is on showing the important role of mathematics in human interaction with the environment. It is known that anthropogenic objects (populated points, various industrial enterprises, transport, etc.) as a result of their functioning have different effects on a person. For the study of these processes, there is a need to develop sciences to forecast the state of the environment and manage the processes of ecological balance in the geological environment, between nature and the technosphere (technological activity of people). In the study of these processes, mathematics is assigned a decisive role. However, the subject of research is invariably complicated, because the study requires the combination of interrelated processes of the most diverse nature. We notice that the organization of these studies is very difficult, because The study of human anthropogenic influence on the environment requires the integration of the activities of a number of specialists in various fields.

For the description and classification of geological objects and ecological systems, for the forecasting of its actions it’s needed to be developed appropriate mathematical models. The process of such model creation is quite difficult and consists of several stages. Data obtained from the observations or experiments are processed by using of statistical analysis. The development of computer technologies made it possible to apply new technologies in geology and ecology. The article describes usage of software package Excel's tools and a number of functions in the statistical analysis. Basic statistical indicators, such as the mean value, dispersion, asymmetry, square root dispersion, excess, etc. are located in one option, some other essential statistical characteristics can be defined by the corresponding functions (mainly by statistical and mathematical), which is described in the article in detail. 

To carry out ecological and geological studies, it is necessary to know the parameters of any object in the entire study area, but for various reasons it is impossible to take samples from some places and, therefore, we cannot determine the parameters of any variable in these places. In order to make a conclusion, a whole range of data is needed. In such a case, in order to determine the value of any variable at a point where it was practically not calculated, we use spatial interpolation.

The use of mathematical methods in ecology makes it possible to obtain results that cannot be achieved by other methods. It is desirable that ecologists would not only be able to use the mathematical apparatus, but would also be able to choose from numerous methods exactly the one that is necessary to achieve the goal, i.e. purposefully use it.

The assessment of the quality of the environment is carried out with the aim of establishing the maximum permissible impact norms, guaranteeing the ecological safety (EB) of the population, preserving the gene pool and ensuring the rational use and reproduction of natural resources in the conditions of sustainable development of economic activity.

The presented work gives a clear idea of how nowadays it is possible to apply filtering algorithms when solving practical tasks for environmental protection (OS). The assessment of the degree of pollution of the environment is carried out with the aim of establishing the maximum permissible impact norms, guaranteeing the ecological safety of the population, ensuring the rational use and reproduction of natural resources in the conditions of sustainable development of economic activity. At the same time, under the influence is generally understood anthropogenic activity connected with the realization of economic, recreational, cultural interests and introducing physical, chemical, biological changes to the natural environment.

The need to study ecological processes leads to the problem of using (or applying) the modern theory of decision making, which includes a developed mathematical apparatus. The main task of ecological research is to accumulate and analyze information about the quantitative nature of the relationship between living organisms and their environment in order to obtain results such as assessing the quality of the studied ecological systems (ES) (ultimately with the aim of the possibility of their use by humans), identifying factors of negative external impact, forecast of sustainability of ES.