Discrete Modeling Dynamical Systems That Determine the Role of Biodiversity in Different Regimes of Using Resources at Different Levels of Organization of Living Matter

Abstract

The paper aims at mathematical modeling of dynamic systems that determine the role of biodiversity in different modes of resource usage at different levels of the organization of living matter. As a measure of biodiversity, the number of different strategies of the performance of a biological system is used, which differ in ways of usage of the resources by this system. This measure can be supplemented, and in some cases, replaced by the degree of evenness of the intensity of different ways of using resources. As a result of modeling with use of a new class of mathematical models called Discrete Models of Dynamical Systems, the appearance of matrices representing the sets of these strategies corresponding to combinations of values of the system's parameters in columns, strategies observed for the regimes of maximum and limited usage of resources was analyzed. Using the case study related to a local fish population in a pond, it was shown that, in comparison with the regimes of limited use of resources, the regime of maximum usage distinguishes by a larger degree of evenness of the intensities of different ways of using resources by the system. Different size-age groups of the population play the role of resources. A similar result was obtained earlier for different regimes of the performance of the human cardiovascular system; in this case, the heart rate and blood pressure played the role of different ways of resources usage. The similarity of the results obtained for such different biological systems allows us to hope for the prospects of developing universal system approaches to the use of generalized biodiversity parameters for the diagnosis of the state of bioobjects, in particular, with the help of aerospace methods. The necessity of such methods is significantly increasing in the context of global climate change.