Population Dynamics: Mathematical Modeling and Reality

Abstract

Application of mathematical modeling for analysis of natural phenomena relies on model reduction techniques, which inevitably raises the question of whether the results of simulation reflect real processes. This work analyzes problems that arise when the results obtained by mathematical modeling of population processes are compared to data collected by monitoring of natural ecosystems. The source of these problems is that the type of dependencies between variables that describe the population dynamics, as well as the choice of numerical values assigned to the parameters of the mathematical model, are often impossible to justify, even based on the monitoring data from a particular ecosystem. This paper proposes an approach to mathematical modeling that would take the impact of the entire complex of biotic and abiotic factors on the population dynamics into account. Its central feature is consideration of ecosystem monitoring data and incorporating them directly into mathematical models of population dynamics. This approach would make it possible, in particular, to evaluate the extent to which individual environmental factors influence both the variations in population abundance recorded during monitoring and those characteristics of population processes that are not directly measured during monitoring, but are obtained by mathematical modeling.