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.

A mathematical model was constructed to describe the evolution of resistance to the Bacillus thuringiensis toxin (Bt) in an insect pest (European corn borer) population on a transgenic crop (Bt corn). The model comprises a set of partial differential equations of the reaction-diffusion type; local interactions of three competing pest genotypes formed by alleles of Bt resistance and susceptibility are described as in the Kostitzin model, and the spread of insects is modeled as diffusion. The model was used to evaluate the influence of pest characteristics on the efficacy of the high-dose/refuge strategy aiming to prevent or delay the spread of Bt resistance in pest populations. It was shown, by contrast, that a model based on Fisher-Haldane-Wright equations and formally incorporating a diffusion term cannot adequately describe the evolution of Bt resistance in a spatially inhomogeneous pest population. Further development of the proposed demo-genetic model is discussed.

We present the results of an analysis of the long-term chlorophyll a dynamics in the Naroch lakes. It was shown that an increase in nutrient load in the 1970s resulted in progressive eutrophication of the Naroch lakes. Then, starting from the mid-1980s, the water transparency began to increase and the concentration of phosphorus and nitrogen began to decrease due to the implementation of an environmental improvement program. In the 1980s, the Naroch lakes experienced an invasion by the zebra mussel (Dreissena polymorpha Pallas). Our analysis showed that the responses of all three lakes to the intensive nutrient load and a further decrease in the nutrient concentration as a result of the environmental-protection measures are correlated. At the same time, the invasion of the zebra mussel Dreissena polymorpha, which causes significant transformation of ecosystem processes, led to divergence in the chlorophyll dynamics; this was manifested as a drastic decline in the correlation between the fluctuations in the chlorophyll concentration in each lake.

The ecosystem of the Naroch Lakes (Belarus) includes three water bodies, Lake Batorino, Lake Myastro and Lake Naroch. These lakes have a common catchment area. At the end of the 80 s, the ecosystem of the Naroch Lakes underwent a transformation, during which the nutrient load on the catchment area decreased, and the concentration of phosphorus as a limiting factor in these water bodies decreased significantly. At the same time, the Naroch Lakes were exposed to zebra mussel (Dreissena polymorpha Pallas) invasion. In the mid-90 s, the biological and hydrochemical characteristics of the ecosystem of the Naroch Lakes stabilized. We show here that complex processes associated with the transformation of the lake ecosystem and affecting both trophic interactions in the Naroch Lakes and the influence of environmental factors on them can be represented using a single parameter, the phase-locking index, PLI. In this case, a statistically significant numerical value of PLI characterizes the phase synchronization of two processes, oscillations of the concentration of total phosphorus, TP, and oscillations of the concentration of chlorophyll, Chl. We show that the phase synchronization of these processes occurs only after the stabilization of the ecosystem of the Naroch Lakes. In the period preceding the transformation of the lake ecosystem, there was no synchronization. Numerical evaluation of PLI as a holistic parameter allows us to characterize the transformation of the lake ecosystem as a whole without resorting to study of complex interactions of various factors involved in this transformation.