[Long-period endogenous oscillations in fish population size: mathematical modeling].

We present a mathematical model of an aquatic community, where the size-and-age structure of hydrobiont populations is taken into account and the corresponding trophic interactions between zooplankton, peaceful fish and predatory fish are described. We show that the interactions between separate components of the aquatic community can lead to long-period oscillations in fish population size. The period of these oscillations is of the order of dozen years. With the use of the model we show also that an increase in the zooplankton growth rate can be followed by a set of the fish population dynamical bifurcations: stationary states --> regular oscillations --> quasicycles --> the dynamical chaos.

[The impact of population dynamics on Y-chromosome microsatellite Polymorphism. Mathematical modeling].

In this article, we use mathematical modeling to study the impact of population dynamics on Y-chromosome STR-polymorphism accumulation in two independently evolving populations, namely, on the changes in genetic distance among the populations. Using two definitions of the genetic distance: (deltamu)2 and ASD, we carry out comparative research on the genetic distance changes and show that in contrast to (deltamu)2, ASD is characterized by a near-linear dependence on time. As the populations undergo oscillations, ASD is shown to be smaller than that in stationary populations. The linear dependence of ASD on time is shown to break down in relatively scanty stationary populations.

[The analysis of commercial fish population size oscillations in Lake Peipus].

With the use of recurrence plots, we show that the irregular oscillations in time, which commercial fish populations in Lake Peipus undergo, are deterministic.

[The impact of the high dose-refuge strategy on the Bt-crop yield. Mathematical simulations].

A mathematical model is presented, which describes interactions between Bt-plants and pests in terms of the plant growth rate, plant annual reseeding, consumption of plant biomass by pests, the action of Bt toxins, and the emergence of Bt-resistant insects. It has been shown that the migration of Bt-susceptible insects affects the Bt-crop yield dynamics and provides the exclusion of Bt-resistant pests if the migration exceeds the threshold value.

[Mathematical model of invasion of mysids (Mysidacea) into the Naroch Lake system].

We present a mathematical model of the invasion of mysid into the Naroch Lake system. The model is parameterized with the use of field observation data. We show that the mysid invasion can lead to an increase in the time-averaged fish population size, and to a decrease in the time-averaged rotifer population size.

[Mathematical modeling of the spatial distribution of the pollen produced by genetically modified crops].

We represent and analyze the results of mathematical simulation of pollen dispersion from the origin, a field sowed by genetically modified plants. Factors responsible for the genetic isolation of such fields are discussed.

[Research of the Bt crop biomass dynamics upon the invasion of Bt-resistant pests. A mathematical model].

The results of simulations of some consequences of the invasion of Bt-resistant pests into an agricultural ecosystem containing a Bt crop are presented. It is shown that the invasion of Bt-resistant pests leads to changes in the plant biomass dynamics, a decrease in the Bt crop production, and the deterioration of the predictability of the Bt crop production. We show that the parameter values at which the badly predictable Bt crop production takes place, occupy a minor area in the model parameter space. The size of the area depends on the insect reproduction period and the duration of the growing season.

[A conceptual mathematical model of aquatic communities in lakes Naroch and Myastro (Belarus)].

A conceptual mathematical model of fish and zooplankton (rotifer) populations inhabiting the lakes Naroch and Myastro has been developed and studied. The parametrization of the model was carried out having regard to the field observation data. The population dynamics was simulated taking into account that the lakes Naroch and Myastro are coupled with each other by a channel. It was shown that both the population coupling and trophic interactions result in regular and irregular oscillations of the population size.

[Invasion of an intermediate predator: the dynamics of fish populations in the mathematical model of a trophic chain (as applied to the Syamozero lake)].

We present a mathematical model of the dynamics of a spatially heterogeneous predator-prey population system. A prototype of the model system is the Syamozero lake fish community. We study the impact of the invader, an intermediate predator, on the dynamics of the fish community. We show that the invasion can lead to the appearance of chaotic oscillations in the population density. We show also that different dynamical regimes resulting from the invasion, i.e., stationary, non-chaotic oscillatory and chaotic ones, can coexist. The "choice" of a specific regime therewith depends on the initial invader density. Our analysis of solutions of the mathematical models shows that the successful invasion of the alien species takes place solely in the absence of the competition between the invaders and the native species.

[Circulation of excitation waves in a model medium containing unexcitable obstacles].

The 3D structure of the heart tissue of Wistar rats from different age groups has been reconstructed by light microscopy of consecutive series of semithin sections. At the histological resolution level, connective tissue segments in the myocardium of aged (18 months) animals were found, while in the myocardium of young (2 months) animals no connective tissue segments were observed. A mathematical model and the results of the 3D reconstruction were used to simulate the formation of excitation wave circulation in the myocardium. The values of conductivity and the excitability threshold, and the pulse frequency rates were found at which the disturbances of the heart rhythm resulting from the excitation wave circulation are predicted by the mathematical modeling.

[Spatial model of development of resistance to transgenic insecticidal crop in a pest as applied to the European corn borer].

A mathematical model of the development of resistance to transgenic Bt-crop in insect-pest populations as applied to the European corn borer has been constructed. The model represents a system of differential equations in special derivatives of the reaction-diffusion type. Local interactions of three competing pest genotypes formed by the allele of Bt-resistance and allele of susceptibility, are described by the same relations as in the Kostitsyn model, and the spread of insects is modelled as diffusion. The model was used to estimate the influence of the pest on the efficiency of the "high dose-refuge" strategy, which is intended for the suppression of development of Bt-resistance in pest populations. It was shown that formal integration of the Fisher-Haldane-Wright model and the diffusion term cannot adequately describe the development of Bt-resistance in a spatially heterogeneous pest population. A further development of the model is discussed.

[Population dynamics: limits of predictability].

Problems pertaining to the complex character of ecological system dynamics are discussed. Examples of the complex dynamics of plankton populations in a heterogeneous environment and agricultural ecosystems under invasion of pests resistant to Bt toxins produced by genetically modified insecticidal crops are given.

[A conceptual model of the dynamics of the Syamozero lake community].

We have developed a conceptual mathematical model of the dynamics of a spatially heterogeneous population system, the prototype of which is the Syamozero lake fish community. Based on the analysis of solutions of the model, we show that interrelations between prey and predator populations in two neighboring habitats (pelagic and offshore zones) can lead to both undamped oscillations and stationary values of the population size. The population density was found to be close to the values oblained in the course of long-term observations of the biota of the Syamozero lake. Besides, we showed that the transition to the stationary states can be accompanied by long-term (dozens and hundreds of years) damped oscillations of the prey and predator population size. In natural waters, long-term transition periods can prevent the attainment of stationary regimes of fish community functioning.

[Evolution of rotifer population dynamics in a heterogeneous habitat: mathematical modeling].

We present the results of mathematical modeling of a rotifer species inhabiting two coupled habitats with different environmental conditions. We use the modified Consensus model and show that the exchange between the habitats can lead to chaotization of originally regular plankton dynamics and synchronization of plankton biomass oscillations. As a result, the invasion of a chaotic regime takes place.

[The rotation of autowaves as a result of their penetration through a system of unexcitable obstacles. A mechanism of arrhythmias associated with aging].

The dependence of the frequency of occurrence of excitation vortices rotating around unexcitable obstacles on the size and the number of the obstacles and also on the medium excitation threshold was studied. It was shown that the vortex formation takes place in a wide range of the model parameter values. The assumption was formulated that the mechanism of formation of excitation vortices under study underlies the increase in the heart arrhythmias associated with aging.

[Effect of the rate of phytoplankton growth on the spaced-time dynamics of plankton communities in an homogeneous environment]. / Vliianie skorosti rosta fitoplanktona na prostranstvenno-vremennuiu dinamiku planktonnykh soobshchestv v neodnorodnoi srede obitaniia.

We use a conceptual mathematical reaction-diffusion model to investigate the mechanisms of spatial structure formation and complex temporal dynamics of plankton in a heterogeneous environment. We take into account basic trophic interactions, namely, "prey-predator" interactions between phytoplankton, zooplankton, and fish in upper layers of natural waters. We consider plankton as a passive contaminant in turbulent waters. We show that plankton structure formation can result from the difference in phytoplankton growth rate in neighboring habitats. Phytoplankton and zooplankton biomass is shown to undergo both regular and chaotic oscillations. The fish predation rate substantially affects the spatial and temporal dynamics of plankton in a heterogeneous environment.

[The study of autowave mechanisms of electrocardiogram variability during high frequency arrhythmias: mathematical modeling data]. / Issledovanie avtovolnovykh mekhanizmov variabel'nosti élektrokardiogramm vo vremia vysokochastotnykh aritmii: rezul'tat matematicheskogo modelirovaniia.

High-frequency cardiac arrhythmias are very dangerous, as they quite often lead to sudden death. These high-frequency arrhythmias are frequently produced by rotating autowaves. In the given work, the dynamics of a rotating three-dimensional excitation scroll wave and the influence of this dynamics on the variability of model electrocardiograms (ECGs) were simulated with the use of the Aliev--Panfilov model for both homogeneous and heterogeneous excitable media. Model ECGs were obtained by summing up local membrane potentials, while ECG variability was estimated numerically through the normalized variability analysis. In the homogeneous medium, the stability of the scroll wave to its filament perturbations was shown to be dependent both on the excitability of the medium and tension of the filament, while in the heterogeneous medium, the scroll was shown to be unstable. It was shown that the scroll wave dynamics affects essentially the variability of the model ECGs, and the ECG variability increases as the excitation threshold value grows. It was found that, at some parameters of the excitable medium, the variability of ECGs in the homogeneous medium is higher than in the heterogeneous medium.

[Learning and selection create new information]. / Obuchenie i otbor sozdaiut novuiu informatsiiu.

Comments on the article of A.V. Melkikh "Can the Organism Select New Valuable Information from Environment?" are given.

[Adaptive mutagenesis accelerates microorganism evolution only while competing for resources: mathematic modeling]. / Adaptivnyi mutagenez uskoriaet évoliutsiiu mikroorganizmov tol'ko pri konkurentsii za resursy: matematicheskoe modelirovanie.

Mathematical simulation of adaptive mutagenesis was carried out. The results obtained indicate that adaptive mutagenesis can play an essential role in the survival of microbial populations. We show that the competition for natural resources is a necessary factor of adaptive mutagenesis.

[Instability of a three-dimnsional linear vortex in a simple model of a heterogenous excitable medium]. / Neustoichivost' trekhmernogo svitka v prostoi modeli geterogennoi vozbudimoi sredy.

We studied the dynamics of three-dimensional linear vortex in a heterogeneous excitable medium. Using the Aliev-Panfilov model we showed that even a small heterogeneity in excitation threshold can lead to drastic deformations of the vortex filament and an instability in its behavior.