[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 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.

[Resource availability and its role in development of invasion processes].

The state of biotic communities inhabiting different water bodies is analyzed aiming to determination of conditions facilitating development of biological invasions. Mass-balance and dynamic models are used to reveal the factors ensuring the invasion of zebra mussel, Dreissena polymorpha, in Naroch Lakes (Byelorussia), and smelt, Osmerus eperlanus, in Lake Syamozero (Karelia). The results obtained indicate that for invasions leading to trophic chain lengthening, the main factor of successful invasion is the availability of resources that are not utilized by aboriginal species. Highest chances for successful invasion belong to invading species feeding on those trophic groups which contribute to the most extent to forming of 'excess' (i.e., available for the invader) production. It is shown that establishment of an alien species in a native community appears to be possible only when total amount of such 'excess' production is higher then some threshold value. Under conditions of spatio-temporal environmental heterogeneity, the timing factor, which determines the exact moment of an alien species intrusion, becomes important as well.

[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.

[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.

[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.