The object of the research is Atlantic salmon in the Ponoi River (Kola Peninsula, Russia). The river harbors one of the largest Atlantic salmon populations, which lives in a poorly accessible part of the region and is less affected by human activities. Earlier research of the brood stock structure, upstream and downstream migrations, distribution of juveniles in spawning and feeding grounds provide data to address some operational issues of fisheries regulation. Meanwhile, elaboration of a theoretical framework for the stock management is crucial both for conserving the existing stock and for augmenting its productivity, but cannot be accomplished without expertise on the population abundance dynamics. To this end, mathematical simulation was applied. Broadly used to study abundance dynamics and to streamline fisheries, the quantitative approach proved to be efficient. This was the first time when such a research was conducted for Atlantic salmon of the Ponoi River. The mathematical simulation model provides separate descriptions of the processes within a population and of random exterior effects, and it was used to study the dynamic properties of the population. Impacts of fisheries of varying intensity on the population’s behaviour were studied. The behaviour of the simulated population was found to have its own periodical component represented by harmonic sustained oscillations. An increase in the fisheries effort up to some best possible value results in oscillation damping, renders the system steady and leads to abundance growth to a maximum value, which occurs when 73 % of the brood stock is harvested. Overfishing (90 % harvest or more) entails the collapse of a population within several decades. Temperature during downstream migration and the first year at sea was found to be the most crucial environmental driver for the population. Simulation with different temperature modes proved that a decrease in temperature to the lower end of the potential range evens out the autooscillation, while an increase makes it more variable. Random changes in temperature bring some fuzzy fluctuations into the system. The simulation can be recommended for use in monitoring and prediction of Atlantic salmon abundance in the Ponoi River, and in managing fisheries.