Mathematical modeling of the conservation of populations

The system of difference equations describing the process of industrial fish catching while their abundance is maintained is proposed. Population size changing and, consequently, the volume of catch are predicted on the basis of this model study. The impact on the model of the parameters responsible for catch rate and factors that characterize the population growth rate is analyzed taking into account the terms of the equation describing the increase in the population size at the expense of fish farms. The proposed model and the results, in particular, can be used to solve problems of the size reducing of population of the rare breed fish and disappearance of valuable species of fish such as sturgeon.