Optimization and spatial adaptation in a problem of a long-term harvesting of fish populations

The theoretical analysis of the problem of long-term optimization of harvesting of the population migrating in a reservoir is carried out. On the basis of dynamic programming method and theory of monotonous operators the main properties of optimum trade are established. The process of migration is set by a Markov matrix which changes from initial state to some final state under the influence of model processes of adaptation. The regularities of family of final matrixes of migration are discovered on the bases of computer experiments. The key role of the positive own vector of such matrixes which characterizes residence time of population on areas is shown.