About the methods of biological resourse extraction, that provide the maximum average time benefit

Models of structured populations, consisting of individual species or divided in to age groups, are considered. In particular, it can be assumed that different types of fish are being harvested, between which there is a competition for food or habitats. The dynamics of the population, in the absence of exploitation, is given by a system of differential equations and at certain points of time, part of the resource is extracted from the population. Estimation of the average time benefit, which is equal to the limit of the average cost of the resource with an unlimited increase in the moments of withdrawal, is obtained. The method of resource extraction for the long-term collection mode is described, in which a certain part of the population is constantly preserved, which is necessary for its further recovery, and the maximum average time benefit is achieved. The results of the study are illustrated by examples of models of interaction between two types, such as competition and symbiosis.