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We study the influence of fishery on a structured fish population under random changes of habitat conditions. The population parameters correspond to dominant pelagic fish species of Far-Eastern seas of the northwestern part of the Pacific Ocean (pollack, herring, sardine). Similar species inhabit various parts of the Word Ocean. The species body size distribution was chosen as a main population feature. This characteristic is easy to measure and adequately defines main specimen qualities such as age, maturity and other morphological and physiological peculiarities. Environmental fluctuations have a great influence on the individuals in early stages of development and have little influence on the vital activity of mature individuals. The fishery revenue was chosen as an optimality criterion. The main control characteristic is fishing effort. We have chosen quadratic dependence of fishing revenue on the fishing effort according to accepted economic ideas stating that the expenses grow with the production volume. The model study shows that the population structure ensures the increased population stability. The growth and drop out of the individuals’ due to natural mortality smoothens the oscillations of population density arising from the strong influence of the fluctuations of environment on young individuals. The smoothing part is played by diffusion component of the growth processes. The fishery in its turn smooths the fluctuations (including random fluctuations) of the environment and has a substantial impact upon the abundance of fry and the subsequent population dynamics. The optimal time-dependent fishing effort strategy was compared to stationary fishing effort strategy. It is shown that in the case of quickly changing habitat conditions and stochastic dynamics of population replenishment there exists a stationary fishing effort having approximately the same efficiency as an optimal time-dependent fishing effort. This means that a constant or weakly varying fishing effort can be very efficient strategy in terms of revenue.

Based on the time-discrete model, we study the effect of selective proportional harvesting on the population dynamics with age and sex structure. When constructing the model, we assume that the population birth rate depends on the ratio of the sexes and the number of formed pairs. The regulation of population growth is carried out by limiting the juvenile’s survival when the survival of immature individuals decreases with an increase in the numbers of sex and age classes. We consider cases where the harvest is carried out only from a younger age class or from a group of mature females or males. We find that the harvesting of males or females at the optimal level is responsible for changing the ratio of females to males (taking into account the average size of the harem). We show that the maximum number of harvested males is achieved either at such a harvest rate when their excess number is withdrawn and the balance of sexes is established or at such an optimal catch quota at which the sex ratio is shifted towards breeding females. Optimal female harvesting, in which the highest number of them are taken, either maintains a preexisting shortage of adult males or leads to an excess of males or the fixing of a sex balance. We find that, depending on the population parameters for all considered harvesting strategies, the hydra effect can observe, i. e., the equilibrium size of the exploited sex and age-specific group (after reproduction) can increase with the growth of harvesting intensity. The selective harvesting, due to which the hydra effect occurs, simultaneously leads to an increase remaining population size and the number of harvested individuals. At the same time, the size of the exploited group after reproduction can become even more than without exploitation. Equilibrium harvesting with the optimal harvest rate that maximizes yield leads to a population size decrease. The effect of hydra is at lower values of the catch quota than the optimal harvest rate. At the same time, the consequence of the hydra effect may be a higher abundance of the age-sex group under optimal exploitation compared to the level observed in the absence of harvesting.