Dynamic modes of limited structured population under age specific harvest

The paper investigates influence of age specific harvest on the dynamics of populations with density dependent regulation of birth rate. We consider the population which by the end of each reproduction season, consists of two age groups: juveniles (immature individuals) and adults (participants of the reproduction process). A harvest rate growth of any age class is shown to give, as a rule, the dynamics stabilization. However, the system with harvesting demonstrates multimodality phenomenon as well as the population model without exploitation. The phenomenon means different dynamic modes are observed with the same values of the population parameters. As a result, some difficulties occur in predicting population dynamics, because harvest can lead to significant changes of population size due to shifting current population size from one attraction basin to another. To neutralize the oscillations emerged is necessary to change the current population size so that it falls into the attraction basin of the fixed point. The stability loss way of model with juvenile harvesting does not depend on the harvest rate value and is completely determined by the intensity of competitive relationships between the age classes. In the case of adult exploitation, a higher harvest rate can result in growing stationary population size. The changing the time of adult harvesting can lead to both the dynamics population stabilization and the occurrence of fluctuations. Exploitation before the reproduction season allows to have more yield than after reproduction season because mature age group size is higher. Conditions when the age specific harvest gives the maximum sustainable yield are considered.