Harvesting in seasonal environments. (English) Zbl 1066.92057

Xu, Cailin; Boyce, Mark S.; Daley, Daryl J.

J. Math. Biol. 50, No. 6, 663-682 (2005).

Summary: Most harvest theory is based on an assumption of a constant or stochastic environment, yet most populations experience some form of environmental seasonality. Assuming that a population follows logistic growth we investigate harvesting in seasonal environments, focusing on maximum annual yield (M.A.Y.) and population persistence under five commonly used harvest strategies. We show that the optimal strategy depends dramatically on the intrinsic growth rate of the population and the magnitude of seasonality. The ordered effectiveness of these alternative harvest strategies is given for different combinations of intrinsic growth rate and seasonality. Also, for piecewise continuous-time harvest strategies (i.e., open \(/\) closed harvest, and pulse harvest) harvest timing is of crucial importance to annual yield. Optimal timing for harvests coincides with maximal rate of decline in the seasonally fluctuating carrying capacity.
For large intrinsic growth rates and small environmental variability several strategies (i.e., constant exploitation rate, linear exploitation rate, and time-dependent harvest) are so effective that M.A.Y. is very close to maximum sustainable yield (M.S.Y.). M.A.Y. of pulse harvest can be even larger than M.S.Y. because in seasonal environments population size varies substantially during the course of the year and how it varies relative to the carrying capacity is what determines the value relative to the optimal harvest rate. However, for populations with small intrinsic growth rate but subject to large seasonality none of these strategies is particularly effective with M.A.Y. much lower than M.S.Y. Finding an optimal harvest strategy for this case and to explore harvesting in populations that follow other growth models (e.g., involving predation or age structure) will be an interesting but challenging problem.

MSC:

92D40	Ecology
34C60	Qualitative investigation and simulation of ordinary differential equation models
91B76	Environmental economics (natural resource models, harvesting, pollution, etc.)
34C25	Periodic solutions to ordinary differential equations
49N90	Applications of optimal control and differential games

Keywords:

Differential equations; Population dynamics; Environmental seasonality; Maximum annual yield; Population persistence; Wildlife management

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