Optimal control of harvest timing in discrete population models

Abstract

Harvest plays an important role in management decisions, from fisheries to pest control. Discrete-time models enable us to explore the importance of timing of management decisions, including the order of events of particular actions. We derive novel mechanistic models featuring explicit within-season harvest timing and level. We explore optimization of within-season harvest level and timing through optimal control of these population models. With a fixed harvest level, harvest timing is taken as the control. Then both harvest timing and level are used as controls. We maximize an objective functional which includes management goals of maximizing yield, maximizing stock, and minimizing costs associated with both harvest intensity and harvest timing. While standard models with compensatory population dynamics predict it is best to harvest as early as possible in the season, we find instances where harvesting later in the season is optimal. Furthermore, we discover interesting oscillations in the population size, which would be unexpected in the model without time-varying controls. Recommendations for Resource Managers: This paper presents a novel model with variable harvest timing, which can be used as a tool to manage populations. While the usual population models identify harvesting at the beginning of the season as the best timing to maximize yield and/or population size, accounting for harvest costs related to timing can give rise to optimal harvest time at some intermediate point in the season. Controlling the level and the timing of harvest separately when maximizing the yield while minimizing the costs of management can lead to oscillation patterns in the population. Such oscillations would not be seen in these models without these time-varying controls. The level of harvest intensity in a population can affect the optimal time to implement the harvest.