Sustainable Management of a Renewable Fishery Resource with Depensation Dynamics from a Control Systems Perspective

Abstract

Human societies are exploiting natural renewable sources such as fisheries, forests, groundwater basins, rivers, and soil at an increasing intensity. Around the world, these resources are being managed by various institutions or governments. One of the challenges faced by institutions is to develop strategies and policies to effectively manage these renewable resources under social and ecological uncertainties, disturbances, policy implementation difficulties, and measurement errors. In this paper, a fishery is considered as an example and the problem of managing a fishery is approached from a control systems perspective. The justification behind this approach is due to the observation that the problem of managing a renewable resource can be posed as a control systems problem and that the discipline of control systems possesses tools and methods to deal with model uncertainties, external disturbances, measurement errors and implementation issues. For the fishery, a depensation type population dynamics model is considered. Depensatory models are used in social/ecological systems in order to model dynamics of certain species of fish populations. An optimal control strategy based on Pontryagin’s Maximum Principle is derived and its sustainability and robustness properties with respect to parametric uncertainties, measurement errors and disturbances are examined. Finally, a sub-optimal but more robust control strategy is proposed and its robustness properties are provided. The main objective of the paper is to show that a control systems engineering approach can be applied to a social-ecological problem and it can provide easy to implement management strategies, insight, and guidance into the management of renewable resources.