Long-Run Average Sustainable Harvesting Policies: Near Optimality

TL;DR

This paper proposes near-optimal sustainable harvesting strategies for predator populations in stochastic predator-prey systems with jump disturbances, using diffusion approximations and ergodic control techniques.

Contribution

It introduces a novel approach to approximate jump-diffusion ecological models with controlled diffusions for near-optimal long-term harvesting policies.

Findings

Development of control policies with near-optimal long-run average performance

Establishment of diffusion approximation for jump ecological systems

New methods for handling ergodicity in population dynamics

Abstract

This paper develops near-optimal sustainable harvesting strategies for the predator in a predator-prey system. The objective function is of long-run average per unit time type. To date, ecological systems under environmental noise are usually modeled as stochastic differential equations driven by a Brownian motion. Recognizing that the formulation using a Brownian motion is only an idealization, in this paper, it is assumed that the environment is subject to disturbances characterized by a jump process with rapid jump rates. Under broad conditions, it is shown that the systems under consideration can be approximated by a controlled diffusion system. Based on the limit diffusion system, control policies of the original systems are constructed. Such an approach enables us to develop sustainable harvesting policies leading to near optimality. To treat the underlying problems, one of the main difficulties is due to the long-run average objective function. This in turn, requires the handling of a number of issues related to ergodicity. New approaches are developed to obtain the tightness of the underlying processes based on the population dynamic systems.