Optimal sustainable harvesting of populations in random environments

TL;DR

This paper develops a framework for optimal sustainable harvesting of populations in stochastic environments, identifying unique threshold-based strategies that maximize long-term yield.

Contribution

It introduces a novel approach to maximize asymptotic harvesting yield in random environments, characterizing optimal strategies via threshold policies under weak assumptions.

Findings

Existence of a unique optimal harvesting threshold

Optimal strategies are of a local time push-type

Explicit solutions for specific population models, including logistic growth

Abstract

We study the optimal sustainable harvesting of a population that lives in a random environment. The novelty of our setting is that we maximize the asymptotic harvesting yield, both in an expected value and almost sure sense, for a large class of harvesting strategies and unstructured population models. We prove under relatively weak assumptions that there exists a unique optimal harvesting strategy characterized by an optimal threshold below which the population is maintained at all times by utilizing a local time push-type policy. We also discuss, through Abelian limits, how our results are related to the optimal harvesting strategies when one maximizes the expected cumulative present value of the harvesting yield and establish a simple connection and ordering between the values and optimal boundaries. Finally, we explicitly characterize the optimal harvesting strategies in two different cases, one of which is the celebrated stochastic Verhulst Pearl logistic model of population growth.