Viable harvest of monotone bioeconomic models

TL;DR

This paper explores how monotonicity properties in discrete-time bioeconomic models can be used to estimate viability kernels, aiding sustainable management strategies, with applications to fisheries like Chilean sea bass and Alfonsino.

Contribution

It introduces methods to estimate viability kernels in monotone bioeconomic models under constraints, enhancing understanding of sustainable management domains.

Findings

Upper and lower estimates of viability kernels are derived.

Numerical examples demonstrate application to fisheries management.

Monotonicity assumptions facilitate delineation of viable management zones.

Abstract

Some monospecies age class models, as well as specific multi-species models (with so-called technical interactions), exhibit useful monotonicity properties. This paper deals with discrete time monotone bioeconomics dynamics in the presence of state and control constraints. In practice, these latter "acceptable configurations" represent production and preservation requirements to be satisfied for all time, and they also possess monotonicity properties. A state $x$ is said to belong to the viability kernel if there exists a trajectory, of states and controls, starting from $x$ and satisfying the constraints. Under monotonicity assumptions, we present upper and lower estimates of the viability kernel. This helps delineating domains where a viable management is possible. Numerical examples, in the context of fisheries management, for the Chilean sea bass (\emph{Dissostichus eleginoides}) and Alfonsino (\emph{Beryx splendens}) are given.