Optimal Harvesting of Size-Structured Populations with Environmental Feedback and Fixed Recruitment Flux

Abstract

We study a nonlinear size-structured transport model with distributed harvesting and prescribed recruitment flux, where environmental feedback is determined by a scalar population functional. After establishing global well-posedness on $L^1$, we reduce stationary equilibria to a scalar closure equation. This reduction reveals that loss of equilibrium uniqueness occurs through a generic fold, mathematically characterizing critical population transitions. On uniformly nonresonant equilibrium branches, we prove the existence of optimal stationary harvesting policies via the direct method of the calculus of variations. We then derive a boundary-corrected adjoint equation and establish an identity equating equilibrium sensitivity with the adjoint loop gain. This relation yields explicit criteria for the persistence and creation of optimal harvesting thresholds. Collectively, these results provide a unified analytical framework connecting environmental feedback, equilibrium structure, and optimal harvesting.

Disclosure

“ships that could have appeared to influence the work reported in this paper. Funding sources This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. Declaration of generative AI use In writing this article, the author used Gemini 3 to polish the language. This content has been reviewed and edited by the author to ensure accuracy. Data Availability Statement Data sharing is not applicable as this study do”

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2026-08-24T00:28:51.963Z

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