# Size-Selective Threshold Harvesting under Nonlocal Crowding and Exogenous Recruitment

arXiv: https://arxiv.org/abs/2603.27368 · HTML: https://mlsanity.com/paper/2603.27368/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Mar 2026.

## Built on by (most cited first, 1 of 1)

- [FTU-Seek: Foundation Model-Guided Hard-Negative Learning for Sparse Functional Tissue Unit Segmentation](https://mlsanity.com/paper/2609.00704/) (2026)

## Abstract (arXiv)

We propose a nonlinear size-structured fishery model for externally recruited stocks under size-selective harvesting. The population density satisfies a McKendrick--von Foerster transport equation in which growth and natural mortality depend on a nonlocal crowding index, while harvesting acts as a bounded size-dependent mortality control. Unlike standard self-recruiting formulations, recruitment is prescribed as a lower-boundary inflow, making the model suitable for enhancement fisheries or analyses conditional on juvenile input. For the no-harvest baseline, we derive the stationary size profile and reduce the nonlinear equilibrium problem to a scalar closure equation, proving existence and uniqueness under a net monotonicity condition. We introduce an intrinsic replacement index and show why, in this externally forced setting, it is a viability diagnostic rather than a persistence threshold. A formal state--adjoint system yields a bang--bang switching rule; under weak coupling and single crossing, the optimal policy has a threshold structure. Numerical experiments validate the approximation and sensitivity trends