MSY and MEY for a multi-site, single-species fishery, incorporating general growth laws with a strong Allee effect and stock-dependent catchability

Research Question

How do spatial refuge, fast resource migration, and environmental noise affect coexistence, oscillations, and collapse in an intraguild predation system?

Abstract

We consider a single-species, multi-site fishery consisting of fishing sites connected by fish movement. Our study incorporates general growth models, specifically those featuring a strong Allee effect, and catch functions where catchability depends on local fish stock. We derive analytical expressions for the global Maximum Sustainable Yield (MSY) in the limiting case of infinitely rapid migration and compare them to the sum of local MSYs for isolated zones. Our results demonstrate that, as in the logistic case, the total MSY cannot exceed the sum of local MSYs, with equality achieved when fish distribute themselves across zones according to a generalized ideal free distribution determined by the local production-maximizing biomasses. This reduces to the classical carrying-capacity proportional distribution only when patches share the same dimensionless growth shape. Our framework includes Gompertz growth and extends the comparison to strong Allee effects and stock-dependent catchability. In contrast to the MSY outcome, we show numerically that interconnection can increase the Maximum Economic Yield (MEY) for some parameter regimes. Our theoretical findings are illustrated through numerical simulations.

What This Paper Does

The paper reduces a two-patch ecological model using time-scale separation, analyzes equilibria and bifurcations, and tests the robustness of the resulting dynamics under environmental stochasticity.

My Contribution

• Analyzed equilibrium points and their stability in the proposed dynamical system and conducted theoretical analysis of the stochastic PDE model under Brownian perturbations.
• Implemented Maple simulations to validate analytical results and generate numerical figures and drafted paper.