Spatial-economic feedbacks in a diffusive predator-prey fishery: Harvest viability and Turing bifurcation

The interaction between endogenous market forces and spatial population dynamics is an important source of complex behavior in harvested ecosystems. This paper proposes a reaction–diffusion bioeconomic model that incorporates adaptive harvesting effort and price responsiveness. Mathematical analysis and numerical simulations show that the coupling between economic feedback and diffusion can induce Turing instability, transforming spatially uniform populations into stable heterogeneous patterns. Such patterns reflect a nontrivial redistribution of biomass driven by market-regulated harvesting and dispersal. Moreover, the system may exhibit bistability, allowing a high-biomass equilibrium and a low-biomass equilibrium to coexist over a range of parameters. Owing to the endogenous dependence of price on resource abundance, these alternative states can generate markedly different economic returns, and the low-biomass regime may yield higher revenue under scarcity-driven price responses. These findings illustrate how nonlinear feedbacks between market dynamics and spatial ecology can generate rich spatiotemporal structures and multiple long-term outcomes in bioeconomic systems, providing insight into the coupled ecological and economic consequences of adaptive harvesting.