Impact of spatial diffusion on the maximum sustainable yield in single-species reaction–diffusion models with harvesting

We investigate the impact of spatial diffusion on the Maximum Sustainable Yield (MSY) for a broad class of single-species reaction–diffusion models with harvesting in heterogeneous environments. The analysis covers three major dispersal mechanisms: linear diffusion, biased diffusion, and directed diffusion. Our main theoretical result shows that spatial diffusion consistently reduces the MSY, with the maximum yield attained in the absence of diffusion. Explicit zero-diffusion benchmarks are provided for the logistic, Richards, and Gompertz growth models. Numerical simulations in one-dimensional and two-dimensional heterogeneous landscapes illustrate and support the theoretical predictions, highlighting the roles of environmental heterogeneity and movement strategy in shaping the decline of yield with increasing diffusion. The results have direct implications for the management of spatially structured harvested populations, emphasizing the importance of controlling mixing to preserve high-yield areas.