Increase maximum economic yield in a patchy environment

In this work, we study the model of a fish species growing logistically exploited by a fishing fleet in a heterogeneous environment. The environment is made up of a network of fishing patches connected by fish migrations taking place on a fast time scale. We are interested in the maximum economic yield (MEY) which corresponds to the maximum profit made by the fishing fleet. We show that the total MEY profit of the fishery made up of all the connected fishing patches can be greater than the sum of the MEY profits of isolated patches in the absence of migration. We study the general case with any number of connected patches then focus on the case of a system composed of two patches. In the latter case, we show that asymmetry in fish migration plays an important role in increasing the total profit at the MEY by connecting patches. We illustrate our results with numerical simulations allowing us to compare the MEY fishery system with connected patches compared to the system with isolated patches.