Marine fisheries are an important source of food supply and play an important economic role in many regions worldwide. However, due to aggressive fishing practices they are increasingly overexploited. Marine reserves have the potential to alleviate this problem and moreover, they also provide a physical area where an alternative economic activity can exist without being in conflict with fishing gear. Here we explore the idea of combining multiple economic activities in a marine ecosystem, namely: fishing and tourism. We use a model in which the fish population evolves according to a reaction-diffusion partial differential equation, and we consider the interactions between fishing and tourism. We use optimal control theory to find, depending on the model parameters, the optimal management strategy. The results show that, subject to certain conditions, it is possible to have two different revenue streams in the same habitat in contrast with the classical view of competing uses. We also corroborate that marine reserves emerge as the optimal strategy and that the presence of visitors in these areas generates larger profits than if only fishing was considered.

中文翻译：

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多用途海洋栖息地的最佳空间管理：平衡渔业和旅游业

海洋渔业是粮食供应的重要来源，在全球许多地区发挥着重要的经济作用。然而，由于激进的捕捞活动，它们越来越被过度开发。海洋保护区有可能缓解这个问题，此外，它们还提供了一个物理区域，可以在其中存在替代经济活动而不会与渔具发生冲突。在这里，我们探讨了在海洋生态系统中结合多种经济活动的想法，即：捕鱼和旅游。我们使用鱼类种群根据反应-扩散偏微分方程演化的模型，并考虑渔业和旅游业之间的相互作用。我们使用最优控制理论根据模型参数找到最优管理策略。结果表明，在某些条件下，同一个栖息地可能有两种不同的收入来源，这与传统的竞争用途观点不同。我们还证实，海洋保护区成为最佳策略，并且与仅考虑捕鱼相比，这些地区游客的存在产生更大的利润。