Takashina Nao
Biodiversity and Biocomplexity Unit, Okinawa Institute of Science and Technology Graduate University, Okinawa, Japan.
PeerJ. 2020 Aug 25;8:e9798. doi: 10.7717/peerj.9798. eCollection 2020.
Marine reserves are an essential component of modern fishery management. Marine reserves, which represent a management tradeoff between harvesting and conservation, are fundamental to maintenance of fisheries. Finding optimal reserve sizes that improve fishing yields is not only of theoretical interest, but also of practical importance to facilitate decision making. Also, since the migratory behavior of some species influences the spillover effect of a marine reserve, this is a key consideration when assessing performance of marine reserves. The relationship between optimal reserve size and migration rate/mode has not been well studied, but it is fundamental to management success. Here, I investigate optimal reserve size and its management outcome with different levels of spillover via a simple two-patch mathematical model. In this model, one patch is open to fishing, and the other is closed. The two-patch model is aggregated by single-population dynamics when the migration rate is sufficiently larger than the growth rate of a target species. At this limit, I show that an optimal reserve size exists when pre-reserve fishing occurs at fishing mortality larger than , the fishing mortality at the maximum sustainable yield (MSY). Also, the fishing yield at an optimal reserve size becomes as large as MSY at the limit. Numerical simulations at various migration rates between the two patches suggest that the maximum harvest under management with a marine reserve is achieved at this limit. This contrasts with the conservation benefit which is maximized at an intermediate migration rate. Numerical simulations show that the above-mentioned condition for an optimal reserve size to exist derived from the aggregated model is necessary when the migration rate is not sufficiently large, and that a moderate migration rate is further necessary for an optimal reserve size to exist. However, high fishing mortality reduces this requirement.
海洋保护区是现代渔业管理的重要组成部分。海洋保护区体现了捕捞与保护之间的管理权衡，对渔业的维持至关重要。找到能提高捕鱼产量的最佳保护区规模不仅具有理论意义，对促进决策制定也具有实际重要性。此外，由于某些物种的洄游行为会影响海洋保护区的溢出效应，这是评估海洋保护区绩效时的关键考虑因素。最佳保护区规模与洄游率/洄游模式之间的关系尚未得到充分研究，但这对管理成功至关重要。在此，我通过一个简单的双斑块数学模型研究了不同溢出水平下的最佳保护区规模及其管理结果。在这个模型中，一个斑块开放用于捕鱼，另一个则关闭。当洄游率远大于目标物种的生长率时，双斑块模型由单种群动态聚合而成。在此极限情况下，我表明当保护区建立前的捕捞死亡率大于最大可持续产量（MSY）时的捕捞死亡率时，存在一个最佳保护区规模。而且，在该极限情况下，最佳保护区规模下的捕鱼产量会达到与MSY一样高。两个斑块之间不同洄游率的数值模拟表明，在这个极限情况下，通过海洋保护区管理可实现最大捕捞量。这与在中等洄游率下保护效益最大化形成对比。数值模拟表明，当洄游率不够大时，从聚合模型得出的上述最佳保护区规模存在的条件是必要的，并且最佳保护区规模的存在还需要适度的洄游率。然而，高捕捞死亡率会降低这一要求。
