Adaptive management of marine protected areas (MPAs) to determine whether they are meeting their intended goals requires predicting how soon those goals will be realized. Such predictions have been made for increases in fish abundance and biomass inside MPAs. However, projecting increases in fishery yield (“fishery spillover”) is more complex because it involves both how the fishery is managed and uncertainty in larval connectivity. We developed a two-patch, age-structured population model, based on a renewal equation approach, to project the initial timing of increase in fishery yield from larvae exported from a no-take MPA. Our results link our understanding of the predicted timing of increases in biomass (and thus reproduction) in MPAs with the time-lags associated with new recruits entering the fishery. We show that the time-lag between biomass peaking within the MPA and the increased fishery yield outside the MPA reaching its maximum depends, in a predictable way, on the age-dependent patterns of growth, natural mortality, and fishing mortality. We apply this analysis to 16 fishery species from the US Pacific coast; this difference ranged from 7 to 18 years. This model provides broadly applicable guidance for this important emerging aspect of fisheries management.

中文翻译：

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预测实施海洋保护区后渔业产量初步增加的时间表

对海洋保护区（MPA）进行自适应管理以确定其是否达到了预期目标，需要预测这些目标将在多长时间内实现。已经做出了这样的预测，即海洋保护区中鱼类的丰度和生物量将增加。但是，预计渔业产量的增加（“渔业外溢”）更为复杂，因为这涉及到渔业的管理方式和幼体连通性的不确定性。我们基于更新方程方法开发了一个两阶段，按年龄结构的种群模型，以预测从无捕捞MPA出口的幼虫渔业产量增加的初始时机。我们的结果将我们对MPA中生物量（进而繁殖）增加的预测时间的理解与新入场的新员工相关的时滞联系在一起。我们表明，MPA内的生物量达到峰值与MPA以外的增加的渔业产量达到最大之间的时间间隔，以可预测的方式取决于生长，自然死亡率和捕捞死亡率的年龄依赖性模式。我们将此分析应用于美国太平洋沿岸的16种渔业物种。差异从7到18年不等。该模型为渔业管理这一重要的新兴方面提供了广泛适用的指导。