Data from: A quantitative framework for investigating risk of deadly collisions between marine wildlife and boats

Speed regulations of watercraft in protected areas are designed to reduce lethal collisions with wildlife but can have economic consequences. We present a quantitative framework for investigating the risk of deadly collisions between boats and wildlife. We apply encounter rate theory to demonstrate how marine mammal-boat encounter rate can be used to predict the expected number of deaths associated with management scenarios. We illustrate our approach with management scenarios for two endangered species: the Florida manatee Trichechus manatus latirostris and the North Atlantic right whale Eubalaena glacialis. We used a Monte Carlo simulation approach to demonstrate the uncertainty that is associated with our estimate of relative mortality. We show that encounter rate increased with vessel speed but that the expected number of encounters varies depending on the boating activities considered. For instance, in a scenario involving manatees and boating activities such as water skiing, the expected number of encounters in a given area (in a fixed time interval) increased with vessel speed. In another scenario in which a vessel made a transit of fixed length the expected number of encounters decreases slightly with boat speed. In both cases the expected number of encounters increased with distanced travelled by the boat. For whales, we found a slight reduction (~0.1%) in the number of encounters under a scenario where speed is unregulated; this reduction, however, is negligible, and overall expected relative mortality was ~30% lower under the scenario with speed regulation. The probability of avoidance by the animal or vessel was set to 0 because of lack of data, but we explored the importance of this parameter on the model predictions. In fact, expected relative mortality under speed regulations decreases even further when the probability of avoidance is a decreasing function of vessel speed. By applying encounter rate theory to the case of boat collisions with marine mammals, we gained new insights about encounter processes between wildlife and watercraft. Our work emphasizes the importance of considering uncertainty when estimating wildlife mortality. Finally, our findings are relevant to other systems and ecological processes involving the encounter between moving agents.

保护区内船舶限速规定旨在降低与野生动物发生致命碰撞的风险，但同时可能带来经济层面的影响。本研究提出了一套用于量化船舶与野生动物致命碰撞风险的分析框架。我们运用相遇率理论（encounter rate theory），阐明了如何利用海洋哺乳动物与船舶的相遇率来预测不同管理场景下的预期死亡数量。我们以两种濒危物种为例展示该分析框架的应用：佛罗里达海牛（*Trichechus manatus latirostris*）以及北大西洋露脊鲸（*Eubalaena glacialis*）。我们采用蒙特卡洛模拟（Monte Carlo simulation）方法，展示了相对死亡率估算中存在的不确定性。研究表明，相遇率随船舶航速提升而升高，但预期相遇次数会因所考量的船舶作业类型不同而存在差异。例如，在涉及海牛与滑水等船舶作业的场景中，特定区域内（固定时段内）的预期相遇次数会随船舶航速提升而增加。而在船舶进行固定航程航行的另一场景中，预期相遇次数则会随航速提升小幅下降。在上述两种场景中，预期相遇次数均随船舶航行距离增加而上升。针对露脊鲸的分析显示，在无航速限制的场景下，相遇次数仅出现约0.1%的小幅下降；但这一降幅可忽略不计，而在实施限速规定的场景中，整体预期相对死亡率可降低约30%。由于缺乏相关数据，本研究将动物或船舶的避让概率设为0，但我们同时探讨了该参数对模型预测结果的重要影响。事实上，当避让概率随船舶航速提升而降低时，限速规定下的预期相对死亡率还会进一步下降。通过将相遇率理论应用于海洋哺乳动物与船舶碰撞场景，我们对野生动物与船舶的相遇过程获得了全新的认知。本研究强调了在估算野生动物死亡率时考量不确定性因素的重要性。最后，本研究的发现可推广至其他涉及移动主体相遇的系统与生态过程。