The Canadian lynx and snowshoe hare pelt data by the Hudson Bay Company did not fit the classical predator–prey theory. Rather than following the peak density of the hare, that of the lynx leads it, creating the hares-eat-lynx (HEL) paradox. Although trappers were suspected to play a role, no mathematical model has ever demonstrated the HEL effect. Here we show that the long-held assumption that the pelt number is a proxy of the wild populations is false and that when the data are modeled by the harvest rates by the trappers, the problem is finally resolved: both the HEL paradox and the classical theory are unified in our mechanistic hare-lynx-competitor-trapper (HLCT) model where competitor stands for all predators of the hares other than the lynx. The result is obtained by systematically fitting the data to various models using Newton’s inverse problem method. Main findings of this study include: the prey-eats-predator paradox in kills by an intraguild top-predator can occur if the top-predator prefers the predator to the prey; the benchmark HLCT model is more sensitive to all lynx-trapper interactions than to the respective hare-trapper interactions; the Hudson Bay Company’s hare pelt number maybe under-reported; and, the most intriguing of all, the trappers did not interfere in each other’s trapping activities.

中文翻译：

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一个相反的问题：捕猎者驾驶野兔吃山猫

哈德逊湾公司的加拿大猞猁和雪鞋野兔毛皮数据不符合经典的捕食者-猎物理论。猞猁并没有跟随野兔的峰值密度，而是引领它，从而造成野兔吃猞猁（HEL）悖论。尽管有人怀疑捕手起了作用，但没有数学模型证明过 HEL 效应。在这里，我们表明毛皮数量代表野生种群的长期假设是错误的，并且当数据由捕猎者的收获率建模时，问题最终得到解决：HEL 悖论和经典悖论理论在我们的机械野兔-猞猁-竞争者-捕手（HLCT）模型中是统一的，其中竞争者代表除猞猁以外野兔的所有捕食者。结果是通过使用牛顿反问题方法系统地将数据拟合到各种模型而获得的。本研究的主要发现包括：如果顶级捕食者更喜欢捕食者而不是猎物，则会出现公会内顶级捕食者杀死猎物的猎物-捕食者悖论；基准 HLCT 模型对所有 lynx-trapper 交互比对各自的 hare-trapper 交互更敏感；哈德逊湾公司的野兔毛皮数量可能被低估了；而且，最有趣的是，诱捕者并没有干涉彼此的诱捕活动。基准 HLCT 模型对所有 lynx-trapper 交互比对各自的 hare-trapper 交互更敏感；哈德逊湾公司的野兔毛皮数量可能被低估了；而且，最有趣的是，诱捕者并没有干涉彼此的诱捕活动。基准 HLCT 模型对所有 lynx-trapper 交互比对各自的 hare-trapper 交互更敏感；哈德逊湾公司的野兔毛皮数量可能被低估了；而且，最有趣的是，诱捕者并没有干涉彼此的诱捕活动。