Abstract Correct modelling of relationships between predators and prey is crucial to ecological and population dynamics models. However, and despite a long-standing competition between ratio and prey-dependent models (and a few alternative intermediate forms) in the literature, most equations currently used to represent such relationships do not meet theoretical criteria for biological consistency. This research proposes a set of universally applicable criteria for all predation equations and shows that the most commonly used predation equations in the literature fail to meet these same criteria. We follow with a proposal for a new predation equation that does meet these criteria, which combines both prey and ratio-dependent concepts while giving reasonable predictions in the cases of both high predator or high prey densities. We show its empirical performance by applying the new equation, along with existing alternatives, to various experimental predation datasets from the literature. Results show that the new equation is not only more mathematically consistent than existing equations, but also performs more consistently empirically across different datasets from various ecological situations. This research is the first to propose a systematic set of criteria to evaluate predation equations and then to offer an equation that meets these criteria and also performs well both theoretically and empirically across datasets from a wide range of predation systems.

中文翻译：

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建模捕食：捕食者-猎物系统函数形式方程的理论标准和经验评估

摘要 捕食者和猎物之间关系的正确建模对于生态和种群动态模型至关重要。然而，尽管文献中比率模型和猎物依赖模型（以及一些替代的中间形式）之间存在长期竞争，但目前用于表示这种关系的大多数方程并不符合生物学一致性的理论标准。本研究为所有捕食方程提出了一套普遍适用的标准，并表明文献中最常用的捕食方程无法满足这些相同的标准。我们随后提出了一个满足这些标准的新捕食方程的建议，它结合了猎物和比例相关的概念，同时在高捕食者或高猎物密度的情况下给出了合理的预测。我们通过将新方程以及现有替代方案应用于文献中的各种实验捕食数据集来展示其经验性能。结果表明，新方程不仅在数学上比现有方程更一致，而且在来自各种生态情况的不同数据集上的经验表现也更一致。这项研究首次提出了一套系统的标准来评估捕食方程，然后提供一个满足这些标准的方程，并且在来自各种捕食系统的数据集上也能在理论上和经验上表现良好。结果表明，新方程不仅在数学上比现有方程更一致，而且在来自各种生态情况的不同数据集上的经验表现也更一致。这项研究首次提出了一套系统的标准来评估捕食方程，然后提供一个满足这些标准的方程，并且在来自各种捕食系统的数据集上也能在理论上和经验上表现良好。结果表明，新方程不仅在数学上比现有方程更一致，而且在来自各种生态情况的不同数据集上的经验表现也更一致。这项研究首次提出了一套系统的标准来评估捕食方程，然后提供一个满足这些标准的方程，并且在来自各种捕食系统的数据集上也能在理论上和经验上表现良好。