In inverted biomass pyramids (IBPs) prey are outnumbered by their predators when measured by biomass. We investigate how prey should behave in the face of danger from higher predator biomass, and how anti‐predator behavior (in the form of vigilance) can, in turn, affect the predator–prey system. In this study, we incorporate anti‐predator behaviors into a Lotka–Volterra predator–prey model in the form of fixed and facultative vigilance. Facultative vigilance models behavior as a dynamic foraging game, allowing us to assess optimal behavioral responses in the context of IBPs using a dynamical fitness optimization approach. We model vigilance as a tradeoff between safety and either the prey's maximum growth rate or its carrying capacity. We assess the population dynamics of predators and prey with fear responses, and investigate the role fear plays on trophic structure. We found that the ecology of fear plays an important role in predator–prey systems, impacting trophic structure and the occurrence of IBPs. Fixed vigilance works against IBP structure by always reducing the predator–prey biomass ratio at equilibrium with increasing levels of vigilance. Facultative vigilance can actually promote IBPs, as prey can now adjust their vigilance levels to cope with increased predation and the costs associated with vigilance. This is especially true when the effectiveness of vigilance is low and predators are very lethal. In general, these trends are true whether the costs of vigilance are felt on the prey's maximum growth rate or its carrying capacity. Just as the ecology of fear, when first introduced, was used to explain why top carnivores are rare in terrestrial systems, it can also be used to understand how big fierce predators can be common in IBPs.

中文翻译：

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恐惧和倒置的生物金字塔的生态

在倒置生物量金字塔（IBP）中，当用生物量进行测量时，猎物的数量要比它们的掠食者多。我们研究了面对更高捕食者生物量的危险时猎物应如何表现，以及反捕食者的行为（以警惕的形式）又会如何影响捕食者-猎物系统。在这项研究中，我们以固定和兼职警惕的形式将反捕食者行为纳入Lotka–Volterra捕食者–猎物模型。兼职警惕将行为建模为动态觅食游戏，从而使我们能够使用动态适应性优化方法在IBP情况下评估最佳行为反应。我们将警惕性建模为安全性与猎物最大增长率或其承载能力之间的折衷。我们用恐惧反应评估捕食者和被捕食者的种群动态，并研究恐惧在营养结构中的作用。我们发现，恐惧的生态系统在捕食者－猎物系统中起着重要作用，影响营养结构和IBP的发生。固定的警惕性通过始终提高警惕性水平始终降低平衡状态下的捕食者与被捕食者生物量之比，来对抗IBP结构。兼职警惕实际上可以促进IBP，因为猎物现在可以调整其警惕水平，以应对日益增加的捕食和与警惕相关的成本。当警惕性低并且掠食者非常致命时，尤其如此。总的来说，无论警觉成本是在猎物的最大增长率上还是在其承载能力上，这些趋势都是正确的。就像恐惧生态最初引入时一样，