Honest signals and cues have been observed as part of interspecific and intraspecific communication among animals. Recent theories suggest that existing signaling systems have evolved through natural selection imposed by predators. Honest signaling in the interspecific communication can provide insight into the evolution of anti-predation techniques. In this work, we introduce a deterministic three-stage, two-species predator-prey model, which modulates the impact of honest signals and cues on the interacting populations. The model is built from a set of first principles originated from signaling and social learning theory in which the response of predators to transmitted honest signals or cues is determined. The predators then use the signals to decide whether to pursue the attack or save their energy for an easier catch. Other members from the prey population that are not familiar with signaling their fitness observe and learn the technique. Our numerical bifurcation analysis indicates that increasing the predator's search rate and the corresponding assimilation efficiency gives a journey from predator-prey abundance and scarcity, a stable transient cycle between persistence and near-extinction, a homoclinic orbit pointing towards extinction, and ultimately, a quasi-periodic orbit. A similar discovery is met under the increment of the prey's intrinsic birth rate and carrying capacity. When both parameters are of sufficiently large magnitudes, the separator between honest signal and cue takes the similar journey from a stable equilibrium to a quasi-periodic orbit as it increases. In the context of modeling, we conclude that under prey abundance, transmitting error-free honest signals leads to not only a stable but also more predictable predator-prey dynamics.

中文翻译：

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提出诚实信号和线索的捕食者-猎物相互作用的建模研究

诚实的信号和线索已被观察到作为动物种间和种内交流的一部分。最近的理论表明，现有的信号系统是通过捕食者强加的自然选择进化而来的。种间通信中的诚实信号可以提供对反捕食技术演变的洞察。在这项工作中，我们引入了一个确定性的三阶段、两种捕食者-猎物模型，该模型调节诚实信号和线索对相互作用种群的影响。该模型是根据一组源自信号和社会学习理论的第一原理构建的，其中确定了掠食者对传输的诚实信号或线索的反应。然后捕食者使用这些信号来决定是继续攻击还是节省能量以便更容易地捕获。来自猎物种群的其他不熟悉信号的成员观察并学习该技术。我们的数值分岔分析表明，增加捕食者的搜索率和相应的同化效率，可以从捕食者-猎物的丰富和稀缺、持久性和接近灭绝之间的稳定瞬态循环、指向灭绝的同宿轨道以及最终的准- 周期轨道。在猎物的内在出生率和承载能力的增加下，也会遇到类似的发现。当两个参数都足够大时，诚实信号和提示之间的分隔符随着它的增加从稳定平衡到准周期轨道的过程类似。在建模的背景下，我们得出结论，在猎物丰富的情况下，