Code for: Threshold assessment, categorical perception, and the evolution of reliable signaling

Animals often use assessment signals to communicate information about their quality to a variety of receivers, including potential mates, competitors, and predators. But what maintains reliable signaling and prevents signalers from signaling a better quality than they actually have? Previous work has shown that reliable signaling can be maintained if signalers pay fitness costs for signaling at different intensities and these costs are greater for lower quality individuals than higher quality ones. Models supporting this idea typically assume that continuous variation in signal intensity is perceived as such by receivers. In many organisms, however, receivers have threshold responses to signals, in which they respond to a signal if it is above a threshold value and do not respond if the signal is below the threshold value. Here, we use both analytical and individual-based models to investigate how such threshold responses affect the reliability of assessment signals. We show that reliable signaling systems can break down when receivers have an invariant threshold response, but reliable signaling can be rescued if there is variation among receivers in the location of their threshold boundary. Our models provide an important step towards understanding signal evolution when receivers have threshold responses to continuous signal variation.

Methods
A full descripition of the methods can be found in the main text and the appendix of the assossicated publication.

动物常通过评估信号向各类接收者传递自身品质相关信息，接收者涵盖潜在配偶、竞争者与捕食者。但究竟是什么机制维持了信号的可靠性，同时避免信号发出者虚报自身实际品质？已有研究证实，若信号发出者为不同强度的信号传递支付适合度成本，且低品质个体所需承担的此类成本高于高品质个体，即可维持可靠的信号传递。支持该观点的模型通常假定，接收者会如实感知信号强度的连续变化。然而在诸多生物类群中，接收者对信号存在阈值响应：即当信号强度高于某一阈值时接收者才会做出响应，反之则不产生响应。本研究同时采用分析模型与基于个体的模型，探究此类阈值响应会如何影响评估信号的可靠性。研究结果表明，当接收者采用固定不变的阈值响应时，可靠的信号传递系统可能会崩溃；但若不同接收者的阈值边界位置存在差异，则可挽救可靠的信号传递。本研究模型为理解接收者对连续信号变化存在阈值响应时的信号演化进程提供了重要研究进展。

方法
完整的方法说明可参阅相关发表论文的正文与附录。