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.