When is False Modesty a False Economy? An Optimality Model of Escalating Signals

Animals making advertisement displays are sometimes faced with a choice of producing a cheap signal with low likelihood of success or a more expensive signal with a higher likelihood of success. We construct a caricature model of such displays, applicable both to agonistic and courtship situations. The model assumes that receivers respond only to the largest signal so far, and predicts when a single `honest' signal might be abandoned in favour of a display consisting of more than one escalating signal, starting low and only rising in intensity subsequent to the initial cheap signal proving unsuccessful. We describe how the optimal behaviour will differ among members of a population. Although there are potential difficulties in observation of escalating signals, we speculate how our results may be of relevance in understanding the calling contests of male Blanchard's cricket frogs.