Perceptual advertisement by the prey of stalking or ambushing predators

There has been previous theoretical explorations of the stability of signals by prey that they have detected a stalking or ambush predator, where such perceptual advertisement dissuades the predator from attacking. Here we use a game theoretical model to extend the theory to consider some empirically-motivated complexities: (i) many perceptual advertisement signals appear to have the potential to vary in intensity, (ii) higher intensity signals are likely to be most costly to produce, and (iii) some high-cost signals (such as staring directly at the predator) can only be utilised if the prey is very confident of the existence of a nearby predator (that is, there are reserved or unfakable signals). We demonstrate that these complexities still allow for stable signalling. However, we do not find solutions where prey use a range of signal intensities to signal different degrees of confidence in the proximity of a predator; with prey simply adopting a binary response of not signalling or always signalling at the same fixed level. However this fixed level will not always be the cheapest possible signal, and we predict that prey that require more certainty about proximity of a predator will use higher-cost signals. The availability of reserved signals does not prohibit the stability of signalling based on lower-cost signals, but we also find circumstances where only the reserved signal is used. We discuss the potential to empirically test our model predictions, and to develop theory further to allow perceptual advertisement to be combined with other signalling functions.