Is there a role for amplifiers in sexual selection?

The amplifier hypothesis states that selection could favour the evolution of traits in signallers that improve the ability of receivers to extract honest information from other signals or cues. We provide a formal definition of amplifiers based on the receiver's mechanisms of signal perception and we present a game-theoretical model in which males advertise their quality and females use sequential-sampling tactics to choose among prospective mates. The main effect of an amplifier on the female mating strategy is to increase her mating threshold, making the female more selective as the effectiveness of the amplifier increases. The effects of the amplifier on male advertising strategy depends both on the context and on the types of the amplifier involved. We consider two different contexts for the evolution of amplifiers (when the effect of amplifiers is on signals and when it is on cues) and two types of amplifiers (the 'neutral amplifier', when it improves quality assessment without altering male attractiveness, and the 'attractive amplifier', when it improves both quality assessment and male attractiveness). The game-theoretical model provides two main results. First, neutral and attractive amplifiers represent, respectively, a conditional and an unconditional signalling strategy. In fact, at the equilibrium, neutral amplifiers are displayed only by males whose advertising level lays above the female acceptance threshold, whereas attractive amplifiers are displayed by all signalling males, independent of their quality. Second, amplifiers of signals increase the differences in advertising levels between amplifying and not-amplifying males, but they decrease the differences within each group, so that the system converges towards an 'all-or-nothing' signalling strategy. By applying concepts from information theory, we show that the increase in information transfer at the perception level due to the amplifier of signals is contrasted by a decrease in information transfer at the emitter level due to the increased stereotypy of male advertising strategy.