A receiver–signaler equilibrium in the evolution of communication in noise

Communication in noise differs in a fundamental way from communication without noise, because a receiver faces four possible outcomes every time it checks its input. These outcomes present inevitable trade-offs for a receiver in adjusting its threshold for response. A signaler also faces trade-offs, in this case between costs and benefits as the exaggeration of signals increases. Furthermore, a receiver’s and signaler’s performances are mutually interdependent. The utility of a receiver’s threshold depends on the signaler’s exaggeration (the level of the signal in relation to the level of noise), and the utility of a signaler’s exaggeration depends on the receiver’s threshold. Diminishing returns for both receiver and signaler suggest the possibility of a joint evolutionary equilibrium for a receiver’s threshold and a signaler’s exaggeration. The present analysis combines previous expressions for the utility of a receiver’s threshold (Ur) and the utility of a signaler’s exaggeration (Us) in order to explore the possibility of this joint equilibrium. Utilities for both parties are expressed as survival × fecundity, an approximate measure of the spread of genes associated with a phenotype. Thus, Ur and Us, as functions of both the receiver’s threshold (t) and the signaler’s exaggeration (e), represent the adaptive landscapes for each party, and the reciprocal partial derivatives of these utilities, ∂Ur/∂e and ∂Us/∂t , approximate the selection gradients for the receiver’s threshold and the signaler’s exaggeration. With parameters for both the receiver’s and the signaler’s performances set to plausible values for many cases of mate choice, the resulting analysis shows that there exists a joint optimum for the receiver’s threshold and the signaler’s exaggeration. This optimum is a Nash equilibrium at which neither party can do better by a unilateral change in behavior. In some conditions, the equilibrium for communication in mate choice occurs at a higher threshold and higher exaggeration than the equilibrium for communication with warning signals. In general, these results indicate that the normal situation for communication in noise is honesty with deception — honesty on average but with instances of disadvantageous outcomes for receivers or signalers. Furthermore, the relationship between honesty and costs is more complex than currently recognized. Most important, the joint optimum for receiver and signaler indicates that communi© 2013 Koninklijke Brill NV, Leiden DOI:10.1163/1568539X-00003063 958 Receiver–signaler equilibrium cation in noise cannot escape the problems created by noise. Noise is an inevitable component of communication, and perfection in communication is not expected in natural conditions.