Signalling among relatives. II. Beyond the tower of Babel.

Models of costly signalling are commonly employed in evolutionary biology in order to explain how honest communication between individuals with conflicting interests can be stable. These models have focused primarily on a single type of honest signalling equilibrium, the separating equilibrium in which any two different signallers send distinct signals, thereby providing signal receivers with complete information. In this paper, we demonstrate that in signalling among relatives (modelled using the Sir Philip Sidney game), there is not one but a large number of possible signalling equilibria, most of which are pooling equilibria in which different types of signallers may share a common signal. We prove that in a general Sir Philip Sidney game, any partition of signallers into equi-signalling classes can have a stable signalling equilibrium if and only if it is a contiguous partition, and provide examples of such partitions. A similar (but slightly stricter) condition is shown to hold when signals are transmitted through a medium with signalling error. These results suggest a solution to a problem faced by previous signalling theory models: when we consider the separating equilibrium, signal cost is independent of the frequency of individuals sending that signal and, consequently, even very rare signaller types can drastically affect signal cost. Here, we show that by allowing these rare signallers to pool with more common signallers, signal cost can be greatly reduced.