General solution to biological signalling games: costly signalling and beyond

Explaining signal reliability poses a central problem in animal communication. According to Zahavis Handicap Principle (HP), signals are honest only when they are costly at the evolutionary equilibrium - hence the term handicap; otherwise, deception evolves, and communication breaks down. The HP has no theoretical or empirical support, despite claims to the contrary, and yet this idea remains immensely popular. Theoretical evaluations of the HP are difficult, however, because finding the equilibrium cost function in signalling games is notoriously complicated. Here we show how cost functions can be calculated for any arbitrary pairwise asymmetric signalling game at the evolutionary equilibrium. We clarify the relationship between signalling costs at equilibrium and the conditions for reliable signalling. We show that these two terms are independent and the costs of signalling at honest equilibrium have no effect on the stability of communication. We show that honest signals can take any cost value, even negative, being beneficial for the signaller independently of the receivers response at equilibrium, without requiring further constraints. Our results are general, and apply to seminal signalling models, including Grafens model of sexual selection and Godfrays model of parent-offspring communication. Our results refute the claim that signals must be costly at the evolutionary equilibrium to be reliable, as predicted by the HP and so-called "costly signalling" theory. The handicap paradigm can thus be fully rejected. We provide testable predictions to help advance the field and establish a better explanation for honest signals.