A Continuous Evolutionary Simulation Model of theAttainability of Honest Signalling EquilibriaSeth

A particular game-theoretic model (Grafen, 1990) of the evolutionary stability of honest signalling, which attempts a formal proof of the validity of Zahavi's (1975, 1977) handicap principle, is generalised and rendered as an evolutionary simulation model. In addition to supporting new theoretical results, this allows the eeects of diiering initial conditions on the attainability of signalling equilibria to be explored. Furthermore, it allows an examination of the manner in which the character of equilibrium signalling behaviour varies with the model's parameters. It is demonstrated that (i) non-handicap signalling equilibria exist, (ii) honest signalling equilibria need not involve extravagant signals, and (iii) the basins of attraction for such equilibria are, however, relatively small. General conditions for the existence of honest signalling equilibria (which replace those ooered by Zahavi) are provided, and it is demonstrated that previous theoretical results are easily accommodated by these general conditions. It is concluded that the supposed generality of the handicap principle, and the coherence of its terminology, are both suspect. Abstract A particular game-theoretic model (Grafen, 1990) of the evolutionary stability of honest signalling, which attempts a formal proof of the validity of Zahavi's (1975, 1977) handicap principle, is generalised and rendered as an evolutionary simulation model. In addition to supporting new theoretical results, this allows the eeects of diiering initial conditions on the attainability of signalling equilibria to be explored. Furthermore, it allows an examination of the manner in which the character of equilibrium signalling behaviour varies with the model's parameters. It is demonstrated that (i) non-handicap signalling equilibria exist, (ii) honest signalling equilibria need not involve extravagant signals, and (iii) the basins of attraction for such equilibria are, however, relatively small. General conditions for the existence of honest signalling equilibria (which replace those ooered by Zahavi) are provided, and it is demonstrated that previous theoretical results are easily accommodated by these general conditions. It is concluded that the supposed generality of the handicap principle, and the coherence of its terminology, are both suspect.