Behavioural attainability of evolutionarily stable strategies in repeated interactions

Theory for the evolution of social interactions based on continuous strategies often assumes for simplicity that expressed behaviours are independent of previous encounters. In reality, however, such dependencies are likely to be widespread and often strong, generating complex behavioural dynamics. To model this process and illustrate potential consequences for the evolution of behavioural interactions, we consider the behavioural dynamics of the interaction between caring parents and their demanding offspring, a prime example of long series of interdependent and highly dynamic interactions. These dynamics can be modelled using functions describing mechanisms for how parents and their offspring respond to each other in the interaction. We establish the general conditions under which the behavioural dynamics converge towards a proximate equilibrium and refer to such converging interactions as behaviourally stable strategies (BSSs). We further demonstrate that there is scope for behavioural instability under realistic conditions; that is, whenever parents and/or offspring 'overreact' beyond some threshold. By applying the derived condition for behavioural stability to evolutionary models of parent-offspring conflict resolution, we show by numerical simulations that evolutionarily stable strategies (ESSs) of current models are not necessarily behaviourally stable. Because behavioural instability implies that expressed levels of behaviours deviate from the ESS, behavioural stability is required for strict evolutionary stability in repeated behavioural interactions. (C) 2009 The Association for the Study of Animal Behaviour. Published by Elsevier Ltd. All rights reserved.