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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.

The distribution of food among altricial bird nestlings is the result of an interaction between parental feeding decisions and scramble competition between nestmates. Both young and parents can potentially be in control of the outcome of this interaction. In great tits, each parent feeds from a fixed location on the nest rim, thereby forcing nestlings to choose between the father's and the mother's location. It was previously found that hungry nestlings approached the female preferentially and were more likely to be fed, appearing as if females showed a stronger preference to feed hungry young than males. However, nestlings were free to move in that study, and the effects of nestling positioning could not be disentangled from those of parental food allocation decisions. Here, we experimentally divided broods into two halves and randomly assigned each half of the brood to one side of the nest cup where only one parent could feed them. One nestling in each half-brood was food deprived to manipulate short-term hunger state. Both parents showed a similar preference to feed the more hungry nestlings, suggesting that the previously observed difference was due to offspring positioning rather than active parental choice. Our study shows that food allocation is partially under nestling control and suggests that nestlings adjust positioning and begging behaviour to the profitability of a given position in the nest cup.