Sibling competition stabilizes signalling resolution models of parent-offspring conflict

Young of altricial birds use conspicuous displays to solicit food from their parents. There is experimental evidence that the intensity of these displays is correlated with the level of food deprivation of young, and that parents respond to increased levels of solicitation by increasing the rate of food delivery to the nest. Game-theoretical models based on the handicap principle show that, when solicitation is costly, there is a signalling equilibrium at which there is a one-to-one correspondence between the condition of the young and the intensity of their display. Parents use this information to adjust their levels of investment on the current offspring. However, the models also have a non-signalling equilibrium, and computer simulations show that only the non-signalling equilibrium is stable. Here I show that when direct sibling competition is introduced into the model, in such a way that parents have control on the amount of food provided to the nest, but not on the way the food is allocated among siblings, the non-signalling equilibrium disappears and the signalling equilibrium becomes stable.