Parents and offspring in an evolutionary game: the effect of supply on demand when costs of care vary.

Current models of parent-offspring communication do not explicitly predict the effect of parental food supply on offspring demand (ESD). However, existing theory is frequently interpreted as predicting a negative ESD, such that offspring beg less when parental supply is high. While empirical evidence largely supports this interpretation, several studies have identified the opposite case, with well-fed offspring begging more than those in poorer condition. Here, we show that signalling theory can give rise to either a negative or a positive ESD depending on the precise form of costs and benefits. Introducing variation among parents in the cost of care, we show that the ESD may change sign depending upon the quantitative relation between two effects: (i) decreased supply leads to increased begging because of an increase in marginal fitness benefit of additional resources to offspring, (ii) decreased supply leads to reduced begging because it is associated with a decrease in parental responsiveness, rendering begging less effective. To illustrate the interplay between these two effects, we show that Godfray's seminal model of begging yields a negative ESD when care is generally cheap, because the impact of supply on the marginal benefits of additional resources then outweighs the associated changes in parental responsiveness to begging. By contrast, the same model predicts a positive ESD when care is generally costly, because the impact of care costs on parental responsiveness then outweighs the change in marginal benefits.