A unified modelling approach for producer–scrounger games in complex ecological conditions

• We model the producer–scrounger foraging game using the linear operator learning rule.
• We explore the effect of eight ecological parameters on the expected equilibrium mixture of search and join tactics.
• Our model replicates almost every producer–scrounger prediction and experimental result published to date.
• This model furthermore provides a means to explore the effect of more realistic foraging conditions.
• We illustrate this by predicting that increased variance in patch richness should increase joining.

Animal decision making in frequency-dependent situations, where the payoff of an action depends on the actions of others, has gained prominence in behavioural ecology and in social foraging in particular. One such situation involves cases where an animal can search for a new resource (produce) or join what others have already found (scrounge). A number of game-theoretic models have been proposed to predict the equilibrium combination of producer and scrounger strategists based on the evolutionarily stable strategy. However, each game model can only handle a few environmental parameters at a time and none address the flexible use of tactics that allows individuals to respond quickly and adaptively to changes in payoffs. In this study we propose an agent-based model using a linear operator learning rule as the decision mechanism. The model provides a unified framework from which to predict the effects on the expected equilibrium of producers and scroungers of group size, metabolic requirement, finder's advantage, food intake rate, cost of searching, cost of joining, patch encounter probability and patch richness. The simulation results replicate almost every producer–scrounger prediction and experimental result published to date such that the simulation provides a more general tool than any single game-theoretic model to predict behaviour under frequency-dependent conditions. The model furthermore allows us to develop a novel prediction about foraging behaviour in a more realistic environment of variable patch richness. By modelling the operation of a plausible decision rule, we can explore the validity of the behavioural gambit, the assumption that the unspecified decision mechanisms of game-theoretic models faithfully reproduce outcomes expected of natural selection operating over generations on fixed alternatives. We suggest that this simulation model can provide a tool for others to explore and predict the effect of more complex and hence realistic foraging conditions on individual levels of producer and scrounger use.