Stochastic dynamics of social patch foraging decisions

Animals typically forage in groups. Social foraging can help animals avoid predation and decrease their uncertainty about the richness of food resources. Despite this, theoretical mechanistic models of patch foraging have overwhelmingly focused on the behavior of single foragers. In this study, we develop a mechanistic model that accounts for the behavior of individuals foraging together and departing food patches following an evidence accumulation process. Each individual's belief about patch quality is represented by a stochastically accumulat-ing variable, which is coupled to another's belief to represent the transfer of information. We consider a cohesive group, and model information sharing by considering both intermittent pulsatile coupling (only communicate decision to leave) and continuous diffusive coupling (communicate throughout the deliberation process). Groups employing pulsatile coupling can obtain higher foraging efficiency, which depends more strongly on the coupling parameter compared to those using diffusive coupling. Conversely, groups using diffusive coupling are more robust to changes and heterogeneities in belief weighting and departure criteria. Efficiency is measured by a reward rate function that balances the amount of energy accumulated against the time spent in a patch, computed by solving an ordered first passage time problem for the patch departures of each individual. Using synthetic departure time data, we can distinguish between the two modes of communication and identify the model parameters. Our model establishes a social patch foraging framework to identify deliberative decision strategies and forms of social communication, and to allow model fitting to field data from foraging animal groups.