The two analysed models can be described in terms of transitions between commitment states by individuals.

The commitment states are ‘committed to foraging patch i’ (Xi) or ‘uncommitted’ (XU). Both models have the same positive and negative feedback for independent transitions: quality-dependent discovery and constant abandonment (leak a). The difference lies in the social feedback; one model (blue) has quality-insensitive recruitment (ri = ρ) but no negative social feedback (z = 0). The other model (red) has both quality-sensitive recruitment (ri = ρqi) and quality-insensitive self-inhibition (z > 0), as reported by field observations [30]. In these representative models, we set rates as constant and (linear) quality-sensitive functions of the quality according to the best function we obtain with numerical optimisation (see S1 Text).