Chicks make stochastic decisions based on gain rates of different time constants.

The marginal value theorem (MVT) predicts that optimal foragers leave a patch when the instantaneous gain rate decreases to the average long-term gain rate. However, various animals systematically deviate from this optimum by staying too long or overharvesting relative to this optimum. We hypothesised that animals do not represent their optimal stay time but instead determine their departure point probabilistically. To test this hypothesis, we conducted behavioural experiments and modelling using chicks. The chicks ran on a treadmill with feeders on both sides, and their travel time to the feeder was experimentally controlled. As predicted by the MVT, the chicks stayed longer at the feeder when forced to run more. However, they stayed even longer than predicted by the MVT. Therefore, we constructed and compared stochastic decision-making models with the MVT-based model. The stochastic models explained the chicks' behaviour better than the MVT-based model. These results suggest that chicks leave probabilistically based on their immediate foraging history rather than representing an optimal stay time.