Modelling antipredator vigilance and flight response in group foragers when warning signals are ambiguous

The trade-off between feeding and vigilance in flocks of birds has been extensively studied and modelled. An assumption of many models is that if one bird spots the predator, it gives a signal and the rest of the flock takes flight. However, it has been observed that birds do not always respond to signals and in fact many signals turn out to be false alarms. Since taking flight is both costly in time and energy, it may be advantageous for birds not to respond to all alarm calls. A model is developed to show under what circumstances birds should respond to a signal. The model predicts that under most, but not all, circumstances, birds should respond to multiple detections but not to single detections. The model also predicts that if birds respond to all flights, they will have to compensate for the time lost to feeding and the greater energy requirement of spending more time in flight, by being less vigilant, and they have a lower probability of survival than birds which only respond to multiple detections.