Direction of predator approach and the decision to flee to a refuge

How close should an animal allow a potential predator to approach before fleeing to a refuge? Fleeing too soon wastes time and energy that could be spent on other important activities, but fleeing too late is potentially lethal. A model to predict flight initiation distance was developed, based on the assumption that animals would flee at a distance that allows them to reach the refuge ahead of the predator by some margin of safety. This model predicts that (1) flight initiation distance should increase with distance from the refuge (which has been supported by studies on several species) and (2) the rate of increase of flight initiation distance with distance from a refuge should be higher when the refuge is between the predator and prey (prey runs towards the predator) than when the prey is between the predator and the refuge (prey runs away from the predator).