Fleeing to refuge: Escape decisions in the race for life

Economic escape theory that predicts that flight initiation distance (FID=predator-prey distance when a prey begins to flee from an approaching predator) increases as predation risk increases has been overwhelmingly supported. However, the vast majority of empirical tests have focused on effects of single predation risk factors. Even studies that have included multiple risk factors have not predicted how they jointly affect FID. I present a model that predicts joint effects of several predation risk factors that affect the outcome of a race between predator and prey to the prey's refuge. As a prey's distance to refuge and predator attack speed increase, and as the prey's location forces it to flee more toward a predator to reach refuge, FID increases. A published model proposed and experiment showed that FID is longer when prey flee directly toward than directly away from a predator to a refuge. We present a new geometric model that predicts FID for all angles between the prey's and predator's paths to refuge, distance of the prey from refuge when escape begins, predator and prey speeds, and a margin of safety allowing the prey to reach refuge before the predator. The model provides many new, testable predictions about relationships among its variables and FID. Most notably, it predicts that FID increases sigmoidally as the angle between predator and prey paths to refuge increases. Although the model is not economic (cost-benefit), we discuss its relationship to economic escape theory.