Interactive effect of starting distance and approach speed on escape behavior challenges theory

Escape theory predicts flight initiation distance (FID, predator-to-prey distance when escape begins) based on fixed functions relating costs and benefits of fleeing to distance between a prey and an approaching predator. Theory accurately predicts effects of costs for fixed functions and changes in functions due to changes in predator behavior approach. Less obvious is how the effect of starting distance (predator-to-prey distance when approach begins) on FID can be explained when predator behavior does not change during approach. We simulated predators to study effects of starting distance on FID in Balearic lizards (Podarcis lilfordi). Starting distance and approach speed affected FID interactively. It increased as starting distance increased during faster, but not slower, approaches. Because risk functions are considered fixed for a given approach speed, we must explain why FID varies with starting distance, why only for rapid approach, and how risk is assessed. Because prey approached slowly assess risk as small until the predator is very close, approach from greater distance has little effect on risk curves. Because continued rapid approach suggests that the predator has detected the prey and is attacking, not merely approaching, risk varies with starting distance. Theoretical difficulty in explaining the effect of starting distance on FID disappears if risk curves vary among starting distances at faster approach speeds, but each curve is fixed. This might occur if prey use a temporal rule of thumb assigning increasing risk as duration of rapid approach increases.