Optimal strategies for predator avoidance: the relative importance of speed and manoeuvrability

The relative importance of speed and manoeuvrability in predator-prey chases was assessed by investigating whether or not a pursuing predator could catch its prey in a simple turning gambit initiated by the prey animal. The turning radius and velocity of the prey were normalized by dividing them by those of the predator. With the use of numerical methods to solve implicit equations it was determined for what values of relative radii and velocity the prey could escape. When escape was possible the optimal time of initiation of the prey's turn and the minimum closure distance of the predator were computed. It was found initially by numerical and subsequently by analytic techniques that, in order for the prey to escape the predator in the turning gambit, its normalized velocity must be related to its normalized radius by the inequality: $\text{v>r}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ over the interval 0 ? r ? 1. Situations in which the results of the turning gambit may be expected to give realistic predictions of capture or escape are discussed together with physical factors governing the relationship between turning radius and velocity, and the conditions under which the prey might profitably trade higher velocity for a smaller turning radius. Lastly, a number of specific predator-prey combinations are treated with a view towards illustrating the application of the theory and promoting the collection of simultaneous turning radii and velocity data.