Do 3-D predators attack the margins of 2-D selfish herds?

To explain the evolution of grouping, Hamilton's selfish herd theory assumes that predators attack the nearest prey and that both are acting on a 2-dimensional (2-D) plane. This proximity assumption in his theory is one explanation for marginal predation, the phenomenon whereby predators attack peripheral members of a prey group. However, in some ecological circumstances, predators move in 3-dimensional (3-D) space and prey in 2 dimensions. Because a predator coming from above or below the group may have relatively equal access to all members, marginal predation cannot be assumed. In this paper, we test whether marginal predation occurs in such a 3-D/2-D geometry. We carried out 3 controlled laboratory experiments in which fish attack prey grouped at the water's surface. Predators were bass (Micropterous salmoides) or goldfish (Carassius auratus), and prey groups were either free-swimming whirligig beetles (Dineutes discolor) or a constrained group of tadpoles (Bufo bufo). In all 3 experiments, predators were significantly more likely to attack the periphery of prey groups. Our experiments also show that marginal predation is robust to differences in overall density within a prey group and that the fish are not reacting to observable state or behavioral correlates to position within a prey group. Furthermore, our results showed that predators will attack group margins even when there is no variation, due to position, in nearest neighbor distance.