  Animal grouping behaviors have been widely studied due to their implications
for understanding social intelligence, collective cognition, and potential
applications in engineering, artificial intelligence, and robotics. An
important biological aspect of these studies is discerning which selection
pressures favor the evolution of grouping behavior. In the past decade,
researchers have begun using evolutionary computation to study the evolutionary
effects of these selection pressures in predator-prey models. The selfish herd
hypothesis states that concentrated groups arise because prey selfishly attempt
to place their conspecifics between themselves and the predator, thus causing
an endless cycle of movement toward the center of the group. Using an
evolutionary model of a predator-prey system, we show that how predators attack
is critical to the evolution of the selfish herd. Following this discovery, we
show that density-dependent predation provides an abstraction of Hamilton's
original formulation of ``domains of danger.'' Finally, we verify that
density-dependent predation provides a sufficient selective advantage for prey
to evolve the selfish herd in response to predation by coevolving predators.
Thus, our work corroborates Hamilton's selfish herd hypothesis in a digital
evolutionary model, refines the assumptions of the selfish herd hypothesis, and
generalizes the domain of danger concept to density-dependent predation.
