The Selfish Herd Revisited: Do Simple Movement Rules Reduce Relative Predation Risk?

Over two decades ago, W. D. Hamilton argued that animal grouping behavior could evolve if individuals selfishly avoided predation by reducing their domains of danger (Voronoi polygons). We examined this hypothesis through dynamic simulations of individual movement directed by a nearest-neighbor and other simple rules. Results from 500 simulations of 100 individuals moving towards their nearest neighbors for 100 moves (time-steps) showed a 20% increase in relative predation risk and a 1·2% decrease when adjusted for edge effects. This increase was 16% less than that of a random movement rule. When the two rules competed in a two-strategy game simulation, the nearest-neighbor rule always performed better than the random-movement rule with up to 41% differences in relative predation risk. The use of more complicated rules, based on consideration of multiple neighbors, decreased relative predation risk as much as 67%. We conclude that these more complicated, yet still simple movement rules, are adequate to explain the evolution of grouping behavior.