Many-eyes and sentinels in selfish and cooperative groups

Collective vigilance describes how animals in groups benefit from the predator detection efforts of others. Empirical observations typically find either a many-eyes strategy with all (or many) group members maintaining a low level of individual vigilance, or a sentinel strategy with one (or a few) individuals maintaining a high level of individual vigilance while others do not. With an analytical treatment that makes minimal assumptions, we show that these two strategies are alternative solutions to the same adaptive problem of balancing the costs of predation and vigilance. Which strategy is preferred depends on how costs scale with the level of individual vigilance: Many-eyes strategies are preferred where costs of vigilance rise gently at low levels but become steeper at higher levels (convex; e.g., an open field); sentinel strategies are preferred where costs of vigilance rise steeply at low levels and then flatten out (concave; e.g., environments with vantage points). This same dichotomy emerges whether individuals act selfishly to optimize their own fitness or cooperatively to optimize group fitness. The model is extended to explain discrete behavioral switching between strategies, differential levels of vigilance such as edge effects, and turn-taking.