FEATURE ARTICLE
Animal Contests as Evolutionary Games
Paradoxical behavior can be understood in the context of evolutionary stable strategies. The trick is to discover which game the animal is playing
Mike Mesterton-Gibbons, Eldridge Adams
Reward Structure in a Game
Several years ago, one of us (Adams), in collaboration with Roy Caldwell at the University of California, Berkeley, observed a series of contests between stomatopods, or mantis shrimps, of the species Gonodactylus bredini. These crustaceans inhabit cavities in coral rubble. If one intrudes upon another, the resident often defends its cavity by threatening with a pair of claw-like appendages. These threat displays often deter intruders, so that contests are settled without any physical contact. A surprising observation is that when stomatopods are weakened by molting, so that they are completely unable to fight, they threaten more frequently than animals that are between molts. Furthermore, threats by weaklings often deter much stronger intruders, who would easily win a fight if there were one. In other words, the weaklings bluff. But if the very weakest members of the population can threaten profitably, then why don't all animals threaten? If the display can be given by animals that cannot back it up, then why do their opponents respect it?
To explore this paradox, we developed a game in which a resident can either threaten or not threaten, and an intruder responds by either attacking or fleeing. We assume that animals vary in weakness, that is, in how much their strength falls short of the maximum strength to be found in the population. We also introduce a reward structure that differs from that assumed by models of "honest" signaling. Specifically, threat displays increase the vulnerability of the signaler to injury inflicted by its opponent. The threat is thus a display of bravado that bears no special cost if the signaler is not attacked, but which adds an additional cost, the threat cost, if it is attacked by a stronger opponent. In addition, if there is a fight, both contestants pay a combat cost, consisting of a fixed cost, which even the strongest animal pays, and a variable cost that increases with weakness at a constant rate of marginal cost.
The threat cost, the fixed cost and the marginal cost together comprise the model ecotype. We also assume that, if there's a fight, the stronger animal wins. Finally, because the molt condition of stomatopods is not externally visible, we assume (as in the war-of-attrition game) that each contestant is unaware of its opponent's strength. So its own strength must determine its behavior.
For this particular reward structure, there is always an evolutionary stable strategy at which the weakest and strongest animals both threaten when resident, whereas those of intermediate strength do not (Figure 4, left). Why such a counterintuitive result? All residents face a similar trade-off: Threats deter some opponents without the necessity of fighting, but if the opponent is stronger and chooses to attack, then the threat increases the vulnerability of the signaler. The weaker the signaling animal, the more likely it is to pay the price of its increased vulnerability. That's why animals of intermediate strength cannot afford to threaten, but stronger animals can. This is essentially an instance of the handicap principle. However, the model illustrates a point lacking from previous discussions of handicaps, namely that the benefits of threats are greater for weaker animals, particularly those that have no other means of driving off competitors. These animals would be unlikely to win any of the contests against opponents that are deterred by threats. So the model shows a potential resolution of the paradox: The net costs of bluffing are lower for weak animals than they are for stronger ones. Bluffing therefore forms a part of the evolutionary stable strategy.
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