The origin and the evolutionary stability of cooperation between unrelated individuals is one of the key problems of evolutionary biology. In this paper, a cooperative defense game against a predator is introduced which is based on Hamilton’s selfish herd theory and Eshel’s survival game models. Cooperation is altruistic in the sense that the individual, which is not the target of the predator, helps the members of the group attacked by the predator and during defensive action the helper individual may also die in any attack. In order to decrease the long term predation risk, this individual has to carry out a high risk action. Here I show that this kind of cooperative behaviour can evolve in small groups. The reason for the emergence of cooperation is that if the predator does not kill a mate of a cooperative individual, then the survival probability of the cooperative individual will increase in two cases. If the mate is non-cooperative, the–according to the dilution effect, the predator cofusion effect and the higher predator vigilance–the survival probability of the cooperative individual increases. The second case is when the mate is cooperative, because a cooperative individual has a further gain, the active help in defence during further predator attacks. Thus, if an individual can increase the survival rate of its mates (no matter whether the mate is cooperative or not), then its own predation risk will decrease.
Hamilton’s “selfish herd” theory (1971) claims that predation risk is lowered when animals huddle in groups, and is lowest for those that are in the middle of the “herd”. Buffalo are a good example. We call them selfish since if one Buffalo is attacked, the others don’t generally help it, they just run. But, as a group they are safer in large numbers.
The trouble with such a theory is it doesn’t explain how altruistic behavior (helping out a fellow group member at the risk to oneself) would develop. Garay’s paper aims to help make sense of how this is possible.
His argument hinges on a Game Theoretic model that shows that although in the short term, a non-altruistic strategy confers a better survival rate, in the long term the altruistic strategy does.
If there are only 2 animals, A and B, and we assume that a predator can only realistically attack one at a time, then the probability of A being attacked is 1/2 in a single round of predation. So, in a one-shot game, if B is attacked, A’s best strategy is to cut and run, since helping B may result in injury or death.
But, if the same game is played over and over (that is, if they run the risk of being attacked often, as is the case in real life), then A’s best strategy is to help out B. This might seem incongruous, but it isn’t.
If B dies in the first attack, then A’s probability of being attacked in the next round is 100%! If he has a less than 100% chance of dying by way of helping B in the first attack than he is better off helping B since on the next round he’ll still have only a 50% chance of being attacked. 50% is certainly better than 100%!
The above is true even if B NEVER helps out A. That is, if A is the only Altruistic one in the (2 man) group, then it is still to his advantage to continue to be altruistic. But, if B also is altruistic (helps A when A is attacked) then this is all the better for A. Also, B would then enjoy the same benefits as A.
What is interesting to me is that this argument doesn’t hinge on kin selection at all. Kin selection is the idea that an individual is far more likely to come to aid of another individual who shares a large portion of their genome (like children, siblings, ect) than they are to a total (genetic) stranger. But, here, the two don’t need to be related at all. The risk of predation is enough to “glue” them to one another.
Garay, Jozsef. 2009. “Cooperation in Defence against a predator.” Journal of Theoretical Biology. 257 (2009) 45-51.
Hamilton, W.D., 1971. “Geometry for the selfish herd.” Journal of Theoretical Biology. 31, 295-311.
Wilson, E.D. 1975. Sociobiology. The Belknap Press Harvard University Press, Boston.