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Game Theory Applied to Primate Infanticide

http://www.sciencedirect.com.proxy.library.cornell.edu/science/article/pii/S0022519311000099

www.santafe.edu/~bowles/Dominance/Papers/vanSchaikEtal’04.pdf

While game theory is often applied to conscious human decisions, it can also be used to explain the instinctive behaviors of animals, such as non-human primates.

In primate groups, when the former dominant male is removed (by death or incapacitation), other males become the new dominant males and compete with each other for the top-ranking position in the primate group. These males may be from outside the group or they may be formerly lower-ranking males. Each newly dominant male has a goal to increase his reproductive success by siring as many offspring as possible. Often, this results in a newly dominant male committing infanticide: killing the infants of females with which they want to mate. This allows the female to conceive again much sooner than she would if she were still nursing an infant. Dominant males are normally effective protectors of infants, if they choose to protect them. This leaves newly dominant males with three options (per female): to attack the infant, to defend the infant, or to act indifferently towards the infant. This can be modeled as a game!

As the first article accomplishes, game theory can be applied to these male strategies. Each male is a player, and the infanticide decision can be modeled as a two-player game with three strategies per player. The strategies are listed as options above, and each option’s payoff is a combination of the benefit it gives to the male and the cost that it carries with it. The fate of the infant depends on the choices made by the two males. The strategy to attack the infant gives a benefit of allowing the male to sire another infant with the female (if the attack is successful). However, this strategy could be a mistake if there is a chance that the infant is actually that male’s offspring. The higher the probability that the male sired the infant, the less likely the male is to kill the infant. The cost to reproductive success is very high if the male kills his own infant. The next option is to defend the infant from the other male. The defending male only benefits (through better reproductive success) if he sired the infant, and thus as the probability that he is the father of the infant decreases, the probability of the male defending the infant also decreases. The cost to defending the infant is possible injury from the attacking male (if the other male does, in fact, choose to attack the infant). The third strategy is to act indifferently toward the infant. This option carries the benefit of possibly allowing the infant to survive if the other male does not attack it, and is only a benefit if the male sired the infant. The cost to this strategy and also to the defending strategy is possibly allowing an infant that the male did not sire to live, and thus increasing the time he must wait to impregnate the female.

How does the male know which strategy to choose? It depends mostly on the probability that he sired the infant in question, and also on what strategy the male thinks the other male will choose (which depends on the probability that the other male sired the infant). The male’s priorities are protecting the infant if he is the father, and if it is not his, getting the female to conceive again as soon as possible. If the female was more promiscuous prior to the birth of her infant, she may be able to prevent infanticide by having many males recognize the potential that they may have sired her infant, and thus the males would either defend the infant or act indifferently toward it. However, by spreading around the probability of paternity, the female risks the probabilities being low enough that the males would kill the infant or act indifferently toward it while another male attacks it.

Evidently, a male keeps tabs on the females with which he has mated, including how many times he has mated with her, the quality of the sexual experience, and how many other males have mated with her. This gives the male some idea of the probability of paternity and whether or not he will kill the infant in question. The payoffs and Nash equilibria can be quite complicated, but somehow primate males decide on a strategy without ever taking a course in game theory.

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