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
Information Structure in a Game
A few years ago, Jim Marden of Pennsylvania State University, in collaboration with Jonathan Waage of Brown University, staged a series of territorial contests between male damselflies (Calopteryx maculata). The male pairs in these contests had various, unequal reserves of fat, an indicator of strength. A common expectation for such contests (derived from game-theory models) is that each animal compares its own strength to that of its opponent and withdraws when it judges itself to be the probable loser. This has been confirmed by experimental studies on a variety of animals. The duration of such contests is greatest when the opponents are of nearly equal fighting ability, so that it is more difficult to judge which is likely to win. This is the same reason that many human sporting events are longer and more exciting when teams are evenly matched.
But the duels between the damselflies failed to follow this logic. Although the weaker animal ultimately conceded to its opponent in more than 90 percent of these encounters, Marden found no negative correlation between the duration of a contest and the difference in the relative strengths of the males. Here was a paradox, all the more baffling because the expected relationship had emerged repeatedly in studies of other species. Could there be something amiss in our assumptions about damselfly contests?
One possibly errant assumption is simply the belief that animals can assess one another's strength. Because it is such a good assumption for contests between animals with good visual acuity (such as bighorn sheep), and because so much of a behavioral ecologist's intuition about contest behavior had developed in that context, it was an easy assumption to overlook. But fat is stored internally in insects, so a damselfly cannot directly observe its opponent's reserves. (Marden also found no correlation between fat reserves and traits that surely are observable, such as body length or wing span.) Thus there emerged the intriguing possibility that damselflies do not assess their opponents' strength at all.
Accordingly, in a collaboration with Marden and Lee Dugatkin of the University of Louisville, one of us (Mesterton-Gibbons) developed a model in which a key assumption is that players know only their own reserves. In the resultant game, known as a "war of attrition," a strategy is the proportion of an animal's initial reserves that it is prepared to expend in a prolonged contest over a disputed site. A second key assumption is that the value of winning is proportional to the winner's remaining reserves. The more an animal has left, the more successful it will be in attracting a mate, finding food or defending its territory (and hence in producing surviving offspring). These assumptions determined the strategy set and the reward formula.
But what about the ecotype? Since a model is merely a caricature of nature, it effectively reduces a real ecological environment to a few parameters, with different values for different ecotypes. In the war-of-attrition game, there are only two such parameters, each a number between zero and one. The first, a coefficient of variation, measures the dispersion of energy reserves about their mean. For example, a coefficient of variation of 0.6 means that one standard deviation in fat reserves is 60 percent of the mean. The second parameter, a cost/benefit ratio, compares the reproductive cost of a spent unit of fat reserves to the eventual winner's reproductive benefit from a saved unit.
With each component of the game identified, we can look for an evolutionary stable strategy. In general, because an evolutionary stable strategy is a population strategy, the ecological parameters determine whether one exists. In this particular game, an evolutionary stable strategy exists (for reasons described below) if the coefficient of variation exceeds a critical threshold, which increases with the cost/benefit ratio but is never much more than about 0.5. The coefficient of variation for Marden's damselflies is 0.51, which would fall below critical if the cost/benefit ratio were between 0.99 and 1. However, in practice the cost/benefit ratio is likely to be considerably less than 0.99. Thus we could assume that fat reserves among damselflies are variable enough that an evolutionary stable strategy involving no assessment of opponents' strength could exist.
At this evolutionary stable strategy, both contestants are prepared to expend at least 50 percent of their initial reserves on the contest, although only the loser actually does so. We can verbally describe the reason for the stability of the no-assessment strategy. Being prepared to expend too small a proportion of initial reserves may mean ceding needlessly to weaker opponents (who would otherwise lose), whereas too high a proportion may mean wasting reserves needlessly against much stronger opponents (who would win in any case). Although animals do not know the reserves of their actual opponents, they achieve a balance between trade-offs by responding to the distribution of reserves among the population.
Marden later staged further damselfly duels in conjunction with Bob Rollins of Pennsylvania State University, and he pooled his data sets. Although the percentage of wins by fatter males fell from 90 percent to 86 percent, it was still remarkably high. Now, judicious approximation is the essence of modeling—effects that are small in a real population are typically absent from a model. For example, we would expect an 86 percent win rate for fatter males in the real world to translate into a 100 percent win rate for fatter males in the model. And this is precisely what happens because both contestants are prepared to deplete their initial reserves by the same proportion. The skinnier one invariably gives up first. In other words, although there is no assessment, the fatter male always wins.
Thus the assessment and no-assessment hypotheses both predict that fatter males always win. But there is also a difference. The assessment hypothesis predicts a negative correlation between strength difference and contest duration. Although, in the pooled data, Marden detected such a correlation in contests exceeding 500 seconds, the variation in strength difference could explain only 14 percent of the variation in contest duration. By contrast, in the no-assessment model, a contest ends when the loser gives up after using a fixed proportion of its reserves. So the no-assessment hypothesis predicts a positive correlation between final loser reserves and contest duration. And, in contests over 500 seconds, the variation in loser reserves was found to explain 29 percent of the variation in duration.
It is tempting to infer from these results that the no-assessment hypothesis is twice as likely to be correct. But we should desist, because 14 percent and 29 percent are both so much less than 100 percent. The results are really inconclusive. Nevertheless, our attempt to resolve the initial paradox has yielded a valuable new insight on animal contest behavior, namely, that a pattern of victory by stronger animals need not imply that strength is being assessed. Moreover, the analysis indicates the kind of population in which we could expect to find such a no-assessment evolutionary stable strategy: one with a high coefficient of variation.
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