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
The Ecotype in a Game
As the damselflies exemplify, contests between animals of unequal strength are usually won by the stronger one. Suppose, however, that the animals are equally strong. What advantage could either then have? One possibility in competitions for resources is ownership. Indeed evidence abounds, in species as diverse as baboons, butterflies, lions and red deer, that if animals perceive themselves to be in the separate roles of owner and intruder when contesting a permanent resource, then the owner usually retains it with little serious fighting. There is nothing paradoxical about such respect for ownership. But wouldn't it surprise you if animals avoided serious fighting, not because intruders retreated, but rather because owners fled? That is what appears to happen in a species of Mexican spider, Oecobius civitas.
According to a study by J. Wesley Burgess, populations of this tiny spider live in darkness on the undersides of rocks. If a spider is disturbed from its hiding place, it is apt to enter the hiding place of another, which, if in residence, does not attack the intruder, but instead departs to find a new retreat. A domino effect can ensue, with retreats successively changing ownership until eventually a spider finds one unoccupied. This behavior is inherently paradoxical because, assuming a home-court advantage, the prize always goes to the contestant likelier to lose an actual fight. How can we make sense of this?
As usual, when a behavior is fixed, we expect to understand it as the evolutionary stable strategy of an evolutionary game, with effects that are small in the real population being absent from a model. Thus, we expect butterfly behavior to correspond to an evolutionary stable strategy at which owners always (as opposed to usually) win, and O. civitas behavior to an evolutionary stable strategy at which owners always lose. And, in both cases, we expect fighting to be absent (as opposed to rare). That is, in Maynard Smith's terminology, we expect butterfly behavior to follow a Bourgeois strategy—attack if an owner but be non-aggressive (or display) if an intruder. O. civitas behavior reflects an anti-Bourgeois strategy—display if an owner but attack if an intruder. Likewise, animals that invariably attack, regardless of whether they are owners or intruders, follow a Hawk strategy, and those that display in either role follow a Dove strategy. These four strategies imply an information structure, namely, that animals know their roles.
Using a simple game with these four strategies, Maynard Smith showed that only the Hawk strategy is evolutionarily stable if costs are low enough, whereas the Bourgeois and anti-Bourgeois strategies are evolutionarily stable if costs are high enough. But when two evolutionary stable strategies exist, the population can only be at one of them, and Maynard Smith's game could not say which.
One of us (Mesterton-Gibbons) incorporated Maynard Smith's strategy set into a more elaborate model. Each animal has a finite number of periods in which to find a site, which is essential for reproduction. It does not matter whether the site is acquired early or late, as long as it is owned by the end of the last period. The number of periods is unknown, but all animals have the same probability of surviving predation each period. There are more sites than animals, but the search for a site is random. So a vagrant animal may search in vain, and even if it finds a site it may be occupied. In that case, the animal can either continue to search or contest the site. If it wins, then it becomes an owner, and the previous owner must search again.
There's a catch to this, however. When there's a serious fight, the loser is so seriously injured that it can no longer search, and hence cannot reproduce. Even a winner may suffer injury, and have lower reproductive success than an uninjured animal. So there's a trade-off between the uncertainty of search and the risk of injury. The owner's probability of winning an actual fight is called its resource-holding potential. It is a number between 0.5 and one, indicating that the owner is more likely to win.
Whether animals fight depends on their strategies. A Bourgeois owner and an anti-Bourgeois intruder, or two Hawks, would always fight; an anti-Bourgeois owner and a Bourgeois intruder, or two Doves, would merely display; and a Hawk would always scare off a Dove, in either role. This reward and information structure results in a six-parameter ecotype.
Although the evolutionary stable strategy depends on all six ecological parameters, in terms of our paradox it depends critically on the animal's fighting ability and the probability of its survival. From Figure 6 it is evident that only the Hawk strategy is evolutionarily stable if survival is sufficiently low. Despite the risk of injury, it is better to fight than to hope to find a vacant site before the competition ends. At higher probabilities of survival, however, the Bourgeois or the anti-Bourgeois strategy is evolutionarily stable. To see why, suppose that the resource-holding potential remains constant, but that predation decreases slowly with time (so that the probability of survival increases slowly with time) and that the population tracks its changing environment by continually evolving to a new evolutionary stable strategy. Then we think of the population as a point moving horizontally to the right in Figure 6. As this point migrates, the Hawk strategy must eventually cease to be evolutionarily stable.
Why? Consider a lone Bourgeois mutant in an otherwise Hawk population. Because the Bourgeois animal behaves like a Hawk at home, being an owner has no effect on its reward. So a mutant Bourgeois has a higher reward than the population strategy if a Bourgeois intruder does better than an Hawk intruder. Now, a Bourgeois intruder runs from a Hawk owner, hoping to find an empty site eventually, but a Hawk intruder fights, hoping to win a site immediately. If predation is sufficiently low and the resource-holding potential is sufficiently high, however, the first hope is much more likely to be realized than the second. Thus the Bourgeois fares better than the Hawk and so will spread in the population.
Similarly, a mutant anti-Bourgeois in a Hawk population will behave differently only as an owner. It runs from an intruding Hawk, hoping eventually to find a vacant site, whereas a Hawk owner would fight, hoping to win immediately. If predation and the resource-holding potential are both sufficiently low, then the first of these hopes is much more likely to be realized than the second. Thus the anti-Bourgeois fares better than the Hawk and so will spread in the population.
In summary, under decreasing predation, a Hawk population evolves to Bourgeois if the resource-holding potential is relatively large, but the Hawk population evolves to anti-Bourgeois if the resource-holding potential is relatively small (Figure 6). If predation falls sufficiently, then the population will remain at either the Bourgeois or the anti-Bourgeois strategy depending on the initial resource-holding potential. In either case, a non-fighting population evolves from a population of fighters.
To the extent that lower predation increases the chance that not fighting and searching will eventually yield a site without injury, these results agree with those of Maynard Smith. But the new model goes further to suggest a resolution of our paradox. If an ownership asymmetry exists, then the resource-holding potential is almost always high enough to keep the population in a Bourgeois strategy under conditions of low predation. However, there are rare environments in which the resource-holding potential is low enough to keep the population in an anti-Bourgeois strategy under conditions of low predation. Does O. civitas represent such an exception? Perhaps. But without any empirical evidence that the resource-holding potential is indeed low in O. civitas, we can do no more than conjecture.
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