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Choosing a Nest Site: Contests and Catalysts

Game theory is an invaluable tool for analyzing and understanding conflicts in nature. The pioneering article was that of Maynard Smith and Price (1973), which introduced the concept of an evolutionarily stable strategy, but now hundreds of articles apply game theoretic ideas to biological problems. The three books by Maynard Smith (1982), Hofbauer and Sigmund (1988), and Sigmund (1994) are not exhaustive but do show the enormous scope of the applications. Here we are concerned with an n-player game that models the arrival of a population of birds at a nesting area. The sites have a variety of values, as measured by the expected number of offspring. The birds arrive sequentially and may decide either to occupy a vacant site (which need not be the best one) or to challenge for one that is occupied. The loser of such a challenge suffers a penalty (due to injury or loss of energy) and must then choose one of the unoccupied sites. We shall see that the interplay of strategies can be extremely complex. The purpose of this note is to demonstrate that some strategies may need the temporary presence of catalysts in order to establish themselves. In what follows, we shall use the word bird ambiguously to denote a nesting pair of birds as well as an individual. At the beginning of the nesting season, birds that arrive at a colonial site have to decide whether to accept a free nest area or to challenge a sitting bird for a (usually better) site. The problem is to determine how the birds should behave in order to maximize their own fitness. We shall suppose that the value of a site is fixed and known to each bird but accrues only to the bird finally in possession. If a contest takes place, then the loser of the fight is presumed to suffer a cost C and has to go to a vacant site before the arrival of the next bird. These assumptions ensure that the displaced bird is not in the same situation as a new arrival. Another basic simplifying assumption is that the probability, p, that a resident bird wins a contest is always the same. We are also applying similar ideas to hierarchies, and this assumption must then be modified. Of course, more complicated types of models can be imagined, but the central feature (choose a free site or fight) would seem to be basic, and our model is amenable to analysis. From the species' point of view, the best thing to do is simply fill the sites in an orderly fashion with no disputations. Such a solution is not stable because it is invadable by individuals (or gene copies) that do better for themselves. These "selfish" strategies will tend to be preferred by natural selection. We can treat the birds as if they were rational individuals because natural selection will tend to produce the strategy that such individuals would decide on. For the purposes