DERIVING POPULATION PARAMETERS FROM INDIVIDUAL VARIATIONS IN FORAGINGBEHAVIOR .1. EMPIRICAL GAME-THEORY DISTRIBUTION MODEL OF OYSTERCATCHERS HAEMATOPUS-OSTRALEGUS FEEDING ON MUSSELS MYTILUS-EDULIS

1. The basic structure is described of a game theory model of the dist ribution of a wintering shorebird, the oystercatcher Haematopus ostral egus, foraging on 12 mussel Mytilus edulis beds whose quality as feedi ng areas for the birds differed. Model parameters were derived from fi eld studies made over 15 years. A companion paper tests model predicti ons and illustrates how the model can be used to derive survival curve s and predict estuary carrying capacity. 2. Mussel-bed quality was mea sured as the intake rate achieved by an oystercatcher of average compe tance foraging at random over the bed, and varied threefold across bed s. Each individual in the model was given its own foraging efficiency, drawn at random from a normal distribution whose mean and variance de pended on the bird's age and feeding method. Its susceptibility to int erference from other foraging birds was calculated from its local domi nance score, the percentage of wins it had over the other individuals currently on the same bed. A bird's local dominance score on a particu lar mussel bed was calculated from the proportion of birds on that bed having a lower global dominance rank, a measure of a bird's competiti ve ability relative to those of all other birds on the estuary. Across individuals, foraging efficiency and susceptibility to interference w ere unrelated. 3. In every iteration, the model calculated a bird's pu tative intake rate on each bed by subtracting the reduction in intake rate due to interference from the intake rate the bird could achieve t here in the absence of interference. Each individual could then move t o the mussel bed which, at that time, gave it the highest intake rate, provided the differences were suffciently large (3%) for it to discri minate. 4. The main model limitations were the absence of: (i) a real- time base, so time-lags due to learning were not included; (ii) the en ergy costs associated with moving between beds; (iii) the opportunity for birds to increase their dominance score or foraging efficiency thr ough familiarity with a mussel bed; (iv) the opportunity for individua ls to control the amount of competition to which they are exposed by s electing particular times in the tidal cycle at which to feed; and (v) factors known to affect bed attractiveness to oystercatchers, such as the consistency of the substrate. None the less, the model was regard ed as a suitable starting point for exploring how the proportion faili ng to acquire enough food, and either emigrating or starving, is affec ted by population size.