THE RELATIONSHIP BETWEEN CONTINUOUS INPUT AND INTERFERENCE MODELS OF IDEAL FREE DISTRIBUTIONS WITH UNEQUAL COMPETITORS

Fretwell's (1972, Populations in a Seasonal Environment, Princeton University Press) ideal tree model predicts the ideal distribution when individuals in a habitat are free to move between patches. In this paper, the relationship between the 'continuous input' and 'interference' ideal free models of Sutherland & Parker (1985, In: Behavioural Ecology: Ecological Consequences of Adaptive Behaviour, ed. by R. M. Sibly & R. H. Smith, pp. 255-274, Blackwell) and Parker & Sutherland (1986, Anim. Behav., 34, 1222-1242) are examined. Continuous input describes cases where resource items arrive at patches containing groups of waiting competitors. Increasing their density in a patch reduces individual gain rates because the resource items arrive at a fixed rate, and are shared between competitors. Interference describes cases where foragers search for prey items hidden within the patches. Increasing competitor density in a patch can reduce individual gain rates due to interference between individuals. Both can be modelled using the form: individual gain rate = Qini-m, in which Qi is the input rate or prey density in patch i, ni is the number of competitors, and m is a constant which increases with the strength of interference. A previous formulation of the above model in which individuals have unequal competitive abilities is extended to cover the case where phenotypic differences are reflected by a scaling of Qi (rather than by a scaling of the level of m). Here, many different mixed distributions of phenotypes can exist as ideal free equilibria, provided that relative competitive abilities stay constant across patches. Many different phenotypes can occur across several patch types. However, where phenotypic differences are best reflected by a scaling of m, then these mixed distributions of phenotypes are not possible, and no more than one phenotype can play a mixed strategy across the same pair of patch types. Typically, a truncated distribution of phenotypes between the patches can be expected, with the best phenotypes in the best patches. Some general conditions are proposed for ideal free distributions of unequal competitors. © 1992.