Journal of Animal Ecology 2001 70, 1062– 1069 © 2001 British Ecological Society Blackwell Science Ltd Unequal competitor ideal free distributions: predictions for differential effects of interference between habitats STUART HUMPHRIES*†, GRAEME D. RUXTON* and JAAP VAN DER MEER‡ *Division of Environmental and Evolutionary Biology, Institute of Biomedical and Life Sciences, Graham Kerr Building,University of Glasgow, Glasgow G12 8QQ, UK; †Freshwater Biological Association, The Ferry House, Far Sawrey, Ambleside, Cumbria, LA22 0LP, UK; and ‡Nederlands Instituut voor Onderzoek der Zee, PO Box 59, NL-1790 AB Den Burg, Texel, The Netherlands Summary 1. Unequal competitor ideal free distribution (IFD) models that deal with the effects of interference allow for the relaxation of several unrealistic assumptions of the basic IFD model. We used the recently developed interaction-matrix method to examine the general case where the effect of interference can vary between patches, one previously unexplored in the literature. 2. An analytical approach revealed that mixed solutions are not possible for the case of differential interference between patches. However, simulations from an individual- based model suggest that, when numbers of individuals similar to those commonly used in empirical tests of the IFD are considered, mixed solutions are in fact predicted. 3. This discrepancy can only be detected by the use of individual-based models, and may help to explain the lack of certain previously predicted distributions in empirical tests of the theory. We suggest that future work should employ individual-based models to better link empirical tests with analytic theory. Key-words: ideal free distribution, interference, interaction-matrix, unequal competitors. Journal of Animal Ecology (2001) 70, 1062– 1069 Introduction The ideal free distribution (IFD) (Fretwell & Lucas 1970; Fretwell 1972) is an important pillar of theoretical ecology and forms the basis of most attempts to predict the distribution of individuals between different resources. In the IFD as originally defined, individual animals are equal in their competitive abilities, are free to move between resource patches, and have perfect knowledge of the qualities of all available patches. Much attention has been given to elaborating the model to include assumptions that are more realistic (for an overview see Tregenza 1995) and the IFD has been extensively tested, modified and improved. In particu- lar, many studies have relaxed the assumption that all individuals are intrinsically equal in their competitive ability. However, these studies, almost without excep- tion, assume that the ratio of the competitive abilities of two phenotypes will remain unchanged, regardless of the identity of the patch that they occupy. For instance, if an individual of phenotype A has twice the competitive ability of an individual of phenotype B in one patch of the system, then it is assumed that it will have twice the com- petitive ability of the B individual in all patches in that system, even if the absolute competitive abilities of indi- viduals of the two phenotypes change between patches. Intuitively, we might expect relative competitive ability to vary between patches when patches contain different prey types or require different foraging strategies. For example, Cresswell, Smith & Ruxton (2001) found that free-living European blackbirds Turdus merula L. differed in their relative foraging rates and susceptibility to interference, dependent on the amount of leaf litter in foraging patches. Despite the prevalence of such variation in the real world, surpris- ingly little effort has been spent on investigation of such cases, and there is growing evidence that the assump- tion of constant competitive abilities does not hold in some systems. For instance, demonstrations of varia- tion in the strength of interference with resource den- sity on different patches for snow buntings Emberiza nivalis L. (Dolman 1995), differences in the relative competitive ability of cichlid fish Aequidens portaleg- rensis (Hensel) (Tregenza & Thompson 1998) and Correspondence: S. Humphries, Division of Environmental and Evolutionary Biology, Institute of Biomedical and Life Sciences, Graham Kerr Building, University of Glasgow, Glasgow G12 8QQ, UK (fax + 44 141 3305971; e-mail s.humphries@bio.gla.ac.uk).