Evol Ecol Res 4: 471-493 (2002) Full PDF if your library subscribes.
The ideal free distribution: an analysis of the perceptual limit model
Edmund J. Collins,* Alasdair I. Houston and Alison Lang
Centre for Behavioural Biology, School of Biological Sciences, University of Bristol, Woodland Road, Bristol BS8 1UG, UK
Address all correspondence to E.J. Collins, Department of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK.
Since the introduction of the ideal free distribution in the 1970s, amendments have attempted to explain observations that deviate from the prediction of input matching. We consider a perceptual limit model that relaxes the assumption that animals are ideal. Under the model, individuals move to the location with the highest potential intake rate, unless the potential intake rates differ by less than some fixed amount, in which case the animals move at random. The random movements of the animals mean that there are often many feasible distributions. Here we present a new method of implementing the model in which we treat movements between the feasible distributions as a Markov chain. Analysis of this model shows that the range of feasible distributions is determined by the limits on the random movements of the animals. This new method allows us to compute the equilibrium probability of observing each feasible distribution, to compute the expected long-term rate of intake overall and on each site, and to compute differences in the expected total intake of individual animals depending on their initial site and the initial number on that site. We show that observed limits from feeding trials could be used to provide a more robust test of the perceptual limit model than comparing predicted average distributions.
Keywords: ideal free distribution, input matching, Markov chain model, perceptual limit.
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