The ideal free distribution: an analysis of the perceptual limit model
Edmund J. Collins, Alasdair I. Houston & Alison Lang.
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.