### Abstract

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 Emits from feeding trials could be used to provide

Translated title of the contribution | The ideal free distribution: an analysis of the perceptual limit model |
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Original language | English |

Pages (from-to) | 471 - 493 |

Number of pages | 24 |

Journal | Evolutionary Ecology Research |

Volume | 4 (4) |

Publication status | Published - 10 Apr 2002 |

### Bibliographical note

Publisher: University of ArizonaOther identifier: IDS number 552FN

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## Cite this

Collins, EJ., Houston, AI., & Lang, A. (2002). The ideal free distribution: an analysis of the perceptual limit model.

*Evolutionary Ecology Research*,*4 (4)*, 471 - 493. http://www.evolutionary-ecology.com/issues/v04n04/ccar1274.pdf