Matching and ideal free distributions.

Ideal free distributions characterise how a group of animals should be distributed between sources of food. In a simple case, the ratio of the number of animals matches the ratio of input rates, a result known as input matching. The matching law characterises how an animal should allocate responses to sources of food. If matching holds then the ratio of behaviour allocated to the sources matches the ratio of rewards obtained. Several authors have drawn attention to the analogy between input matching and the matching law. I present a critical review of this topic, and go on to investigate the claim that the distribution of animals should be analyzed in the same way that the generalized matching law is analyzed. This involves assuming that the relationship between the ratio of animals and the ratio of resources obeys a power law with two parameters, one corresponding to bias and the other to sensitivity. On this view, a plot of the log of the ratio of animals against the log of the ratio of input rates will be a straight line and its intercept and slope will provide estimates of bias and sensitivity. I show that this approach can give a good fit even when the underlying model does not result in a power law. A consequence is that the parameters estimated cannot be interpreted as bias and sensitivity. I conclude that there are no compelling reasons for analyzing the distribution of animals using log-log plots, and the method has the disadvantage of encouraging the mistaken view that deviations from input matching follow a power law. [ABSTRACT FROM AUTHOR]