The ideal free distribution when the resource is variable

On the basis of the ideal free distribution (IFD) model, two stochastic models that incorporate the uncertainty of the information used for decision making were considered to investigate the effects of the variability in the resource supply rate on the IFD under continuous input conditions. In the uncertain-information model, competitors cannot trace the variation of the supply rate and use the expectation of the supply rate or previous payoffs for decision making. Both submodels predict matching of means, in which the average number of competitors for each patch is proportional to the average supply rate in the patch. In the perfect-information model, competitors continuously know and trace the environment conditions. Numerical predictions depend on the relative size of the resource variance between patches. When the resource variance in the good patch is sufficiently larger than that in the poor patch, it predicts undermatching of means; when the variance of the supply rate for each patch is small and proportional to the average of the supply rate in the patch, it predicts matching of means; and when the resource variance in the poor patch is larger than (or equal to) that in the good patch, it predicts overmatching of means. These results indicate the importance of clarifying the assumption on the uncertainty in information for decision making and the type of the resource variance for the test of the IFD under conditions where the resource supply rate is stochastic.