The ideal free distribution when the resource is variable

On the basis of the ideal free distribution (IFD) model, twostochastic models that incorporate the uncertainty of the informationused for decision making were considered to investigate theeffects of the variability in the resource supply rate on theIFD under continuous input conditions. In the uncertain-informationmodel, competitors cannot trace the variation of the supplyrate and use the expectation of the supply rate or previouspayoffs for decision making. Both submodels predict matchingof means, in which the average number of competitors for eachpatch is proportional to the average supply rate in the patch.In the perfect-information model, competitors continuously knowand trace the environment conditions. Numerical predictionsdepend on the relative size of the resource variance betweenpatches. When the resource variance in the good patch is sufficientlylarger than that in the poor patch, it predicts undermatchingof means; when the variance of the supply rate for each patchis small and proportional to the average of the supply ratein the patch, it predicts matching of means; and when the resourcevariance in the poor patch is larger than (or equal to) thatin the good patch, it predicts overmatching of means. Theseresults indicate the importance of clarifying the assumptionon the uncertainty in information for decision making and thetype of the resource variance for the test of the IFD underconditions where the resource supply rate is stochastic.