Balance studies on compartmental systems with stochastic inputs.

For a population of identical one compartment systems with daily inputs which are random samples from a stationary distribution the mean of the daily balance (balance = input minus excretion) taken over the population of compartments or over days for one compartment is linearly dependent on input with a slope which is independent of the distribution of the inputs and an intercept which depends only on the mean of the distribution of intakes. Analytical and simulation studies on a model with three daily inputs gives essentially similar results. Even if the inputs are not from a stationary distribution but the inputs to a population of compartments are all from the same distribution, one still obtains a linear regression of the mean of the daily balance over the population of compartments , on intake for any particular day but this no longer holds from day to day. This provides a theoretical basis for the interpretation of balance studies on populations of individuals when the daily intakes of an element under study cannot be kept constant.