BULLETIN OF THE TORREY BOTANICAL CLUB 316 (Vou. 91 The problem of developing mathematical models to deseribe and predict the concentration of a given radionuelide in a particular ecosystem is perhaps too complex to be solved by the application of simple, empirical, or deterministic proportionality constants. A major source of the complexity of this problem is the wide variability of radionuclide concentrations in the biotie and abiotic components of a given ecosystem. Geographic variability may be ~ even greater. . 3, Other Deterministic Models. In the case of short-lived radionuclides such as I-131, a deterministic model may be adequate for quantitative studies during the acute phase of environmental contamination. French (1909) has used such a model to account for the acitvity of jack rabbit thyroids following a single release of radioiodine. The formula used by French is as follows : e “tp a “DE A=IxFx (<=) A =activity in thyroids I = total [-131 ingested on first day F = fraction of I-131 reaching thyroid Ag = effective I-131 decay constant in jack rabbits Ap = physical deeay constant for 1-131 e = 2.7183 t = time If ‘‘A’’ is known,‘‘I’’ can be estimated by transposition; and this value can be interpreted as an estimate of plant contamination, but there are several possible sources of error. French found that F varied from 15% in the ’ summer to 29% in the winter while Ag varied from .693/1.5 in winter to .693/2.5 in summer. This model assumes that the loss of I-181 activity from plants is equal to the physical decay constant (A,), but Chamberlain (1958) has reported that the loss of radioiodine from plants may occur at a greater rate. It is possible, therefore, that some expression should be ineluded in the formula to account for this source of variability.* 4, The Need for Stochastic Models. Mathematical models for longer-lived isotopes require expressions to account for an even greater variety of variables. In considering the circulation of radiostrontium, for example, in a simple desert ecosystem, it would be necessary to consider several input and several output factors for each of the major abiotic and biotic components of the system (Fig. 5). To account for the radiostrontium in or on plants (= animal diets) the input factors would be related to fallout (external de* Studies completed since this paper was written (Turner and Martin 1963, 1964) have used field data to test this model; and the model has been rewritten, in stochastic form, to estimate the frequency distribution of “A” based on limited, random variations in the other parameters,