PLUTONIUM IN A GRASSLAND ECOSYSTEM 437 



identical size and preparation. According to these workers, "The much greater 

 translocation of ^^^Pu ... suggests that solubilization of the "^^^PuOt occurs to a 

 significant degree within the dog ... ." 



The previous two paragraphs do little to help explain the animal IRdata. A possible 

 explanation may be had in statistical bias that heretofore has gone undetected. Basically, 

 the bias has to do with the fact that both ^^^Pu and ^^*Pu are probably lognormally 

 distributed in environmental compartments. Therefore the ratio of ^^^Pu to •^^^Pu 

 should also be lognormally distributed (Aitchison and Brown, 1969, p. 11). Unfortu- 

 nately, the distribution of both ^^^Pu and ^^^Pu was censored; i.e., some proportion of 

 the data points was below a detectable limit (Aitchison and Brown, 1969). Shaeffer and 

 Little (1978) have shown that both the mean ratio and the variance of the ratio of two 

 censored lognormal variates will be decreased relative to ratios of uncensored variates if 

 the denominator (^^^Pu) has a lower magnitude than the numerator (^"'^Pu). The 

 magnitude of the decrease in mean ratio and variance is influenced by the relative 

 closeness to the detection limit of the two variates. 



This appears to be essentially the case with the IR data presented herein. The soil, 

 vegetation, and litter compartments had relatively high plutonium concentrations and 

 also relatively large IR"s. As the plutonium concentration began to approach the 

 detection limit, e.g., in arthropods and small mammals, the IR also decreased. Therefore, 

 if the censoring is large, an estimate of the mean or median of the uncensored ratios will 

 be in error because of the effect of censoring. 



A solution for the problem of ratios of two censored distributions is to try to 

 estimate the population parameters for each distribution and then use method R2 , i.e., 

 mean ratio equals mean ^^^Pu divided by mean '^^Pu, as suggested by Doctor and 

 Gilbert (1977). Kushner (1976) discusses two methods of estimating such parameters. 



Lognormality was assumed, and the methods of Hald (1949) as modified by Kushner 

 (1976) were used to calculate population parameters. Then, a method of Aitchison and 

 Brown (1969, p. 45) was used to calculate the "minimum variance unbiased estimator" of 

 the arithmetic mean isotopic ratio tor hide. The mean ratio of hide by these methods was 

 found to be 37. The median ratio published in this chapter was 20, and the mean ratio 

 calculated by summing all hide ratios and dividing by the number of ratios (method R3 in 

 Doctor and Gilbert, 1977) was 29. Therefore, although no confidence interval was 

 calculated, the mean IR in hide calculated by Kushner's (1976) method would be little 

 different from the mean IR in soil. Unfortunately, some of the small-mammal tissue data 

 are censored to such a degree that some of the functional values are extreme enough that 

 they were not tabulated by Hald (1949), one of Kushner's (1976) prime references. 

 Therefore the parameters of most of the censored small-mammal data cannot be 

 estimated by the methods of Kushner (1976) and Hald (1949). 



In summary, the median IR was constant in soil and vegetation compartments. 

 However, the median IR's also suggest that *^'^^Pu is preferentially mobile in animal 

 compartments of the grassland relative to '^^^Pu and soil. There is reason to believe that 

 the IR data are biased toward lower magnitudes as influenced by their nearness to the 

 detection limit. The mean IR for hide estimated with procedures of Kushner (1976) and 

 Hald (1949) suggested that these data may be similar to soil IR's. Other small-mammal 

 tissues were not compatible with these estimation procedures. Further field sampling to 

 eliminate the censoring difficulties is probably necessary if the question of differential 

 concentration of "^ ^"^Pu and ^ ''^^Pu in small mammals is to be resolved. 



