906 RADIATION BIOLOGY 



the precursor affected are given by the successive terms of the binomial 



expansion [(1 — p) + p]". It may be assumed that precursors with a 



x 

 proportion of from to - cells altered can still develop normally, while 



ft 



x + 1 

 those with a proportion of from — to all cells altered will give rise to 



a changed character, the degree of abnormality being determined by the 

 number of stricken cells. The larger p becomes on raising the dose, 

 (1) the relatively smaller will be the proportions of animals in the classes 

 with 0, 1, 2, . . . , x cells affected, i.e., the greater the incidence of 

 abnormality, and (2) the larger will be the mean, pn, i.e., the higher the 

 average degree of abnormality. The result, mentioned in the preceding 

 section, that irradiation under hypoxia is equivalent in end result to 

 lower dose treatment in air, indicates that for any given dose, p is lower 

 under hypoxia, since n and x are presumably constant. The fact that 

 irradiation at a stage subsequent to that of maximum sensitivity may still 

 yield abnormality with a higher dose can be explained either by decrease, 

 with age of precursor, in p for a given dose because of some biological 

 reason, e.g., slowing in rate of mitosis, or merely by increase in n (pro- 



x 

 vided - > pn), or by a combination of these factors. 



The above statistical considerations on incidence and degree show that 

 there could be variability in results even in perfectly uniform material, a 

 fact which has not generally been recognized. As it is, however, such 

 variability would be superimposed on three biological variables: (1) 

 genetic variability, which can, however, easily be controlled by the use of 

 inbred material ; (2) environmentally determined variability existing even 

 in genetically homogenous material of a given developmental age; 

 (3) differences in developmental age between and within litters of a given 

 chronological age (Allen and MacDowell, 1940) ; these probably account 

 in part for the finding that certain abnormalities are obtainable with low 

 incidence by irradiating on the days adjacent to the main critical period. 



The effect of genetic constitution on radiosensitivity to the induction of 

 certain abnormalities has been studied by Russell and Russell (1950b), 

 choosing characters (homeotic shifts in vertebral borders and related 

 changes in the thorax) in which there is normal variability between as 

 well as within inbred strains. Genetic constitution determines the loca- 

 tion of the strain on a scale of developmental potencies, while environ- 

 mental factors, mostly intangible, cause individuals to be distributed 

 about this mean. Because of thresholds of expression, the finally 

 observed characters fall into alternate categories. Data indicate that 

 differences between three strains in the final visible result of a given dose 

 of radiation — and thus in the apparent ease of radiation shift — are not 

 attributable to differences in the underlying effect. For example, 200 r 



