A Study of Aging, Thermal Killing, and Radiation Damage by Information Theory 307 



uglandis at three stages of growth in air and nitrogen. Rough survivorship 

 curves are given using eclosion as the criterion of survival. The haploid males 

 apparently do not exhibit an exponential survival. This point should be studied 

 further but it may be that the male haploid insects also exhibit a redundancy 

 in the genetic information similar to Chlamydonwnas in spite of their haploid 

 character. The argument used to derive equation (9) applies in these cases 

 as well as in the diploid case. 



So far in the discussion it has been argued that deviations from the ideal 

 fonn of the survivorship curves were due to the deleterious agent and p{H, 0) 

 was regarded as having the same form. The fact that many organisms, parti- 

 cularly hybrids, do not exhibit the survivorship curves corresponding to 

 equation (9) is shown in Fig. 3. This behavior is closely associated with the 

 genetic constitution of the organisms. There are a number of facts which 

 support this conclusion. 



Consider the survivorship curves of vestigial Drosophila melanogaster in 

 Fig. 2 which differs from the wild type, whose survivorship curve is shown in 

 Fig. 3 by a single gene. The same general effect has been reported by Clarke 

 and Smith (47) for Drosophila subobscura. The hybrids between two inbred lines 

 designated 'B' and 'K' exhibit a life span essentially double that of the parent 

 inbred strains. The data are not sufficiently extensive to determine the mathe- 

 matical form of the survivorship curve, but the inbred strains seem to have 

 roughly the same type as the vestigial Drosophila melanogaster of Pearl 

 and Parker shown in Fig. 2 while the hybrid has the same form as the wild 

 type shown in Fig. 3. This effect is also shown by mice. The survivorship 

 curves for nonnal aging are given in Fig. 3 for two hybrid strains and for the 

 hybrids of each with the C57 strain. 



It is therefore a very plausible conclusion that the survivorship curve is 

 very sensitive to the genetical character of the ensemble and that the change 

 of shape can be ascribed to the form of p(H, 0). 



This function p(H, 0) plays a role in information theory not unlike the 

 equation of state in thermodynamics. We are at liberty to admit many types 

 of probability distribution in //but it must be the same one in a given ensemble 

 of organisms for all experiments. That this is the case is illustrated for mice 

 by the resemblance between the survivorship curves for gamma- and x-irradia- 

 tion and those for normal aging. The purposes of most of the work in this 

 field, particularly in the case of acute killing, are served by obtaining an LDgQ. 

 The results are ordinarily reported by probit analysis and the life table is not 

 given. We will not attempt to review the very extensive literature, which was 

 not developed for the present purpose. Rather we will quote one experiment 

 which involved a very large number of mice and which has been extensively 

 studied and reported (48, 49, 50). In Fig. 5 the acute killing from atomic 

 bomb radiation as a function of dose is shown from Cronkite et al. (51), 

 on LAFj mice. This is to be compared with the normal aging survivorship 

 curve obtained from the controls. All curves on this figure are normalized 

 by being passed through the 3 per cent survivorship point, after the custom 

 of Pearl. The data of Murray and Hoffman (52) and Murray (53) giving 

 normal aging life tables for hybrid and in-bred mice are also shown. The 

 agreement, of course, is not exact but the curves for gamma-ray acute lethality 



