298 Hubert P. Yockey 



hapJoid survivorship, diploid survivorship, and to the role of equivocation in 

 the germ line. 



II. SURVIVORSHIP FOR THE HAPLOID CASE 



Otto Rahn (1,2) was the first to suggest in two pioneer papers published 

 in 1929 and 1930 that the genetic structure is the sensitive element in the cell 

 for radiation damage, thermal killing, and the action of some chemicals. He 

 later reviewed the data on disinfectant action and confirmed this opinion (3). 

 Lea (4) was a strong supporter of this idea and used it in his development of 

 the target theory. This is generally an accepted view today (5) although the 

 role of gene mutations and chromosome aberrations is a matter of debate (6, 7). 



In a previous article in this volume we showed that this notion follows 

 directly from the application of information theory to the current conception 

 of the storage and transfer of genetical information in the cell and the synthesis 

 of proteins. It is therefore of interest to continue the argument and attempt 

 to calculate survivorship curves. We also showed that error will exist in the 

 genetical information of all real organisms. The organism will live and multiply 

 according to Dancoff's principle (8), in spite of these errors. We argued 

 previously that there must be a distribution of message entropy values among 

 the elements of the ensemble of organisms. Suppose that the number of errors 

 in the genetical infoiTnation is increased as a result of, say, radiation. Those 

 elements of the ensemble near the lethal limit will succumb even though they 

 were quite viable before irradiation. 



This is a notion peculiar to information theory. The communications 

 analogy is Shannon's channel capacity theorem (9). This theorem shows that 

 if a channel has a capacity C, it is possible, by proper coding, to send information 

 at rate C or less through the channel with as small a frequency of errors as desired. 

 Thus, though the noise level in the channel will affect the channel capacity C, 

 it will not prevent nearly perfect transmission of information. This can be 

 assured by proper coding. As long as this limit C is not exceeded, it is impossible 

 for the recipient to know the noise level in the channel or information source. 



With these points in mind, we now return to the suggestions of Rahn and 

 Lea, keeping further in mind the idea of Watson and Crick that a mutation 

 is a change in the order of nucleotide bases in DNA (or some other information- 

 bearing molecule). We have proposed that the action of radiation or other 

 deleterious agent at the molecular level is such that the nucleotide pair mimes 

 some other nucleotide pair insofar as protein synthesis and replication are 

 concerned (10). The action of radiation may therefore be thought of as causing 

 lethality through gene mutation by decreasing the message entropy of some 

 members of the ensemble below the lethal limit. This is essentially the suggestion 

 of Rahn and of Lea phrased in the language of information theory, and it 

 follows from the argument given in the previous article in this volume. On 

 this basis we may proceed to calculate the force of mortality on the ensemble. 



The distribution of message entropy in the ensemble will be represented 

 by a probability distribution p(H, A), where A is a measure of the magnitude 

 of the deleterious agent and the initial distribution is p{H, 0). This distribution 

 will vary with the genetic character of the ensemble of organisms. It can 

 probably be derived from first principles, at least for simple cases, when more 



