138 Discussion 



Nigrelli: Is that true of well-fed and of starved tadpoles ? Well- 

 fed tadpoles should not metamorphose as rapidly as starved ones. 



Verzdr: In the cases which I know of the tadpoles were well fed. 



Lindop: Mr. Sacher, you were trying to put something forward 

 mathematically, using your concept of lifespan. I tried to relate 

 your criterion to what we were doing, and I found that I could not 

 apply it. In a discussion group like this, where there are so many 

 different disciplines, and we are each putting forward our own 

 specialist information, a short discussion on what is the most useful 

 concept of lifespan for us to be able to compare our different groups 

 might be helpful. People who have experiments which are half-way 

 through would then know what others want them to do for the rest 

 of them. 



Can you use your mathematical interpretations to get a mathe- 

 matical correlation between lifespan in naturally occurring popula- 

 tions and in populations where we ha^^e altered the lifespan ? By 

 irradiation we have altered lifespans both by your definition and 

 ours, but we have not changed the index of cephalization. 



Sacher: There are certainly many factors affecting length of life. 

 The thing has to be put into perspective. I have used the lifespan I 

 defined above — the maximum attained life — only in the present 

 context of doing a comparative study on a very broad scale. When 

 I am working on laboratory data I usually use the life expectation, 

 and specifically the after-expectation of life from the beginning of 

 exposure. In order to characterize the effects of radiations on popul- 

 ations, we have found that it is particularly convenient to discuss 

 these in terms of the log rate of mortality (Gompertz) curve (Sacher, 

 1956; Brues A. M., and Sacher, G. A. (1952). In Symposium on 

 Radiobiology, ed. Nickson, J. J., p. 441. New York: John Wiley). 

 Before discussing this I wish to point out that any one of the life- 

 table functions contains the same amount of statistical information 

 as any other, as long as you have not lost information by rounding, 

 setting up large class intervals, etc. The reason for preferring some 

 particular analytical function of the basic data is that it seems to give 

 the clearest insight into underlying mechanisms. 



Cohorts of mice kept under laboratory conditions have life-tables 

 such that the plot of logarithm of rate of mortality (Gompertz 

 transform) either is a straight line or shows a moderate amount of 

 curvature. In various mouse strains, the slope of the best-fitting 

 straight line at advanced ages (omitting the mortality primarily due 

 to infectious disease in young mice) does not vary significantly. In 

 hybrids showing marked hybrid vigour the slope again remains 

 unchanged, and the increased survival is due to a decrease in the 



