Group Discussion 293 



borne in mind that this is an oversimpHfied form, suitable for dis- 

 cussing general principles. In application to data, more complicated 

 expressions are used. Each major disease category needs a separate 

 Gompertz term, as has been shown by Simms (1940. Science, 91, 7). 

 In addition the experiment need not be simply proportional to age, 

 a?, but may be a function of x. Thus the general expression for the 

 description of mortality in terms of a summation of Gompertz terms 

 is 



gx = 2 A^efi^^) 



i = l 



Perks : If you are fitting mathematical expressions to your data of 

 statistical distribution, then clearly you estimate the parameters, 

 and your estimated values for the parameters sum up the statistics. 

 I thought the problem we were really talking about was how to 

 characterize statistics for which you have not got a mathematical 

 expression. For a single measure to be sufficient the distribution 

 would have to be a very simple one, such as l^ = an exponential, in 

 which case you have got a single parameter and the measure might 

 be the constant rate of mortality or the half-life. In any other case, 

 you cannot sum up the distribution by a single measure, and you 

 cannot even say that any particular measure is the best one. All you 

 can say is that for some purposes one measure may be better than 

 another. You have to accept that the expectation of life or the half- 

 life or mode or whatever you may regard as the lifespan, gives you 

 only part of the information contained in the statistics. 



When the life-tables of different animals are compared, it may be 

 that the lifespan is good enough, and I think that view was expressed 

 yesterday. When the mortalities of the same species in different 

 environments are compared, I would agree that expectation of life 

 is probably as good as any. In general terms, if you are going to have 

 more than one figure as a measure of a death curve, probably the 

 1st, 2nd, and 3rd moments of the death curve would be as good as 

 any. It is not until you get a mathematical expression for the death 

 curve that you can really say that any parameters are better 

 estimators than any others. 



Benjamin: All this discussion of lifespan seems to be only a means 

 to an end ; we really want to get away from lifespans to considering 

 the ageing effects, for example, of changes in environment. For that 

 we really want two things. First, we need some kind of function 

 which is as discriminating as possible of the effects of ageing, so that 

 it is very sensitive. That suggests that what is wanted is the middle 

 part of the survival curve where a small change in the survival risk 



