OLD AGE AND NATURAL DEATH 



running are very small indeed. The upshot of this is that young 

 animals will always outnumber old. 



Let us in imagination mark a group of 100,000 animals at 

 birth and follow it through life, supposing that the chance of 

 dying within any small interval of time is constant, and equal 

 to one-tenth per annum of those that remain alive to submit 

 to the hazard. The survivors at the end of the first year will be 

 90,000; at the end of the second year, nine-tenths of those alive 

 at its beginning, namely 81,000; and so on, through 72,900, to 

 numbers which obviously get very small. In a population with a 

 4ife table"* such as this, supposing that it is not decreasing in 

 numbers, a certain steady state of ages will be reached, a 

 certain definite age-spectrum or composition with regard to 

 age. At this steady stage, youngsters are being fed into the 

 lower reaches of each age-group at the same rate as death and 

 the passage of time remove them from it. The shape of this 

 ""stable age distribution"* (which is moulded, odd though it may 

 seem, by the birth-rate per head alone) is that of a die-away 

 exponential curve, such as one so often meets in the numerical 

 treatment of natural data. The number of animals in each 

 age-group bears a constant ratio, greater than unity, to the 

 number of animals in the age-group following next. 



What is important from our point of view is that the con- 

 tribution which each age-class makes to the ancestry of future 

 generations decreases with age. Not because its members 

 become progressively less fertile; on the contrary, it is one of 

 our axioms that fertility remains unchanged, so that the repro- 

 ductive value per head is constant;^ but simply because, as age 

 increases, so the number of heads to be counted in each age- 

 group progressively falls. It is at least as good a guess as 

 Weismann made, that the process of senescence has been 

 genetically moulded to a pattern set by the properties of this 



^ The term is teclmically defined in R. A. Fisher, The Genetical Theory 

 of Natural Selection, Chap. 2, Oxford, 1930. 



37 



