AN UNSOLVED PROBLEM OF BIOLOGY 



ageing. Test-tubes will do, since they are clearly ""mortar, and 

 I shall peremptorily assume that they do not become more 

 fragile with increasing age.* 



Imagine now a chemical laboratory equipped on its founda- 

 tion with a stock of 1000 test-tubes, and that these are acci- 

 dentally and in random manner broken at the rate of 10 per 

 cent, per month. Under such an exaction of mortality, a 

 monthly decimation, the activities of the laboratory would soon 

 be brought to a standstill. We suppose therefore that the 

 laboratory steward replaces the broken test-tubes monthly, 

 and that the test-tubes newly added are mixed in at random 

 with the pre-existing stock. The steward will obviously be 

 obliged to buy an average of 100 test-tubes monthly, and I am 

 going to assume that he scratches on each test-tube the date 

 at which he bought it, so that its age-in-stock on any future 

 occasion can be ascertained. 



Now imagine that this regimen of mortality and fertility, 

 breakage and replacement, has been in progress for a number 

 of years. What will then be the age-distribution of the test-tube 

 population; that is, what will be the proportions of the various 

 groups into which it may be classified by age? The answer is 

 illustrated in Fig. 3. The population Avill have reached the 

 stable or ''life-table'' age-distribution in which there are 100 

 test-tubes aged 0-1 month, 90 aged 1-2 months, 81 aged 2-3 

 months and so on. This pattern of age-distribution is char- 

 acteristic of a ''potentially'' immortal population, i.e. one in 



* [In real life, of course, test-tubes could undergo senescence of both the 

 types, (a) and (6), which I have distinguished in the text. 'Innate senescence' 

 might be represented by the slow crystallization of the glass, which will 

 happen whether the test tubes are used or not, and 'traumatic senescence' 

 by the accumulation of tiny chips or cracks which, without making the 

 test-tube unusable, make it a good deal more likely to be broken in 

 everyday use. A life table for glass tumblers has been worked out by G. W. 

 Brown and M. M. Flood, Journal of the American Statistical Association, 

 42, p. 562, 1947.] 



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