Relation of Lifespan to Brain and Body Weight 117 



as much as 20 per cent. There is a good reason for this, as will 

 be discussed below. 



One objection that has been raised to the use of lifespans is 

 that the estimated lifespan will increase as the sample on 

 which the estimate is based increases. Until recently there 

 was no comprehensive statistical treatment of this question. 

 With the publication of Gumbel's (1958) treatise on the 

 Statistics of Extremes, we now have a statistical theory that 

 is adequate to deal with most questions that arise. The 

 characteristic oldest age (the age attained when one survivor 

 remains of the initial cohort) is an easily computed statistic in 

 terms of which we can discuss the dependence of lifespan on 

 cohort size. If the survivorship curve is of the Gompertz type, 

 in which the age-specific rate of mortality increases exponenti- 

 ally with age, the characteristic oldest age increases as a double 

 logarithmic function of the cohort size. This is illustrated in 

 Fig. 1, where the characteristic oldest age is shown in relation 

 to cohort size for an actual life-table of the Gompertz type, 

 drawn from Comfort's analysis (1958) of the life-table of 

 thoroughbred mares. It can be seen that increasing the cohort 

 size by a factor of 10^ would increase the characteristic oldest 

 age by only one-third. The lifespan itself, i.e. the age at death 

 of the oldest survivor, would vary more slowly than this. 



The typical mammalian life-table can be adequately des- 

 cribed by the Gompertz-Makeham equation, in which the 

 relation of rate of mortality to age contains a constant term 

 in addition to the Gompertz term: 



q^ =Ae^ + B (1) 



The Makeham term, B, is markedly influenced by environ- 

 mental conditions, whereas the Gompertz term is influenced 

 to only a small degree. However, the Gompertz term will 

 always dominate at advanced ages, and the lifespan therefore 

 tends to behave like an extremum statistic of a Gompertz life- 

 table. Since the inherent ageing parameters characteristic of 

 the species are embodied in the parameters A and a of the 



