Data for the Problem of Evolution in Man. 167 



obtain a rough approximation to the effect of reproductive selection in 

 modifying the duration of life. It has been shown* that if there be no 

 assortative mating the average deviation, /^, of an array of offspring 

 from the mean of the general population of offspring due to parents 

 deviating h-2 and h s from the means of the general populations of 

 parents is given by : 



hi = fa Ai-r-ris *8j 



"2 0-3 



where r^ and r 13 are coefficients of parental inheritance, and a- v o- 2 , o- 3 , the 

 standard deviations in offspring and parents for the character in ques- 

 tion. When that character is longevity our data are not yet complete, 

 but two of us have shown that the value of ri20"i/<r 2 for father and son, 

 i.e., the regression coefficient for inheritance of duration of life, is about 

 0-1682, f if the sons die having lived at least 21 years. We have not 

 yet completed our data for the inheritance of the duration of life in 

 the case (i) of minors, or (ii) in the case of the female line, although 

 we have nearly reached the requisite amount of material. Hence the 

 following statements must be taken as tentative and suggestive only. 

 We will assume 0-1682 to be the regression coefficient for both sexes, 

 and for all ages of the offspring, minors or adults. In this case if m l be 

 the mean of the unweighted and m. 2 of the weighted fathers, mi of the 

 unweighted and m.{ of the weighted mothers, we should expect an 

 increased duration of life in the offspring due to reproductive selec- 

 tion of 



hi = OT682(m 2 - mi) + 0-1682 (w 2 '-TOi') 



- 0-1682 (6-328 + 4-996) \ f ,, . 



v ' >for the Americans 



= 0-1 682 (2-656 + 1-900) 1 , ,, ,-, r , 

 = . 77U 'j> for the English 



Thus the increased duration of life would be about 2 years per 

 generation from the American data, and about 9 to 9'5 months per 

 generation from the English data. 



The result for the American series shows us how an especially low 

 expectation of life, due possibly in this case to some family character,! 

 will be rapidly Raised by reproductive selection, if there be no opposing 



* ' Phil. Trans.,' A, vol. 187, p. 288. 



t ' Roy. Soc. Proc.,' vol. 65, p. 297. The Landed Gentry would appear to 

 be closer than the Peerage to our present material. 



J It is by no means certain that this is the true view of the case. We have 

 seen that the American women have their maximum mortality in early middle- 

 life, and only a secondary maximum at 70. The maximum mortality of the table 

 prepared by J. P., F.R.S., for the years 1728-57 (' A Collection of the Yearly 

 Bills of Mortality from 1657 to 1758 inclusive,' London, 1759) occurs about 41 

 years, and there is no evidence of a maximum at 70 at all. Thus the American 

 data appear to resemble London data of two centuries back. 



