294 



POPULATIONS 



Table 21. Computation Schedule: Ratio of Total Births in Two Consecutive Generations 

 According to Fertility and Mortality in 1920 (White Females only) (From Dublin and Lotka) 



ratio of 1.166 to 1. Furthermore, our data 

 determine a definite rate of growth per genera- 

 tion, and hence, if we know the mean length 

 of one generation in years, they determine a 

 rate of growth per annum. This mean length 

 of one generation is found, in close approxima- 

 tion, as the mean age of the mothers in a 

 cohort, at the time of the births of their 

 children. I'his mean age is . . . 28.5 years. 

 The net result, so far, is that the conditions of 

 fertility and mortality prevailing in 1920, if 

 continued unchanged, would have resulted in 

 an increase of births in successive generations 

 at such a rate that a cohort of 1,000 newborn 

 girls would, by the end of their reproductive 

 period, have given rise to 1,166 daughters. Tin's 

 corresponds to an increase in total births at a 

 rate of 166 per 1,000 per generation. It can be 

 shovni that this is also the ultimate rate of 

 increase of the population as a whole, after 

 the stable form of the age distribution has be- 

 come established." 



This rate of increase of 166 per 1000 

 per generation can be converted into a 

 rate of increase per vear. This is the true 

 rate of natural increase, and, for our exam- 

 ple, is 5.41 per 1000 per annum.* If now 

 we c( mpare this figure, 5.41, with the 

 crude rate of natural increase, 10.99 (i.e., 

 crude birth rate minus crude death rate), 



° To convert rate per generation to rate per 

 j'ear, Dublin and Lotka present the following 

 algebraic solution: 



e"«= 1.166 



r = ^log,1.166 = 0.00541 



we see that the latter has a spurious opti- 

 mism about it. By taking into account the 

 age distribution with its consequent eflFects 

 on mortality and natality, the true rate is 

 only half the magnitude of the crude rate." 



THE LIFE TABLE 



One of the most useful of all numerical 

 aids for the population student is the life 

 table, a device that records in systematic 

 fashion those facts basic to the age distri- 

 bution of mortality. In short, a life table 

 "keeps the books on death." 



In this discussion we wish to show 

 briefly what a simple life table is and then 

 present several illustrations taken from the 

 literature of human and other population 

 studies. Since the life table underlies actu- 

 arial matters and "life insurance," it has, 

 of course, a voluminous bibliography. For 

 our purposes the two best general treat- 

 ments are those of Dublin and Lotka 

 (1936) and Pearl's (1940) biometry text. 

 Deevey (1947) has published a most useful 

 review of the hfe table as a tool in the 

 study of natural populations. 



Structure of the Life Table 



Conventionally, a life table is a series of 

 columns each of which describes something 



' After the above was written, a first-rate 

 discussion of this method as applied to insect 

 populations was published by Birch (1948). 

 This paper not only interprets the index, but 

 shows clearly the steps in its computation. See 

 also Leslie and Park, 1949. 



