CERTAIN DEMOGRAPHIC BACKGROUNDS FOR POPULATION STUDIES 293 



This illustration of a specific death rate 

 nicely demonstrates some of the advantages 

 of the statistic, not only for human popula- 

 tions, but for others as well. 



We now have discussed birth rates and 

 death rates in enough detail to illustrate 

 certain of their attributes and limitations. 

 That they are the basic statistics of human 

 populations is incontestable, and that eco- 

 logical population students can utilize them 

 with profit should be equally clear. In 

 short, some knowledge of these rates should 

 be part of the equipment of the modem 

 ecologist. Nevertheless, from tlie point of 

 view of population growth trends, it is 

 meaningless to consider a birth rate inde- 

 pendent of a death rate or a death rate 

 independent of a birth rate. As was stressed 

 in the last chapter, the interaction between 

 the two is significant. We now wish to dis- 

 cuss an index, the true rate of natural in- 

 crease, that expresses this interaction. 



THE TRUE RATE OF NATURAL INCREASE* 



The "true rate of natural increase" is a 

 statistic that has been championed by A. ]. 

 Lotka. Since it has much to recommend 

 it and since an understanding of the under- 

 lying principles clears up a number of 

 points about birth rates and deaths, we con- 

 sider it advisable to discuss it in some de- 

 tail. We follow closely the excellent treat- 

 ment, as well as the example, presented in 

 Dublin and Lotka (1936, pp. 242-247). 



In 1920 the observed birth rate for the 

 white population of the United States was 

 23.40; the death rate, 12.41. The diflFerence 

 between these two, 10.99, is frequently 

 called the "rate of natural increase." Dub- 

 lin and Lotka question the validity of this 

 index and propose instead the "true rate 

 of natural increase," now to be discussed. 

 True natural increase takes into account the 

 age distribution of the population. This is 



• In earlier years demographers frequently 

 used a statistic known as the "vital-index" or 

 birth-death ratio to express the interaction of 

 natality with mortality. This index is defined as 

 100 births divided by deaths, and, upon solu- 

 tion, yields the number of births per each 100 

 deaths per desi^ated time interval. When the 

 index exceeds 100, the population is growing; at 

 less than 100, it is declining. The vital index 

 finds little adoption today because it is "open to 

 misinterpretation as a measure of population 

 reproductivity since it is partly determined by 

 the age composition of the population" (Linder 

 and Grove, 1943). 



sound procedure for two reasons: (1) be- 

 cause the death rate, as we have seen, 

 varies with the age-class composition of the 

 group, and (2) because, in the human 

 population, reproduction is concentrated 

 essentially between the female ages fifteen 

 to fifty years. For these reasons, Lotka 

 rightly beheves that a measure of popula- 

 tion increase that does not evaluate the 

 particular age distribution is not so accu- 

 rate as it should be. 



Age distribution itself is not a random 

 distribution; it has a pattern of its own. It 

 has been shown (Sharpe and Lotka, 1911) 

 that if the fertility of females at each age 

 (i.e., the average number of children bom 

 in a particular year of hfe) and the mor- 

 tality at each age remain constant, the age 

 distribution eventually assumes a form that 

 can be predicted by calculation. From this 

 distribution the birth rate, death rate, and 

 true rate of natural increase characteristic 

 of this population can be computed. These 

 rates "represent more correctly the inherent 

 power for growth of the population." 



The ultimate course of events in a popu- 

 lation rests on the ratio of total births in 

 two consecutive generations. Dublin and 

 Lotka illustrate these data for twenty-three 

 states in 1920 as contrasted with 1930. 

 Their basic figures appear in Table 21. 



In 1920 the total white female births by 

 women twenty to twenty-four years old was 

 186,302. The total number of white women 

 in the population was 2,548,435. Their re- 

 productive rate, as shown in Table 21, was 

 7310 daughters per 100,000 (i.e., 186,302: 

 2,548,435 = X: 100,000). We now follow 

 the history of a cohort of 100,000 female 

 babies, assuming they are subjected to the 

 mortality characteristic of 1920. As they 

 mature their number is reduced by deaths. 

 At twenty-two years of age the table shows 

 85,509 surviving. These reproduce at a rate 

 of 7310 girls per 100,000, or give rise to 

 6251 per annum. Thus, in five years there 

 are 31,255 girl births (5x6251). After 

 the fifty-fifth year the cohort will have pro- 

 duced 116,635 girls. This means that for 

 the age schedule operative in 1920, the 

 ratio of total female births in two successive 

 generations would have been 1.166. Dub- 

 lin and Lotka comment on this point as 

 follows: 



"Evidently, we have here the requisite 

 conditions for a growing population, each 

 generation exceeding its predecessor in the 



