THE GROWTH FORM OF POPULATIONS 



315 



time the population of the world was esti- 

 mated to have been about 445,500,000 per- 

 sons and when industrial and commercial 

 procedures started to come to the fore with 

 their consequent acceleration of population 

 growth. The upper asymptote, attained in 

 2100, estimates the world's population at 

 that time to be in the neighborhood of 

 2,645,500,000 individuals. The fit between 

 points and curve is only moderate. 



An instructive feature arising from 

 Figure 107 is that one logistic curve is not 

 considered adequate to describe the growth 

 of the human population over its entire his- 

 tory. Pearl has repeatedly pointed out that 

 a population follows a particular logistic 

 curve only so long as there has been "no 

 serious or cataclysmic alteration of the con- 

 ditions (climatic, geological, biological or 

 social) under which its earlier grovv^h has 

 taken place." He has also suggested that 

 several curves can be arranged one upon 

 the other to describe a population's growth 

 as it meets and adjusts to major changes in 

 its total environmental relationships (see 

 discussion of Logistic Curve, p. 301). Thus, 

 one might speculate, somewhat boldly to 

 be sure, that before the middle of the 

 seventeenth century the population had 

 passed through a series of logistic cycles 

 representing adjustments from hunting, to 

 pastoral, to agricultural, modes of living. 

 Then, vidth the advent of industrialism, 

 commerce, and public health practices, a 

 new and excessively steep cycle of growth 

 originated. 



There are, of course, other logical possi- 

 bilities as to the quantitative state of the 

 world population before 1650. These are 

 recognized by Pearl and Gould and sche- 

 matized in Figure 108. In this figure the 

 "first hypothesis" is that just discussed. The 

 "second hypothesis" holds that for thou- 

 sands of years the population stood rela- 

 tively stable between roughly four and five 

 hundred million persons. This stability 

 represents an asymptote of a growth cycle 

 long before consummated. The "third hy- 

 pothesis" maintains that "during some 

 period or periods in this vast .span of at 

 least 100,000 years of man's life on the 

 earth the world population was much higher 

 than 445 million, and subsequently less- 

 ened, for reasons wholly unknown, to reach 

 that figure when reasonably reliable popu- 

 lation history begins." 



These three possibilities are examined by 

 Pearl and Gould. They exclude the third 

 immediately as untenable. It is more diffi- 

 cult (they argue) to judge between the 

 first and the second, although they decide 

 that "on the balance"' there are more data 

 supporting the first, which, consequently, is 

 tentatively accepted as the most probable 

 representation of world population growth. 



EQUILIBRIUM 



In the discussion of equilibrium, as in the 

 following treatment of Fluctuations and 

 Oscillations, it must be remembered that, 

 while it is possible to define these growth 

 forms with mathematical precision, as ac- 

 tual illustrations it is possible to diflFerentiate 

 them in relative terms only. The point can 

 be put diflFerently. There probably exists no 

 "perfect case" of equilibrium or oscillation. 

 There are many instances for which it is 

 difficult to say "This is the one" and "This 

 is the other," since elements of both are 

 present. There are, of course, many other 

 instances for which this is not the case, and 

 then it is easy to separate one growth form 

 from another. In final analysis the issue be- 

 comes a matter of judgment. Does the fact 

 that it would be possible to arrange an ex- 

 tensive series of population data all the way 

 from marked fluctuation, grading into oscil- 

 lation, or into equilibrium detract from our 

 definition of these three growth forms as 

 true descriptive population characteristics? 

 We think not. In fact, we believe that this 

 strengthens the concept since it is just the 

 way a series of biodemographic units, such 

 as the population, might be expected to be- 

 have. Therefore, in speaking of equilibrium, 

 oscillation, and fluctuation we recognize 

 that they are relative rather than absolute 

 concepts, but that they have great descrip- 

 tive value in depicting the course of popu- 

 lations, irrespective of the type, through 

 time. 



Equilibrium could be defined in various 

 ways, some more or less complex. It seems 

 appropriate and adequate enough to define 

 it simply as mean numerical stability, i.e., 

 the average size held by a population over 

 a considerable period of time. To illustrate 

 fhis it is necessary to find examples in 

 which the oscillation and/or fluctuation is 

 at a minimum, examples in which the 

 equilibrium approaches a straight, horizon- 

 tal line. 



