340 Relations within the Species 



form. Illustrations of such curves of growth for laboratory cultures 

 of Protozoa, yeasts, Drosophila, flour beetles, and water fleas, and for 

 natural populations of bees, ants, thrips, sheep, and other animals are 

 discussed in further detail by Alice et al. (1949, Ch. 21). The growth 

 of man's population follows a similar pattern whether examined in 

 individual regions or in the world as a whole. A plot of the census 

 records for the United States for the years up to 1940 is shown in Fig. 

 9.12, and the curve has been extrapolated by fitting the logistic func- 



1700 20 40 60 80180020 40 60 801900 20 40 60 80 2000 20 40 60 802100 



Year 

 Fig. 9.12. Growth curve of the population of the United States, showing census 

 counts from 1790 to 1950. The logistic function has been fitted to the counts 

 from 1790 to 1910 and extrapolated to 2100. The agreement of the extrapolation 

 with the counts for 1920 to 1950 is shown, and a cessation of growth about the 

 year 2000 is indicated. (Modified from Pearl, Reed, and Kish, 1940.) 



tion. The agreement of the 1950 census figure of 151 million with 

 the extrapolated curve and the indication of an asymptote at about 

 184 million in the year 2100 may be observed. 



Equilibrium and Fluctuation 



The logistic curve discussed in the previous section applies only to 

 periods of population growth (when A^ M) and to situations in 

 which the rate of increase is controlled only by density-dependent 

 factors. Since the inhabitants of a natural area have mostly been 

 present for a long time, we see the initial stages of population growth 

 only in special instances. The early part of population increase is 



