THE GROWTH FORM OF POPULATIONS 



313 



data would be quantitative studies of the 

 colonization of bare rock surfaces by single 

 species of sessile, marine organisms. 



Riley (1943) has reported some interest- 

 ing data on growth form for diatoms. He 

 studied in detail one diatom, Nitschia clos- 

 terium, as a laboratory population and then 

 drew certain parallels between these find- 

 ings and the "spring flowerings" of natural 

 populations of phytoplankton sampled from 

 Georges Bank oflF New England. The growth 

 curve for the experimental population of 

 Nitschia is shown in Figure 105, in which 

 it is seen that growth is sigmoid in charac- 



that resembled the curve for cultures of 

 Nitschia shown in Figure 105. 



This investigation is helpful for our 

 purposes since it provides (1) an exception 

 to logistic growth, because such a curve 

 apparently can not be fitted, owing to the 

 irregularities around the asymptote; and 

 (2) an excellent documentation of the point 

 that laboratory ecology has something to 

 contribute to field ecology, and contrariwise. 



Human Populations 



Examples of the logistic curve applied to 

 human populations are extremely numer- 



200 



1700 



'80 1800 



'80 1900 



'80 2000 



'80 2100 



YEAR 



Fig. 106. The logistic function fitted to the census counts of the population of the United 

 States from 1790 to 1940, inclusive. Broken line is extrapolation of the curve. (From Pearl, 

 Reed, and Kish.) 



ter through the point of inflection of the 

 curve. There is an initial lag period, a 

 period of rapid growth, followed by a 

 period of reduced relative growth rate. 

 After the inflection point, however, "all re- 

 semblance to the sigmoid type of popula- 

 tion curve ended. Instead of coming slowly 

 to an asymptote, the rate of growth re- 

 mained constant for a few days and then 

 abruptly dropped to a negative value, indi- 

 cating a sharp peak in the population level, 

 followed by a gradual decrease." Riley 

 found that many dominant species of phy- 

 toplankton (e.g., Nitschia closteritim, Tha- 

 lassionema nitschioides, Leptocijlindricus 

 danicus, and AsterioneUa japonica) had 

 positive growth forms as natural poptdations 



ous in the hterature. The curve has been 

 apphed to various sorts of demographic 

 units: counties, cities, states, countries, and 

 the world. A number of apphcations are to 

 be found in Pearl (1930) (e.g., for Sweden, 

 United States, France, England and Wales, 

 Germany, and so on). We choose two cases 

 for our purposes: the growth of the United 

 States population (Pearl, Reed, and Kish, 

 1940) and the growth of the population of 

 the world (Pearl and Gould, 1936). 



Figure 106 graphs the logistic curve of 

 growth for the United States population 

 through the 1940 census. The curve can be 

 extrapolated between 1700 and 1790 and 

 between 1940 and 2100. The observed 

 points covering these 150 years of censu.« 



