CERTAIN DEMOGRAPHIC BACKGROUNDS FOR POPULATION STUDIES 303 



portunity for growth is indicated by the 



ratio — ^ , which approaches one on the 



first day and is reduced to 0.016 on the 

 fourth day, when few additional paramecia 



(Cause's 1 - ^^7^). The last entry of 



the table indicates the rate of population 

 growth. This is actually the arithmetical 

 solution of the logistic equation. The figures 



400 



CO 



<300 



Q 

 > 



200 



100 



DAYS 



Fig. 1)4. The growth of a laboratory population of Paramecium caudatum fitted to the lo- 

 gistic equation. Circles are observed counts; line is the fitted curve. ( From Cause. ) 



are added to the total. The reason the po- 

 tential increase becomes successively lower 

 as the population grows is related to the 

 fact that the utiUzed opportunity for growth 



show that the population grows rapidly be- 

 tween the first and second day, after which 

 the rate of increase slackens. For example, 

 44.5 individuals are added to the culture 



Table 23. The Growth of a Population of Paramecium caudatum 



N (number of individuals; derived from the logistic 

 equation) 



bN (potential increase of the population per 24 hour 

 period) 



K — N . . 



— ^7 — (unutihzed opportunity for population growth) 

 xv 



N . . 



r7 (utiUzed opportunity for population growth) 



dN , ^^ K - N , , , 



-r- = dN — p — (rate of population growth) 



Time in Days 



20.4 



47.1 

 0.945 



0.055 



44.5 



137.2 



316.8 

 0.633 



0.367 



200.0 



319.0 



736.6 

 0.149 



0.851 



109.7 



369.0 



852.0 

 0.016 



0.984 



13.6 



(designated by Cause as "environmental during the first twenty-four hours: 200.0 



resistance") approaches 1.0 with time, and during the second twenty-four hours; 109.7 



as the population nears its asymptote the during the third, and only 13.6 during the 



potential increase remains almost entirely fourth. 



T J ,,, ^1 . ^, ^. N Cause designates these relationships as 



unrealized. We express this as the ratio — « , ^ • . • r ,-■..■ » / u„ 



^ K characteristics of competition and has 



