38 



THE STRUGGLE FOR EXISTENCE 



values bN given in Table IV express the potential rate of increase of 

 the whole population at different moments of growth, or the number 

 of offspring which a given population of Paramecia can potentially 

 produce within 24 hours at these moments. We must repeat here 

 what has been already said in calculating the value b. The potential 

 rate bN exists only within an infinitesimal time and should these condi- 

 tions exist during 24 hours the values shown in Table IV would be 



TABLE IV 



The growth of population of Paramecium caudatum 

 b (coefficient of multiplication; potential progeny per individual per day) 

 2.309. 



K (maximal population) = 375. 



AT (number of individuals according to the 



logistic curve) 



bN (potential increase of the population per 



day) 



K-N 



(degree of realization of the potential 



K 



increase) 



K-N . , . 

 1 — — =- (environmental resistance) 



dN K-N r , ' , 



— = bN — 77~ (rate of growth of the popu- 

 dt A 



lation) 



dN 



hN ~Jt 

 dN 

 dt 

 istence) 



(intensity of the struggle for ex- 



TIME IN DATS 



20.4 

 47.1 



0.945 

 0.055 



44.5 



0.058 



137.2 

 316.8 



0.633 

 0.367 



200.0 



0.584 



319.0 

 736.6 



0.149 

 0.851 



109.7 



5.72 



369.0 

 852.0 



0.016 

 0.984 



13.6 



61.7 



K-N 



obtained. The expression — = — shows the relative number of yet 



unoccupied places. At the beginning of the population growth when 



K — N 

 N is very small the value — r- — approaches unity. In other words 



the potential rate of growth is almost completely realized. As the 



K M 

 population grows, — ^ — approaches zero. The environmental re- 



K 



