STRUGGLE FROM VIEWPOINT OF MATHEMATICIANS 



39 



sistance can be measured by that part of the potential increase which 

 has not been realized — the greater the resistance the larger the un- 



K — N 



realized part. This value can be obtained by subtracting — = — from 



unity. At the beginning of growth the environmental resistance is 



mm* ■ K — N 



small and 1 ^ — approaches zero. As the population increases 



A 



M 



aY* 



A* 



& 



Rate of growths <p/ Environmental 



y 



A 



/Degree of realization of 

 S the potential fncreai 



Intensity of the 

 struggle for 

 existence 



Ddys 



Fig. 5. The characteristics'of competitiorfin'ajhomogeneous population of 

 Paraviecium caudatum. 



K - N 



the environmental resistance increases also and 1— == — ap- 



K 



proaches unity. This means that the potential increase remains 



K — N 



almost entirely unrealized. Multiplying bN by = — for a given 



dN 

 moment we obtain a rate of population growth -=— , which increases 



at first and then decreases. The corresponding numerical data are 

 given in Table IV and Figure 5. 



