150 



THE STRUGGLE FOR EXISTENCE 



n X 2.3026. In order to verify the calculations it is necessary to insert all the 



-pr 



parameters into the logistic equation: N = -and by substituting differ- 



1 + e ° bt 



ent values in place of t to find the "calculated curve," which must approach 



closely the observations. A more detailed account is to be found in the book 



of Raymond Pearl: An introduction to medical biometry and statistics, and in 



the paper of Gause and Alpatov ('31). 



2. Calculation of the equations of the struggle for existence. We have deter- 



zo 



VO €o So 



Hours ft) 



too 



no 



Fig. 41. Calculation of the logistic curve for the separate growth of the 

 yeast, Schizosaccharomyces kephir, grown under anaerobic conditions (1931). 



mined the maximal masses and the coefficients of multiplication : 6i, b 2 , K\, K 2 , 

 and following the instructions of Chapter IV we have calculated the coefficients 

 of the struggle for existence a and /3. The curves corresponding to the system 

 of the differential equations of the struggle for existence must now be found 

 for a verification of the numerical values of a and 13. 

 We have a system of equations: 



dNi t xr A', - (Ni + aN 2 ) ) 

 -aT = blNl K, 



dm . __ K % - (AT 2 + ffli) 



— - = b 2 N 2 =; 



dt A 2 



