78 THE STRUGGLE FOR EXISTENCE 



volume; in the smaller species Schizosaccharomyces there are 57.70 

 cells in one unit of yeast volume. Starting from these averages, we 

 have calculated the volumes occupied by each species in the mixed 

 population at a given moment, according to the number of cells of 

 each species observed in the mixed population. (In the experiments 

 of 1932 which are given further on we did not use such general aver- 

 ages for our calculations, but started every time from the average 

 number of cells observed at a given moment of time.) 



The sum of the calculated volumes of both species in the mixed 

 culture at a given moment should agree with the actual volume of 

 mixed population at this moment determined by the method of cen- 

 trifugation. In the first series the totals of calculated volumes are 

 somewhat smaller than the volumes actually observed, and we know 

 the causes of this disagreement. In the second series these causes 

 have been eliminated, and the coincidence between the totals of the 

 volumes calculated and the volumes actually observed is a satisfac- 

 tory one. 



(2) Figures 14 and 15 give the curves of the growth of the yeast 

 volume in Saccharomyces and Schizosaccharomyces cultivated sepa- 

 rately and in a mixed population. The curves of the separate growth 

 of each species are expressed with the aid of simple logistic curves of 

 the following type (the details of these calculations are to be found in 

 the Appendix) : 



dN ,, T K-N 

 -dt= hN -K-> 



where N is yeast volume, t is time, b and K are constants. The fitting 

 of the logistic curves has given us the following values of the param- 

 eters for the separate growth of our species (Sp. No. 1 is Saccharo- 

 myces, No. 2 is Schizosaccharomyces) : 



Maximal volumes: K x = 13.0; K 2 = 5.8 



Coefficients of geometric increase: 



&i = 0.21827; b 2 = 0.06069 



The calculated coefficients of geometric increase show that per 

 unit of time (one hour) every unit of volume of Saccharomyces can 

 potentially give an increase equal to 0.21827 of this unit, and in 

 Schizosaccharomyces equal to only 0.06069. 



