70 



THE STRUGGLE FOR EXISTENCE 



to itself, and the growth of the number of cells in this culture followed 

 a common S-shaped curve and then stopped. In an experimental 

 culture a change of the medium was made at very short intervals of 

 time (every 3 hours). Here the conditions were all the time main- 

 tained constant and favorable for growth. Under these conditions 

 the multiplication of yeast followed the law of geometric increase: 

 in every moment of time the increase of the population constituted a 

 certain definite portion of the size of the population. The relative 

 rate of growth (i.e., the rate of growth per unit of population) re- 

 mained constant all the time, or in other words there was no auto- 

 catalysis here. Figure 10 represents the data of Richards. To the 

 left are shown the growth curves of the number of cells per unit of 

 volume: the S-shaped curve in the control culture, and the exponen- 



300 



tied i urn changed 

 every 3nrj 



every n hYevery 2Vtfr' 



jConirof 



=5? 



v. 

 o 



/ipJium changed 

 every 3t>rr t 



' eyery I2hn ' 



^^ifvtryVth 



Control 



rt>) 



no hours o 



to so 



Time 



no 



Fig. 10. Growth curves of the yeast Saccharomyces cerevisiae. (a) Growth 

 of the number of cells, (b) The same, plotted on logarithmic scale. From 

 Richards ('28a). 



tially increasing one with continuously renewed medium. One can 

 in the following manner be easily convinced that the exponentially 

 increasing curve corresponds to the geometric increase: if against 

 the absolute values of time we plot the logarithms of cell numbers, a 

 straight line will be obtained (see the right part of Figure 10 taken 

 from Richards). As is well known this is a characteristic property 

 of a geometric increase. Nearly the same results were recently 

 obtained by Klem ('33). 



The experiments made by Richards show clearly that the growth 

 of the yeast population is founded on a potential geometric multiplica- 

 tion of yeast cells (&iiVi), but the latter can not be completely realized 

 owing to the limited dimensions of the microcosm and consequently 

 to the limited number of places (K). As a result the geometric 

 increase becomes S-shaped. It is easy to see that the experimenta- 



