76 THE STRUGGLE FOR EXISTENCE 



The accumulation of the yeast volume at the moment of the cessa- 

 tion of growth is everywhere marked by K, and the amount of volume 

 at a given moment is N. Alcohol production per unit of yeast volume 

 is rather constant, and increases somewhat only before growth is 

 checked (see Fig. 11). Taking the alcohol production per unit of 

 yeast volume as a constant for the entire process of growth of the 

 population as the very first approximation to reality, we can easily 

 pass from the given (N) and maximal (K) amount of yeast, through 

 multiplying them by certain coefficients, to the given and critical 

 concentrations of alcohol. 



(5) It is easy to see that, while we give up any attempt to discover 

 a certain universal growth equation forecasting the level of the satu- 

 rating population under any conditions, if we use the logistic equation 

 we express rationally, very simply, and in complete agreement with 

 experimental data, the mechanism of growth of a homogeneous 

 population of yeast cells. The attempts to find universal equations 

 will scarcely lead to satisfactory results, and in any case all this would 

 be too complicated for a mathematical theory of the struggle for exist- 

 ence in a mixed population of two species. One of the leading ideas 

 of this book is that all the quantitative theories of population growth 

 must be only constructed for strictly determined cycles or epochs of 

 growth, within which the same limiting factors dominate and a certain 

 regulating mechanism remains invariable. 



Experiments with yeast point also to a very important circum- 

 stance in the experimental analysis of populations. All the condi- 

 tions of cultivation ought to be so arranged that the growth depends 

 distinctly on only one limiting factor. In the case of yeast we must 

 have a sufficiently high concentration of sugar and other necessary 

 substances in the nutritive medium so that the alcohol can in full 

 measure manifest its inhibitory action. As we shall see in the next 

 chapter in experimenting with Protozoa, it is very easy to arrange 

 experiments under such complicated conditions and with the inter- 

 ference of such a great number of various factors that the attempts to 

 discover certain fundamental quantitative relations in the struggle 

 for existence will never have any success. 



IV 



(1) Our study of the growth of homogeneous populations of yeast 

 cells was only a preparation before we pass on to the investigation of 



