MECHANISM OF COMPETITION IN YEAST CELLS 61 



struggle for existence are just such theoretical equations that have 

 been deduced from hypotheses about potential coefficients of multi- 

 plication of species and the participation of these species in the utiliza- 

 tion of a limited opportunity for growth. The verification of such a 

 theoretical equation of the struggle for existence may be reduced to 

 the following: (1) we must determine experimentally the potential 

 coefficients of multiplication of the species; (2) by means of a direct 

 study of the factors limiting growth we must evaluate the degree of 

 influence of one species on the opportunity for growth of another, 

 i.e., the coefficients of the struggle for existence; (3) by inserting all 

 these values into a theoretical equation we must obtain a complete 

 agreement with the experimental data, if our mathematical theory 

 connects correctly the coefficients furnished by experimentation. It 

 seems to us that these three steps of verifying our theoretical equa- 

 tions must be somewhat modified, taking into account the compli- 

 cated situation in the competition between two species for a common 

 place in the microcosm. We proceed as follows: (1) having deter- 

 mined the potential coefficients of multiplication b\, b 2 and the maxi- 

 mal biomasses K\, K 2 we pass on at once to (3), i.e., on the basis of the 

 experimental data, taking our equations as purely empirical expres- 

 sions or, in other terms, considering that they must describe the values 

 observed, we calculate those empirical coefficients of the struggle for 

 existence with which the equations actually describe the experimental 

 data. It is only then that we pass to (2), and compare these empiri- 

 cally found coefficients of the struggle for existence with those which are 

 to be expected from a direct study of the factors limiting growth. If the 

 empirical coefficients coincide with the theoretical ones, the correctness of 

 the mathematical theory will be proved. 



This mode of verification of the mathematical theory has been 

 adopted by us because the coincidence of theoretical coefficients with 

 the empirical ones is but rarely to be expected. Such a rare case 

 representing, most likely, rather an exception than a rule is described 

 in this chapter. This small probability of a coincidence of the co- 

 efficients is connected with the fact that usually the growth of popu- 

 lations depends on numerous factors, many of which (e.g., waste-prod- 

 ucts) we often cannot specify exactly, and the influence of one species 

 on the opportunity of growth of another under these conditions is 

 realized in a very complicated manner. Hence the empirical coeffi- 

 cients of the struggle for existence, calculated by an equation which 



