108 THE STRUGGLE FOR EXISTENCE 



On the fifth day of growth of a mixed population the biomass of 

 P. caudatum (in volume units) is equal to about 25, and of P. aurelia 

 to about 65. If we calculate the total of these biomasses in equiva- 

 lents of P. aurelia, we shall have: (25 X 1.64) -f- 65 = 106 (maximal 

 free growth of P. aurelia is equal to 105). The total of the biomasses 

 expressed in equivalents of P. caudatum will be (65 X 0.61) + 25 = 

 65 (with the free growth 64). This means that on the fifth day of 

 growth of the mixed population the food resources of the microcosm 

 are indeed completely taken hold of. 



(4) The first period of competition up to the fifth day is not all 

 so simple as we considered it in the theoretical discussion of the third 

 chapter, or when examining the population of yeast cells. The na- 

 ture of the influence of one species on the growth of another does not 

 remain invariable in the course of the entire first stage of competition, 

 and in its turn may be divided into two periods. At the very begin- 

 ning P. caudatum grows even somewhat better in a mixed population 

 than separately (analogous to Fig. 22), apparently in connection 

 with more nearly optimal relations between the density of Paramecia 

 and that of the bacteria in accordance with the already mentioned 

 data of Johnson ('33). At the same time P. aurelia is but very 

 slightly oppressed by P. caudatum. As the food resources are used 

 up, the Johnson effect disappears, and the species begin to depress 

 each other as a result of competition for common food. 



It is easy to see that all this does not alter in the least the essence 

 of the mathematical theory of the struggle for existence, but only 

 introduces into it a certain natural complication: the coefficients of 

 the struggle for existence, which characterize the influence of one 

 species on the growth of another, do not remain constant but in their 

 turn undergo regular alterations as the culture grows. The curves 

 of growth of every species in a mixed population in Figure 24 up to 

 the fifth day of growth have been calculated according to the system 

 of differential equations of competition with such varying coefficients. 

 In the first days of growth the coefficient 13 is negative and near to 

 — 1, i.e., instead of —(3Ni we obtain -J-JVi- In other words, the 

 presence of P. aurelia does not diminish, but increases the pos- 

 sibility of growth of P. caudatum, which proceeds for a certain time 

 with a potential geometrical rate, outrunning the control culture 



( 2 — 1 remains near to unity I. At this time the coefficient 



