COMPETITION FOR COMMON FOOD IN PROTOZOA 111 



every moment of time according to the unutilized opportunity for 

 growth. We have only had to change the interpretation of this un- 

 utilized opportunity. 



(7) It seems reasonable at this point to coordinate our data with 

 the ideas of the modern theory of natural selection. It is recognized 

 that fluctuations in numbers resembling the dilutions we have arti- 

 ficially produced in our microcosms play in general a decisive role in 

 the removal of the less fitted species and mutations (Ford, '30). An 

 interesting mathematical expression of this process proposed by 

 Haldane ('24, '32) can be formulated thus: how does the rate of 

 increase of the favorable type in the population depend on the 

 value of the coefficient of selection k? In its turn the coefficient of 

 selection characterizes an elementary displacement in the relation 

 between the two types per unit of time — one generation. Therefore 

 the problem resolves itself into a determination of the functional rela- 

 tionship between the increase of concentration of the favorable type 

 and the elementary displacement in its concentration. A recent 

 theoretical paper by Ludwig ('33) clearly shows how the fluctuation 

 in the population density alters the relation between the two types 

 owing to the fact that one of them has a somewhat higher probability 

 of multiplication than the other. It seems to us that there is a great 

 future for the Volterra method here, because it enables us not to 

 begin the theory by the coefficient of selection but to calculate theo- 

 retically the coefficient itself starting from the process of interaction 

 between the two species or mutations. 



IV 



(1) How complicated are processes of competition under the condi- 

 tions approaching those of nature can be seen from the experiments 

 made by Gause, Nastukova and Alpatov ('35). They studied the in- 

 fluence of biologically conditioned media on the growth of a mixed 

 population of Paramecium caudatum and P. aurelia. The analysis 

 of the relative adaptation of the two species at different stages of 

 population growth has shown that P. caudatum has an advantage 

 over P. aurelia in the coefficient of geometric increase (in the absence 

 of Bacillus pyocyaneus in the nutritive medium which in the experi- 

 ments described above inhibited P. caudatum by its waste products) 

 whilst P. aurelia surpasses P. caudatum in the resistance to waste 

 products. Therefore if the decisive factor of competition is a rapid 



