110 THE STRUGGLE FOR EXISTENCE 



Were the species similar in their properties, each one of them would 

 again increase by to, and there would not be any alteration in the 

 relative quantities of the two species. However, as one species grows 

 quicker than another, it succeeds not only in regaining what it has 

 lost but also in seizing part of the food resources of the other species. 

 Therefore, every elementary movement of the population leads to a 

 diminution in the biomass of the slowly growing species, and produces 

 its entire disappearance after a certain time. 



(6) The recovery of the population loss in every elementary move- 

 ment is subordinate to a system of the differential equations of com- 

 petition. In the present stage of our researches we can make use of 

 these equations for only a qualitative analysis of the process of dis- 

 placement. They will show us exactly what particular species in the 

 population will be displaced. However, the quantitative side of the 

 problem, i.e., the rate of the displacement, still requires further experi- 

 mental and mathematical researches and we will not consider it at 

 present. 



The qualitative analysis consists in the following. Let us assume 

 that the biomass of each component of the saturating population is 

 decreased by yu- Then according to the system of differential equa- 

 tions, inserting the values of the coefficients of multiplication and of 

 the coefficients of food consumption, we shall be able to say how each 

 one of the components can utilize the now created possibility for 

 growth. The result of the calculations shows that P. aurelia, pri- 

 marily owing to its high coefficient of multiplication, has an advan- 

 tage and increases every time comparatively more than P. caudatum* 



In summing up we can say that in spite of the complexity of the 

 process of competition between two species of infusoria, and as one 

 may think a complete change of conditions in passing from one period 

 of growth to another, a certain law of the struggle for existence which 

 may be expressed by a system of differential equations of competition 

 remains invariable all the time. The law is that the species possess 

 definite potential coefficients of multiplication, which are realized at 



2 It is obvious that in these calculations it is necessary to introduce varying 

 coefficients of the struggle for existence. At the same time with our technique 

 of cultivation corrections to the "elementary movements" must be also in- 

 cluded in an analysis of the first stage of growth of a mixed population (an 

 approximation to the asymptote). But at the present stage of our researches 

 we have neglected them. 



