126 



THE STRUGGLE FOR EXISTENCE 



the time of the fourth immigration the predator had already devoured 

 all the prey, had become reduced in size and degenerated. The prey 

 introduced into the microcosm originates a new cycle of growth of the 

 prey population. Such periodic changes repeat themselves further on. 

 Comparing the results of different similar experiments with immi- 

 gration made in a homogeneous microcosm, we come to the same 

 conclusions as in the preceding paragraph. Within the limits of each 

 cycle when there is a great number of both Paramecium and Didinium 

 it is possible by means of certain differential equations to predict the 

 course of the process of the struggle for existence for some time to 



| 



I 



8 



Days 



10 



n 



iv 



16 



Fig. 32. The interaction between Didinium nasutum and Paramecium 

 caudatum in a microcosm with immigrations (1 Didinium + 1 Paramecium). 

 Causes of too low peak of Didinium in the first cycle of growth are known. 

 From Gause ('34a). 



come. However, at the critical moments, when one cycle of growth 

 succeeds another, the number of individuals being very small, "mul- 

 tiplicity of causes" acquires great significance (compare first and 

 second cycles in Fig. 32). As a result it turns out to be impossible 

 to forecast exactly the development in every individual microcosm 

 and we are again compelled to deal only with the probabilities of 



change. 



(5) Let us briefly sum up the results of the qualitative analysis of 

 the process of destruction of one species by another in a case of two 

 infusoria. The data obtained are schematically presented in Figure 



y 



