DESTRUCTION OF ONE SPECIES BY ANOTHER 137 



delay of the inflow after the threshold has been reached increases the 

 dimensions of the relaxations (the importance of this problem for 

 epidemiology has been pointed out by Kermack and McKendrick 

 ('27)). When relaxation is going on, slight impulses do not disturb it 

 seriously until crossing of the abscissa by the integral curves, and later 

 on up to their intersection with the line of horizontal tangents (Fig. 

 38). After this the impulses lead to a return on the ordinate and the 

 process begins again. 



(1) The theory of the preceding section shows that the consump- 

 tion of one species by another in the population studied is so active 

 that the classical oscillations in numbers are transformed into an 

 elementary relaxation and the coordinates of the singular point 

 around which such oscillations could be theoretically expected are 

 exceedingly small. This fact except its independent interest enables 

 us to predict that were we in a position to reduce the intensity of 

 consumption we could increase the coordinates of the singular point, 

 and in this way observe the classical oscillations of Lotka-Volterra. 

 The situation is entirely analogous to that of classical physiology. 

 The rate of propagation of nervous impulses is under usual conditions 

 too high and it is sometimes desirable to decrease it, to cool the nerve, 

 in order to be able to observe certain phenomena. How can one de- 

 crease the intensity of consumption of one species by another? 



The simplest way is to investigate a system where this intensity is 

 naturally low. This has been recently made by Gause ('35b) who 

 analyzed the properties of the food chain consisting of Paramecium 

 bursaria and Paramecium aurelia devouring small yeast cells, Schizo- 

 saccharomyces pombe and Saccharomyces exiguus. Special arrange- 

 ments allowed of controlling artificially the mortality of predators by 

 rarefying them, and of avoiding the settling of yeast cells on the 

 bottom by a slow mixing of the medium. Figure 39 shows that under 

 such specialized conditions fluctuations of the Lotka-Volterra type 

 actually take place, and in this manner the conditions of the equation 

 (21a) are realized in general features. 



It must be remarked that the equation (21a) does not hold abso- 

 lutely true because the oscillations do not apparently belong to the 

 "conservative" type. In other terms they do not keep the magnitude 

 initially given them but tend to an inherent magnitude of their own 



