DESTRUCTION OF ONE SPECIES BY ANOTHER 



131 



epidemics and fluctuations in our protozoan population. A certain 

 potential or a certain state is here built up by a continuous process 

 and the conditions become less and less stable until a state is reached 

 at which a discharge (or epidemics) must take place. It is evident 

 that the interaction between the two components instead of periodic- 

 ity leads here to an interruption of contact (depending from specific 

 biological conditions in the case of epidemics and from a disappear- 

 ance of predators and prey in our Protozoa), and then ceases until the 

 next critical threshold. Such oscillations with an interruption of con- 

 tact bear in physics the name of "relaxation oscillations." 



AJ (concentration of the predator ) 



Fig. 34. Diagrams illustrating two types of innate periodic fluctuations in 

 numbers of animals. 1. "Classical" fluctuation of Lotka-Volterra. 2. "Re- 

 laxation fluctuations." 



It is easy to visualize the difference between these two types of 

 oscillations employing the illuminating graphs so often used by Lotka. 

 On the coordinate paper we usually plot time on the abscissae and 

 densities of predators (iV 2 ) and prey (iVi) on the ordinates. But if 

 we abstract from time and plot iV 2 on the abscissae and Ni on the 

 ordinates we obtain a clear idea of the nature of interspecific inter- 

 action. As Figure 34 shows in the case of classical oscillation we must 

 have a closed curve. 4 



4 The transformation of the usual time-curves into such graphs is illustrated 

 by a numerical example reproduced in Fig. 35. The upper part of it presents a 



