STRUGGLE FROM VIEWPOINT OF MATHEMATICIANS 



51 



dt 





eft 



[*-*■(£ 



n 2 + |i 



2 A 2 



(19) 



The result of the transformation shows that the equation (12) coin- 

 cides with Volterra's equation (18), but it does not include any param- 

 eters dealing with the food consumption, and simply expresses the 

 competition between species in terms of the growing populations 

 themselves. As will be seen in the next chapter, the equation (12) 

 is actually realized in the experiment. 



IV 



(1) In the present book our attention will be concentrated on an 

 experimental study of the struggle for existence. In this connection 

 we are interested only in those initial stages of mathematical re- 

 searches which have already undergone an experimental verification. 

 At the same time we are writing for biological readers and we would 

 not encumber them by too numerous mathematical material. All 

 this leads us to restrict ourselves to an examination of only a few 

 fundamental equations of the struggle for existence, referring those 

 who are interested in mathematical questions to the original investi- 

 gations of Volterra, Lotka and others. 



We shall now consider the second important set of equations of the 

 struggle for existence, which deals with the destruction of one species 

 by another. The idea of these equations is very near to those of 

 Ross which we have already analyzed. They were given for the 

 first time by Lotka ('20b) and independently by Volterra ('26). 

 After the previous discussion these equations ought not to present 

 any difficulties. Let us consider the process of the prey iVi being 

 devoured by another species, the predator iV 2 . We can put it in a 

 general form: 



