10 THE STRUGGLE FOR EXISTENCE 



process of propagation Ross came to the conclusion that he was deal- 

 ing with a peculiar case of a struggle for existence between the malaria 

 Plasmodium and man with a participation of the mosquito. Ross 

 formulated mathematically an equation of the struggle for existence 

 for this case, which closely approached in its conception those equa- 

 tions of the struggle for existence which the Italian mathematician 

 Volterra proposed in 1926 without knowing the investigations of Ross. 



Whilst Ross was working on the propagation of malaria the Ameri- 

 can mathematician Lotka ('10, '20a) examined theoretically the 

 course of certain chemical reactions, and had to deal here with equa- 

 tions of the same type. Later on Lotka became interested in the 

 problem of the struggle for existence, and in 1920 he formulated an 

 equation for the interaction between hosts and parasites ('20b), and 

 gave a great deal of interesting material in his valuable book, Ele- 

 ments of Physical Biology ('25). Without being acquainted with 

 these researches the Italian mathematician Vito Volterra proposed in 

 1926 somewhat similar equations of the struggle for existence. At 

 the same time he advanced the entire problem considerably, investi- 

 gating for the first time many important questions of the theory of 

 competition from the theoretical point of view. Thus three distin- 

 guished investigators came to the very same theoretical equations 

 almost at the same time but by entirely different ways. It is also 

 interesting that the struggle for existence only began to be experi- 

 mentally studied after the ground had been prepared by purely theo- 

 retical researches. The same has already happened many times in 

 the fields both of physics and of physical chemistry: let us recollect 

 the mechanical equivalent of heat or Gibbs' investigations. 



(11) The study of the struggle for existence will undoubtedly 

 rapidly progress in the future, but it will have to overcome a certain 

 gap between the investigations of contemporary biologists and mathe- 

 maticians. There is no doubt that the struggle for existence is a 

 biological problem, and that it ought to be solved by experimentation 

 and not at the desk of a mathematician. But in order to penetrate 

 deeper into the nature of these phenomena we must combine the 

 experimental method with the mathematical theory, a possibility 

 which has been created by the brilliant researches of Lotka and Vol- 

 terra. This combination of the experimental method with the 

 quantitative theory is in general one of the most powerful tools in 

 the hands of contemporary science. 



