32 THE STRUGGLE FOR EXISTENCE 



tions or in the quantities of each species can lead to the result that 

 instead of the second species supplanting the first it is the first species 

 itself that begins to supplant the second. As Jennings ('33) points 

 out, there exists a strong strain of uniformitarianism in many biolo- 

 gists. The idea that we can observe one effect, and then the opposite, 

 seems to them a negation of science. 



In the spreading of malaria something analogous actually takes 

 place. Ross came to the following interesting conclusion about 

 this matter: (1) Whatever the original number of malaria cases 

 in the locality may have been, the ultimate malaria ratio will 

 tend to settle down to a fixed figure dependent on the number 

 of Anophelines and the other factors — that is if these factors remain 

 constant all the time. (2) If the number of Anophelines is suffi- 

 ciently high, the ultimate malaria ratio will become fixed at 

 some figure between per cent and 100 per cent. If the number 

 of Anophelines is low (say below 40 per person) the ultimate 

 malaria rate will tend to zero — that is, the disease will tend to 

 die out. All these relations Ross expressed quantitatively, and later 

 they were worked out very elegantly by Lotka. This example shows 

 that a change in the quantitative relations between the components 

 can change entirely the course of the struggle for existence. Instead 

 of an increase of the malaria infection and its approach to a certain 

 fixed value, there may be a decrease reaching an equilibrium with a 

 complete absence of malaria. In spite of all this there remains a 

 certain invariable law of the struggle for existence which Ross's equa- 

 tions express. In this way we see what laws are to be sought in the 

 investigation of the complex and unstable competition processes. 

 The laws which exist here are not of the type the biologists are 

 accustomed to deal with. These laws may be formulated in terms 

 of certain equations of the struggle for existence. The parameters in 

 these equations easily undergo various changes and as a result a whole 

 range of exceedingly dissimilar processes arises. 



ii 



(1) The material just presented enables one to form a certain idea 

 as to what constitutes the essence of the mathematical theories of the 

 struggle for existence. In these theories we start by formulating the 

 dependence of one competitor on another in a verbal form, then trans- 

 late this formulation into mathematical language and obtain differen- 



