40 THE STRUGGLE FOR EXISTENCE 



(4) We must now analyze a very important principle which was 

 clearly understood by Darwin, but which is still waiting for its ra- 

 tional quantitative expression. I mean the intensity of the struggle 

 for existence between individuals of a given group. 3 The intensity of 

 the struggle for existence is measured by the resistance which must be 

 overcome in order to increase the number of individuals by a unit at a 

 given moment of time. As we measure the environmental resistance 

 by the eliminated part of the potential increase, our idea can be 

 formulated thus : what amount of the eliminated fraction of the po- 

 tential increase falls upon a unit of the realized part of the increase at 

 a given moment of time? The intensity of the struggle for existence 

 keeps constant only for an infinitesimal time and its value shows 

 with what losses of the potentially possible increment the establish- 

 ment of a new unit in the population is connected. The realized 

 value of increase at a given moment is equal to 



dN ,„K-N 



Tt= hN -ir~ 



and the unrealized one: 



,,,/, K-N\ ... . AT K-N ... 

 bN ( 1 = — 1 = bN — bN — = — = bN — 



dN 

 dt ' 



Then the amount of unrealized potential increase per unit of realized 

 increase, or the intensity of the struggle for existence (i), will be 

 expressed thus: 



unrealized part of the . .. dN 



potential increase dt ,„^ 



i = — - = (10) 



realized part of the dN 



potential increase dt 



3 As we have seen in Chapter II, botanists are beginning to deal with the 

 intensity of the struggle for existence, simply characterizing it by the per cent 

 of destroyed individuals. Haldane investigating the connection of the inten- 

 sity of competition with the intensity of selection ('31) and in his interesting 

 book The Causes of Evolution ('32) specifies the intensity of competition by Z 

 and determines it as the proportion of the number of eliminated individuals to 

 that of the surviving ones. Thus if the mortality is equal to 9 per cent, Z = 

 9/91, i.e., approximately 0.1. 



