48 THE STRUGGLE FOR EXISTENCE 



express quantitatively the process of competition between two species 

 for the possession of a certain common place in the microcosm. They 

 are founded on the idea that every species possesses a definite po- 

 tential coefficient of multiplication but that the realization of these 

 potentialities (biNi and b 2 N 2 ) of two species is impeded by four proc- 

 esses hindering growth: (1) in increasing the first species diminishes 

 its own opportunity for growth (accumulation of Ni), (2) in increas- 

 ing the second species decreases the opportunity for growth of the 

 first species (aNz), (3) in increasing the second species decreases its 

 own opportunity for growth (accumulation of N 2 ), and (4) the in- 

 crease of the first species diminishes the opportunity for growth of 

 the second species (/3iVi). Whether the first species will be victori- 

 ous over the second, or whether it will be displaced by the second 

 depends, first, on the properties of each of the species taken sepa- 

 rately, i.e., on the potential coefficients of increase in the given condi- 

 tions (&i, 62), and on the maximal numbers of individuals (K\, K 2 ). 

 But when two species enter into contact with one another, new coeffi- 

 cients of the struggle for existence a and /3 begin to operate. They 

 characterize the degree of influence of one species upon the growth of 

 another, and participate in accordance with the equation (12) in 

 producing this or that outcome of the competition. 



(4) It is the place to note here that the equation (12) as it is written 

 does not permit of any equilibrium between the competing species 

 occupying the same "niche," and leads to the entire displacing of one 

 of them by another. This has been pointed out by Volterra ('26), 

 Lotka ('32b) and even earlier by Haldane ('24), and for the experi- 

 mental confirmation and a further analysis of this problem the reader 

 is referred to Chapter V. We can only remark here that this is 

 immediately evident from the equation (12). The stationary state 



dNi idN 2 ., u .,, ., (dN x dN 2 \ 

 occurs whenever —z— and — 3— both vanish together I —z— = —7— = CM, 



and the mathematical considerations show that with usual a and /3 

 there cannot simultaneously exist positive values for both Ni tao 

 and N 2 , w . One of the species must eventually disappear. This 

 apparently harmonizes with the biological observations. As we 

 have pointed out in Chapter II, both species survive indefinitely only 

 when they occupy different niches in the microcosm in which they have 

 an advantage over their competitors. Experimental investigations 

 of such complicated systems are in progress at the time of this writing. 



