46 THE STRUGGLE FOR EXISTENCE 



growth of another, or the coefficient a, will be equal to zero. But if 

 the species lay claim to the very same "niche," and are more or less 

 equivalent as concerns the utilization of the medium, then the coeffi- 

 cient a will approach unity. And finally if one of the species utilizes 

 the environment very unproductively, i.e., if each individual con- 

 sumes a great amount of food or excretes a great quantity of waste 

 products, then it follows that an individual of this species occupies as 

 large a place in the microcosm as would permit another species to pro- 

 duce many individuals, and the coefficient a will be large. In other 

 words an individual of this species will occupy the place of many 

 individuals of the other species. If we remember here the specificity 

 of the metabolic products, and all the very complex relations which 

 can exist between the species, we shall understand how useful we 

 may find the coefficient of the struggle for existence a, which objec- 

 tively shows how many places suitable for the first species are occu- 

 pied by one individual of the second. 



Taking the coefficient a, we can now express in the following man- 

 ner the unutilized opportunity for growth of the first species in a 



mixed population : — * — . The unutilized opportunity 



for growth of the second species in a mixed population will have a 



similar expression : — -J — • The coefficient of the strug- 



A 2 



gle for existence |8 indicates the degree of influence of every individual 

 of the first species on the number of places suitable for the life of the 

 second species. These two expressions enable one to judge in what 

 degree the potential increase of each species is realized in a mixed 

 population. 



(3) As we have already mentioned in analyzing the Ross equations, 

 an important feature of mixed populations is the simultaneous influ- 

 ence upon each other of the species constituting them. The rate of 

 growth of the first species depends upon the number of places already 

 occupied by it as well as by the second species at a given moment. 

 As growth proceeds the first species increases the number of places 

 already occupied, and thus affects the growth of the second species as 

 well as its own. We can introduce the following notation: 



—^, —r^- = rates of growth of the number of individuals of the 

 first and second species in a mixed population at a 

 given moment. 



