lotka: discontinuous evolution 



51 



d Mi \ it 



COMMONLY 



(1) 



(2) 



A h (- 



*A H ) 



^4 k 



.4, 



/Ik 



SPECIAL CASE 



or 



We now proceed to discuss in greater detail a case of the type 

 (2) noted in our table: 



Ah(->A 



H 



A, 



that is to say a kindred-group A\ feeds on the waste products 

 A H of other groups which we denote collectively by Ah. Thus 

 for example Ah may represent a number of carnivorous species, 

 A H the carbon dioxide and other matter excreted by them, and 

 Ai some green plant which assimilates such waste products, 

 but is not itself consumed by Ah. 



Fixing our attention first on A i We note that 



dflf, 

 dt 



= Bi- Z, 



(1) 



where B\ is the total food consumed by Ai per unit of time, and 

 Z\ is the total waste matter (including the bodies of dead indi- 

 viduals) discarded by A f per unit of time. 

 We will write 



dM x 



dt 



= (6,-2i)Mi = r,Mi 



Similarly we have for A H 



dM n 

 dt 



Bn~ Z n 



(2) 



(3) 



We will suppose that the groups A h have had time to arrive 

 at a state of equilibrium with their environment, and that the 

 waste products A H exert at most a negligible influence on A h . 

 Then we have for the mass M h of the groups A h 



M h = constant (4) 



