6 lotka: discontinuous evolution 



in mass. The simplest example in point comes to us from physi- 

 cal chemistry. In general a change of state, such as crystallisa- 

 tion from a supersaturated solution, involves a change in com- 

 position, as well as in mass, of one or more phases. 



When we turn to biological systems, composed of a number of 

 "kindred-groups," we observe an analogous state of affairs. In 

 general the individuals comprised within a kindred-group are 

 not all precisely similar. Thus, expressing the matter analytic- 

 ally, out of a total N } of individuals of some group A h a certain 

 fraction 



-W1C1 (P> 0.1 r > - • • ) dpdqdr . . . 



will have the values of certain characteristic features P, Q, R, 

 . . . comprised between the limits 



p and (p + dp) 

 q and (q -f- dq) 

 r and (r + dr) 



A similar statement holds for each of the other groups A 2 , 



A.3, 



As time goes on both the values of JVi, N 2 , . • • will in 

 general change, and also the form of the frequency functions 

 Ci, C 2 , . . . In other words, the matter of the system under- 

 goes a change in distribution: (1) among the several kindred- 

 groups; (2) among the several types of individuals of which each 

 group is composed. The former change may be spoken of as 

 "Inter-Group Evolution," the latter as "Intra-Group Evolu- 

 tion." 5 



It is intra-group evolution, the change in time of the character 

 of a species, with the possibility of the origin of a new species as 

 its outcome, which has hitherto mainly engaged the attention of 

 the biologist. 



We, on the contrary, will here turn our attention chiefly to 

 certain aspects of inter-group evolution. 



6 Annalen der Naturphilosophie, p. 69. 1911. 



