288 



from 16 to 60, with an average of 34— and comparing the aver- 

 age of their coefficients of mutual association with the general 

 average coefficient for the entire group, with its 82 occurrences 

 to the species. From Table V. it appears that this general co- 

 efficient for the seven least frequent species take a separately is 

 1.85, while that for the whole group of thirteen (Table I.) is 

 2.02 — a coincidence probably as close as could be expected in 

 view of the fact that the former number is an average of only 

 21 coefficients and the latter of 78. The coefficient expressing 

 frequency of mutual association among these least frequent 

 species, is thus so close to the general coefficient for the entire 

 group that even the former species may be said to occur fre- 

 quently enough in the collections for the purposes of this dis- 

 cussion. 



Relations to Physical Environment. 



I have next to study the interrelations of this group of dart- 

 ers by means of another and widely different set of data, to be 

 derived from an analysis of collectors' records concerning the 

 kinds of waters and the classes of situations from which the 

 several collections came; and to compare the conclusions thus 

 reached concerning the physical relations of the species with 

 those already derived from an analysis of their relations of asso- 

 ciation. For this purpose these records have been organized in 

 a way to show the relative frequency of the occurrence of each 

 species in our collections in each of the three sections — northern, 

 central, and southern Illinois, as the state is commonly divided; 

 in each of the ten stream systems, or river basins, distinguished 

 by us; and in each kind or class of body of water — whether 

 stream, lake, pond, or marsh— the classification made express- 

 ing differences in size, in water movement, and in the charac- 

 ter of the bottom. 



Equalization of the Data. 



The data available are not equally numerous under these 

 various heads. Those concerning the size and general charac- 

 ter of water bodies, and the distribution by stream systems 



