GENERAL AND INTERIOR DISTRIBUTION XC111 



RELATIONS OF EACH DISTRICT TO ALL THE OTHERS 



In the foregoing discussions and analyses the fishes of the various 

 districts have been compared with those of the largest and most cen- 

 tral district as a type ; but a fuller and more accurate idea of the com- 

 position of the fish population of Illinois and of its relations in the 

 various hydrographic divisions of the state may be obtained by a 

 comparison of the species of each of our ten districts successively 

 with those of all the others. This may lie done in an exact and uni- 

 form manner by determining for each pair of districts the ratio which 

 the number of species common to the pair bears to the whole number 

 of species occurring within the area of both the districts taken to- 

 gether as one. In the Galena district, for example, there are 44 spe- 

 cies recorded, and in the Saline River basin there are 55, a total of 99 ; 

 but as 26 of these species have been found in both these districts, this 

 number has been taken twice in the above addition, and the number 

 of species found by us in the entire area of these two districts is con- 

 sequently 73. The ichthyological affinity of these two areas is evi- 

 dently to be measured by the ratio which the number of species com- 

 mon to both bears to the whole number of species found in either or 

 both the areas — in this case, the ratio of 26 to 73, or 36 per cent. 

 That is, 36 per cent, of the fishes found in either of these two districts 

 have been found by us in both of them. 



A similar analysis of the data for each of the forty-five pairs 

 which it is possible to make up from our ten hydrographic districts, 

 yields the material for the following table of common species and of 

 ratios of affiliation. This table shows, in the lower left-hand part, 

 the number of species common to each pair of districts, and in the 

 upper right-hand part the ratios which these numbers bear to the 

 number of species occurring in each pair of districts taken as one. 

 The number of species common to any two districts will be found 

 in the lower left-hand part of the table, where the column for one 

 district intersects with the line for the other, and the ratio of affil- 

 iation for the same pair of districts will be found in the opposite 

 part of the table at the intersection of the line for the first with 

 the column for the second. A simple inspection of the figures in 

 the latter part shows at once which districts are most alike and 

 which are most unlike in respect to their fish inhabitants. Thus, the 

 Rock and Illinois basins and the Mississippi are the most closely re- 

 lated, according to these data, with affiliation ratios of 68-72 per 

 cent, and an average of 70; and the Michigan, Galena, and Big 

 Muddy districts are the least alike, with ratios of 20-28 per cent. 



