410 
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. 
and an average of 23. The two highest single ratios of ichthyo- 
logical affiliation are those of the Illinois and Mississippi rivers (. 72) 
and of the Big Muddy and Saline (.70). 
The data of this table may be generalized by bringing into com- 
parison the average of the ratios of affiliation for each district with 
those for all the rest, as shown in the column of figures farthest to 
the right. If the ten districts are arranged in the order of the size of 
their average ratios, they readily fall into two groups, the first of six 
districts, with relatively high ratios, and the second of four, with 
relatively low ratios. The first group comprises the basins of the 
larger rivers—the Mississippi, the Rock, the Illinois, the Kaskaskia, 
the Wabash, and the Ohio, each with its more or less complex system 
of tributaries. ‘The average ratio for this group 4s 52:7 er cemr 
The second group is made up of small, widely separated districts, 
containing only small streams and lakes, except that one of them in- 
cludes a little of the shallow southwestern border of Lake Michigan. 
In this group are the northwestern driftless area, the Saline River 
and its tributaries, the Big Muddy district, and the Michigan dis- 
trict, with an average affiliation ratio of 37.6. 
If we average separately, for these groups, the ratios of each dis- 
trict to all the other districts of its group, we obtain for the first and 
higher group a ratio of mutual affiliation of 63 per cent., and for the 
lower group a similar ratio of 33 per cent. It is thus made clear 
that the districts most typical of our Illinois fauna are the first six 
