280 



species: Multiply the number of collections made from the common 

 area of the species by the number containing one or more represent- 

 atives of both; multiply the number of collections containing one or 

 more representatives of one of the species by the number containing 

 one or more of the other; and divide the first product by the second. 

 The quotient will be the coefficient of association. 



Discussion of Associative Tables. 



I have computed, by the above-described method, for thirteen 

 species of Illinois darters— each of which was obtained more 

 than fifteen times in my collections— the coefficients of the as- 

 sociation of each species with each of the other twelve, and 

 have arranged these seventy-eight coefficients (apparently one 

 hundred and fifty-six, since each of them is entered t twice) in 

 Tables I.-V. for comparison and discussion. In computing the 

 coefficients of two species, Diplesion blennioides and Etheostoma 

 zonule, the first of which is found only in the eastern part of 

 the state and the second only in the northern half, I have used 

 as the value of a in my formula, not the entire number of col- 

 lections made throughout the state, but the number made in 

 the stream systems in which these species occur. 



In Table I. the coefficients in each column are in serial or- 

 der, the highest to the lowest from above downwards; and the 

 columns for the several species are placed in the order of the 

 average coefficients for the columns, the highest at the left. 



We notice first, that the total of the one hundred and fifty- 

 six coefficients of this table is 315.8 — a general average associa- 

 tive coefficient of 2.02 for all the thirteen species. As the nor- 

 mal chance average would be but 1, we conclude, from these 

 data, that darters were found together in my collections about 

 twice as frequently as mere chance would indicate. This ratio 

 of 1 to 2 is thus an approximate and provisional measure of the 

 ecological bond in this family taken at large. 



We notice next, the unlike totals and averages of the co- 

 efficients for the several species, these running from 1.22 to 

 2.69 — an indication that the associative bond is more than 2.2 

 times as strong for Radropterus phoxocephulus and Etheostoma 



