282 



cients of those species which exhibit strong associative affinities 

 we omit those which have the weaker affinities, and so have a 

 group of select associates whose average coefficient must be 

 higher than that of the whole thirteen species, including, as 

 this does, some with strong and others with feeble associative 

 tendencies. 



The same fact is illustrated in Table II., in which all the 

 coefficients of the seventy-eight possible pairs of my thirteen 

 species are arranged in the order of the magnitude of their co- 

 efficients of association with ILnlroptci-iisaspro (1421 ). Taking 

 the hrst twenty-one coefficients of the six most frequent asso- 

 ciates of Hddruptpnis aspi'o, we hnd that they average 3.27, 

 while the last twenty-one coefficients of the six least frequent 

 associates of HiK/rupfcnis aspro average 1.4. That is, the twen- 

 ty-one coefficients at the upper left angle of Table II. (above 

 the l)lack line) average two and a half times as much as the 

 twenty-one coefficients at the lower right angle of that table 

 (to the right of the black line). The most frequent associates 

 of this species are associated with each other about two and a 

 half times as frequently as are its least frequent associates. 



It is also significant that five of the list of six most fre- 

 quent mutual associates made up from Table I., are the same as 

 those of the corresponding list made up from Table II., of Ha- 

 (1r(>j)tcnis (ispiv and its five closest associates, the two tables con- 

 taining the same figures, differently arranged. We further 

 notice that the three least frequently associated species are the 

 same on both lists. Whether the data indicating frecjuency of 

 association are arranged under each species independently, in 

 the order of frequency, as in Table I., or with reference only to 

 a single leading species, as in Table II., the results are nearly 

 identical as to the darters most typical and least typical of the 

 group. 



Sufficiency of the Collections. 



With respect to the sutficiency of the collections for the use 

 which is here made of them, some additional evidence may be 

 found by tabulating separately the seven species which appear 

 least frequently in them— ranging in number of occurrences 



