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to learn to what extent the species of this subfamily are ecolog- 

 ically affiliated, which of the species are most typical of the 

 subfamily as an ecological group, which are to be regarded as 

 lagging or wandering members of it, and which, if any, do not 

 belong ecologically with their taxonomic relatives. 



I shall be obliged, in these studies, to assume provisionally 

 that my collections are large enough and numerous enough 

 fairly to represent actual field conditions in Illinois, and that 

 they are so numerous that they may reasonably be treated, for 

 the present purpose, as homogeneous and similar, each collec- 

 tion as a unit substantially like every other, important differ- 

 ences among them disappearing, in aggregates and averages, 

 by the process of mutual cancelation. In other words, I must 

 assume provisionally, testing my supposition later by the con- 

 stancy and reasonableness of the results, that these random 

 samples of Illinois darters represent the subfamily as a whole 

 sufficiently well to justify their use as materials for a study in 

 statistical ecology. 



The Method of the Investigation. 



The species of darters which are most frequently found in 

 each others' company are, of course, those most likely to be 

 closely related ecologically; and the ratio of the number of 

 collections containing both of any two-species to the total num- 

 ber of collections containing either, may be used as a provi- 

 sional measure of the ecological affinity of the two. 



Furthermore, given a certain average frequency of occur- 

 rence of each of two species inhabiting a common territory, and 

 assuming a uniform distribution of each in this territory, un- 

 influenced by ecological relationships, the average frequency 

 of the joint occurrence of these species in collections may be 

 computed; and any very marked departure, positive or negative, 

 from this computed average will point to some ecological 

 bond if the difference is positive, or to some cause of ecolog- 

 ical separation if it is negative. 



If, for example, it appears that several species ought to be 

 found together, on an average, in one out of twenty of our col- 



