15 
Such are some of the products of a study of the populations of 
predetermined habitats. It remains to be seen to what extent these 
habitat populations coincide with real ecological groups of most fre- 
quent associates—to what extent our habitat characters are the real de- 
terminers of the actual associative distribution of our fishes. It may 
be that the effective sensibilities of fishes are not altogether what we 
have supposed them to be, a priori; that things we have not thought of 
in that connection have much to do with their assemblage in more or 
less definite and in more or less permanent societies. This is especially 
possible with fishes, because we can see so little of them as a rule, and 
because their power of free and rapid locomotion enables them to as- 
semble and to disperse so readily and so rapidly. To get at the funda- 
mental facts we must find a means of learning what and where definite 
associations among fishes really exist; what is the local center and what 
are the optimum conditions of each such associate assemblage; and what 
are its most typical and constant components—what species, that is to 
say, are the most clearly and constantly characteristic of it. This means 
that we must study the details of the distribution, and hence of the 
associate grouping of fishes, with reference at first to their location only; 
and then, when our associations have thus been determined, located, and 
described, we must see how they compare with the habitat system ar- 
rived at by our preliminary analysis of the environment. 
This sort of critical study of the essential details of ecological dis- 
tribution has almost never been made, at least for animals, and even 
the methods of it are scarcely agreed upon. Those which I shall briefly 
describe to you were devised for the purpose of utilizing, for ecological 
description and inference, the product of extensive collections of IIli- 
nois fishes, made in the long course of the natural history survey of 
the state. They are based upon the obvious fact that a biological asso- 
ciation is made up of species which are associated with one another more 
frequently than they are with other species; from which it follows that 
to find an association one must find a group of such most frequent asso- 
ciates; and to determine the center of its location and the extent of its 
range we must find where this associative frequency—this frequency of 
joint occurrence—of the several species of the group is greatest, and 
how far in each direction each species of it continues to be more fre- 
quently associated with the other members of the group than with any 
other species. If, for example, we make a hundred collections over a 
given area of complex ecological composition, and find that we have 
