IN THE NORFOLK BROADS DISTRICT. 
79 
but it would be exceedingly difficult to arrange the species 
into associations with any accuracy by separating them 
according to their habitats. A method has, however, occurred 
to me by which it seems possible to determine which species 
are more commonly associated together, and as this method 
depends upon statistics and not upon impressions, I believe 
it is reliable. 
From complete lists of the species of every collection we 
can quite easily extract the percentage of occurrences of all 
the species in all the collections. Similarly, if we separate 
out all collections containing a certain species “ A,” we can 
extract the percentage of occurrences of all the species in the 
“ A ” collections, that is, we can find out how many times 
each of the other species has occurred in company with “ A.” 
We have not, however, in such a series of figures got the 
true value of each species as an associate of “ A,” because 
those species which exceed “ A ” in number of occurrences 
in the general collections can occur in ioo % of the “ A ” 
collections, while a species scarcer than “ A ” in the general 
collections cannot possibly turn up in ioo % of the “ A ” 
collections. We must therefore find the value of each species 
as an associate of “ A ” in terms of its own commonness in 
the general collections. Perhaps this can be made clear by 
•an illustration. 
Species “ A ” occurs in 50 % of all collections and we wish 
to find the values of “ B,” “ C,” and “ D ” as associates of 
“ A.” Species “ B ” occurs in 75 % of all collections, “ C ” in 
20 % and “ D ” in 15 %. Now since “ B ” occurs in more 
of the general collections than “ A ” does, the largest per- 
centage that it could show' in the “ A ” collections would be 
100. On the other hand, “ C ” only occurs in 20 out of every 
100 general collections, and therefore cannot possibly turn 
up in more than 40 % of the “ A ” collections. Thus if “ B ” 
occurs in all the “ A ” collections it occurs in 100 — 75, i.e., 25 % 
more of the “ A " collections than of all the collections, while 
if “ C ” occurs in 40 % of the “ A ” collections, the best it 
•can do, it occurs in 40 — 20, i.e., in 20 % more of the “ A ” 
•collections than of the general collections. It appears 
therefore as if “ B ” were more important than “ C ” as an 
