30 GLEASON: SOME APPLICATIONS OF THE QUADRAT METHOD 
discrepancy between actual and theoretical number should be, 
and is, greatest in species of high frequency, FI 95 or more. 
It is not possible to draw any accurate conclusions as to the relation 
between theoretical and actual number of individuals, but in 
general, the theoretical number is one fifth to two thirds as large 
as the actual, and results any more accurate than this are prob- 
ably of little or no value in ecological description. 
The determination of the proper size of the major quadrat 
involves reducing the original series of quadrats to a smaller num- 
ber of larger quadrats, thereby increasing the frequency index of 
selected species to 99 or more. With FI 99 or more for all the 
important species, it may be assumed that this quadrat is large 
enough to serve as a fair sample of the association. 
In the original equation 1 — ( I— x)= FI, substitute for g 
the number of quadrats actually counted, use for PI the index of 
the least common one of the important species, and solve for 7. 
Substitute again the determined value for 7 and 99 for the original 
FI and solve for g. The equation is I — ee \.O1 (presuming 
100 quadrats were counted), from which g may be easily determined. 
For example, in a certain association, it is desired to determine 4 
major quadrat which will probably contain all the species with 
FI 60 or more. 
I 90 ;-— . 
I Fae V.o1: g = 20 (fractions omitted) 
That is, the original 100 quadrats redivided into 20 larger 
quadrats should show FI 99 or 100 for all species which originally 
had FI 60 or more; or the major quadrat should be five times as 
large as the original. The error concerned in computing the value 
of 2, due to imperfect distribution of the species, does not affect 
this last equation, and experience has shown that it gives surpris- 
ingly good results. On the average, four major quadrats out of 
ve, the location of which is chosen at random, present all the 
important species for which they were computed. 
