24 GLEASON: SOME APPLICATIONS OF THE QUADRAT METHOD 
to be representative of the whole association, of sufficient number 
to permit drawing logical conclusions, and of a size suitable to the 
character of the vegetation concerned. Several ecologists have 
devised statistical methods toward this end, which have been 
more or less successful. One of the earliest was Drude (1890), 
who described plants as social, gregarious, copious, or rare, de- 
pending on their number, their distribution, and their grouping. 
He also proposed the determination of the frequence of plants on a 
large scale by dividing an area into quadrats of 100 square kilo- 
meters. Pound and Clements (1898, 1900) adopted the same 
terminology in their first studies on the subject, but determined 
abundance within a single association by actual counts of the 
number of individuals in a quadrat 5 meters square, and investi- 
gated enough quadrats to warrant them in drawing averages. It 
is obvious, however, that averages from figures obtained in this 
way are not entirely trustworthy, since some species are mutually 
exclusive, while the averages might indicate that they normally 
grew together. Jaccard (1901) adopted the study of several 
adjacent quadrats as a method in his study of alpine vegetation, 
and developed the idea of the frequency index and the community 
coefficient. His results are, however, probably somewhat faulty, 
inasmuch as he used few quadrats in any one association and lo- 
cated them adjacent to one another. Harper (1917 and several 
other articles) has also attempted a statistical expression of car- 
window observations, which corresponds to some extent to the fre- 
quency index as here used. Raunkiaer (1909) used essentially 
the same method described here. 
The present writer first attempted the use of statistical methods : 
to determine and express the structure of vegetation in 1993 
(1907). He improved his method somewhat in 1908 (1910) and 
adapted it to class work with students in 1910. In the summer 
of 1911 he began the intensive study of the quadrat method and 
its applications at the Biological Station of the University of 
Michigan, and during the following four summers obtained a long 
series of data upon which the present paper is based. The 
statistics used in TasLEs I and II were secured from the aspen 
(Populus tremuloides and P. grandidentata) association. 
In practice, the following method is adopted. The size of the 
