296 GLEASON: SOME APPLICATIONS OF THE QUADRAT METHOD 
the counts. Some of the rarer ones will be missed completely. 
For example, during five years experience in the aspen association 
of northern Michigan, during which some thousands of quadrats 
have been counted by the writer or his students, Cypripedium 
acaule, a plant of great rarity in this habitat, has appeared but once 
in the quadrats. These rarer ones, while of the greatest interest 
to the systematist or the phytogeographer in their relation to 
plant distribution in general, as emphasized so interestingly by 
Fernald (1919), and to the ecologist through the evidence which 
they frequently offer concerning the past or future development 
of the association, are nevertheless of negligible value in formu- 
lating a verbal description of the association. But the important 
species all do occur, provided the number and location of the 
quadrats has been properly chosen with reference to the size and 
character of the association, as the writer has demonstrated fre- 
quently in his own work. 
If the whole association were included in a single quadrat, 
the frequency index of each species would be roo and would give 
no idea of the comparative value of the species. In general, if the 
quadrats are too large, the frequency indices are also large and 
tend to approximate near 100. Conversely, if they are too small 
the indices are also small, and tend to approximate near unity, 
while the number of omitted species tends to become large and 
may even include some of the more important ones. The optimum 
size is one in which there is a wide divergence in the indices, from 
1 to 90 or even more, so that the variation is an indication of the 
relative importance of the species. This is illustrated in the first 
three columns of figures in TABLE I,* of which the second column 
based on quadrats two meters square, presents probably the best 
series of indices. 
a te 
* The frequency indices given in TABLE I are not considered typical of the ae 
associationi n general. The association consists of a sparse growth of two species © 
aspen and the: paper birch, alternating with treeless areas dominated by bracke 
The 240 quadrats counted for this paper were located entirely within a treeless area, 
and do not take account of the conspicuous difference encountered in the shade, - 
Neither 40 
reeless areas 
where Melampyrum lineare and Diervilla Lonicera are both abundant. 
they cover an extent wide enough to give a fair representation of the t 
in general, since these omit completely such relatively common species as Vaccinium oe 
pithamacus- — 
canadense, Panicum depauperatum, Oryzopsis pungens, and Convolvulus s 
n fern. 
are 
