GLEASON: SOME APPLICATIONS OF THE QUADRAT METHOD 29 
The relative abundance of a species is a fair measure of its 
ability to maintain itself under the conditions of environment and 
competition prevalent within the association. Long-established 
species of an old association have frequently become diffused 
thoroughly over the whole area, and their abundance may be 
determined by counting, but recent immigrants into old associa- 
tions or any species of young associations are not uniformly 
distributed. The number of individuals of such plants is there- 
fore zero in those parts which they have not yet reached and is too 
high to show their relative adjustment in those parts which they 
have reached. 
But there is a definite relation between the number of individ- 
uals of a species and its frequency index. If only one is present in 
the area covered by the quadrats, the frequency index naturally 
cannot exceed 1. If only two are present, it can not exceed 2 
and may be only 1 if both happen to occur in the same quadrat. 
While it is possible for a species to be represented by a large 
number of individuals all of which occur in a single quadrat only, 
the chance of such a thing actually happening is very small indeed. 
Similarly, while 100 individuals might be so thoroughly distributed 
that they would occur one in each quadrat, there is again very slight 
probability of it. The mathematical possibilities are capable of 
solution according to the laws of probability and chance. If 
plants are scattered at random over g quadrats, the probability 
of any one quadrat being occupied is expressed by the formula 
n 2 
ees (: we . Thus for 2 plants in 5 quadrats I — (: _ ; 
I 6/5 
= 0.36 = FI 36. Or for 65 plants in 100 quadrats I -(: gee 
= FI48. Or, conversely, FI 48 should indicate a total of 65 indi- 
viduals within the 100 quadrats. But since plants are not dis- 
tributed entirely atfrandom, the actual number is therefore always 
greater than indicated by the mathematical formula, which may 
be expressed, when g = 100, as” = ree . Thus, Pleris 
aquilina, determined by actual count to have an average abun- 
dance of 4,400 in 100 quadrats, has FI 99, corresponding to a 
theoretical number of only 455 individuals. Obviously, the 
