Difference between entropy and maximum entropy
As illustrated in Fig. 3, the ratio of the entropy factor to total mass
quantity s /C T was positively related to
ln(N ) at high levels of correlation in both Plots I
(R2 = 0.9449, Fig. 3a) and II (R2 =
0.9950, Fig. 3b). Sinces m/C T = ln(N ), the
difference between the observed s /C T and
ln(N ) was resulted from the difference between s and its
maximum s m. Combining the linear regression
equation with Eq. 5 gives
s /C T =
∑x iln(1/x i) =a ln(N ) =a (s m/C T) (9)
The logical variation range of the proportional factor a will be
0 ≤ a ≤ 1 as a = 0, s /C T =
ln(N 0) = 0, which is a special case for a
single species system while a = 1,s /C T = ln(N ) =s m/C T, which is the
potential limit at which s reaches its maximums m.
The increase in s /C T with increasing
ln(N ) is a process of increase in species richness while the
approach of s to s m is a process of
increase in species evenness. The proportional factor a can thus
be regarded as an index for species evenness. The higher value ofa found for Plot II (0.7059) than that for Plot I (0.2218)
indicated that the level of species evenness was much higher in Plot II
than in Plot I. The cause for the smaller difference between sand s m in Plot II was its metal contaminated
condition that inhibited the growth of the species and reduced the
difference among them.