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.