Calculation
For comparison, the Shannon-Wiener index (the Shannon form of the
information entropy) was calculated by
SI=∑(m i/M )ln(M /m i)
= ∑p iln(1/p i) M =
∑m i, p i=∑m i/M , i = 1, 2, …, N (1)
where m i denotes the number of individuals of the
ith plant species, M denotes the total number of individuals of
the plant community, N denotes the total number of species of the
plant community and p i stands for the relative
abundance of the ith plant species (Eq. 1 referring to Eq. 15 in the
theoretical section).
The thermodynamic factors h , s and f (enthalpyH , entropy S and Gibbs free energy G divided,
respectively, by gas constant R and temperature T ) were
calculated by
h = H /(RT ) =C Tln(N m) =C Tln(66) C T =
∑C i (2)
s = TS /(RT )= S /R =
∑C iln(1/x i)x i =C i/C T,C i = ∑c ij, j = 1, 2, …,m i (3)
f = G /(RT ) = h – s =C Tln(66) -
∑C iln(1/x i) (4)
s /C T =(1/C T)∑C iln(C T/C i)
= ∑x iln(1/x i) (5)
f/C T = ln(N m) -s/C T = ln(66) - s/C T (6)
where c ij denotes the net dry biomass quantity of
the jth plant for the ith species, C i denotes the
total net dry biomass quantity of the ith species,C T denotes the total net dry biomass quantity of
the plant community, x i denotes the mass ratio
for the ith species, and N m stands for the
maximum number of plant species (Eqs. 2-4 referring to Eqs. 11-13, 24 in
the theoretical section). As an upper limit of N ,Nm for a given habitat is a constant. The
enthalpy factor h is a linear function ofCT and use of any Nm value
will not change its basic relation with the Gibbs free energy factorf and entropy factor s . Since, as a potential limit,Nm is a parameter related to regional species
richness, the highest number of plant species 66 observed in the
non-polluted surrounding area nearby the metal contaminated site was
used as Nm for calculating h .
For comparing the difference among plant species, the standard deviation
for relevant parameters was calculated by
SD = ∑[(Z i –Z )2/(N -1)]1/2 Z =
∑Z i/N (7)
where Z i denotes a parameter for the ith species
and Z denotes its mean value.