System diversity
The SI data listed in Table 2 do not fully prove the use of the
traditional applied Shannon-Wiener index SI for comparing the
biodiversity among the investigated plant communities. The patterns in
Fig. 2 indicate that SI i is not a proper
parameter for species abundance in terms of mass quantity and internal
energy. There is a theoretical flaw to use SI as a biodiversity
index for description of an ecosystem simply because the biodiversity of
an ecosystem is not a single function of the number of individualsm i or its ratio p i.
According to the principle of invalidity of a single factor, a system
state cannot be determined by a single factor unless some of other
factors are kept constant. The relative abundance of a species on a
habitat cannot thus be uniquely determined by m iunless the individuals both within and across species are identical, or
at least, with no significant differences in their concerned physical
properties and quantities. As a matter of fact, use ofpi as a relative abundance index also disobeys
the principle of additivity. The number of individuals of a herb species
cannot be added to that of a tree species simply because a small grass
is hardly comparable to a big tree with respect to their ecological
functions in a plant community. The value of M would be in
particular meaningless at an ecosystem approach if it should stand for
the total number of individuals of all organisms co-existed in the
ecosystem.
Unlike SI , which is a single function of individual number ratiop i, s is a function of mass quantityC i and mass ratio x i. As
been discussed in the theoretical section, the rationality for
calculating x i is based on the assumption that
the biomass of different plant species possesses the same unit energy
value in terms of standard chemical potential. If this criterion is not
fulfilled, the weighted biomass quantity C iγshould be used for calculating the total equivalent mass quantityC Tγ. As a state function (rather than a
probability variable), s is a system property linked to system
composition, and can thus be generally applied as a system diversity
index. Use of s for determining the diversity state of a system
also follows the principle of relative validity of a single factor. From
Eq. 5, we see that ln(N m) is a constant, and
given C T, both f and s can be
uniquely determined by x i. The analytical results
obtained in the present study give support to use of s as a
system diversity index (Tables 1 and 2, Fig 2). Since the related
principle holds in general with no exceptions, s can be used as a
diversity index for all types of thermodynamic systems.
It is necessary to mention that SI can be a useful index in
particular cases. Apart from that SI does not differ froms /C T in both concept and quantity in
systems with uniform individuals (see discussions in the theoretical
section), the number of individuals m i orSI i is a meaningful index to reflect the ability
of a species to reproduce at a given habitat. TheSI i patterns for different plots depicted in Fig.
2 show its importance for comparing the ability of species to survive
under different site conditions. Reproduction is also an energy
consumption process. It should take a longer time for a tree species
with a larger body size to multiply its individual number since more
energy is required in its reproduction.