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 should be used for calculating the total equivalent mass quantityC . 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.