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Sources: Cavalier-Smith (1985), Li and Grauer (1991) and Lewin (1994).

Sources: Cavalier-Smith (1985), Li and Grauer (1991) and Lewin (1994).

Finally, the specific exergy of 1 g of biomass of ith species is equal to ex,. = T0(infchem + infbio1) = To(62.3 + 0.174^f) J/g. (7.8)

The total exergy of ecosystem can be found by summing up the contributions, originating from all n components including detritus (i = 1, g1 = 0)

i=i where c, are the biomasses of corresponding components expressed in grams. By introducing the weighting factor ¡3, = exi/ex1, i = 1,..., n we are able to cover the exergy for various organisms in the detritus equivalent unit D = 62.3 J/K g:

The weighting factor defined as exergy content in relation to detritus (see Table 5.1) might be considered as a quality factor, reflecting how developed are the various groups and to what extent they contribute to the exergy due to their information content, reflected in the computation. This is completely in accordance with Boltzmann (1905), who gave the following relationship for the work, A, that is embodied in the thermodynamic information; we have A = RT ln w where w is the number of possible states, among which the information has been selected, i.e. w for species is the inverse value of probability spontaneously to obtain the valid amino acid sequence.

The total exergy of an ecosystem cannot be calculated exactly, as we cannot measure the concentrations of all the components or determine all possible contributions to exergy in an ecosystem. If we calculate the exergy of a fox, for instance, the above calculations will only give us the contributions coming from the biomass and the information embodied in the genes, but what is the contribution from the blood pressure, the hormonal activity and so on? These properties are at least partially covered by the genes, but is that an entire picture? We can calculate the contributions from the dominant components, for instance, by the use of a model or measurements that cover the most essential components for a focal problem.

Exergy calculated using the above method has some clear shortcomings:

• We apply the model of ideal dilution to such a non-ideal substance as detritus.

• We do not know the non-nonsense gene for all the organisms.

• We calculate the exergy embodied in the proteins (enzymes) only in principle, while there are other components important for life processes. These components are contributing less to the exergy than the enzymes, and the information embodied in the enzymes controls the formation of other components, for instance hormones. It cannot, however, be excluded that these components will contribute to the total exergy of the system.

• We do not include the exergy of the ecological network. If we calculate the exergy of models, the network will always be relatively simple and the contribution coming from the information content of the network is negligible.

• We will always use a simplification of the ecosystem, for instance by a model or a diagram or similar. This implies that we only calculate the exergy contributions of the components included in the simplified image of the ecosystem. The real ecosystem will inevitably contain more components which are not included in our calculations.

It is therefore proposed to consider the exergy found by these calculations as a relative minimum exergy index to indicate that there are other contributions to the total exergy of an ecosystem, although they may be of minor importance. In most cases, however, a relative index is sufficient to understand the reactions of ecosystems because the absolute exergy content is irrelevant for the reactions. It is in most cases the change in exergy which is of importance to understand the ecological reactions.

The weighting factors presented in Table 5.1 have been applied successfully in several structurally dynamic models and furthermore in many illustrations of the maximum exergy principle that will be presented in Chapter 12. The relatively good results in the application of the weighting factors, in spite of the uncertainty of their assessment, only seem to be explicable by the robustness of the application of the factors in modelling and other quantifications. The differences between the factors of the microorganisms, the vertebrates and invertebrates, are so clear that it does not matter if the uncertainty of the factors is very high—the results are not affected.

On the other hand, it would be important progress not only from a theoretical point of view to get better weighting factors but it also would enable us to model the competition between species that are closely related.

5.8. Other methods for the exergy calculation

Fonseca et al. (2000) have proposed another method to estimate the weighting factors based on the overall DNA content. It could be argued that all DNA contribute to the information content and that all DNA would have some function, for instance as spare parts for damaged DNA. We slightly modify this method taking into account the pair correlations between amino acids (see Section 4.9, Chapter 4). According to modified Fonseca et al.'s proposal the genetic information contained in the biomass of ith species (group of species, taxon), inf^t, is defined as (infbit>l = Inuc):

i bit 6

where Lnuc (n in Section 4.9) is the nucleotide length of single-stranded DNA. If C is the amount of DNA contained in the organism (in picograms per cell) then Lnuc = (1/2) X 0.98 X 109C (nucleotides). The weighting factors BDNA are calculated by the method described in Section 5.7. In Fonseca et al. (2000) a table can be found with the B-values estimated according to their method. Table 5.2 is our modification of their table.

The advantage of this method is that the C-value is known for the higher number of organisms than the number of non-nonsense genes, which of course is not needed if the estimation method is wrong. If we compare two columns in Table 5.2 then we can see that for some organisms Bi > BDNA (Bacteria, Fungi, Molluscs, Crustaceans and Fish),

Table 5.2

Lowest DNA contents (Ci) and weighting factors (BDNA) for living organisms

Table 5.2

Lowest DNA contents (Ci) and weighting factors (BDNA) for living organisms

Organisms

Ci

BNA

ßi

Detritus

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