## How to Calculate Eco Exergy of Organic Matter and Organisms

The following expression for what we could call the ecological exergy per unit of volume has been presented; see eqn [7]:

where R is the gas constant, T is the temperature of the environment, c; is the concentration ofthe ;th component expressed in a suitable unit, and c; , is the concentration of the ;th component at thermodynamic equilibrium and n is the number of components. c; is very low for living component because the probability that living components are formed at thermodynamic equilibrium is very low. It implies that living components get a high eco-exergy. c; is not zero for organisms, but will correspond to a very low probability of forming complex organic compounds spontaneously in an inorganic soup at thermodynamic equilibrium. c; on the other hand is high for inorganic components, and although c; still is low for detritus, it is much higher than for living component.

The exergy of structurally complicated material can be estimated based on the elementary composition. This has, however, the disadvantage that a higher organism and a microorganism with the same elementary composition will get the same exergy which is in complete disagreement with the lower probability to form a more complex organism, that is, the lower concentration of c; in the equation. The composition will not account for the contribution of Kullbach's measure of information, which is often the major part of the eco-exergy, as it is shown below.

The problem related to the assessment of Cj has been discussed and a possible solution proposed. For dead organic matter, detritus, which is given the index 1, it can be found from classical thermodynamics.

For the biological components, 2,3,4,... ,N, the probability, p; , consists at least ofthe probability ofproducing the organic matter (detritus), that is, p1 , and the probability, pja, to find the correct composition of the enzymes determining the biochemical processes in the organisms. Living organisms use 20 different amino acids and each gene determines in average the sequence of about 700 amino acids. pia, can be found from the number of permutations among which the characteristic amino acid sequence for the considered organism has been selected. It means that

where a is the number of possible amino acids = 20, N is the number of amino acids determined by one gene = 700, and g, is the number of non-nonsense genes. The following two equations are available:

The exergy contribution of the ith component can be found by combining eqns [12] and [14]:

Ex = RTc, ln c,/(px0a - Ngc0a ) = (^1 -)c, - ct lnp,,a = (^1 - ) c, - c, ln (a - Ng, )

The total eco-exergy can be found by summing up the contributions originated from all components. The contribution by inorganic matter can be neglected as the contributions by detritus and even to a higher extent from the biological components are much higher due to an extremely low concentration of these components in the reference system (thermodynamic equilibrium for the system). The contribution by detritus, dead organic matter, is 18.7 kJg-1 times the concentration (in gram per unit of volume) corresponding to the composition of detritus, namely lipids, carbohydrates, and proteins mainly, while the eco-exergy of living organisms with approximations consists of

Ex1chem = 18.7kJg-1 times the concentration c, (gram per unit of volume)

R = 8.314J mole-1 and if we presume a molecular weight of an average 105 for the enzymes, we obtain the following equation for Exibio at 300 K:

where the concentration now is expressed in g per unit of volume and the exergy in kilojoules per unit of volume.

For the entire system the eco-exergy, Ex-total = exergy-chemical + exergy-biological can be found as

Ex-total = 18.7^ ct - 0.052^^ c, g,[ML - 1T - 2] [18] i=i i=1

where g for detritus (i = 1) of course is 0. Table 1 shows the weighting factor, which is introduced to be able to cover the exergy for various organisms in the unit detritus equivalent or chemical exergy equivalent:

The calculation of eco-exergy accounts for the chemical energy in the organic matter as well as for the (minimum) genetic information embodied in the living organisms. The latter contribution is measured by the extremely small probability to form the living components, for instance algae, zooplankton, fish, mammals, etc., spontaneously from inorganic matter. Weighting factors defined as the exergy content relatively to detritus (see Table 1 ) may be considered quality factors reflecting how developed the various groups of organisms are and to what extent they contribute to the exergy due to their content of information which is reflected in the computation. The ^-values in Table 1 are found on basis of latest knowledge of the genome size and the complexity of different organisms. A /3-value of 2.0 means that the eco-exergy embodied in the organic matter and the information are equal. As the ^-values in Table 1 are much bigger than 2.0 (except for virus, where the /3-value is 1.01) the information eco-exergy is the most significant part of the eco-exergy of organisms.

The eco-exergy due to the 'fuel' value of organic matter (chemical energy) is about 18.7 kJg-1 (compare with coal: about 30 kJg-1 and crude oil: 42 kJg-1). It can be transferred to other energy forms for instance mechanical work directly, and be measured by bomb calorimetry, which requires destruction of the sample (organism), however. The information eco-exergy = (fl — 1) c is taken care of by the control and function of the many biochemical processes. The ability of the living system to do work is contingent upon its functioning as a living dissipative system. Without information eco-exergy, the organic matter could only be used as fuel similar to fossil fuel. But due to the information eco-exergy, organisms are able to make a network of the sophisticated biochemical processes that characterize life. The eco-exergy (of which the major part is embodied in the information) is a measure of the organization. This is the intimate relationship between energy and organization that Schr0dinger was struggling to find.

As calculated here, eco-exergy is a result of evolution and of what Elsasser calls re-creativity to emphasize that the information is copied and copied again and again in a long chain of copies where only minor changes are introduced for each new copy. The energy required for the copying process is very small, but it has of course required a lot of energy to come to the 'mother' copy through the evolution for instance from prokaryotes to human cells.

Kullback's measure of information covers the gain in information when the distribution is changed from pion to

 Early organisms Plants Animals Detritus 1.00 Virus 1.01 Minimal cell 5.8 Bacteria 8.5 Archaea 13.8 Protists (Algae) 20 Yeast 17.8 33 Mesozoa, Placozoa 39 Protozoa, amoebe 43 Phasmida (stick insects) Fungi, molds 61 76 Nemertina 91 Cnidaria (corals,sea anemones, jelly fish) Rhodophyta 92 97 Gastroticha Prolifera,sponges 98 109 Brachiopoda 120 Plathyhalminthes (flatworms) 133 Nematoda (round worms) 133 Annelida (leeches) 143 Gnathostomulida Mustard weed 143 165 Kinorhyncha Seedless vascular plants 158 163 Rotifera (wheel animals) 164 Entoprocta Moss 174 167 Insecta (beetles, flies, bees, wasps, bugs, ants) 191 Coleodiea (Sea squirt) 221 Lepidoptera (butterflies) 232 Crustaceans 246 Chordata Rice 275 Gymnosperms (incl. Pinus) 314 310 Molluska, bivalvia, gastropodea 322 Mosquito Flowering plants 393 499 Fish 688 Amphibia 833 Reptilia 980 Aves (birds) 2127 Mammalia 2138 Monkeys 2145 Anthropoid apes 2173 Homo sapiens

ß-values = exergy content relatively to the exergy of detritus (Jorgensen et al.).

ß-values = exergy content relatively to the exergy of detritus (Jorgensen et al.).

p[. Note that K is a specific measure (per unit of matter). Expressed by the Kullbach's measure of information, we get the following equation for eco-exergy:

ß is therefore RTK.

The total eco-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, then the above shown calculations will only give the contributions coming from the biomass and the information embodied in the genes, but what is the contribution from blood pressure, sexual hormones, network interactions, etc.? These properties are at least partially covered by the genes but is that the entire story? 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. The 'difference' in eco-exergy by 'comparing' two different possible structures (species composition) is decisive here. Moreover, eco-exergy computations give always only relative values, as the eco-exergy is calculated relatively to the reference system.

Eco-exergy calculated using the above equations has some clear shortcomings:

1. We have made some although minor approximations in the equations presented above.

2. We do not know the genes in all details for all organisms.

3. We calculate only in principle the eco-exergy embodied in the proteins (enzymes), while there are other components of importance for the life processes. These components are contributing less to the exergy than the enzymes and the information embodied in the enzymes control the formation of these other components, for instance hormones. It can however not be excluded that these components will contribute to the total exergy of the system. The life processes are of course considered indirectly as the enzymes determine the life processes.

4. We do not include the eco-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 considerably less than the exergy contribution from the organisms. The real ecological network may contribute much more to the total exergy. When network models are compared it may also be relevant to compare exergy of different networks.

5. 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 eco-exergy found by these calculations as a 'relative minimum eco-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. In most cases, the change in eco-exergy is of importance to understand ecological responses.

The weighting factors presented in Table 1 have been applied successfully to calculate eco-exergy applied as an indicator to assess ecosystem health and in several structurally dynamic models to express the model goal function, and furthermore in many illustrations of the maximum eco-exergy principle, that is presented below. Structural dynamic models are able to take a shift of species composition into account: which combinations of properties are able to offer most survival? Further information about structural dynamic models is given in

Structural Dynamic Models. The relatively good results in applying the weighting factors in this context, in spite of the uncertainty of their assessment, seems only to be explicable by the robustness of the application of the factors in modeling and other quantifications. The differences between the factors of the microorganism, the vertebrates, and invertebrates are so clear that it does not matter if the uncertainty of the factors is very high -the results are influenced slightly.

On the other hand, from a theoretical point of view it would be an important progress to get better weighting factors but also because it would enable us to model the competition between species which are closely related.

The key to find better ^-values maybe the proteomes (the total compositions of the proteins that as enzymes determine the life processes). Our knowledge about the composition of proteomes in various organisms is, however, more limited than for the number of the genes.