Support to the Maximum Eco Exergy Hypothesis

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Eight supporting arguments for the hypothesis presented above. More evidence has been provided; but the eight supporting evidences presented here give a good idea of the theoretical support for the hypothesis.

1. The exergy-storage hypothesis might be taken as a generalized version of 'Le Chatelier's Principle.' Biomass synthesis can be expressed as a chemical reaction:

Energy + nutrients = molecules with more free energy (exergy) and organization + dissipated energy

According to Le Chatelier's Principle, if energy is put into a reaction system at equilibrium the system will shift its equilibrium composition in a way to counteract the change. This means that more molecules with more free energy and organization will be formed. If more pathways are offered, those giving the most relief from the disturbance (using most of the inflowing energy) by using the most energy, and forming the most molecules with the most free energy, will be the ones followed in restoring equilibrium.

2. The sequence of organic matter oxidation takes place in the following order: by oxygen, by nitrate, by manganese dioxide, by iron (III), by sulfate, and by carbon dioxide. This means that oxygen, if present, will always outcompete nitrate which will outcompete manganese dioxide, etc. The amount of exergy stored as a result of an oxidation process is measured by the available kJmole—1 electrons which determine the number of adenosine tri-phosphate molecules (ATPs) formed. ATP represents an exergy storage of 42 kJ mole—1. Usable energy as exergy in ATPs decreases in the same sequence as indicated above. This is as expected if the exergy-storage hypothesis was valid (Table 3). If more oxidizing agents are offered to the system, the one giving the resulting system the highest storage of free energy will be selected.

3. Numerous experiments have been performed to imitate the formation of organic matter in the primeval atmosphere on Earth 4 billion years ago. Energy from various sources were sent through a gas mixture of carbon dioxide, ammonia, and methane. Analyses showed that a wide spectrum of compounds, including several amino acids contributing to protein synthesis, is formed under these circumstances. There are obviously many pathways to utilize the energy sent through simple gas mixtures, but mainly those forming compounds with rather large free energies (high exergy storage, released when the compounds are oxidized again to carbon dioxide, ammonia, and methane) will form an appreciable part of the mixture.

4. There are three biochemical pathways for photosynthesis: (1) the C3 or Calvin-Benson cycle, (2) the C4 pathway, and (3) the Crassulacean acid metabolism (CAM) pathway. The latter is least efficient in terms of the amount of plant biomass formed per unit of energy received. Plants using the CAM pathway are, however, able to survive in harsh, arid environments that would be inhospitable to C3 and C4 plants. CAM photosynthesis will generally switch to C3 as soon as sufficient water becomes available. The CAM pathways yield the highest biomass production, reflecting exergy storage, under arid conditions, while the other two give highest net production (exergy storage) under other conditions. While it is true that one gram of plant biomass produced by each of the three pathways has different free energies, in a general way improved biomass production by any ofthe pathways can be taken to be in a direction that is consistent, under the conditions, with the exergy-storage hypothesis.

5. Givnish and Vermelj observed that leaves optimize their size (thus mass) for the conditions. This may be interpreted as meaning that they maximize their free-energy content. The larger the leaves the higher their respiration and evapotranspiration, but the more solar radiation they can capture. Deciduous forests in moist climates have a leaf area index (LAI) of about 6%. Such an index can be predicted from the hypothesis of highest possible leaf size, resulting from the tradeoff between having leaves of a given size versus maintaining leaves of a given size. Size of leaves in a given environment depends on the solar radiation and humidity regime, and while, for example, sun and shade leaves on the same

Table 3 Yields of kJ and ATPs per mole of electrons, corresponding to 0.25 moles of CH2O oxidized

Reaction

kJ/(mole )

ATPs/(mole )

CH2O + O2 $ CO2 + h2o

125

2.98

CH2O + 0.8 NO3— + 0.8 H+ $ CO2 + 0.4 N2 +1.4 H2O

119

2.83

CH2O + 2 MnO2 + H+ $ CO2 + 2 Mn2+ + 3 H2O

85

2.02

CH2O + 4 FeOOH + 8 H+ $ CO2 + 7 H2O + Fe2+

27

0.64

CH2O + 0.5 SO42— + 0.5 H+ $ CO2 + 0.5 HS— + H2O

26

0.62

CH2O + 0.5 CO2 $ CO2 + 0.5 CH4

23

0.55

The released energy is available to build ATP for various oxidation processes of organic matter at pH = 7.0 and 25 °C.

The released energy is available to build ATP for various oxidation processes of organic matter at pH = 7.0 and 25 °C.

plant would not have equal exergy contents, in a general way leaf size and LAI relationships are consistent with the hypothesis of maximum exergy storage.

6. The general relationship between animal body weight, W, and population density, D, is D = A/W, where A is a constant. Highest packing of biomass depends only on the aggregate mass, not the size of individual organisms. This means that it is biomass rather than population size that is maximized in an ecosystem, as density (number per unit area) is inversely proportional to the weight of the organisms. Of course the relationship is complex. A given mass of mice would not contain the same exergy or number of individuals as an equivalent weight of elephants. Also, genome differences (example 1) and other factors would figure in. Later we will discuss exergy dissipation as an alternative objective function proposed for thermodynamic systems. If this were maximized rather than storage, then biomass packing would follow the relationship D = A/W 0-65-0-75. As this is not the case, biomass packing and the free energy associated with this will lend general support for the exergy-storage hypothesis.

7. If a resource (for instance, a limiting nutrient for plant growth) is abundant, it will typically recycle faster. This is a little strange, because a rapid recycling is not needed when a resource is nonlimiting. A modeling study indicated that free-energy storage increases when an abundant resource recycles faster. Figure 4 shows such results for a lake eutrophication model. The ratio, R, of nitrogen (N) to phosphorus (P) cycling which gives the highest exergy is plotted versus log (N/P). The plot in Figure 4 is also consistent with empirical results. Of course, one cannot 'inductively test' anything with a model, but the indications and correspondence with data

Figure 4 Log-log plot of the turnover rate ratio of nitrogen to phosphorus, R, at maximum exergy versus the logarithm of the nitrogen/phosphorus ratio, log N/P. The plot is consistent with Vollenweider (1975).

do tend to support in a general way the exergy-storage hypothesis.

8. Dynamic models whose structure changes over time are based on nonstationary or time-varying differential or difference equations. We will refer to these as 'structurally dynamic models'. A number of such models, mainly of aquatic systems, have been investigated to see how structural changes are reflected in free-energy changes. The latter were computed as exergy indexes.

Time-varying parameters were selected iteratively to give the highest exergy index values in a given situation at each time step. Changes in parameters, and thus system structure, not only reflect changes in external boundary conditions, but also mean that such changes are necessary for the ongoing maximization of exergy. For all models investigated along these lines, the changes obtained were in accordance with actual observations (see references). These studies therefore affirm, in a general way, that systems adapt structurally to maximize their content of exergy. It is noteworthy that Coffaro et al, in their structural dynamic model of the Lagoon of Venice, did not calibrate the model describing the spatial pattern of various macrophyte species such as Ulva and Zostera, but used exergy-index optimization to estimate parameters determining the spatial distribution of these species. They found good accordance between observations and model, as was able by this method 'without' calibration to explain more than 90% of the observed spatial distribution of various species of Zostera and Ulva.

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