towards athermodynamics of biological …towards athermodynamics of biological systems s.e....

TOWARDS A THERMODYNAMICS OF BIOLOGICAL SYSTEMS

S.E. JØRGENSENDFU, Institute A, Section for Environmental Chemistry, University Park 2, 2100 Copenhagen Ø, Denmark.

ABSTRACTThis paper presents a tentative ecosystem theory based on the thermodynamic variable eco-exergy, whichmeasures an ecosystem’s distance from thermodynamic equilibrium. The hypothesis, as a basis for the ecosystemtheory, may be formulated as follows: a system that receives a flow of exergy (e.g. solar radiation) will use thisflow of exergy, after the exergy needed for maintenance of the system has been covered, to move the systemfurther from thermodynamic equilibrium, reflected by the growth of gradients. If there is more than one pathwayto depart from equilibrium, the one yielding the most storage of exergy in the form of gradients under the pre-vailing conditions, i.e. gives the most ordered structure furthest from equilibrium, will tend to be selected. Threepossible types of application of this hypothesis have been presented to: (i) provide a theoretical explanation forecological observations, (ii) develop a structurally dynamic modelling approach that can describe adaptationand shifts of species composition, and (iii) use exergy and specific exergy as ecological indicators to describe thedevelopment of ecosystems.As these applications have been promising they are also a support for the hypothesis.Keywords: biodiversity, ecological indicators, ecosystem development, entropy, exergy, structural dynamicmodelling.

1 INTRODUCTIONDuring the last decade there has been an increasing understanding for the need of an integratedecological management of our environment. However, this is possible only if we understand and canexplain the reactions of ecosystems to changed impacts (called forcing functions in modelling). There-fore, there is an urgent need for an ecosystem theory that can be used to predict an ecosystem’s reactionto the steadily changing conditions: climatic changes, changes induced by humans—controlled forc-ing functions, whether the changes are increasing or decreasing loadings, or are they a result of thevarious available restoration methods.

This paper presents an ecosystem theory, which has been applied in the development of ecologicalmodels, to explain ecological observations and to assess the health and development of the ecosystem.The theory is based on the thermodynamic variable exergy or rather a modification of the exergy calledeco-exergy. These concepts and their use in the formulation of an ecosystem theory are presented inthe next section, followed by a section where supporting evidences for the hypothesis are presented.

Section 4 of this paper mentions how this theory has been applied to develop a more ecologicallycorrect modelling approach. An example is presented to illustrate how the approach is able to explainobserved structural changes in shallow lakes. This example demonstrates the ability of what is calleda structurally dynamic modelling approach to make prognoses on structural changes that other typeof models cannot do.

Section 5 illustrates how eco-exergy can be applied to describe ecosystem development and assessecosystem health. The consistency of the presented theory based on eco-exergy with other ecosystemtheories is presented in Section 6 together with a conclusive discussion on how to apply this integratedtheory to explain ecological observations. The concluding section of the paper proves clearly thatwe have an ecosystem theory and that it should be applied much more widely to explain ecologicalobservations than is the case today.

2 AN ECOSYSTEM THEORY BASED ON ECO-EXERGYExergy is defined as the amount of work a system can perform when it is brought into equilibriumwith its environment. Exergy can be considered as the amount of energy that can be utilized for doing

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doi:10.2495/978-1-84564- - /654 7 02

Figure 1: An illustration of the definition of exergy.

Figure 2: The exergy content of the system is calculated in the text for the system relative to a referenceenvironment of the same system at the same temperature and pressure, but as an inorganicsoup with no life, biological structure, information or organic molecules.

work, in contrast to the heat released at the temperature of the environment that cannot be utilized todo work. Figure 1 illustrates the definition of exergy [1]. When we want to find the work capacity of anecosystem, we are interested in the chemical energy of the biomass and the complicated biochemicalcomponents. Minor differences in pressure and temperature are uninteresting. For ecological use wehave therefore defined another exergy, called eco-exergy, which is defined in Fig. 2 [1, 2]. As seenthe eco-exergy content is the chemical energy embodied in the biomass and the complex biochemicalconstituents. Eco-exergy measures, according to the definition, the distance from thermodynamic

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Table 1: Genome size, repetition genes and β-values.

Organisms Genome (Mb) Repeat (%) β

Human 2900 46 2966Mouse 2500 38 2935Tiger fish 400 9 689Mosquito 280 16 445Squirt 155 10 264Fruit fly 137 2 254Yeast 12 2 22Amoeba 34 0.5 64Worm 97 0.5 183Mustard weed 128 14 203Rice 400 50 379Virus 1.01Reptiles 1150*Birds 1340*

*Found indirectly.

equilibrium and can be expressed as the chemical energy difference between the system and thethermodynamic equilibrium:

Eco-exergy = RTn∑

i=0

ci ln ci/

ci0. (1)

To illustrate the application of this equation, let us calculate the formation constant for high molecularweight organic compounds. We use:

−�G = RT ln K ,(2)−�G = −18.7 kJ/g × 104400 g/mole = 1952 MJ/mole = 8.2 J/mole × 300 ln K ,

which implies thatln K = −793496 or K is about 10−344998. (3)

The eco-exergy for organisms is expressed as

Eco-exergy =∑

βici,

where β is a weighting factor = RT ln ci/ci0, considering that the concentration at thermodynamicequilibrium can be expressed as the probability of forming the organism at these conditions, i.e. whatis the probability of forming the right sequence of the amino acids in the enzymes that determine thelife processes. Or how much information does an organism contain? The genome size is known forsome organisms from the gene mapping project and for other organisms we can find the β-values bycomparison of many different measures of the complexity of the organisms [3]. Table 1 summarizesthe genome size and the repetition genes which are not directly required for the determination of theamino acid sequence and therefore do not count in our calculations of the β-value.

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Prigogine [4] has discussed how systems can move away from thermodynamic equilibrium in spiteof the Second Law of Thermodynamics, which is formulated by the use of eco-exergy as follows: theeco-exergy of all closed systems will decrease until the system reaches thermodynamic equilibrium.But ecosystems are open systems and can therefore receive energy (and working capacity = exergy)from outside, which explains how the system can gain exergy. A certain amount of eco-exergy isused in the system (eco-exergy decreases as indicated in the Second Law of Thermodynamics) formaintenance; but if the input of eco-exergy, e.g. from solar radiation, is bigger than the amount ofeco-exergy used for maintenance, the stored eco-exergy can increase. When we consider the evolutionof an ecosystem or follow an ecosystem under development, it is clear that ecosystems strive towardsmoving away from thermodynamic equilibrium [5], as they store biomass and information in theform of the genes. The question is whether it is possible to propose a hypothesis that can describe inmore detail how an ecosystem develops. For the level of organisms, Darwin has already formulatedsuch a description of the development: survival of the fittest. It means that those organisms that underthe prevailing conditions can yield the best survival (most stored biomass and information) will takeover. If we translate Darwin’s theory to thermodynamics using eco-exergy, it is possible to proposethe following hypothesis [1, 6, 7, 8]:

If a system receives an input of exergy, it will—after the exergy needed for maintenance of thesystem has been covered—move the system further from thermodynamic equilibrium, reflectedby the growth of gradients. If there is more than one pathway to depart from equilibrium, theone yielding the most storage of exergy in the form of gradients under the prevailing conditions,i.e. gives the most ordered structure furthest from equilibrium, will tend to be selected.

3 SUPPORTING EVIDENCESIn this section, supporting evidences for the hypothesis are presented (based upon Jørgensen et al. [9]),and many more supporting evidences can be found in the literature [1]. In addition, the applicability ofstructurally dynamic models to explain observed structural changes can also be considered a supportfor the hypothesis, as described in the following section.

3.1 Example 1: Size of genomes

In general, biological evolution has been towards organisms with an increasing number of genesand diversity of cell types [10]. If a direct correspondence between free energy and genome sizeis assumed, this can reasonably be taken to reflect the increasing exergy storage accompanying theincreased information content and processing of ‘higher’ organisms.

3.2 Example 2: Sequence of organic matter oxidation

The sequence of organic matter oxidation [11] takes place in the following order: by oxygen, by nitrate,by manganese dioxide, by iron (III), by sulphate and by carbon dioxide. This means that oxygen, ifpresent, will always outcompete nitrate, which will outcompete manganese dioxide and so on. Theamount of exergy stored as a result of an oxidation process is measured by the kJ/mole electronsavailable, which determines the number of adenosine triphosphate molecules (ATPs) formed. ATPrepresents an exergy storage of 42 kJ/mole. Usable energy as exergy in terms of ATPs decreases inthe same sequence as indicated above. This is as expected if the exergy storage hypothesis was valid(Table 2). If more oxidizing agents are offered to the system, the one giving the highest storage offree energy to the resulting system will be selected.

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Table 2: ATPs formed by the oxidation of organic matter by microbiological processes with variousoxidation agents.

Reaction kJ/mole e− ATPs/mole e−

CH2O + O2 → CO2 + H2O 125 2.98CH2O + 0.8NO−

3 + 0.8H+ → CO2 + 0.4N2 + 1.4H2O 119 2.83CH2O + 2MnO2 + H+ → CO2 + 2Mn2+ + 3H2O 85 2.02CH2O + 4FeOOH + 8H+ → CO2 + 7H2O + Fe2+ 27 0.64CH2O + 0.5SO2−

4 + 0.5H+ → CO2 + 0.5HS− + H2O 26 0.62CH2O + 0.5CO2 → CO2 + 0.5CH4 23 0.55

3.3 Example 3: Formation of organic matter in the primeval atmosphere

Numerous experiments have been performed to imitate the formation of organic matter in the primevalatmosphere on earth 4 billion years ago [12]. Energy from various sources was sent through a gasmixture of carbon dioxide, ammonia and methane. Analyses have shown that a wide spectrum ofcompounds, including several amino acids contributing to protein synthesis, is formed under thesecircumstances. There are obviously many pathways to utilize the energy sent through simple gasmixtures, 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 forman appreciable part of the mixture [12].

3.4 Example 4: Photosynthesis

There are three biochemical pathways for photosynthesis: (i) the C3 or Calvin–Benson cycle, (ii) theC4 pathway and (iii) the crassulacean acid metabolism (CAM) pathway. The third pathway is the leastefficient in terms of the amount of plant biomass formed per unit of energy received. Plants using theCAM pathway are, however, able to survive in harsh arid environments that would be inhospitableto C3 and C4 plants. CAM photosynthesis will generally switch to C3 as soon as sufficient waterbecomes available [13]. The CAM pathways yield the highest biomass production, reflecting exergystorage, under arid conditions, while the other two give highest net production (exergy storage) underother conditions. While it is true that 1 g of plant biomass produced by each of the three pathwayshas different free energies, in a general way, improved biomass production by any of the pathwayscan be taken to be in a direction that is consistent, under the prevailing conditions, with the exergystorage hypothesis.

3.5 Example 5: Biomass packing

The general relationship between animal body weight, W , and population density, D, is D = A/W ,where A is a constant [14]. The highest packing of biomass depends only on the aggregate massand not the size of individual organisms. This means that it is biomass rather than population sizethat is maximized in an ecosystem, as density (number per unit area) is inversely proportional to theweight of the organisms. Of course, the relationship is complex. A given mass of mice would notcontain the same exergy or number of individuals as an equivalent weight of elephants. Also, genomedifferences (Example 1) and other factors would figure in. Later we will discuss exergy dissipation

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Figure 3: Log–log plot of the ratio of nitrogen (N) to phosphorus (P) turnover rates, R, at maximumexergy versus the logarithm of the nitrogen/phosphorus ratio, log N/P. The plot is consistentwith Vollenweider [16].

as an alternative objective function proposed for thermodynamic systems. If this were maximizedrather than storage, then biomass packing would follow the relationship D = A/W 0.65−0.75 [14]. Asthis is not the case, biomass packing and the free energy associated with it lend general support forthe exergy storage hypothesis.

3.6 Example 6: Cycling

If a resource (e.g. a limiting nutrient for plant growth) is abundant, it will typically recycle faster. Thisis a little strange because a rapid recycling is not needed when a resource is non-limiting. Previousmodelling studies [1, 9] have indicated that free-energy storage increases when an abundant resourcerecycles faster. Figure 3 shows these results for a lake eutrophication model. The ratio, R, of nitrogen(N) to phosphorus (P) cycling that gives the highest exergy is plotted versus log N/P. The plot inFig. 1 is also consistent with empirical results [16]. Of course, one cannot ‘inductively test’ anythingwith a model, but the indications and the correspondence with data do tend to support the exergystorage hypothesis in a general way.

4 STRUCTURALLY DYNAMIC MODELSIf we follow the general modelling procedure, we will obtain a model that describes the processesin the focal ecosystem, but the parameters will represent the properties of the state variables asthey are in the ecosystem during the examination period. They are not necessarily valid for anotherperiod because we know that an ecosystem can regulate, modify and change them, if needed, asa response to the changes in the prevailing conditions, determined by the forcing functions andthe interrelations between the state variables. Our present models have rigid structures and a fixedset of parameters, reflecting that no changes or replacements of the components are possible. Weneed, however, to introduce properties of the biological components in the models that can changeaccording to changing forcing functions and general conditions for the state variables (components),as illustrated in Fig. 4. In accordance with the proposed ecosystem theory it is possible to optimize

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Figure 4: Conceptualization of how the external factors steadily change the species composition. Thepossible shifts in species composition are determined by the gene pool, which is steadilychanged owing to mutations and new sexual recombinations of genes. The developmentis, however, more complex. This is indicated by: (i) arrows from ‘structure’ to ‘externalfactors’ and ‘selection’ to account for the possibility that the species are able to modify theirown environment (see below) and thereby their own selection pressure; (ii) an arrow from‘structure’ to ‘gene pool’ to account for the possibilities that the species can to a certainextent change their own gene pool.

continuously the ability of the system to move away from thermodynamic equilibrium. So, we mayhypothesize that the change of these properties (parameters) can be accounted for in our model bythe use of eco-exergy as an ecological goal function. The idea is currently to test if a change of themost crucial parameters produces a higher eco-exergy of the system and, if that is the case, to usethat set of parameters (see the procedure in Fig. 5).

The type of models that can account for the change in species composition as well as for the abilityof the species to change their properties, i.e. to adapt to the prevailing conditions imposed on thespecies, are sometimes called structurally dynamic models, to indicate that they are able to capturestructural changes. They may also be called the next (or fifth) generation of ecological models tounderline that they are radically different from previous modelling approaches and can do more,namely describe changes in species composition or changes in the properties of the species.

It could be argued that the ability of ecosystems to replace present species with other better-fittedspecies can be considered by construction of models that encompass all actual species for the entireperiod that the model attempts to cover. This approach however has two essential disadvantages.First, the model becomes very complex, as it will contain many state variables for each trophic level.This also implies that the model will contain many more parameters that have to be calibrated andvalidated, which will introduce a high degree of uncertainty in the model’s results and will renderthe application of the model very case specific [17, 18]. In addition, the model will still be rigidand will not have the property of the ecosystems of having continuously changing parameters evenwithout changing the species composition. It can be shown to be very important that ecologicalmodels reflect the flexibility and adaptability that characterize organisms. If a model includes manyrigid state variables (species), there will be only one species that will have a combination of properties

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Figure 5: The procedure applied to develop structurally dynamic models.

that gives the best chance for survival in a given situation. The other species will have a combinationof the properties that makes survival and growth more difficult, and they cannot compete [17, 18].

Several goal functions have been proposed, but only very few models that account for the changein species composition or for the ability of the species to change their properties within some limitshave been developed. Exergy has been used most widely as a goal function in ecological models. Ithas been applied to date in 16 case studies, where significant changes in the species composition orthe properties of the species were observed:

1–6 for six shallow lakes (Søbygård Lake, Denmark [1], Glumsø Lake, Denmark [1], Mogan Lake,Turkey [19, 20], Lake Balaton, Hungary [21] and Nielsen [17, 18]),

7–9 for three population dynamic models [1],10 for Mondego Estuary, Portugal [22],11 for Lake Annone, Italy [15],12 for the lagoons of Venice [23],13 to explain the success and failure of biomanipulation [24],14 to explain the intermediate disturbance hypothesis [21],15 to explain the change in the properties of Darwin’s finches [25] and16 to explain the hysteresis in the shift from submerged vegetation to phytoplankton-dominated

eutrophication and back again to submerged vegetation by reduction of the nutrient input[19, 20].

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For all 16 case studies, the models were able to simulate the observed changes with a standard deviationsimilar to other model studies, and in most cases the calibration and validation were improved.

Moreover, it has been found possible to improve the parameter estimation by the use of exergy. Ifone parameter is not known with sufficient accuracy, it is possible to find this parameter as the valuethat yields the highest exergy for the model of the considered ecosystem [1, 26]. For eutrophicationmodels an attempt has also been made to combine a normal calibration of some parameters with adetermination of the combination of other parameters that give the highest exergy [27, 28].

Finally, it should be mentioned that it is possible to obtain a better calibration of models developedfor ecosystems that show seasonal changes of species composition, e.g. an eutrophication modelwhere the phytoplankton and zooplankton species in the spring, summer and fall are often different.The usually applied calibration procedure finds one parameter set covering the entire year, whereasby the use of exergy optimization we can find the current change of parameters that reflects the changeof species’ composition, the so-called succession. The application of a current optimization of theexergy will therefore, not surprisingly, offer a better accordance between the model simulations andobservations [19, 20, 28]. Exergy optimization is only used for the parameters of the organisms,whereas physical–chemical parameters are calibrated according to the usually applied procedure.

The results obtained using structurally dynamic models are promising and also urgently neededfor the modelling of various ecosystems, as they behave in a non-linear manner and rapidly showstructural changes and hysteresis behaviour. Particularly for lakes, the use of structurally dynamicmodels is very important. Carnivorous fish and zooplankton are dominant in lakes below 60 µg/l,while planktivorous fish and phytoplankton are dominant above 125 µg P/l, when phosphorus is thelimiting factor. Between 60 and 125 µg P/l both structures are possible depending on the history. Thisexplains why biomanipulation alone is successful between 60 and 125 µg P/l, provided phosphorusis the liming factor. The exergy of a lake ecosystem, calculated based upon an eutrophication model,is highest for the carnivorous fish and zooplankton structure below 60 µg P/l, but highest for plank-tivorous fish and phytoplankton structure above 125 µg P/l. Between the two concentrations bothstructures give approximately the same exergy result.

Scheffer et al. [29] have reviewed the structural change of shallow lakes, where a shift betweenphytoplankton dominance and submerged vegetation may take place. Below 100 µg P/l submergedvegetation is dominant and above 250 µg P/l phytoplankton is dominant, when phosphorus is thelimiting nutrient. Between 100 and 250 µg P/l both structures are possible and have the same exergy,calculated based upon a model. The resulting structure between 100 and 250 µg P/l depends on thehistory. If the phosphorus concentration in the lake is reduced from a high phosphorus concentration,the phytoplankton dominance will be maintained until 100 µg P/l. In contrast, when the phosphorusconcentration increases from a low phosphorus concentration, the submerged vegetation will remainuntil 250 µg P/l. The reaction to the changed phosphorus concentration shows, in other words, ahysteresis behaviour.

Figure 6 shows the result obtained from a structurally dynamic model. As seen in the figure, themodel’s results follow the above-mentioned rule based upon Scheffer et al. [29], which may beconsidered a strong support for the applicability of structurally dynamic models and at the same timean important progress in modelling, because we now know new ways of developing better modelsand modelling the structural changes.

5 THE APPLICATION OF EXERGY AS AN ECOLOGICAL INDICATORAbout 15 years ago there was a proposal by environmental managers to find ecological indicatorsthat could be used to assess the integrity of ecosystems or ‘take the pulse’ of the ecosystem. Theidea was to be able to assess, preferably quantitatively, not only the ecosystem integrity but also,

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Figure 6: Total phosphorus in the form of submerged plants are plotted versus total phosphorus ofall forms in the lake water. As seen in the figure, the submerged plants first increase owingto the increased concentration of phosphorus, then at about 150 µg P/l the submergedplant phosphorus decreases and at about 250 µg P/l the submerged vegetation disappears.When the phosphorus concentration decreases at a later stage the submerged vegetationwill reappear at about 100 µg P/l.

if possible, to set up a diagnosis with the help of a few indicators. If the ecosystem were not sound,what would we name the disease? It was realised that the first step in a process of cure would be toset up a quantitative diagnosis. How bad was the eutrophication or the toxic substance pollution forinstance? Exergy and specific exergy = exergy/biomass have been applied as ecological indicators:

1. by a comparison and integrity assessment of eutrophied lakes [1],2. by a comparison and integrity assessment of coastal zones [9, 30, 31],3. by integrity assessment of Mondego Estuary in Portugal [30, 31],4. by integrity assessment of Chinese lakes [32],5. as ecological indicators for coastal lagoons in Europe [33],6. for integrity assessment of different farming systems [1] and7. for integrity assessment in a situation where toxic contamination of ecosystems has taken place.

The application of exergy as an ecological indicator is presented here by an example—the formationof Surtsey Island south of Iceland by a volcanic eruption in 1963. The observations are taken fromSurtsey Research Reports [34]. When a new island is formed life starts from level zero, and it wouldtherefore be a very illustrative case to follow the development of ecological indicators and see ifthey, in accordance with the expectation, would increase and reflect the increasing life on the islandover time. The following information is valid for Surtsey Island: (i) it has an area of about 1.5 km2;(ii) it was formed as a result of a volcanic eruption in 1963; (iii) measurements have been taken sinceNovember 1964.

The eco-exergy calculated for plants and nesting birds based upon the available observations isshown in Fig. 7. The plant biodiversity is also determined and shown in Fig. 8. These two figuresreflect the expected development. In addition, in this context, exergy seems to be an applicable,holistic, ecological indicator for the development of life on the island. There is a relatively goodlinear correlation between time and exergy, but a logistic expression may be better able to cover therelationship between time and exergy.

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Figure 7: The eco-exergy of plants and nesting birds on Surtsey Island plotted versus the year.

Figure 8: The plant biodiversity on Surtsey Island plotted versus the year.

6 A PATTERN OF ECOSYSTEM THEORIESSeveral ecosystem theories have been presented in the scientific literature during the last two to threedecades. At first glance they look very different and seem to be inconsistent, but a further examinationreveals that they are not so different and that it should be possible to unite them in a consistent pattern[35]. It has been accepted among system ecologists since 1998/1999, but as a result of a meetinginvolving several system ecologists in 2000, it can now be concluded that a consistent pattern ofecosystem theories has been formed. Several system ecologists have agreed on the pattern presented

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below as a working basis for further development in system ecology. This is of the utmost importancefor progress in system ecology, because with a theory in hand it will be possible to explain many rulesthat are published in ecology and applied ecology, which again explain many ecological observations.In other words, we should be able to attain the same theoretical basis that characterizes physics: afew basic laws which can be used to deduce rules that explain observations. It has therefore also beenagreed that one of the important goals in system ecology would be to demonstrate (prove) the linksbetween ecological rules and ecological laws.

Ten to fifteen years ago the presented theories seemed very inconsistent and chaotic. How couldE.P. Odum’s attributes [36], H.T. Odum’s maximum power [37], Ulanowicz’s ascendancy [38],Patten’s indirect effect [39], Kay and Schneider’s maximum exergy degradation [40, 41], Jørgensen’smaximum exergy principle [1, 2, 6, 7, 42], and Prigogine’s [43] and Mauersberger’s minimum entropydissipation [44, 45] be valid at the same time? New results and an open discussion among the con-tributing scientists have led to the formation of a pattern, where all the theories contribute to the totalpicture of ecosystem development.

The first contribution to a clear pattern of the various ecosystem theories came from the networkapproach used often by Patten (see e.g. Fath and Patten [46]). Fath and Patten [46] have shown,by a mathematical analysis of networks in steady state (representing for instance an average annualsituation in an ecosystem with close to balanced inputs and outputs for all components in the network),that the sum of throughflows in a network (which is maximum power) is determined by the inputand the cycling within the network. The input (solar radiation) is again determined by the structureof the system (the stored exergy, the biomass). Furthermore, the greater the structure the greater isthe maintenance needed, and therefore more exergy must be dissipated and the greater are the inputs.Cycling on the other hand means that the same energy (exergy) is utilized better in the system, andtherefore more biomass (exergy) can be formed without increase of the inputs. It has been shownpreviously that more cycling means an increased ratio of indirect to direct effects, while increasedinput does not change the ratio of indirect to direct effects [1].

Fath and Patten [46] used these results to determine the development of various variables used asgoal functions (exergy, power, entropy, etc.). An ecosystem is, of course, not setting goals, but a goalfunction is used to describe the direction of development an ecosystem will take in an ecologicalmodel. Their results can be summarized as follows:

1. increased inputs (more solar radiation is captured) mean more biomass, more exergy stored, moreexergy degraded, therefore higher entropy dissipation also, more throughflow (power), increasedascendancy, but no change in the ratio of indirect to direct effects or in the retention time for theenergy in the system = total exergy/input exergy per unit of time;

2. increased cycling implies more biomass, more exergy stored, more throughflow, increased ascen-dancy, increased ratio of indirect to direct effects, increased retention, but no change in exergydegradation.

Almost simultaneously Jørgensen et al. [9] published a paper which claims that ecosystems showthree growth forms:

I. Growth of physical structure (biomass), which is able to capture more of the incoming energyin the form of solar radiation, but also requires more energy for maintenance (respiration andevaporation).

II. Growth of the network, which means more cycling of energy and matter.III. Growth of information (develop more plants and animals with more genes), from r-strategists

to K-strategists, which waste less energy but also usually carry more information.

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Figure 9: The exergy captured expressed as solar radiation % is plotted versus the exergy of theecosystem.

These three growth forms may be considered an integration of E.P. Odum’s attributes whichdescribe changes in the ecosystem associated with development from the early stage to the maturestage. Eight of the most applied attributes associated with the three growth forms should be mentioned:

1. ecosystem biomass (physical structure) increases,2. more feedback loops (including recycling of energy and matter) are built,3. respiration increases,4. respiration relative to biomass decreases,5. bigger animals and plants (trees) become more dominant,6. the specific entropy production (relative to biomass) decreases,7. the total entropy production will first increase and then stabilizes at approximately the same level

and8. the amount of information increases (more species, species with more genes, the biochemistry

becomes more diverse).

Growth form I covers attributes 1, 3 and 7. Growth form II covers attributes 2 and 6, and growthform III covers attributes 4, 5, 7 and 8.

In the same paper [9], Fig. 9 was presented to illustrate the concomitant development of ecosystems,exergy captured (most of which was degraded) and exergy stored (biomass, structure, information).The points in the figure correspond to ecosystems in different stages of development (see Table 3).Debeljak [47] obtained the same shape of the curve when determining the exergy captured and theexergy stored in managed forests and virgin forests in different stages of development (Fig. 10).

Holling [48] has suggested how an ecosystem progresses through the sequential phases of renewal(mainly growth form I), exploitation (mainly growth form II), conservation (dominant growth form III)

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Table 3: Exergy utilization and storage in a comparative set of ecosystems.

Ecosystem Exergy utilization (%) Exergy storage (MJ/m2)

Quarry 6 0Desert 2 0.073Clear-cut forest 49 0.594Grassland 59 0.940Fir plantation 70 12.70Natural forest 71 26.00Old-growth deciduous forest 72 38.00Tropical rain forest 70 64.00

Figure 10: The plot shows the results of Debeljak [47], who examined managed and virgin forestsin different stages of development. Gap has no trees, while the virgin forest changesfrom optimum to mixed to regeneration and back to optimum, although the virgin forestcan be destroyed by catastrophic events such as fires or storms. The juvenile stage isa developmental stage between the gap and the optimum. Pasture is included for thecomparison.

and creative destruction (Fig. 11). The latter phase also fits into the three growth forms but will requirea further explanation. The creative destruction phase is a result of either external or internal factors. Inthe first case (e.g. hurricanes and volcanic activity), further explanation is not needed as an ecosystemhas to use the growth forms under the prevailing conditions which are determined by the externalfactors. If the destructive phase is a result of internal factors, the question is ‘why would a system beself-destructive?’. A possible explanation is that a result of the conservation phase is that almost allnutrients will be contained in organisms, which implies that there are no nutrients available to test new

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Figure 11: Holling’s four stages are expressed in terms of biomass and specific exergy. Notice thatthe trend of each further cycle is towards higher exergy storage.

and possibly better solutions to move further away from thermodynamic equilibrium or, expressed inDarwinian terms, to increase the probability of survival. This is also implicitly indicated by Holling, ashe talks about creative destruction. Therefore, when new solutions are available, it would, in the longrun, be beneficial for the ecosystem to decompose the organic nutrients into inorganic componentsthat can be utilized to test the new solutions. The creative destruction phase can be considered to be amethod to utilize the three other phases and the three growth forms more effectively in the long run.

Five hypotheses have been proposed to describe ecosystem growth and development, namely:

A. The entropy production tends to be minimum (this was proposed by Prigogine [4, 43] for linearsystems at a steady non-equilibrium state, not for far from equilibrium systems). It was appliedby Mauersberger [44, 45] to derive expressions for bioprocesses at a stable stationary state.

B. Natural selection tends to make the energy flux through the system a maximum, so far as it iscompatible with the constraints to which the system is subjected [37]. This is also called themaximum power principle.

C. Ecosystems will organize themselves to maximize the degradation of exergy [40].D. A system that receives a throughflow of exergy will have a propensity to move away from

thermodynamic equilibrium, and if more combinations of components and processes are offeredto utilize the exergy flow, the system has the propensity to select the organization that gives thesystem as much stored exergy as possible [1, 2, 6, 7, 26, 38].

E. Ecosystems will have a propensity to develop towards a maximization of the ascendancy [38].

The usual description of ecosystem development illustrated, for instance, by the recovery of YellowStone Park after a fire, an island born after a volcanic eruption, reclaimed land, is well covered byE.P. Odum [36]: at first the biomass increases rapidly which implies that the percentage of captured

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Table 4: Accordance between growth forms and the proposed descriptors.

Hypothesis

Growth form I Growth form II Growth form III

Exergy storage Up Up UpPower/throughflow Up Up UpAscendancy Up Up UpExergy dissipation Up Equal EqualRetention time Equal Up UpEntropy production Up Equal EqualExergy/biomass = specific exergy Equal Up UpEntropy/biomass = specific Equal Down Down

entropy productionRatio indirect/direct effects Equal Up Up

incoming solar radiation increases and also the energy needed for the maintenance. Growth form I isdominant in this first phase, where exergy stored increases (more biomass, more physical structureto capture more solar radiation), and the throughflow (of useful energy), the exergy dissipation andthe entropy production increase owing to the increased need of energy for maintenance.

Growth forms II and III become dominant later, although an overlap of the three growth formstakes place. When the percentage of solar radiation captured reaches about 80%, it is not possibleto increase the amount of captured solar radiation further (due in principle to the second law ofthermodynamics). Therefore, further growth of the physical structure (biomass) does not improvethe energy balance of the ecosystem. In addition, all or almost all the essential elements are in theform of dead or living organic matter and not as inorganic compounds ready to be used for growth.Therefore, growth form I will not proceed, but growth forms II and III can still operate. The ecosystemcan still improve the ecological network and can still change r-strategists with K-strategists, smallanimals and plants with bigger ones and less developed organisms with more developed ones withmore information genes. A graphical representation of this description of ecosystem development isalready presented in Fig. 9.

The accordance with the five descriptors + specific entropy production and the three growth formsbased on this description of ecosystem development is shown in Table 4.

Debeljak [47] found the same results presented in Fig. 9, as the development from gap to juvenile(see also Fig. 10) corresponds to growth form II, while the development from juvenile to optimumrepresents growth forms I and II. The development from optimum to mixed forest is dominantgrowth form III. These results are also consistent with those of Johnson [49, 50], who found thatwhen ecosystems are relatively isolated, competitive exclusion results in a relatively homogeneoussystem configuration that exhibits relatively low dissipation.

Based upon the results, it is possible to formulate the following hypothesis (Ecological Law ofThermodynamics, which is consistent with the hypothesis on eco-exergy proposed in Section 2 ofthis paper) uniting the five hypotheses:

Ecosystem development in all phases will move away from thermodynamic equilibrium and hasthe propensity to select the components and the organization that yields the highest flux of usefulenergy throughout the system and the most exergy stored in the system. This also correspondsto the highest ascendancy.

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Ecosystem development is accomplished by three growth forms, all increasing the throughflow,the exergy stored and the ascendancy:

1. Tends according to growth form I to reach the highest possible rate of exergy captured (whichis of the order of 80% of the incoming solar radiation) and thereby also of exergy degradation.This growth form may therefore best be measured by a determination of the exergy degradationrate.

2. Growth of the number of network linkages and thereby of recycling of matter and energy whichimplies a better utilization of the incoming energy, and therefore an increase in throughflow andexergy storage without an increase in exergy dissipation. It means that specific exergy degradationand specific entropy production is decreasing.

3. Growth of information, as the number of components in the network and replacement of r-strategistand small organisms with K-strategists and bigger and often more developed organisms.

7 CONCLUSIONSA hypothesis that we may call the Ecological Law of Thermodynamics has been presented. Thehypothesis has been applied to explain ecological observations, to develop structurally dynamicmodels and to assess ecosystem health. These applications support the hypothesis. Furthermore, ithas been shown that the hypothesis is consistent with other hypotheses on ecosystem development.Therefore, there is a basis for the application of the hypothesis as an element in an ecosystem theory,which would encompass eight to ten basic laws including the thermodynamic laws [51]. It maytherefore be concluded that we have a tentative ecosystem theory that can be applied to explainecological observations. The tentative theory will, of course, develop further in the coming years,but the prerequisite for the development is that the tentative theory is used in ecology. It is thereforevery important to encourage all ecologists to assist in building a network of explanation in ecology,as in the case of physics, so that the development of an applicable ecosystem theory can be ensured.

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towards athermodynamics of biological …towards athermodynamics of biological systems s.e....

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