TOWARDS A THERMODYNAMICS OF BIOLOGICAL SYSTEMS

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1 P a g e 1 TOWARDS A THERMODYNAMICS OF BIOLOGICAL SYSTEMS S.E. JØRGENSEN DFU, Institute A, Section for Environmental Chemistry, University Park 2, 2100 Copenhagen Ø, Denmark. ABSTRACT This paper presents a tentative ecosystem theory based on the thermodynamic variable eco-exergy, which measures an ecosystem s distance from thermodynamic equilibrium. The hypothesis, as a basis for the ecosystem theory, may be formulated as follows: a system that receives a flow of exergy (e.g. solar radiation) will use this flow of exergy, after the exergy needed for maintenance of the system has been covered, to move the system further from thermodynamic equilibrium, reflected by the growth of gradients. If there is more than one pathway to depart from equilibrium, the one 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. Three possible types of application of this hypothesis have been presented to: (i) provide a theoretical explanation for ecological observations, (ii) develop a structurally dynamic modelling approach that can describe adaptation and shifts of species composition, and (iii) use exergy and specific exergy as ecological indicators to describe the development 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 dynamic modelling. 1 INTRODUCTION During the last decade there has been an increasing understanding for the need of an integrated ecological management of our environment. However, this is possible only if we understand and can explain the reactions of ecosystems to changed impacts (called forcing functions in modelling). Therefore, there is an urgent need for an ecosystem theory that can be used to predict an ecosystem s reaction to the steadily changing conditions: climatic changes, changes induced by humans controlled forcing functions, whether the changes are increasing or decreasing loadings, or are they a result of the various available restoration methods. This paper presents an ecosystem theory, which has been applied in the development of ecological models, 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 called eco-exergy. These concepts and their use in the formulation of an ecosystem theory are presented in the 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 ecologically correct modelling approach. An example is presented to illustrate how the approach is able to explain observed structural changes in shallow lakes. This example demonstrates the ability of what is called a structurally dynamic modelling approach to make prognoses on structural changes that other type of models cannot do. Section 5 illustrates how eco-exergy can be applied to describe ecosystem development and assess ecosystem health. The consistency of the presented theory based on eco-exergy with other ecosystem theories is presented in Section 6 together with a conclusive discussion on how to apply this integrated theory to explain ecological observations. The concluding section of the paper proves clearly that we have an ecosystem theory and that it should be applied much more widely to explain ecological observations than is the case today. 2 AN ECOSYSTEM THEORY BASED ON ECO-EXERGY Exergy is defined as the amount of work a system can perform when it is brought into equilibrium with its environment. Exergy can be considered as the amount of energy that can be utilized for doing doi: / / 02

2 2 P a g e 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 reference environment of the same system at the same temperature and pressure, but as an inorganic soup 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 to do work. Figure 1 illustrates the definition of exergy [1]. When we want to find the work capacity of an ecosystem, we are interested in the chemical energy of the biomass and the complicated biochemical components. Minor differences in pressure and temperature are uninteresting. For ecological use we have therefore defined another exergy, called eco-exergy, which is defined in Fig. 2 [1, 2]. As seen the eco-exergy content is the chemical energy embodied in the biomass and the complex biochemical constituents. Eco-exergy measures, according to the definition, the distance from thermodynamic

3 P a g e 3 Table 1: Genome size, repetition genes and β-values. Organisms Genome (Mb) Repeat (%) β Human Mouse Tiger fish Mosquito Squirt Fruit fly Yeast Amoeba Worm Mustard weed Rice Virus 1.01 Reptiles 1150* Birds 1340* *Found indirectly. equilibrium and can be expressed as the chemical energy difference between the system and the thermodynamic equilibrium: Eco-exergy = RT n / c i ln c i ci0. (1) i=0 To illustrate the application of this equation, let us calculate the formation constant for high molecular weight organic compounds. We use: G = RT ln K, G = 18.7kJ/g g/mole = 1952 MJ/mole = 8.2J/mole 300 ln K, (2) which implies that ln K = or K is about (3) The eco-exergy for organisms is expressed as Eco-exergy = β i c i, where β is a weighting factor = RT ln c i /c i0, considering that the concentration at thermodynamic equilibrium can be expressed as the probability of forming the organism at these conditions, i.e. what is the probability of forming the right sequence of the amino acids in the enzymes that determine the life processes. Or how much information does an organism contain? The genome size is known for some organisms from the gene mapping project and for other organisms we can find the β-values by comparison of many different measures of the complexity of the organisms [3]. Table 1 summarizes the genome size and the repetition genes which are not directly required for the determination of the amino acid sequence and therefore do not count in our calculations of the β-value.

4 4 P a g e Prigogine [4] has discussed how systems can move away from thermodynamic equilibrium in spite of the Second Law of Thermodynamics, which is formulated by the use of eco-exergy as follows: the eco-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 is used in the system (eco-exergy decreases as indicated in the Second Law of Thermodynamics) for maintenance; but if the input of eco-exergy, e.g. from solar radiation, is bigger than the amount of eco-exergy used for maintenance, the stored eco-exergy can increase. When we consider the evolution of an ecosystem or follow an ecosystem under development, it is clear that ecosystems strive towards moving away from thermodynamic equilibrium [5], as they store biomass and information in the form of the genes. The question is whether it is possible to propose a hypothesis that can describe in more detail how an ecosystem develops. For the level of organisms, Darwin has already formulated such a description of the development: survival of the fittest. It means that those organisms that under the prevailing conditions can yield the best survival (most stored biomass and information) will take over. If we translate Darwin s theory to thermodynamics using eco-exergy, it is possible to propose the following hypothesis [1, 6, 7, 8]: If a system receives an input of exergy, it will after the exergy needed for maintenance of the system has been covered move the system further from thermodynamic equilibrium, reflected by the growth of gradients. If there is more than one pathway to depart from equilibrium, the one 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 EVIDENCES In 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 of structurally dynamic models to explain observed structural changes can also be considered a support for 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 genes and diversity of cell types [10]. If a direct correspondence between free energy and genome size is assumed, this can reasonably be taken to reflect the increasing exergy storage accompanying the increased 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, if present, will always outcompete nitrate, which will outcompete manganese dioxide and so on. The amount of exergy stored as a result of an oxidation process is measured by the kj/mole electrons available, which determines the number of adenosine triphosphate molecules (ATPs) formed. ATP represents an exergy storage of 42 kj/mole. Usable energy as exergy in terms of ATPs decreases in the 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 of free energy to the resulting system will be selected.

5 P a g e 5 Table 2: ATPs formed by the oxidation of organic matter by microbiological processes with various oxidation agents. Reaction kj/mole e ATPs/mole e CH 2 O + O 2 CO 2 + H 2 O CH 2 O + 0.8NO H+ CO N H 2 O CH 2 O + 2MnO 2 + H + CO 2 + 2Mn H 2 O CH 2 O + 4FeOOH + 8H + CO 2 + 7H 2 O + Fe CH 2 O + 0.5SO H + CO HS + H 2 O CH 2 O + 0.5CO 2 CO CH Example 3: Formation of organic matter in the primeval atmosphere Numerous experiments have been performed to imitate the formation of organic matter in the primeval atmosphere on earth 4 billion years ago [12]. Energy from various sources was sent through a gas mixture of carbon dioxide, ammonia and methane. Analyses have shown 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 [12]. 3.4 Example 4: Photosynthesis There are three biochemical pathways for photosynthesis: (i) the C3 or Calvin Benson cycle, (ii) the C4 pathway and (iii) the crassulacean acid metabolism (CAM) pathway. The third pathway is the 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 [13]. 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 1 g of plant biomass produced by each of the three pathways has different free energies, in a general way, improved biomass production by any of the pathways can be taken to be in a direction that is consistent, under the prevailing conditions, with the exergy storage 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 mass and 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

6 6 P a g e Figure 3: Log log plot of the ratio of nitrogen (N) to phosphorus (P) turnover rates, R, at maximum exergy versus the logarithm of the nitrogen/phosphorus ratio, log N/P. The plot is consistent with Vollenweider [16]. 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 [14]. As this is not the case, biomass packing and the free energy associated with it lend general support for the 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. This is a little strange because a rapid recycling is not needed when a resource is non-limiting. Previous modelling studies [1, 9] have indicated that free-energy storage increases when an abundant resource recycles 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 in Fig. 1 is also consistent with empirical results [16]. Of course, one cannot inductively test anything with a model, but the indications and the correspondence with data do tend to support the exergy storage hypothesis in a general way. 4 STRUCTURALLY DYNAMIC MODELS If we follow the general modelling procedure, we will obtain a model that describes the processes in the focal ecosystem, but the parameters will represent the properties of the state variables as they are in the ecosystem during the examination period. They are not necessarily valid for another period because we know that an ecosystem can regulate, modify and change them, if needed, as a response to the changes in the prevailing conditions, determined by the forcing functions and the interrelations between the state variables. Our present models have rigid structures and a fixed set of parameters, reflecting that no changes or replacements of the components are possible. We need, however, to introduce properties of the biological components in the models that can change according 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

7 P a g e 7 Figure 4: Conceptualization of how the external factors steadily change the species composition. The possible shifts in species composition are determined by the gene pool, which is steadily changed owing to mutations and new sexual recombinations of genes. The development is, however, more complex. This is indicated by: (i) arrows from structure to external factors and selection to account for the possibility that the species are able to modify their own 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 certain extent change their own gene pool. continuously the ability of the system to move away from thermodynamic equilibrium. So, we may hypothesize that the change of these properties (parameters) can be accounted for in our model by the use of eco-exergy as an ecological goal function. The idea is currently to test if a change of the most crucial parameters produces a higher eco-exergy of the system and, if that is the case, to use that 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 ability of the species to change their properties, i.e. to adapt to the prevailing conditions imposed on the species, are sometimes called structurally dynamic models, to indicate that they are able to capture structural changes. They may also be called the next (or fifth) generation of ecological models to underline 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-fitted species can be considered by construction of models that encompass all actual species for the entire period 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 and validated, which will introduce a high degree of uncertainty in the model s results and will render the application of the model very case specific [17, 18]. In addition, the model will still be rigid and will not have the property of the ecosystems of having continuously changing parameters even without changing the species composition. It can be shown to be very important that ecological models reflect the flexibility and adaptability that characterize organisms. If a model includes many rigid state variables (species), there will be only one species that will have a combination of properties

8 8 P a g e 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 combination of 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 change in species composition or for the ability of the species to change their properties within some limits have been developed. Exergy has been used most widely as a goal function in ecological models. It has been applied to date in 16 case studies, where significant changes in the species composition or the 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] and 16 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].

9 P a g e 9 For all 16 case studies, the models were able to simulate the observed changes with a standard deviation similar 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. If one parameter is not known with sufficient accuracy, it is possible to find this parameter as the value that yields the highest exergy for the model of the considered ecosystem [1, 26]. For eutrophication models an attempt has also been made to combine a normal calibration of some parameters with a determination 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 developed for ecosystems that show seasonal changes of species composition, e.g. an eutrophication model where 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, whereas by the use of exergy optimization we can find the current change of parameters that reflects the change of species composition, the so-called succession. The application of a current optimization of the exergy will therefore, not surprisingly, offer a better accordance between the model simulations and observations [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 needed for the modelling of various ecosystems, as they behave in a non-linear manner and rapidly show structural changes and hysteresis behaviour. Particularly for lakes, the use of structurally dynamic models 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 the limiting factor. Between 60 and 125 µg P/l both structures are possible depending on the history. This explains why biomanipulation alone is successful between 60 and 125 µg P/l, provided phosphorus is 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 planktivorous fish and phytoplankton structure above 125 µg P/l. Between the two concentrations both structures give approximately the same exergy result. Scheffer et al. [29] have reviewed the structural change of shallow lakes, where a shift between phytoplankton dominance and submerged vegetation may take place. Below 100 µg P/l submerged vegetation is dominant and above 250 µg P/l phytoplankton is dominant, when phosphorus is the limiting 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 the history. 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 phosphorus concentration increases from a low phosphorus concentration, the submerged vegetation will remain until 250 µg P/l. The reaction to the changed phosphorus concentration shows, in other words, a hysteresis behaviour. Figure 6 shows the result obtained from a structurally dynamic model. As seen in the figure, the model s results follow the above-mentioned rule based upon Scheffer et al. [29], which may be considered a strong support for the applicability of structurally dynamic models and at the same time an important progress in modelling, because we now know new ways of developing better models and modelling the structural changes. 5 THE APPLICATION OF EXERGY AS AN ECOLOGICAL INDICATOR About 15 years ago there was a proposal by environmental managers to find ecological indicators that could be used to assess the integrity of ecosystems or take the pulse of the ecosystem. The idea was to be able to assess, preferably quantitatively, not only the ecosystem integrity but also,

10 10 P a g e Figure 6: Total phosphorus in the form of submerged plants are plotted versus total phosphorus of all forms in the lake water. As seen in the figure, the submerged plants first increase owing to the increased concentration of phosphorus, then at about 150 µg P/l the submerged plant phosphorus decreases and at about 250 µg P/l the submerged vegetation disappears. When the phosphorus concentration decreases at a later stage the submerged vegetation will 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 to set up a quantitative diagnosis. How bad was the eutrophication or the toxic substance pollution for instance? 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] and 7. 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 formation of Surtsey Island south of Iceland by a volcanic eruption in The observations are taken from Surtsey Research Reports [34]. When a new island is formed life starts from level zero, and it would therefore be a very illustrative case to follow the development of ecological indicators and see if they, in accordance with the expectation, would increase and reflect the increasing life on the island over time. The following information is valid for Surtsey Island: (i) it has an area of about 1.5 km 2 ; (ii) it was formed as a result of a volcanic eruption in 1963; (iii) measurements have been taken since November The eco-exergy calculated for plants and nesting birds based upon the available observations is shown in Fig. 7. The plant biodiversity is also determined and shown in Fig. 8. These two figures reflect 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 good linear correlation between time and exergy, but a logistic expression may be better able to cover the relationship between time and exergy.

11 P a g e 11 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 THEORIES Several ecosystem theories have been presented in the scientific literature during the last two to three decades. At first glance they look very different and seem to be inconsistent, but a further examination reveals 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 meeting involving several system ecologists in 2000, it can now be concluded that a consistent pattern of ecosystem theories has been formed. Several system ecologists have agreed on the pattern presented

12 12 P a g e below as a working basis for further development in system ecology. This is of the utmost importance for progress in system ecology, because with a theory in hand it will be possible to explain many rules that 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: a few basic laws which can be used to deduce rules that explain observations. It has therefore also been agreed that one of the important goals in system ecology would be to demonstrate (prove) the links between ecological rules and ecological laws. Ten to fifteen years ago the presented theories seemed very inconsistent and chaotic. How could E.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 s maximum exergy principle [1, 2, 6, 7, 42], and Prigogine s [43] and Mauersberger s minimum entropy dissipation [44, 45] be valid at the same time? New results and an open discussion among the contributing scientists have led to the formation of a pattern, where all the theories contribute to the total picture of ecosystem development. The first contribution to a clear pattern of the various ecosystem theories came from the network approach 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 annual situation 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 input and the cycling within the network. The input (solar radiation) is again determined by the structure of the system (the stored exergy, the biomass). Furthermore, the greater the structure the greater is the 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, and therefore more biomass (exergy) can be formed without increase of the inputs. It has been shown previously that more cycling means an increased ratio of indirect to direct effects, while increased input 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 as goal functions (exergy, power, entropy, etc.). An ecosystem is, of course, not setting goals, but a goal function is used to describe the direction of development an ecosystem will take in an ecological model. Their results can be summarized as follows: 1. increased inputs (more solar radiation is captured) mean more biomass, more exergy stored, more exergy degraded, therefore higher entropy dissipation also, more throughflow (power), increased ascendancy, but no change in the ratio of indirect to direct effects or in the retention time for the energy in the system = total exergy/input exergy per unit of time; 2. increased cycling implies more biomass, more exergy stored, more throughflow, increased ascendancy, increased ratio of indirect to direct effects, increased retention, but no change in exergy degradation. Almost simultaneously Jørgensen et al. [9] published a paper which claims that ecosystems show three growth forms: I. Growth of physical structure (biomass), which is able to capture more of the incoming energy in the form of solar radiation, but also requires more energy for maintenance (respiration and evaporation). II. III. Growth of the network, which means more cycling of energy and matter. 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.

13 P a g e 13 Figure 9: The exergy captured expressed as solar radiation % is plotted versus the exergy of the ecosystem. These three growth forms may be considered an integration of E.P. Odum s attributes which describe changes in the ecosystem associated with development from the early stage to the mature stage. 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 and 8. 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 growth form 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 the exergy 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)

14 14 P a g e Table 3: Exergy utilization and storage in a comparative set of ecosystems. Ecosystem Exergy utilization (%) Exergy storage (MJ/m 2 ) Quarry 6 0 Desert Clear-cut forest Grassland Fir plantation Natural forest Old-growth deciduous forest Tropical rain forest Figure 10: The plot shows the results of Debeljak [47], who examined managed and virgin forests in different stages of development. Gap has no trees, while the virgin forest changes from optimum to mixed to regeneration and back to optimum, although the virgin forest can be destroyed by catastrophic events such as fires or storms. The juvenile stage is a developmental stage between the gap and the optimum. Pasture is included for the comparison. and creative destruction (Fig. 11). The latter phase also fits into the three growth forms but will require a further explanation. The creative destruction phase is a result of either external or internal factors. In the first case (e.g. hurricanes and volcanic activity), further explanation is not needed as an ecosystem has to use the growth forms under the prevailing conditions which are determined by the external factors. If the destructive phase is a result of internal factors, the question is why would a system be self-destructive?. A possible explanation is that a result of the conservation phase is that almost all nutrients will be contained in organisms, which implies that there are no nutrients available to test new

15 P a g e 15 Figure 11: Holling s four stages are expressed in terms of biomass and specific exergy. Notice that the trend of each further cycle is towards higher exergy storage. and possibly better solutions to move further away from thermodynamic equilibrium or, expressed in Darwinian terms, to increase the probability of survival. This is also implicitly indicated by Holling, as he talks about creative destruction. Therefore, when new solutions are available, it would, in the long run, be beneficial for the ecosystem to decompose the organic nutrients into inorganic components that can be utilized to test the new solutions. The creative destruction phase can be considered to be a method 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 linear systems at a steady non-equilibrium state, not for far from equilibrium systems). It was applied by 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 is compatible with the constraints to which the system is subjected [37]. This is also called the maximum 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 offered to utilize the exergy flow, the system has the propensity to select the organization that gives the system 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 Yellow Stone Park after a fire, an island born after a volcanic eruption, reclaimed land, is well covered by E.P. Odum [36]: at first the biomass increases rapidly which implies that the percentage of captured

16 16 P a g e Table 4: Accordance between growth forms and the proposed descriptors. Hypothesis Growth form I Growth form II Growth form III Exergy storage Up Up Up Power/throughflow Up Up Up Ascendancy Up Up Up Exergy dissipation Up Equal Equal Retention time Equal Up Up Entropy production Up Equal Equal Exergy/biomass = specific exergy Equal Up Up Entropy/biomass = specific Equal Down Down entropy production Ratio indirect/direct effects Equal Up Up incoming solar radiation increases and also the energy needed for the maintenance. Growth form I is dominant in this first phase, where exergy stored increases (more biomass, more physical structure to capture more solar radiation), and the throughflow (of useful energy), the exergy dissipation and the 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 forms takes place. When the percentage of solar radiation captured reaches about 80%, it is not possible to increase the amount of captured solar radiation further (due in principle to the second law of thermodynamics). Therefore, further growth of the physical structure (biomass) does not improve the energy balance of the ecosystem. In addition, all or almost all the essential elements are in the form 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 ecosystem can still improve the ecological network and can still change r-strategists with K-strategists, small animals and plants with bigger ones and less developed organisms with more developed ones with more information genes. A graphical representation of this description of ecosystem development is already presented in Fig. 9. The accordance with the five descriptors + specific entropy production and the three growth forms based 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 optimum represents growth forms I and II. The development from optimum to mixed forest is dominant growth form III. These results are also consistent with those of Johnson [49, 50], who found that when ecosystems are relatively isolated, competitive exclusion results in a relatively homogeneous system configuration that exhibits relatively low dissipation. Based upon the results, it is possible to formulate the following hypothesis (Ecological Law of Thermodynamics, which is consistent with the hypothesis on eco-exergy proposed in Section 2 of this paper) uniting the five hypotheses: Ecosystem development in all phases will move away from thermodynamic equilibrium and has the propensity to select the components and the organization that yields the highest flux of useful energy throughout the system and the most exergy stored in the system. This also corresponds to the highest ascendancy.

17 P a g e 17 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 (which is 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 degradation rate. 2. Growth of the number of network linkages and thereby of recycling of matter and energy which implies a better utilization of the incoming energy, and therefore an increase in throughflow and exergy storage without an increase in exergy dissipation. It means that specific exergy degradation and specific entropy production is decreasing. 3. Growth of information, as the number of components in the network and replacement of r-strategist and small organisms with K-strategists and bigger and often more developed organisms. 7 CONCLUSIONS A hypothesis that we may call the Ecological Law of Thermodynamics has been presented. The hypothesis has been applied to explain ecological observations, to develop structurally dynamic models and to assess ecosystem health. These applications support the hypothesis. Furthermore, it has 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 may therefore be concluded that we have a tentative ecosystem theory that can be applied to explain ecological 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 therefore very 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. REFERENCES [1] Jørgensen, S.E., Integration of Ecosystem Theories: A Pattern, Kluwer Academic Publishers: Dordrecht, [2] Jørgensen, S.E., A holistic approach to ecological modelling by application of thermodynamics. Systems and Energy, eds W. Mitsch et al., Ann Arbor Science: Ann Arbor, MI, p. 132, [3] Jørgensen, S.E., Ladegaard, N., Debeljak, M. & Marques, J.C., Calculations of exergy for organisms. Ecological Modelling, 185, pp , [4] Prigogine, I., Etude thermodynamique des phénomenès irreversibles, Desoer: Liège, [5] Morowitz, H.J., Beginnings of Cellular Life, Yale University Press: New Haven and London, [6] Jørgensen, S.E. & Mejer, H.F., Ecological buffer capacity. Ecological Modelling, 3, pp , [7] Jørgensen, S.E. & Mejer, H.F., A holistic approach to ecological modelling. Ecological Modelling, 7, pp , [8] Jørgensen, S.E., Nielsen, S.N. & Mejer, H., Emergy, environ, exergy and ecological modelling. Ecological Modelling, 77, pp , [9] Jørgensen, S.E., Patten, B.C. & Straskraba, M., Ecosystem emerging: 4. Growth. Ecological Modelling, 126, pp , [10] Li, W.-H. & Garuer, D., Fundamentals of Molecular Evolution, Sinauer: Sunderland, MA, [11] Schlesinger, W.H., Biogeochemistry. An Analysis of Global Change, 2nd edn, Academic Press: San Diego, London, Boston, New York, Sydney, Tokyo, Toronto, [12] Morowitz, H.J., Energy Flow in Biology, Academic Press: New York, 1968.

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