Page | 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
WIT Transactions on State of the Art in Science and Engineering, Vol 51, © 2011 WIT Press
www.witpress.com, ISSN 1755-8336 (on-line)
doi:10.2495/978-1-84564-654-7/02
2 | Page
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
WIT Transactions on State of the Art in Science and Engineering, Vol 51, © 2011 WIT Press
www.witpress.com, ISSN 1755-8336 (on-line)
Page | 3
Table 1: Genome size, repetition genes and β-values.
Organisms
Human
Mouse
Tiger fish
Mosquito
Squirt
Fruit fly
Yeast
Amoeba
Worm
Mustard weed
Rice
Virus
Reptiles
Birds
Genome (Mb)
Repeat (%)
β
2900
2500
400
280
155
137
12
34
97
128
400
46
38
9
16
10
2
2
0.5
0.5
14
50
2966
2935
689
445
264
254
22
64
183
203
379
1.01
1150*
1340*
*Found indirectly.
equilibrium and can be expressed as the chemical energy difference between the system and the
thermodynamic equilibrium:
Eco-exergy = RT
n
ci ln ci 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 = −18.7 kJ/g × 104400 g/mole = 1952 MJ/mole = 8.2 J/mole × 300 ln K,
which implies that
ln K = −793496 or K is about 10−344998 .
(2)
(3)
The eco-exergy for organisms is expressed as
Eco-exergy =
β i ci ,
where β is a weighting factor = RT ln ci /ci0 , 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.
WIT Transactions on State of the Art in Science and Engineering, Vol 51, © 2011 WIT Press
www.witpress.com, ISSN 1755-8336 (on-line)
4 | Page
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.
WIT Transactions on State of the Art in Science and Engineering, Vol 51, © 2011 WIT Press
www.witpress.com, ISSN 1755-8336 (on-line)
Page | 5
Table 2: ATPs formed by the oxidation of organic matter by microbiological processes with various
oxidation agents.
Reaction
CH2 O + O2 → CO2 + H2 O
+
CH2 O + 0.8NO−
3 + 0.8H → CO2 + 0.4N2 + 1.4H2 O
+
CH2 O + 2MnO2 + H → CO2 + 2Mn2+ + 3H2 O
CH2 O + 4FeOOH + 8H+ → CO2 + 7H2 O + Fe2+
+
−
CH2 O + 0.5SO2−
4 + 0.5H → CO2 + 0.5HS + H2 O
CH2 O + 0.5CO2 → CO2 + 0.5CH4
kJ/mole e−
ATPs/mole e−
125
119
85
27
26
23
2.98
2.83
2.02
0.64
0.62
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 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
WIT Transactions on State of the Art in Science and Engineering, Vol 51, © 2011 WIT Press
www.witpress.com, ISSN 1755-8336 (on-line)
6 | Page
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 0.65−0.75 [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
WIT Transactions on State of the Art in Science and Engineering, Vol 51, © 2011 WIT Press
www.witpress.com, ISSN 1755-8336 (on-line)
Page | 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
WIT Transactions on State of the Art in Science and Engineering, Vol 51, © 2011 WIT Press
www.witpress.com, ISSN 1755-8336 (on-line)
8 | Page
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
7–9
10
11
12
13
14
15
16
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]),
for three population dynamic models [1],
for Mondego Estuary, Portugal [22],
for Lake Annone, Italy [15],
for the lagoons of Venice [23],
to explain the success and failure of biomanipulation [24],
to explain the intermediate disturbance hypothesis [21],
to explain the change in the properties of Darwin’s finches [25] and
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].
WIT Transactions on State of the Art in Science and Engineering, Vol 51, © 2011 WIT Press
www.witpress.com, ISSN 1755-8336 (on-line)
Page | 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,
WIT Transactions on State of the Art in Science and Engineering, Vol 51, © 2011 WIT Press
www.witpress.com, ISSN 1755-8336 (on-line)
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.
2.
3.
4.
5.
6.
7.
by a comparison and integrity assessment of eutrophied lakes [1],
by a comparison and integrity assessment of coastal zones [9, 30, 31],
by integrity assessment of Mondego Estuary in Portugal [30, 31],
by integrity assessment of Chinese lakes [32],
as ecological indicators for coastal lagoons in Europe [33],
for integrity assessment of different farming systems [1] and
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 1963. 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 km2 ;
(ii) it was formed as a result of a volcanic eruption in 1963; (iii) measurements have been taken since
November 1964.
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.
WIT Transactions on State of the Art in Science and Engineering, Vol 51, © 2011 WIT Press
www.witpress.com, ISSN 1755-8336 (on-line)
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
WIT Transactions on State of the Art in Science and Engineering, Vol 51, © 2011 WIT Press
www.witpress.com, ISSN 1755-8336 (on-line)
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. 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.
WIT Transactions on State of the Art in Science and Engineering, Vol 51, © 2011 WIT Press
www.witpress.com, ISSN 1755-8336 (on-line)
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.
2.
3.
4.
5.
6.
7.
ecosystem biomass (physical structure) increases,
more feedback loops (including recycling of energy and matter) are built,
respiration increases,
respiration relative to biomass decreases,
bigger animals and plants (trees) become more dominant,
the specific entropy production (relative to biomass) decreases,
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)
WIT Transactions on State of the Art in Science and Engineering, Vol 51, © 2011 WIT Press
www.witpress.com, ISSN 1755-8336 (on-line)
14 | P a g e
Table 3: Exergy utilization and storage in a comparative set of ecosystems.
Ecosystem
Quarry
Desert
Clear-cut forest
Grassland
Fir plantation
Natural forest
Old-growth deciduous forest
Tropical rain forest
Exergy utilization (%)
Exergy storage (MJ/m2 )
6
2
49
59
70
71
72
70
0
0.073
0.594
0.940
12.70
26.00
38.00
64.00
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
WIT Transactions on State of the Art in Science and Engineering, Vol 51, © 2011 WIT Press
www.witpress.com, ISSN 1755-8336 (on-line)
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
WIT Transactions on State of the Art in Science and Engineering, Vol 51, © 2011 WIT Press
www.witpress.com, ISSN 1755-8336 (on-line)
16 | P a g e
Table 4: Accordance between growth forms and the proposed descriptors.
Hypothesis
Exergy storage
Power/throughflow
Ascendancy
Exergy dissipation
Retention time
Entropy production
Exergy/biomass = specific exergy
Entropy/biomass = specific
entropy production
Ratio indirect/direct effects
Growth form I
Growth form II
Growth form III
Up
Up
Up
Up
Equal
Up
Equal
Equal
Up
Up
Up
Equal
Up
Equal
Up
Down
Up
Up
Up
Equal
Up
Equal
Up
Down
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.
WIT Transactions on State of the Art in Science and Engineering, Vol 51, © 2011 WIT Press
www.witpress.com, ISSN 1755-8336 (on-line)
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, 2002.
[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, 1982.
[3] Jørgensen, S.E., Ladegaard, N., Debeljak, M. & Marques, J.C., Calculations of exergy for
organisms. Ecological Modelling, 185, pp. 165–176, 2005.
[4] Prigogine, I., Etude thermodynamique des phénomenès irreversibles, Desoer: Liège, 1947.
[5] Morowitz, H.J., Beginnings of Cellular Life, Yale University Press: New Haven and London,
1992.
[6] Jørgensen, S.E. & Mejer, H.F., Ecological buffer capacity. Ecological Modelling, 3, pp. 39–61,
1977.
[7] Jørgensen, S.E. & Mejer, H.F., A holistic approach to ecological modelling. Ecological Modelling, 7, pp. 169–189, 1979.
[8] Jørgensen, S.E., Nielsen, S.N. & Mejer, H., Emergy, environ, exergy and ecological modelling.
Ecological Modelling, 77, pp. 99–109, 1995.
[9] Jørgensen, S.E., Patten, B.C. & Straskraba, M., Ecosystem emerging: 4. Growth. Ecological
Modelling, 126, pp. 249–284, 2000.
[10] Li, W.-H. & Garuer, D., Fundamentals of Molecular Evolution, Sinauer: Sunderland, MA, 1991.
[11] Schlesinger, W.H., Biogeochemistry. An Analysis of Global Change, 2nd edn, Academic Press:
San Diego, London, Boston, New York, Sydney, Tokyo, Toronto, 1997.
[12] Morowitz, H.J., Energy Flow in Biology, Academic Press: New York, 1968.
WIT Transactions on State of the Art in Science and Engineering, Vol 51, © 2011 WIT Press
www.witpress.com, ISSN 1755-8336 (on-line)
18 | P a g e
[13] Shugart, H.H., Terrestrial Ecosystems in Changing Environments, Cambridge University Press:
Cambridge, 1998.
[14] Peters, R.H., The Ecological Implications of Body Size, Cambridge University Press: Cambridge,
1983.
[15] Jørgensen, S.E. & de Bernardi, R., The application of a model with dynamic structure to simulate
the effect of mass fish mortality on zooplankton structure in Lago de Annone. Hydrobiologia,
356, pp. 87–96, 1997.
[16] Vollenweider, R.A., Input-output models with special reference to the phosphorus loading concept in limnology. Schweizerische Zeitschrift fur Hydrobiologie, 37, pp. 53–84, 1975.
[17] Nielsen, S.N.,Application of Maximum Exergy in Structural Dynamic Models [Thesis], National
Environmental Research Institute, Denmark, 1992.
[18] Nielsen, S.N., Strategies for structural-dynamical modelling. Ecological Modelling, 63,
pp. 91–102, 1992.
[19] Zhang, J., Jørgensen, S.E., Tan C.O. & Beklioglu, M., A structurally dynamic modelling—Lake
Mogan, Turkey as a case study. Ecological Modelling, 164, pp. 103–120, 2003.
[20] Zhang, J., Jørgensen, S.E., Tan C.O. & Beklioglu, M., Hysteresis in vegetation shift—Lake
Mogan prognoses. Ecological Modelling, 164, pp. 227–238, 2003.
[21] Jørgensen, S.E. & Padisak, J., Does the intermediate disturbance hypothesis comply with
thermodynamics? Hydrobiologia, 323, pp. 9–21, 1996.
[22] Marques, J.C., Nielsen, S.N., Pardal, M.A. & Jørgensen, S.E., Impact of eutrophication and
river management within a framework of ecosystem theories. Ecological Modelling, 166,
pp. 147–168, 2003.
[23] Coffaro, G., Bocci, M. & Bendoricchio, G., Application of structural dynamic approach to
estimate space variability of primary producers in shallow marine water. Ecological Modelling,
102, pp. 97–114, 1997.
[24] Jørgensen, S.E. & de Bernardi, R., The use of structural dynamic models to explain successes
and failures of biomanipulation. Hydrobiologia, 359, pp. 1–12, 1998.
[25] Jørgensen, S.E. & Fath, B., Modelling the selective adaptation of Darwin’s Finches. Ecological
Modelling, 176, pp. 409–418, 2004.
[26] Jørgensen, S.E., The growth rate of zooplankton at the edge of chaos: ecological models. Journal
of Theoretical Biology, 175, pp. 13–21, 1995.
[27] Jørgensen, S.E., Parameters, ecological constraints and exergy. Ecological Modelling, 62,
163–170, 1992.
[28] Jørgensen, S.E., Ray, S., Berec, L. & Straskraba, M., Improved calibration of a eutrophication
model by use of the size variation due to succession. Ecological Modelling, 153, pp. 269–278,
2002.
[29] Scheffer, M., Carpenter, S., Foley, J.A., Folke C. & Walker, B., Catastrophic shifts in ecosystems.
Nature, 413, pp. 591–596, 2001.
[30] Marques, J.C., Pardal, M.A., Nielsen, S.N. & Jørgensen, S.E., Analysis of the properties of
exergy and biodiversity along an estuarine gradient of eutrophication. Ecological Modelling,
102, pp. 155–167, 1997.
[31] Marques, J.C., Pardal, M.A., Nielsen, S.N. & Jørgensen, S.E., Thermodynamic orientors: exergy
as a holistic ecosystem indicator: a case study [Chapter 2.5]. Ecotargets, Goal Functions and
Orientors. Theoretical Concepts and Interdisciplinary Fundamentals for an Integrated, System Based Environmental Management, eds F. Müller & M. Leupelt, Springer-Verlag: Berlin,
pp. 87–101, 1998.
WIT Transactions on State of the Art in Science and Engineering, Vol 51, © 2011 WIT Press
www.witpress.com, ISSN 1755-8336 (on-line)
P a g e | 19
[32] Xu, F.L., Tao, S. & Xu, Z.R., Restoration of riparian and macrophytes in Lake Chao, an eutrophic
Chinese lake: possibilities and effects. Hydrobiologia, 405, pp. 169–178, 1999.
[33] ISPRA, Application of exergy as an ecological indicator in Mediterranean coastal lagoons,
A. Reyner, M. Plus & J.M. Zaldivar, 2001.
[34] Surtsey Research Reports, Volumes 1–11, Surtsey Research Society: Reykjavik, 1965–2000.
[35] Jørgensen, S.E., Toward a consistent pattern of ecosystem theories. The Scientific World, 1,
pp. 71–75, 2001.
[36] Odum, E.P., The strategy of ecosystem development. Science, 164, pp. 262–270, 1969.
[37] Odum, H.T., System Ecology, Wiley Interscience: New York, 1983.
[38] Ulanowicz, R.E., Growth and Development. Ecosystems Phenomenology. Springer-Verlag:
New York, Berlin, Heidelberg, Tokyo, 1986.
[39] Patten, B.C., Network ecology: indirect determination of the life–environment relationship in
ecosystems. Theoretical Studies of Ecosystems: The Network Perspective, eds M. Higashi &
T.P. Burns, Cambridge University Press: Cambridge, pp. 288–351, 1991.
[40] Kay, J.J., Self-organization in Living Systems [Thesis], Systems Design Engineering, University
of Waterloo, Ontario, Canada, 1984.
[41] Kay, J. & Schneider, E.D., Thermodynamics and measures of ecological integrity. Proceedings
of the International Symposium on Ecological Indicators, eds D.H. McKenzie, D.E. Hyatt &
V.J. McDonald, Elsevier: Amsterdam, pp. 159–182, 1992.
[42] Mejer, H.F. & Jørgensen, S.E., Energy and ecological buffer capacity. State-of-the-Art of Ecological Modelling (Environmental Sciences and Applications, 7), ed. S.E. Jørgensen, Proceedings
of a Conference on Ecological Modelling, 28 August–2 September 1978, Copenhagen, International Society for Ecological Modelling, Copenhagen, pp. 829–846, 1979.
[43] Prigogine, I., From Being to Becoming: Time and Complexity in the Physical Sciences, Freeman:
San Fransisco, CA, 1980.
[44] Mauersberger, P., General principles in deterministic water quality modeling. Mathematical
Modeling of Water Quality: Streams, Lakes and Reservoirs (International Series on Applied
Systems Analysis, 12), ed. G.T. Orlob, Wiley: New York, pp. 42–115, 1983.
[45] Mauersberger, P., Entropy control of complex ecological processes. Complex Ecology: The PartWhole Relation in Ecosystems, eds B.C. Patten & S.E. Jørgensen, Prentice-Hall: Englewood
Cliffs, NJ, pp. 130–165, 1995.
[46] Fath, B. & Patten, B.C., A progressive definition of network aggradation. Advances in Energy
Studies, ed. S. Ulgiati, SGE Editoriali: Padova, pp. 551–562, 2001.
[47] Debeljak, M., Characteristics of Energetics of Managed and Virgin Forest, PhD Thesis,
Ljubljana, 2002.
[48] Holling, C.S., The resilience of terrestrial ecosystems: local surprise and global change. Sustainable Development of the Biosphere, eds W.C. Clark & R.E. Munn, Cambridge University
Press: Cambridge, pp. 292–317, 1986.
[49] Johnson, L., The thermodynamics of ecosystem. The Handbook of Environmental Chemistry,
ed. O. Hutzinger, Vol. 1, The Natural Environment and The Biogeochemical Cycles, SpringerVerlag: Heidelberg, pp. 2–46, 1990.
[50] Johnson, L., The far-from-equilibrium ecological hinterlands. Complex Ecology. The PartWhole Relation in Ecosystems, eds B.C. Patten, S.E. Jørgensen & S.I. Auerbach, Prentice Hall
PTR: Englewood Cliffs, NJ, pp. 51–104, 1995.
[51] Jørgensen, S.E. & Fath, B., Application of thermodynamic principles in ecology. Ecological
Complexity, 1, pp. 267–280, 2004.
WIT Transactions on State of the Art in Science and Engineering, Vol 51, © 2011 WIT Press
www.witpress.com, ISSN 1755-8336 (on-line)