Ecological Modelling 126 (2000) 249 – 284
www.elsevier.com/locate/ecolmodel
Ecosystems emerging:
4. growth
Sven E. Jørgensen a, Bernard C. Patten b,*, Milan Straškraba c
a
DFH, Institute A, Miljøkemi, Uni6ersitetsparken 2, 2100 Copenhagen Ø, Denmark
b
Institute of Ecology, Uni6ersity of Georgia, Athens, GA 30602, USA
c
Biomathematical Laboratory, Czech Academy of Sciences and Uni6ersity of South Bohemia, Braniso6ska 31,
370 05 C& eske Budějo6ice, Czech Republic
Abstract
This fifth paper in the series on Ecosystems Emerging treats the properties of ecosystem growth and development
from the perspective of open (paper four), nonequilibrium, thermodynamic systems. The treatment is nonrigorous and
intuitive, interpreting results for living ecosystems based on parallels between these and the much simpler nonliving
ones treated rigorously in thermodynamic theory. If an (open, nonequilibrium) ecosystem receives a boundary flow
of energy from its environment, it will use what it can of this energy, the free energy or exergy content, to do work.
The work will generate internal flows, leading to storage and cycling of matter, energy, and information, which move
the system further from equilibrium. This is reflected in decreased internal entropy and increased internal organization. Energy degraded in the performance of work is exhausted as boundary outputs to the system’s environment.
This is reflected in decreased organization and increased entropy of the surroundings, the dissipative property (paper
three). All properties rest on the conservation principle (paper two). Growth is movement away from equilibrium,
which occurs in three forms: (I) when there is a simple positive balance of boundary inputs over outputs, which
increments storage; (II) when, with boundary inputs fixed, the ratio of internal to boundary flows increases, which
reflects increase in the sum of internal flows, which contribute to throughflow; and (III) when, somewhat coincident
with but mostly following upon I and II, system internal organization, reflecting its energy-use machinery, evolves the
utilization of information to increase the usefulness for work of the boundary energy supply. These three forms of
growth are, respectively, growth-to-storage, growth-to-throughflow, and growth-to-organization. Forms I and II are
quantitative and objective, concerned with brute energy and matter of different kinds. Form III has qualitative and
subjective attributes inherent in information-based mechanisms that increase the exergy/energy ratio in available
energy supplies. The open question of this paper is, which of many possible pathways will an ecosystem take in
realizing its three forms of growth? The answer given is that an ecosystem will change in directions that most
consistently create additional capacity and opportunity to utilize and dissipate available energy and so achieve
increasing deviation from thermodynamic ground. The machinery for this synthesized from the three identified
growth processes is reflected in a single measure, exergy storage. Abundant and diverse living biomass represents
abundant and diverse departure from thermodynamic equilibrium, and both are captured in this parameter. It is the
* Corresponding author.
E-mail address: [email protected] (B.C. Patten)
0304-3800/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved.
PII: S 0 3 0 4 - 3 8 0 0 ( 0 0 ) 0 0 2 6 8 - 4
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S.E. Jørgensen et al. / Ecological Modelling 126 (2000) 249–284
working hypothesis of this paper that ecosystems continually maximize their storage of free energy at all stages in
their integrated existence. If multiple growth pathways are offered from a given starting state, those producing
greatest exergy storage will tend to be selected, for these in turn require greatest energy dissipation to establish and
maintain, consistent with the second law. Energy storage by itself is not sufficient, but it is the increase in specific
exergy, that is, of exergy/energy ratios, that reflects improved usability, and this represents the increasing capacity to
do the work required for living systems to continuously evolve new adaptive ‘technologies’ to meet their changing
environments. Exergy cannot be found for entire ecosystems as these are too complex to yield knowledge of all
contributing elements. But it is possible to compute an exergy index for models of ecosystems that can serve as
relative indicators. How to compute this index is shown, together with its use in developing models with time-varying
parameters. It is also shown how maximization of exergy storage distinguishes between local and global optimization
criteria. In ecological succession, energy storage in early stages is dominated by Form I growth which builds structure;
the dominant mechanisms are increasing energy capture (boundary inputs) and low entropy production (dissipative
boundary outputs). In middle stages, growing interconnection of proliferating storage units (organisms) increases
energy throughflow (Form II growth). This increases endogenous inputs and outputs and, in consequence,
throughflow/boundary flow ratios, entropy production, and on balance, biomass. In mature phases, cycling becomes
a dominant feature of the internal network, increasing storage and throughflow both. Biomass and entropy
production are maximal, but specific dissipation (as dissipation/storage ratio) decreases, reflecting advanced organization (Form III growth) typified by cycling. Specific exergy (exergy/energy ratio) increases throughout succession to
maturity, in early stages mainly due to mass accrual, and in the later stages to gains in information and organization.
During senescence, storage, entropy production, specific dissipation, and specific exergy all decrease, reflecting a
declining ecosystem returning toward equilibrium. © 2126 Elsevier Science B.V. All rights reserved.
Keywords: Growth; Storage; Throughflow; Organization; Energy; Exergy; Dissipation; Thermodynamics
1. Introduction
The quality of exergy is not sustain’d.
It droppeth as a gentle drain to heaven,
and is thrice bless’d.
(…with apologies to The Bard)
If you have been following this serial on ‘Ecosystems Emerging’, you may recognize in this little
parody on Shakespeare the main themes from our
previous three papers: energy is 1. conserved (Patten et al., 1997), but its ability to do work (exergy)
is not. Quality degrades, and the residues 2. dissipate (Straškraba et al., 1999) from 3. open
(Jørgensen et al., 1999) systems to the vast reaches
of space, giving direction to change. But unlike
‘mercy’, which in The Merchant of Venice is only
twice bless’d, exergy serves in three ways to create
order in ecosystems apace of its running down. It
is this antientropic process — 4. growth — that is
the subject of this paper.
In previous installments, we examined what
properties of ecosystems and how much of a
comprehensive ecosystem theory could be derived
from the first three laws of thermodynamics. The
laws were cast as restrictions to contain growth and
development, whose processes had to satisfy the
conservation principle (first law) for applicable
parameters, and degrade energy (second law) and
evacuate effluent heat to surroundings. Energy flow
through a system, defining it as open (energy–matter permeable) or nonisolated (energy permeable),
is necessary for continued existence (partly deduced
from the third law), and a flow of usable energy is
sufficient to form an ordered structure, called a
dissipative system (Prigogine, 1980). Morowitz
(1992) referred to this latter as a fourth law of
thermodynamics, but it would seem more appropriate if such a law could be expanded to state which
ordered structure among possible ones will be
selected. An hypothesis about this selection has
been offered and advocated by the first author of
this paper for over two decades (Jørgensen and
Mejer, 1977; Mejer and Jørgensen, 1979;
Jørgensen, 1982, 1992a, 1997). This paper explores
some of the ramifications of this hypothesis as a
determinant of growth and development, and its
implications for other properties, of ecosystems.
S.E. Jørgensen et al. / Ecological Modelling 126 (2000) 249–284
Growth of something is defined as increase in a
measurable quantity, often taken in ecology to be
some form of mass or energy, such as population
size or biomass. Here is the ‘thrice blessed’ part
from the Shakespearean paraphrase. Form I
growth is simple accrual of mass – energy due to
an excess of boundary inputs (Sz) over outputs
(Sy). It is characterized by input/output ratios
greater than unity, Sz/Sy \ 1, reflected in increased accumulation. This may be referred to as
growth-to-storage. Form II growth is the increase
in internal mass – energy flows (STint) per unit of
boundary inputs: STint/Sz, where STint +Sz =
TST is total system throughflow. This may be
considered as growth-to-throughflow. Form III
growth is increase in internal order, reflected in
the informational component of exergy which increases exergy/energy ratios, both throughflowspecific, TSTexergy/TSTenergy, and input-specific,
TSTexergy/Szenergy. This may be referred to as
growth-to-organization.
These concepts of growth are inherently atomistic — entity oriented. They do not explicitly
include environmental aspects of growing ‘eco–
systems’, the term we introduced (Patten et al.,
1997, Fig. 2) to refer to open or nonisolated
processes or objects (slow processes) with input
and output environments. What environmentally
oriented definitions might be used to support an
emerging holistic concept of ecosystems? Growth
as the expansion of input or output ‘environs’
(partition units of ecosystems associated with
their component parts — Patten, 1978, 1982)
might be appropriate. Then the growth of entities
could be expressed as growth of their environs, of
input environs defined as ‘‘annexation of resources formerly committed to other uses’’, and of
output environs defined as ‘‘performance of work
to achieve better use and expansion of the resource base’’ (by increase of niches, habitats, biodiversity, etc.). Such definitions would provide
useful perspectives on the three forms of growth
described above, but they lead to complications
and also other definitions are possible. Therefore,
we have chosen to avoid a frontal exposition of
‘environmental growth’ per se, which ‘entity
growth’ necessarily involves, and instead, beginning later in this paper and continuing as our
251
series progresses, to gradually extend our atomistic definition to the ‘outsides’ (the environs) of
eco–systems, which collectively form the ‘insides’
of ecosystems.
In general, then, we will take growth as increase
in the size of a focal system (reflected especially in
Forms I and II), and development as increase in
its size-specific organization (expressed in Form
III). Growth is measured as mass or energy
change per unit of time, for instance kg/y, while
storage-specific growth is measured in 1/units of
time, for instance 1/24 h. Development may take
place with or without change in biomass. Ulanowicz (1986) uses ‘growth’ and ‘development’ as
extensive and intensive aspects of the same process; they may often co-occur. In thermodynamic
terms, a growing system is one moving away from
thermodynamic equilibrium. At equilibrium, the
system cannot do any work. All its components
are inorganic, have zero free energy (exergy), and
all gradients are eliminated. Everywhere in the
universe there are structures and gradients, resulting from growth and developmental processes cutting across all levels of organization. A gradient is
understood as a difference in an intensive thermodynamic variable, such as temperature, pressure,
altitude, or chemical potential. Second-law dissipation acts to tear down the structures and eliminate the gradients, but it cannot operate unless
the gradients are established in the first place. An
obvious question, therefore, is what determines
the buildup of gradients?
Structure and organization can be expressed in
different units, such as number of state variables,
number of connections in an interactive web, and
kJ of exergy which corresponds to distance from
thermodynamic equilibrium. Biological systems,
especially, have many possibilities for moving
away from equilibrium, and it is important to
know along which pathways among possible ones
a system will develop. Invoking the second-lawbased dissipation principle from our earlier paper
(Straškraba, et al., 1999), we suggest as an answer
the following working hypothesis:
Exergy storage hypothesis. If a system receives
an input of exergy, it will utilize this exergy to
perform work. The work performed (1) de-
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grades the exergy, dissipating the residue as
entropy to the system’s surroundings, (2) moves
the system further from thermodynamic equilibrium, reflected in growth of gradients, and
(3) increases the accumulated mass – energy of
the system, representing additional stored exergy. If there is offered more than one pathway
to depart from equilibrium, the one yielding the
most work, dissipation, gradients, and (ultimately) storage under the prevailing conditions,
to give the most ordered structure furthest from
equilibrium, will tend to be selected.
This is a restatment and expansion of Jørgensen
and Mejer (1977). A paradox appears to exist in
conflicting criteria, the joint maximization of two
diametrically opposed properties, storage, which
is buildup, and dissipation, which is teardown.
This paper will try to resolve this paradox in an
ecological context, and in the process expose the
complexity of the interplay between thermodynamics and the growth of order in ecosystems and
the ecosphere.
Just as it is not possible to prove the first three
laws of thermodynamics by deductive methods, so
also can the above hypothesis only be ‘proved’
inductively. We do not attempt such proof or
falsification in any formal way, but in the next
section we do examine a number of concrete cases
which contribute generally to the weight of evidence in favor. The section following will discuss
how significant contributions to exergy, which
cannot be measured in absolute terms for complex
systems, can be incorporated into a usable exergy
index. Then, consistency of the exergy-storage
hypothesis with other theories describing ecosystem development will be examined. Finally, we
discuss how ecosystem growth follows thermodynamic laws and the above hypothesis. By the use
of steady-state models, factors that influence
growth, amount of biomass, and distance from
equilibrium will be explored. Then briefly, at the
end, we will entertain the same question we have
posed for conservation, dissipation and openness
in previous installments: What would the world
be like if the above hypothesis, and others consistent with it, were not valid?
2. Some examples
Below are presented several case studies from
Jørgensen (1997) in which alternative energy-use
pathways representing probably different gains in
stored exergy are compared. A direct relationship
between ‘biomass’ and ‘stored exergy’ will be assumed, understanding that the true exergy–
biomass relationship is inherently complicated in
different cases due to differences in the biomass
qualities of different organisms.
2.1. Example 1, size of genomes
In general, biological evolution has been towards organisms with an increasing number of
genes and diversity of cell types. If a direct correspondence between free energy and genome size is
assumed, this can reasonably be taken to reflect
increasing exergy storage accompanying the increased information content and processing of
‘higher’ organisms.
2.2. Example 2, Le Chatelier’s principle
The exergy-storage hypothesis might be taken
as a generalized version of ‘Le Chatelier’s Principle.’ Biomass synthesis can be expressed as a
chemical reaction:
energy+ nutrients
=molecules with more free energy (exergy)
and organization+ dissipated energy
(1)
According to Le Chatelier’s Principle, if energy
is put into a reaction system at equilibrium the
system will shift its equilibrium composition in a
way to counteract the change. This means that
more molecules with more free energy and organization will be formed. If more pathways are offered, those giving the most relief from the
disturbance (displacement from equilibrium) by
using the most energy, and forming the most
molecules with the most free energy, will be the
ones followed in restoring equilibrium.
For example, the sequence of organic matter
oxidation (e.g. Schlesinger, 1997) takes place in
the following order: by oxygen, by nitrate, by
S.E. Jørgensen et al. / Ecological Modelling 126 (2000) 249–284
manganese dioxide, by iron (III), by sulphate, and
by carbon dioxide. This means that oxygen, if
present, will always out-compete nitrate which will
out-compete manganese dioxide, and so on. The
amount of exergy stored as a result of an oxidation
process is measured by the available kJ/mol of
electrons which determines the number of
adenosine triphosphate molecules (ATPs) formed.
ATP represents an exergy storage of 42 kJ per mol.
Usable energy as exergy in ATP’s decreases in the
same sequence as indicated above. This is as
expected if the exergy-storage hypothesis were valid
(Table 1). If more oxidizing agents are offered to
a system, the one giving the highest storage of free
energy will be selected. In Table 1, the first (aerobic)
reaction will always out-compete the others because it gives the highest yield of stored exergy. The
last (anaerobic) reaction produces methane;
this is a less complete oxidation than the first
because methane has a greater exergy content than
water.
Numerous experiments have been performed to
imitate the formation of organic matter in the
primeval atmosphere on earth 4 billion years ago
(Morowitz, 1968). Energy from various sources was
sent through a gas mixture of carbon dioxide,
ammonia and methane. Analyses showed that a
wide spectrum of compounds, including several
amino acids contributing to protein synthesis, is
formed under these circumstances. There are obviously many pathways to utilize the energy sent
through simple gas mixtures, but mainly those
forming compounds with rather large free energies
(high exergy storage, released when the compounds
are oxidized again to carbon dioxide, ammonia and
methane) will form an appreciable part of the
mixture (Morowitz, 1968).
2.3. Example 3, photosynthesis
There are three biochemical pathways for photosynthesis: (1) the C3 or Calvin–Benson cycle, (2)
the C4 pathway, and (3) the crassulacean acid
metabolism (CAM) pathway. The latter is least
efficient in terms of the amount of plant biomass
formed per unit of energy received. Plants using the
CAM pathway are, however, able to survive in
harsh, arid environments that would be inhospitable to C3 and C4 plants. CAM photosynthesis
will generally switch to C3 as soon as sufficient
water becomes available (Shugart, 1998). 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 a gram of plant biomass
produced by the three pathways has different
free-energies in each case, 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 conditions, with the exergy-storage hypothesis.
2.4. Example 4, leaf size
Givnish and Vermelj (1976) observed that leaves
optimize their size (thus mass) for the conditions.
This may be interpreted as meaning that they
maximize their free-energy content. The larger the
leaves the higher their respiration and evapotranspiration, but the more solar radiation they can
capture. Deciduous forests in moist climates
have a leaf-area index (LAI) of about 6%. Such
an index can be predicted from the hypothe-
Table 1
Yields of kJ and ATP’s per mole of electrons, corresponding to 0.25 mol of CH2O oxidizeda
Reaction
kJ/mol e−
ATP’s/mol e−
CH2O+O2\CO2+H2O
+
CH2O+0.8NO−
3 +0.8H \CO2+0.4N2+1.4H2O
+
CH2O+2MnO2+H \CO2+2Mn2++3H2O
CH2O+4FeOOH+8H+\CO2+7H2O+Fe2+
+
−
CH2O+0.5SO2−
4 +0.5H \CO2+0.5HS +H2O
CH2O+0.5CO2\CO2+0.5CH4
125
119
85
27
26
23
2.98
2.83
2.02
0.64
0.62
0.55
a
253
The released energy is available to build ATP for various oxidation processes of organic matter at pH 7.0 and 25°C.
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S.E. Jørgensen et al. / Ecological Modelling 126 (2000) 249–284
differences (Example 1) and other factors would
figure in. Later we will discuss exergy dissipation
as an alternative objective function proposed for
thermodynamic systems. If this were maximized
rather than storage, then biomass packing would
follow the relationship D=A/W 0.65 – 0.75 (Peters,
1983). As this is not the case, biomass packing
and the free energy associated with this
lend general support for the exergy-storage hypothesis.
2.6. Example 6, cycling
Fig. 1. Log – log plot of the ratio of nitrogen to phosphorus
turnover rates, R, at maximum exergy vs. the logarithm of the
nitrogen/phosphorus ratio, log N/P. The plot is consistent with
Vollenweider (1975).
sis of highest possible leaf size, resulting from
the tradeoff between having leaves of a given
size versus maintaining leaves of a given
size (Givnish and Vermelj, 1976). Size of
leaves in a given environment depends on the
solar radiation and humidity regime, and while,
for example, sun and shade leaves on the same
plant would not have equal exergy contents, in a
general way leaf size and LAI relationships are
consistent with the hypothesis of maximum exergy
storage.
Ulanowicz and Baird (1999), appendix A, p.
171) recently provided an example where a controlling nutrient has a long turnover time. In
general, if a limiting resource is abundant it will
recycle faster. This is counterintuitive because recycling is not needed in nonlimiting circumstances. A modeling study (Jørgensen, 1997)
indicated that free-energy storage increases
when an abundant resource recycles faster. Fig. 1
shows such results for a lake eutrophication model. The ratio, R, of nitrogen (N) to
phosphorus (P) cycling which gives the highest
exergy is plotted versus log (N/P). The plot in Fig.
1 is also consistent with empirical results
(Vollenweider, 1975). Of course, one cannot ‘inductively test’ anything with a model, but the
indications and correspondence with data do tend
to support in a general way the exergy-storage
hypothesis.
2.5. Example 5, biomass packing
2.7. Example 7, fitness
The general relationship between animal body
weight,W, and population density, D, is D = A/
W, where A is a constant (Peters, 1983). Highest
packing of biomass depends only on the
aggregate mass, not the size of individual organisms. This means that it is biomass rather than
population size that is maximized in an
ecosystem, as density (number per unit area) is
inversely proportional to the weight of the
organisms. Of course the relationship is complex.
A given mass of mice would not contain the
same exergy or number of individuals as an
equivalent weight of elephants. Also, genome
Brown et al. (1993), Marquet and Taper (1998)
examined patterns of animal body size. They explained frequency distributions for the number of
species as functions of body size in terms of
fitness optimization. Fitness can be defined as the
rate at which resources in excess of those
required for maintenance are used for reproduction (Brown, 1995). This definition, drawing
on previous examples (especially 1 and 5), suggests channeling of resources to increase the
free-energy pool. Fitness, so interpreted, may be
taken as consistent with the exergy-storage hypothesis.
S.E. Jørgensen et al. / Ecological Modelling 126 (2000) 249–284
255
2.8. Example 8, structural dynamics
2.9. Conclusion
Dynamic models whose structure changes over
time are based on nonstationary or time-varying
differential or difference equations. We will refer
to these as structurally dynamic models. A number of such models, mainly of aquatic systems
(Jørgensen, 1986, 1988, 1990, 1992a,b; Nielsen,
1992a,b; Jørgensen and Padisák, 1996; Coffaro et
al., 1997; Jørgensen and de Bernardi, 1997), have
been investigated to see how structural changes
are reflected in free-energy changes. The latter
were computed as exergy indexes (Section 3).
Time-varying parameters were selected iteratively
to give the highest index values in a given situation at each time step (see Jørgensen and Padisák,
1996). Such informal procedures for system identification are complicated and prone to error.
Final results, and whether local versus global
optima are realized, etc. are very sensitive to
initial choices made. Even so, at the least, it was
always observed that maximum exergy index values could not be achieved without changing
parameter values, that is, without structural dynamics. The technicalities of parameter fitting
aside, this overall result means that system structure must change if its free-energy storage is to be
continually maximized. Changes in parameters,
and thus system structure, not only reflect changes
in external boundary conditions, but also mean
that such changes are necessary for the ongoing
maximization of exergy. For all models investigated along these lines, the changes obtained were
in accordance with actual observations (see references). These studies therefore affirm, in a general
way, that systems adapt structually to maximize
their content of exergy.
It is noteworthy that Coffaro et al. (1997), in
their structurally dynamic model of the Lagoon of
Venice, did not calibrate the model describing the
spatial pattern of various macrophyte species such
as Ul6a and Zostera, but used exergy-index optimization to estimate parameters determining the
spatial distribution of these species. They found
good accordance between observations and
model, as were able by this method without calibration to explain more than 90% of the observed
spatial distribution of various species of Zostera
and Ul6a.
The above case studies do not constitute a
rigorous test of the exergy-storage hypothesis.
This is impossible because exergy strictly defined
cannot be measured for ecological systems. They
are too complex. However, through modeling and
recourse to many examples, a kind of ‘inductive
verification’ is possible. That is what this section
has tried to do, show that the hypothesis provides
a plausible objective function over a broad selection of actual systems and circumstances. Assistance from modeling depends on deriving a valid
substitute measure for absolute exergy, an index
covering the storage of both biomass and information that can be used in modeling studies to
give further credence to the hypothesis. In the
next section such an index is developed.
3. Estimating free energy: exergy index
3.1. Chemical and physical exergy
Exergy is defined as the work a system can
perform when it is brought into equilibrium with
the environment or another well-defined reference
state. If we presume a reference environment for a
system at thermodynamic equilibrium, meaning
that all the components are: (1) inorganic, (2) at
the highest possible oxidation state signifying that
all free energy has been utilized to do work, and
(3) homogeneously distributed in the system,
meaning no gradients, then the situation illustrated in Fig. 2 is valid. Szargut et al. (1988) and
Szargut (1998) distinguish between chemical exergy and physical exergy. The chemical energy
embodied in organic compounds and biological
structure contributes most to the exergy content
of ecological systems. Temperature and pressure
differences between systems and their reference
environments are small in contribution to overall
exergy and for present purposes can be ignored.
We will compute an exergy index based entirely
on chemical energy: Si (mc − mc,o)Ni, where i is the
number of exergy-contributing compounds, c, and
mc is the chemical potential relative to that at a
reference inorganic state, mc,o. Our (chemical) ex-
S.E. Jørgensen et al. / Ecological Modelling 126 (2000) 249–284
256
ergy index for a system will be taken with reference to the same system at the same temperature
and pressure, but in the form of an inorganic
soup without life, biological structure, information, or organic molecules.
thermodynamic equilibrium. The chemical exergy
contributed by components in an open system
with throughflow is (Mejer and Jørgensen, 1979):
n
Ex= RT % [ci ln(ci /ci,eq)− (ci − ci,eq)]
[ML2T − 2]
i=0
(3)
3.2. Deri6ation of exergy index
As (mc − mco) can be found from the definition
of chemical potential, the following expression for
chemical exergy can be obtained by using concentrations to approximate activities:
n
Ex =RT % ci ln(ci /ci,eq)
[ML2T − 2]
(2)
i=0
R is the gas constant, T is the temperature of the
environment and system (Fig. 2), ci is the concentration of the i’th component expressed in suitable units, ci,eq is the concentration of the i’th
component at thermodynamic equilibrium, and n
is the number of components. The quantity ci,eq
represents a very small, but nonzero, concentration (except for i =0, which is considered to cover
the inorganic compounds), corresponding to a
very low probability of forming complex organic
compounds spontaneously in an inorganic soup at
The problem in applying these equations is
related to the magnitude of ci,eq. Contributions
from inorganic components are usually very low
and can in most cases be neglected. Shieh and Fan
(1982) have suggested that the exergy of structurally complicated material be measured on the
basis of elemental composition. For our purposes
this is unsatisfactory because compositionally similar higher and lower organisms would have the
same exergy, which is at variance with our intent
to account for the exergy embodied in
information.
The problem of assessing ci,eq has been discussed and a possible solution proposed by
Jørgensen et al. (1995). The essential arguments
are repeated here. The chemical potential of dead
organic matter, indexed i =1, can be expressed
from classical thermodynamics (e.g. Russell and
Adebiyi, 1993) as:
m1 = m1,eq + RT ln c1/c1,eq,
[ML2T − 2 mol − 1]
(4)
where m1 is the chemical potential. The difference
m1 − m1,eq is known for detrital organic matter,
which is a mixture of carbohydrates, fats and
proteins. Generally, ci,eq can be calculated from
the definition of the probability, Pi,eq, of finding
component i at thermodynamic equilibrium,
which is:
Pi,eq +
ci,eq
n
[1, dimensionless]
(5)
% ci,eq
i=0
Fig. 2. Illustration of the concept of exergy used to compute
the exergy index for an ecological model. Temperature and
pressure are the same for both the system and the reference
state, which implies that only by the difference in chemical
potentials (m1 −m0) can work be done.
If this probability can be determined, then in
effect the ratio of ci,eq to the total concentration is
also determined. As the inorganic component, c0,
is very dominant at thermodynamic equilibrium,
Eq. (5) can be approximated as:
Pi,eq : ci,eq/c0,eq
[1]
(6)
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By a combination of Eq. (4) and Eq. (6), we
get:
P1,eq =[c1/c0,eq] exp[ −(m1 −m1,eq)/RT]
[1]
(7)
For biological components, i =2, 3,…, n (i =0
covers inorganic compounds, and i =1 detritus),
Pi,eq, is the probability of producing organic matter, P1,eq, and in addition the probability, Pi,a, of
assembling the genetic information to determine
amino acid sequences. Organisms use 20 different
amino acids, and each gene determines a sequence
of about 700 amino acids (Li and Grauer, 1991).
Pi,a can be found from the number of permutations among which the characteristic amino acid
sequence for the considered organism has been
selected. This means that the following two equations are available to calculate Pi :
Pi,eq = P1,eqPi,a
Pi,a =20
− 700g
(i ]2)
[1]
(8)
where g is the number of genes. Eq. (6) can be
reformulated to:
ci,eq :Pi,eqc0,eq
[mol l − 3]
(9)
and Eq. (3) and Eq. (9) combined to yield for
exergy:
n
ci
Ex:RT % ci ln
−ci −Pi,eqc0,eq
Pi,eqc0,eq
i=0
[ML2T − 2]
(10)
This equation may be simplified by use of the
following approximations (based upon Pi,eq ci,
Pi,eq P0, 1/Pi,eq ci, 1/Pi,eq c0,eq/ci ): c/c0,eq : 1,
ci :0, Pi,eqc0,eq : 0, and the inorganic component
can be omitted. The significant contribution
comes from 1/Pi,eq (Eq. (8)). We obtain:
n
Ex: − RT % ci ln(Pi,eq)
[ML2T − 2]
(11)
i=1
where the sum starts from 1 because P0,eq :1.
Expressing Pi,eq as in Eq. (8) and P1,eq as in Eq.
(7), we arrive at the following expression for an
exergy index:
n
n
Ex/RT = % [ci ln (c1/c0,eq) − (m1 −m1,eq) % ci /RT
i=1
i=1
n
− % ci ln Pi,a
i=2
[mol l − 3]
As the first sum is minor compared with the
other two (use for instance ci /c0,eq : 1), we can
write:
n
n
i=1
i=2
Ex/RT = (m1 − m1,eq) % ci /RT− % ci ln Pi,a
[mol l − 3]
(12)
This equation can now be applied to calculate
contributions to the exergy index by significant
ecosystem components. If only detritus is considered, we know the free energy released is about
18.7 kJ/g. R is 8.4 J/mol, and the average molecular weight of detritus is around 105. We get the
following contribution of exergy by detritus per
liter of water, when we use the unit g detritus
exergy equivalent/l:
Ex1 = 18.7ci kJ/l or Ex1/RT= 7.34× 105ci
[ML − 3]
[1]
257
(13)
A typical unicellular alga has on average 850
genes. We purposely use the number of genes and
not the amount of DNA per cell, which would
include unstructured and nonsense DNA. In addition, a clear correlation between the number of
genes and complexity has been shown (Li and
Grauer, 1991). Recently it has begun to be realized that nonsense genes play an important role in
repair of genes when they are damaged. With 850
genes, a sequence of (Eq. (8)) 850 ×700= 595 000
amino acids can be determined. This represents a
contribution of exergy per liter of water, using g/l
detritus equivalent as the concentration unit, of:
Exalgae/RT= 7.34× 105ci − ci ln 20 − 595 000
= 25.2× 105ci [g/l]
(14)
The contribution to exergy from a simple
prokaryotic cell can be calculated similarly as:
Exprokar/RT= 7.34× 105ci + ci ln 20329 000
= 17.2× 105ci [g/l]
(15)
Organisms with more than one cell will have
DNA in all cells determined by the first cell. The
number of possible microstates becomes therefore
proportional to the number of cells. Zooplankton
have approximately 100 000 cells and (see Table
2) 15 000 genes per cell, each determining the
sequence of approximately 700 amino acids. Pzoopl
can therefore be found as:
S.E. Jørgensen et al. / Ecological Modelling 126 (2000) 249–284
258
Table 2
Approximate numbers of nonrepetitive genesa
Organisms
Number of
information genes
Detritus
(reference)
Minimal cells
Bacteria
Algae
Yeasts
Fungi
Sponges
Molds
Trees
Jellyfish
Worms
Insects
Zooplankton
Fishes
Amphibians
Birds
Reptiles
Mammals
Humans
0
470
600
850
2000
3000
9000
9500
10 000–30 000
10 000
10 500
10 000–15 000
10 000–15 000
100 000–120 000
120 000
120 000
130 000
140 000
250 000
pressed in g/l, can be converted to kJ/l by multiplication by 18.7, which approximates to the
average energy content of 1 g detritus (Morowitz,
1968). The index i =0 for constituents covers
inorganic components, but in most cases these
will be neglected as contributions from detritus
and living biota are much higher due to extremely
low concentrations of these components in the
reference system. Our exergy index therefore accounts for the chemical energy in organic matter
plus the information embodied in living organisms. It is measured from the extremely small
probabilities of forming living components spontaneously from inorganic matter. The weighting
factors, bi, may be considered as quality factors
reflecting the extent to which different taxa contribute to overall exergy.
Conversion
factorb
1
2.7
3.0
3.9
6.4
10.2
30
32
30–87
30
35
30–46
30–46
300–370
370
390
400
430
740
3.3. Exergy and information
a
Sources: Cavalier-Smith (1985), Li and Grauer (1991),
Morowitz (1992), Lewin (1994).
b
Based on numbers of information genes and the exergy
content of organic matter in the various organisms, compared
with the exergy content of detritus (about 18 kJ/g).
−ln Pzoopl = −ln(20 − 15 000 × 700 ×10 − 5)
:315 ×105
(16)
As shown, the contribution from the numbers
of cells is insignificant. Pi,a values for other organisms can be found using data such as those in
Table 2.
With this, an ecologically useful exergy index
can be computed based on concentrations of
chemical components, ci, multiplied by weighting
factors, bi, reflecting the exergy contents of the
various components due to their chemical energy
and the information embodied in DNA:
Boltzmann (1905) gave the following relationship for the work, W, embodied in thermodynamic information:
W= RT ln N
[ML2T − 2]
(18)
where N is the number of possible microstates
among which the information is selected. For
biota, N denotes the inverse probability of obtaining a valid amino acid sequence spontaneously.
Our exergy index is also consistent with Reeves
(1991), ‘‘…information appears in nature when a
source of energy [exergy] becomes available but
the corresponding (entire) entropy production is
not emitted immediately, but is held back for
some time [as stored exergy].’’
Svirezhev (1998) showed that Eq. (3) can be
written in the form:
n
Ex= RT A % P*i ln(Pi /Pi,eq)+ A ln A/Ao
i=0
− (A− Ao)
(19)
n
Ex= % bi ci
(17)
i=0
Values for bi based on detrital exergy equivalents are available for a number of different species and taxonomic groups (Jørgensen, pers.
comm.). The unit, detrital exergy equivalents ex-
Pi,eq is defined above (Eqs. (5) and (6)), and
Pi +
ci
n
% ci
i=0
A is the total matter:
(20)
S.E. Jørgensen et al. / Ecological Modelling 126 (2000) 249–284
259
n
A= % ci
(21)
i=0
and Ao is the total matter at thermodynamic
equilibrium. The vector P =(P0, P1 ,…, Pn ) describes the structure of the system. The Pi are
intensive variables, and
n
K= % [Pi ln(Pi /Pi,eq)]
(22)
i=0
is the Kullback measure (Aoki, 1993) of information expressing the information change when the
distribution is changed from Pi,eq to Pi. Note that
K is a specific measure (that is, per unit of matter). The product Exinf =AK may be considered
the total amount of information for the entire
system, which has been accumulated in transition
from some reference state corresponding to thermodynamic equilibrium (i.e. some prevital state)
to the current state of living matter. A is an
extensive variable, and DExmat =A ln(A/A0)−
(A− A0) represents the increase of exergy due to
change in the total mass of the system.
Our exergy index can therefore be viewed as a
sum of two terms: Exinf, resulting from structural
changes inside the system, and Exmat, caused by
change in the total mass of the system. This
interpretation of Eq. (3) is consistent with the
derivation of the exergy index, as summarized in
Eq. (5) to Eq. (18).
3.4. Additional points
The total exergy of an ecosystem cannot be
calculated exactly, as we cannot measure the concentrations of all the components or determine all
possible contributions to exergy, physical and
chemical, in an ecosystem. If we calculate our
exergy index for a fox, say, it will only reflect
chemical contributions coming from biomass and
information embodied in the genes. But what are
the contributions from blood pressure, body temperature, enzymes, hormones, and so on? To
some extent these properties are covered by the
genome, but not fully. We are forced to conclude
that, for now at least, exergy calculations based
on dominant components leave out a lot. The
choice, then, is to (1) abandon this line of research
as impractical, or (2) continue it as a placeholding
bridge to the future when more in the way of
measurement may be possible.
It may be useful at this point to summarize
limitations, but also prospects within these, of the
above-derived exergy index:
1. Only chemical, not physical, sources of free
energy are accounted for. This can be improved upon with further research.
2. Within chemical, only contributions from major components of biomass and from genetic
information are taken into account. It is
tempting to just omit contributions from minor elements as being negligible, but this could
be a trap if nature were so rich in its crossscale diversity that most of its exergy contributions came in fact from minor, but
super-abundant, constituents. The door must
be kept open to a full accounting.
3. Information embodied in the structure of interactive networks at and across the different
levels of hierarchical organization is not accounted for. The ascendency approach of
Ulanowicz (1986, 1991, 1997) is recommended
in this regard. We would like to assume that
network information is negligible compared to
that in genes, but the weight of modern approaches in systems ecology and advances in
modeling continue to indicate the opposite,
that network complexity may be equal to, or
possibly even more important than genetic
information in endowing ecosystems with the
capacity to do work. It is ecological networks
which perform natural selection, and this that
establishes reality (as realized genomes) from
potentiality. Ascendency and exergy indices
computed from models are closely correlated
(Jørgensen, 1994a). This is because networks
reflect the ability of biota to build relationships. Two mutually dependent processes play
a role in ecosystem networks: conservative
transfers of energy or mass, or transactions,
and nonconservative transfers of information,
or relations. The transactions (like predation)
are physical and underly the relations (like
competition and mutualism) as necessary conditions. But the relations can also be a source
of alteration of transactions. Which is primary
is a chicken-and-egg question.
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S.E. Jørgensen et al. / Ecological Modelling 126 (2000) 249–284
4. We can never measure or even know all the
constituents of a natural (complex) ecosystem.
Therefore, we must employ simplifying models, and within the sphere of these even imperfect measures such as the present exergy index
may well prove useful.
5. Relative measures may also prove powerful,
for example, in investigating comparative or
alternative organizations of ecosystems. In
fact, even ‘absolute exergy’, if it could be
calculated, would really be relative as free
energy, by its basic definition, is always calculated with respect to some reference system.
4. Other goal functions or orientors
Boltzmann (1905) proposed that ‘‘life is a struggle for the ability to perform work’’, which is
exergy. Herendeen (1998) expressed this idea similarly, referring to a generalized form of the Gibbs
function
from
chemical
thermodynamics
(Straškraba, et al. 1999, Eq. (5)): free energy= energy− TS, and interpreting this to mean energy−
disorder =energy +order. The difference between
free energy and exergy, which we have not emphasized in this paper to this point, is the ability
with exergy to select a case-dependent reference
state. This is a technical matter, and for the
purposes and reference state (see Fig. 2) of this
paper, free energy and exergy can be taken as
congruent (Jørgensen, 1997).
Ecological (and biological) growth and development have very much to do with the evolution of
order in the material of organized matter, and
work must be done to create this order out of the
background (reference state) of somewhat less
order. Purpose is frequently brought into the discussion of origins of order, in the form of ‘objective functions’, ‘goal functions’, ‘optimization
criteria’, ‘extremal principles’, and ‘orientors’ (e.g.
Müller and Leupelt, 1998). This paper’s central
hypothesis, exergy-storage maximization, is one
such goal function, or in Aristotelian terms, a
‘final cause.’ In this section a selection of others is
reviewed, all of them criteria for purposeful ecological growth and development.
4.1. Maximum biomass
Biomass is stored energy, some of which can be
turned into work. This portion is exergy, the
inherent order in which is taken into account in
Eq. (17) through multiplication by bi. Eq. (21)
and Eq. (22) show even more clearly the two
contributions, by A the total matter, and by Kullback’s measure the information. The ability of a
species to perform work in an ecosystem, its exergy or free energy, is thus proportional not only
its information content, but also its biomass.
Margalef (1968), Straškraba (1979, 1980) and
Brown (1995) have all proposed the use of
biomass as an ecological goal function. As
biomass is storage and has exergy, its maximization would be consistent with the exergy-storage
hypothesis. For entire (eco)systems this would
require different weighting factors, as shown in
Eq. (19), to account for the different information
(order) inherent in the different categories, ci (Eq.
(21)), including biological species.
4.2. Maximum power
Lotka (1922) proposed maximum power as a
goal function for energy systems. Power is work
per unit time, dimensioned [ML2T − 3]. Maximum
power refers to maximum work performed per
unit of time, which to achieve in ecosystems requires evolution of appropriate transformations
within and between different energy forms
(Odum, 1983). The transformation of energy to
perform work is correlated with the amount of
exergy available (stored or in passage) in the
system. The more exergy stored, the more is available to be drawn on for work at a later stage,
which requires conversion from storage to
throughflow. In order to achieve storage, however, there must first be boundary flows (inputs)
to sequester. Ecosystems must therefore contain
balanced mixes of diametrically opposed quantities, storages and flows. Throughflow and storage
are nominally inversely related (see Section 2.5).
One can be traded for the other, as determined by
the composition of organic ‘stores’ and biotic
‘storers’ and ‘processors’, which in aggregate determine whole-system turnover. Rapid turnover
S.E. Jørgensen et al. / Ecological Modelling 126 (2000) 249–284
decreases storage and increases throughflow, and
vice versa. A nice link between exergy storage and
work performance was demonstrated for two
lakes with significantly different levels of eutrophication by Salomonsen (1992). He showed
that the exergy/maximum power ratio was approximately the same in both cases. It should be
noted that throughflow and storage are inverse
quantities, one exchangeable for the other, only
when considered in a local sense. In later discussion of what we shall term ‘network aggradation’,
illustrated in Fig. 11, we will show how in a global
(whole-system) perspective both these quantities
can become directly related, and thus jointly maximize, in consequence of network organization.
261
studies. Aoki (1988, 1989, 1993) compared entropy production, which reflects exergy utilization, in terms of maintenance versus exergy
storage in different lake ecosystems. He found
that eutrophic lakes capture and store more exergy, then subsequently use it for maintenance.
This is consistent with the general observation
(e.g. Jørgensen, 1982; Salomonsen, 1992) that eutrophic lakes have more biomass, thus more
stored exergy, but following on this also greater
throughflow and dissipation, though less specific
dissipation, than mesotrophic or oligotrophic
lakes. Biomass-specific exergy, in other words,
decreases with increasing eutrophication.
4.4. Maximum emergy
4.3. Minimum specific entropy
Mauersberger (1983, 1995) proposed a ‘minimum entropy principle’ as an extension of the
principle of least specific dissipation from nearequilibrium thermodynamics (Prigogine, 1947).
Johnson (1990, 1995) investigated least specific
dissipation over a wide range of ecological case
Odum (1983) introduced another goal function,
‘embodied energy’, later contracted to emergy.
Fig. 3 shows the idea behind this concept. Embodied energy is the energy (referenced to the
ultimate solar source) required to construct components in systems at different network distances
from boundary inputs. Everything is expressed in
Fig. 3. Illustration of the concept of emergy (embodied energy), measured by transformity expressed in solar EmJ (‘EmJoules’).
262
S.E. Jørgensen et al. / Ecological Modelling 126 (2000) 249–284
solar energy equivalents. For example, the upper
diagram of Fig. 3 shows energy flows (kJ/m2h) in
a typical food chain operating at 10% transfer
efficiency. The middle diagram shows the reference basis (1000 kJ/m2h boundary inputs). This
becomes the numerator, and the link flows in the
first diagram the denominators, in the calculation
of downpath ‘transformities’ (bottom diagram).
These provide the measure embodiment: 1000/
1000, 1000/100 1000/10, 1000/1 kJ/J. The emergy
increases with distance from the source, reflecting
the system organization that must be in place in
order for the components in question to be synthesized. This is decidedly a systems measure of
‘growth’, because its implicates the whole system
in the production of its individual units. The
specific provenance of all elements in the system is
captured and expressed in energy terms. Though
exergy and emergy are conceptually and computationally very different quantities, and though
emergy calculates how much solar energy it costs
to build a structure whereas exergy expresses the
actual work potential for growth once built, the
two measures correlate well when computed for
models (Jørgensen, 1994b).
4.5. Ascendency
Another network measure of whole-system contributions to growth and development is ascendency (Ulanowicz, 1986, 1997). According to this
theory, in absence of overwhelming external disturbances living systems exhibit a propensity to
increase in an ‘ascendent’ direction. This direction
is given by the ascendency measure, which is the
product of energy or matter throughflow through
the system (extensive measure) and the mutual
information content inherent in its pathway structure (intensive measure). As ascendency is also
well correlated with stored exergy (Jørgensen,
1994b), maximizing ascendency is similar to maximizing exergy storage. The relationship is not
straightforward, however. Considering Example 6
presented earlier, increased cycling at steady state
increases both the throughflow or storage that can
be derived from boundary inputs (Patten et al., in
prep.). One is traded for the other, depending on
the composition of components, which determines
system turnover. Rapid turnover decreases storage and increases throughflow, and vice versa. As
ascendency is dominated by its extensive variable,
throughflow, if this is maximized then storage
must be sacrificed accordingly in the steady-state
relationship. But, as throughflow and storage are
closely coupled, if throughflow is maximized then
so necessarily is the storage to which this may
contribute. Conversely, the greater the storage in
a system, the more of this there is available to be
converted to throughflow as circumstances warrant. Maximization of ascendency, a measure
heavily dominated by throughflow, can thus be
taken as generally consistent with the exergy-storage hypothesis.
4.6. Maximum dissipation
Schneider and Kay (e.g. Kay and Schneider,
1992; Schneider and Kay, 1994a,b) have proposed
an ‘extended version’ of the second law of thermodynamics as an organizing principle for
systems:
Exergy dissipation hypothesis. Given an input of
exergy, thermodynamic systems will use all
means available to degrade this exergy as fully
and quickly as possible.
This is an important idea, as controversial as it
is paradoxical because it invokes ‘destruction’ as a
prior basis for ‘construction.’ That is, it gives
primacy to entropic processes of tearing down
and wearing away rather than, as does the exergystorage hypothesis of this paper, to negentropic
building up.
The basic relationships behind Schneider–Kay
can be seen by considering a biological system
with one or more means of exergy capture, such
as photosynthesis or allochthonous import, Excapt,
and some work-producing mechanisms that degrade and dissipate exergy, such as respiration,
evapotranspiration, and others encountered in different kinds of ecosystems, Eresp + evap + … Then,
although exergy is nonconservative in an ultimate
sense (for example, the weighting factors of Eq.
(19) can change, reflecting improved machinery
for extracting work from energy), a valid balance
S.E. Jørgensen et al. / Ecological Modelling 126 (2000) 249–284
equation can still be written for immediate relations (i.e. with fixed bi ):
DExcapt = DExbiom +DExresp + evap + …
(ML2T − 3)
(23)
Here, DExcapt is the exergy captured by the system
per unit time, DExbiom is the exergy stored (accumulated) as structure per unit time, and DEresp +
evap+ ... is the exergy degraded to heat per unit
time.
Note that these quantities are all energy flows
per unit time, that is, they are differential quantities with the dimensions of power measured in
units that include time, for example kJ/m2d. Such
quantities cannot increase indefinitely. There are
upper limits. For example, it is impossible to
capture all the available solar radiation (or even
85–90%) because of physical constraints. Photosynthetic efficiency is typically only a few percent,
though ice algae coating the dimly lighted under
surfaces of pack ice may achieve \ 50% efficiencies. Szargut et al. (1988) demonstrated that the
ratio of a system’s exergy flux to that of solar
radiation (expressed in J per unit area and time) is
93.27%; for present purposes, this can be taken as
a theoretical absolute upper limit for exergy capture. Since available solar exergy per unit of time
is thus bounded, and because dissipation rises early
in Form I growth to a maximum, exergy degradation per unit of time is not an appropriate descriptor of long-term development of ecosystems. For
this, a measure based on integration of flows over
time is needed. Exergy storage is such an integrated
quantity, measured in units that do not include
time, for instance kJ/m2. Therefore, in principle,
storage has no upper limit and should be able to
increase indefinitely as small increments from each
new day’s allotment of incoming solar exergy.
However, in ecosystems there are catabolic costs to
storage just as in economic systems there are costs
of maintaining inventories. In general, these may
be considered as directly proportional, but at
decreasing rates, to storage quantities. Therefore,
if stored exergy can increase indefinitely then so
can dissipated exergy, but usually this occurs in a
manner to produce least-specific dissipation (that
is, the denominator, storage, increases faster than
the numerator, dissipation (see Section 4.1).
263
Schneider and Kay would hold, in the terms of
this example, that systems will maximize DEresp +
evap+ …, the dissipative component. By comparison, the central hypothesis of this paper claims that
it is exergy storage, Exbiom(t)= R Exbiom(t)dt, that
is maximized. The following facts on the surface
would seem to deny this hypothesis. Usually, in
biological systems, except in early growth stages,
only a small part of the exergy captured per unit
of time is utilized to build new structure, DExbiom.
Most of DExcapt is rapidly degraded to heat. Therefore, DEresp + evap + … is the dominant term on the
right-hand side of Eq. (23), and by this Schneider–
Kay would seem supported: DEresp + evap + … DExbiom. But the situation is more complicated
than this. First, heat dissipated from the ecosphere
can do little or no work referenced to a 300 C
planetary surface. Its exergy can only rise by
passage to the 3 C vacuum of space, and in fact
heat transfer to space removes the last term of Eq.
(23) from any further local significance. It is gone
and forgotten. But, DExbiom stays in place, and in
place is available to accumulate over time to
produce the storage, RExbiom(t)dt, that the working
hypothesis of this paper says is maximized. And as
it is maximized, continually over time, the
gradient between it and any reference system grows
such that to maintain it requires increasing work,
which requires increasing sources of exergy, use of
which occasions even more heat dissipated to space
than otherwise would have occurred in the same
amount of time in absence of accumulating storage.
Exergy storage then, our nominal goal function,
may be seen as one of Schneider and Kay’s ‘all
means available’ to maximize dissipation. This
would make the argument between proponents of
maximum dissipation and maximum storage moot.
Both are mutually entailing: anabolic production
of more storage increases dissipation, and more
storage requires more catabolism (dissipation) for
maintenance. Which comes first in the recursion is
a chicken-and-egg proposition. We give priority to
storage over dissipation because, beginning
with the Big Bang (Patten et al., 1997), mass–
energy had to come into existence and be
conserved before its thermodynamic states could
begin to be degraded. There must have been
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S.E. Jørgensen et al. / Ecological Modelling 126 (2000) 249–284
something to dissipate in the first place. On the
other hand, growth in exergy storage after the
initial conditions could not occur without prior
entropy-generating work. So, the paradox in our
hypothesis produces an impasse. Both Schneider–
Kay and Jørgensen – Mejer are correct, it would
seem, depending on where the ongoing…“ storage“dissipation“ storage “ dissipation “ … recursion cycle is entered. Truly, neither has
precedence over the other in contemporary time;
they are two sides of the same coin. In the long
run, however, exergy storage is the better measure
for the reasons given, especially that dissipation,
which cannot exceed exergy captured, rises
quickly in early-stage growth (Form I) to a theoretical maximum of about 85% of surface solar
radiation where it remains, whereas exergy storage can continue to increase indefinitely. This
implies that later-stage growth of a maturing
ecosystem to throughflow (Form II) and organization (Form III) cannot be described by exergy
dissipation, but can be described by further increases in exergy storage. This will be elaborated
further in the next section.
The
approximation,
DEresp + evap + … :
DExcapt × Exbiom(t), resulting from integration of
DExbiom, determines: the quantity of accumulated
structure, how much exergy the system has in
stock for later consumption, how much exergy it
can capture per unit time in the future, and how
much exergy is dissipated doing the work of
maintenance. It becomes apparent that delaying
dissipation by holding received exergy back in
storage gives rise to greater dissipation later, this
to greater storage, this to still further dissipation,
etc. in an ascending spiral of the two opposed
categories. The outcome of the spiral is system
growth, of all three forms as defined in the
Introduction.
4.7. Goal-function consistency
Finally, the generally consistency with one another of all the goal functions of this section can
be noted (Fath et al., in prep.). The relationship
between biomass and exergy storage is obvious
(Eqs. (19) and (21)). Minimum specific entropy
follows from maximizing the implied denomina-
tor, storage, even if dissipation in the numerator
is maximized. In fact, least specific dissipation,
which bears the imprimatur of far-from-equilibrium thermodynamic theory (Prigogine, 1947),
could be looked upon as another property giving
the weight of priority to storage (denominator) as
opposed to dissipation (numerator) in the above
discussion. Maximum emergy would result from
the same kind of network characteristics (especially cycling) that contribute to maximization of
throughflow or storage in response to given
boundary inputs. Maximum ascendency, in its
throughflow component, would follow any increase in internal flows attending maximum dissipation, and in its mutual information component
would follow, through the bi ’s of Eq. (17), any
increases in exergy storage.
In conclusion, initially different concepts about
how energy and matter are related to one another
in complex systems organization turn out to be
merely nuances in expression of the same central
phenomena, which at base are local negentropy
production (exergy storage), and opposing but
enabling entropy production (exergy dissipation).
5. Growth and development of ecosystems
5.1. Hypothetical entropy principle
Aoki (1998) recently proposed what he termed
a ‘hypothetical entropy principle’ for living systems, from organisms to ecosystems, which accounts for entropy production at different stages
in the growth and development of dynamical systems. Entropy production starts low, increases
during development, attains highest levels during
maturity, then declines with senescence. Thus,
dissipation increases in growing states, is maximal
for mature states, and decreases with degrading
states.
5.2. Succession in state space
Employing the simple model of Eq. (23) and
related text, the last section, ecosystem growth
and development can be described in exergy terms
as illustrated by the state-space-model sequence
S.E. Jørgensen et al. / Ecological Modelling 126 (2000) 249–284
265
Fig. 4. Elements of system transition dynamics as expressed by the state-space model of dynamical change. Change of state is defined
by the state transition function, f, operating on the current state of the system, x(t), together with the input variable, z(t). The
response function, r(t), generates output, y(t), by operating on the same two variables.
shown in Fig. 4. For background in this series on
the state-space formulation of dynamics, see Patten
et al. (1997). The boundary input z(t) = DExcapt(t),
a forcing function, represents source exergy derived
from incident solar radiation fixed in photosynthesis at time t. The boundary output, y(t) =DExresp +
evap+ …(t), is the exergy degraded in respiration
and evapotranspiration to do the work of maintenance. Dx(t)=DExbiomD(t) is the change in exergy
storage at different times t, and x(t)+
DEx(t)Dt = DExbiomD(t)dt is its time integral
representing the standing biomass of component
species and the information in their genes Eqs.
(19)–(22)). Fig. 4 shows a 2-step input–state–output sequence representing changes of state, …
x(t)“x(t+ dt)“ x(t+ 2dt)“ …, and outputs, …
y(t)“ y(t+ dt)“ y(t+ 2dt)“ …, beginning with
time t] t0 and initial state x(t0), in response to
external inputs, z, internal states, x, the system’s
state-transition function, f, and its response or
output function, r. The state variable, x(t), changes
to reflect the amount of exergy accumulated.
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5.3. Exergy trends in succession
Successional development of ecosystems
(Odum, 1969) exemplifies how exergy storage and
utilization are reciprocal concepts. We will notate
the typical stages of terrestrial succession following initial conditions (Stage 0) with roman numerals. This will relate the stages to an empirical
model of ecological dynamics discussed below,
and both of these to the formal state-space model
which underlies them and makes succession a
lawful, rather than ad hoc, growth process. The
discussion will be for an idealized case, as depicted in the modified curve of sigmoid growth
shown in Fig. 5.
5.3.1. Initial condition (0)
Ecologists distinguish between primary succession which starts on bare rock and recently
weathered inorganic parent material, and secondary succession which proceeds on mixed inorganic–organic
substrates
after
later-stage
communities have been reset by disturbance to
some earlier stage. Biotic free energy can be taken
as zero in primary succession, and in secondary
succession it is greater than zero but more or less
recently reduced by disturbance.
Fig. 5. Exergy utilization of a system as a function of exergy
stored, including both biomass and informational components.
The units (kJ, m and d) are arbitrary. For a similar curve
pertaining to ascendency measure, see Ulanowicz (1997), p. 87,
Fig. 4.9).
5.3.2. Early-to-middle succession (I)
This is a period when growth and development
increase at increasing rates. In Fig. 5 it extends
from the initial state to the inflection point of the
sigmoid curve. The second derivative is positive in
this region such that the curve is concave upward,
indicating accelerating growth. An early Stage I
ecosystem has only a small amount of stored free
energy, and also low utilization because its capacity and need for work have not yet developed.
The interactive network is underdeveloped, so
direct relationships are dominant and indirect/direct effects ratios small. Biomass is relatively
small, structure simple, gradients slight, niches as
yet underdeveloped, and only a little exergy is
required for maintenance metabolism and initiation of growth as these processes proceed in proportion to existing biomass. The total surface area
of plants is small relative to available space, so
autotrophic photon capture is also small. The
organisms are functionally and phylogenetically
primitive (atracheophytes, colonizers, ruderals)
reflecting both low environmental and genetic
diversity.
In the transition from early to middle phases,
all these properties change in maturing directions
at generally increasing rates: boundary inputs (exergy capture), biomass (exergy storage, mass component Eqs. (19) and (21)); physical structure
(exergy storage, information component Eqs. (19),
(20) and (22)), network development and connectivity, throughflow (exergy internal distribution,
providing intrasystem inputs and outputs),
metabolic and other work for maintenance,
growth, and development (exergy utilization and
dissipation), and boundary outputs (dissipative
exergy loss and degradation). This latter process is
dominated by the ‘detritus pathway’, which has
been extensively studied both in aquatic and terrestrial systems. Gradients, niches, plant-specific
surface area, representative guilds and phyla, and
environmental and genetic diversity all steepen,
expand, or increase, and the ratio of storage-specific exergy capture to storage itself (i.e. the second derivative) increases (Fig. 5). All three growth
types described in Section 1 occur and increase
during Stage I succession, but because boundary
inputs typically expand faster than boundary out-
S.E. Jørgensen et al. / Ecological Modelling 126 (2000) 249–284
puts making exergy capture exceed dissipation,
Form I growth dominates the early to middle
phases of ecosystem development.
5.3.3. Middle-to-late succession (II)
This period spans the distance in Fig. 5 from
the inflection point to the onset of the upper limit
of growth. This upper limit (Stage III, below) is
analogous to a population carrying capacity; it is
in fact the carrying capacity of the environment
for all populations under the set of evolved conditions. Growth and development still increase, but
at decelerating rates such that second derivatives
are negative and the development curve is concave
downward. As the system matures, its structure
becomes more complicated. Niches and genomes
diversify, interactions expand the complexity of
networks, gradients steepen, and under the
Schneider–Kay impetus to erase these, biota of
more advanced kinds phylogenetically and functionally become supportable. ‘Which comes first,
the niches or the biodiversity?’ is another form of
the chicken-and-egg question we have been asking
in this paper at the thermodynamic level. Complexification is reflected in greater gene frequency
and density, as well as greater environmental
(niche) frequency and density, which confer increasing biomass-specific information upon the
developing ecosystem even though biomass (the
denominator in ‘biomass-specific information’)
per square meter continues to increase.
Particularly noteworthy during mid- to late-successional growth and development is the diversification and steepening of free-energy gradients
referenced to thermodynamic equilibrium (Kay
and Schneider, 1992). Biomass, niches, species
diversity, spatial heterogeneity — all these and
the other attributes that contribute grain to
ecosystem structure — manifest and are manifested by gradients. The second law mandates that
these be broken down, and the Schneider –Kay
rendering of this law says that this should occur
as rapidly as possible utilizing ‘all means available.’ The forces for breakdown increase with the
gradient strength, which reflects distance from
equilibrium, so wherever gradients are steepest
these are sites where biological activity, as agents
of breakdown, can be expected to be greatest. So,
267
the field ecologist finds greatest biodiversity associated with edges, ecotones, riparian and coastal
zones, etc., wherever ecosystems of different descriptions intersect. Gradient breakdown is therefore a property with broad manifestations to be
expected in many of the developmental trends in
ecosystems. A number of the 20 orientors of
Kutsch et al. (1998) listed further below have
obvious gradient-breakdown connotations. The
mechanisms of respiration and evapotranspiration
in our earlier simplified example expend exergy to
do constructive work and produce entropy, and
gradients are leveled in the process in the form of
biochemicals catabolized and energy dissipated to
surroundings. As long as the supply of free energy
in solar radiation continues, dissipative losses can
be made up and the system can maintain or
increase its position far from equilibrium. More
exergy is captured than needed for gradient
maintenance, and the surplus is registered as
stored exergy. The system thereby moves further
from equilibrium and increases the gradient still
more. This ‘antientropic’ or ‘negentropic’ direction, toward structure, grain, order, and organization as reflected in gradients, is the essential
dynamic of any growth process, expressed in thermodynamic terms.
In summary, all the trends of Stage I succession
continue during Stage II, but at generally decelerating rather than accelerating rates. Exergy capture at boundaries, now closer to the Szargut et
al. (1988) maximum of 93.27% of insolation, continues to increase as photosynthetic and other
albedo-reducing biomass and structure expand in
response to steepening gradients to fill diversifying
niches. But because boundary dissipation also increases, Form I growth decelerates in Stage II
succession. This is compensated by a widening
internal distribution, reflected in greater
throughflow, which is due more and more to
cycling. The result is that both Forms II and III
growth increase in importance as maturity approaches. Then, as mass-specific work continues
to increase but at decreasing rates, so therefore do
specific exergy use and dissipation as these approach maximum attainable levels. These relationships are all implied in Fig. 6.
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S.E. Jørgensen et al. / Ecological Modelling 126 (2000) 249–284
Fig. 6. Exergy utilization of a developing ecosystem over time.
A consequence of growth in exergy is an increased requirement
for maintenance.
5.3.4. Climax attractor (III)
Passage from late succession to a dynamic
steady state is the natural outcome of antientropic
development. This is the ecologists’ ‘climax’ condition. Climax ecosystems have become controversial with the recognition that they may not
exist for long in ecospheric time because episodic
disturbances, long-term climatic changes, or
senescence generally cause perturbation or drift
away from established mature conditions. However, as with all state-space dynamical systems
which universally develop directionally in a standard sequence of states from initial through transient to steady states (Patten et al., 1997),
succession of communities in ecosystem seres also
proceeds from initial conditions (‘primary’ or ‘secondary’, as classically distinguished) through succession (transient) to the climax (steady) state. A
mature ecosystem has a high concentration of
biomass (Eq. (21)), meaning steepened gradients,
much information distributed in a wide variety of
organisms (Eq. (22)), including higher organisms,
and diverse genetics and niche and guild development manifested in complex structure, and wellorganized food webs and other interactive
networks. Important indirect effects manifested
by network cycling are a paramount feature of
this stage. The amount of information may con-
tinue to grow indefinitely due to immigration and
establishment of other species, and emergence of
new genes or genetic combinations. Entropy production is maximal, or nearly maximal and continuing to grow, reflecting high costs of
maintenance. Work must be done continually to
maintain the organized structure with its gradients, niches, and biodiversity. The mature system
stops adding biomass when a limiting substance
(nutrients, water, etc.) is either scarce or has been
sequestered in existing pools or structures. At this
point, mass contribution to further exergy increase (Eqs. (19) and (21)) ceases and cycling
comes to regulate subsequent development in
which repair and replacement of lost or damaged
constituents is controlled by regeneration rates.
For example, if water becomes limiting xeric species will enjoy an adaptive advantage and tend to
replace more mesic and hydric forms in proportion to the extent of dryness. By the balance
between limitation (e.g. immobilization) and facilitation (release), mature ecosystems tend to and
perpetuate over relatively long periods of time the
dynamic steady states known as climax communities. Information and organization, hence exergy
accrual (consistent with our working hypothesis,
and Jørgensen–Mejer; Eqs. (19), (20) and (22))
continue indefinitely after primary exergy capture
and dissipative entropy production (Schneider–
Kay) have reached their practical absolute maxima. As a result, storage-specific entropy
generation becomes a minimum, corresponding to
the least specific dissipation principle from thermodynamics (Prigogine, 1947), and biomass-specific exergy storage becomes a good goal function
or orientor to associate with Stage III maturity.
The steady state does not last forever, because the
second law enforces ultimate decline of both organization (derived from Form III growth) and
structure (i.e. storage and throughflow, derived
from growth Forms I and II), and Stage IV
ensues.
5.3.5. Senescence and creati6e destruction (IV)
The climax state, if reached, is subject to longterm processes of aging, spontaneous decay, and
destructive disturbance. The latter has been referred to as ‘creative destruction’ because it is
S.E. Jørgensen et al. / Ecological Modelling 126 (2000) 249–284
always followed by a ‘renewal’ phase (Holling,
1986). In the extended and indefinite phase of
‘old-growth’, all the above-described attributes associated with maturing and maturity decline. Natural disturbance by fires, floods, storms, or
volcanism are important sources of creative destruction. When a forest is burned, for example,
complex organic compounds are converted into
simpler inorganic ones (Botkin and Keller, 1995).
Some of the latter are lost as particles of windblown ash or as vapors that escape into the
atmosphere and become widely distributed. Others are deposited on the surfaces of vegetation,
soils, or water bodies. These compounds are
highly water soluble and readily available for
uptake by vegetation and phytoplankton. Therefore, immediately following a fire there is an
increase in availability of chemical elements,
which are rapidly incorporated into biological
tissue. The pulsed release of inorganic nutrients
produces a pulse in plant growth, which then
ripples through subsequent trophic levels and ultimately propagates throughout the entire food
web. New opportunities to depart further from
thermodynamic equilibrium are thereby created,
and this explains how natural disturbances, so
deleterious in the short run, can have long-term
positive effects on ecosystem health and vitality.
Fig. 7. Holling’s four phases of ecosystems, described in terms
of biomass vs. specific exergy. Modified after Ulanowicz
(1997), p. 90, fig. 4.11).
269
They are nature’s way of breaking the cycle
ofnormal state-space development toward static,
and stagnant, steady states and initiating new
pathways of renewal.
Holling’s ‘lazy-8’ model of ecosystem dynamics
is interesting in this regard (Holling 1986). It
recognizes four phases in the life cycle of ecosystems arrayed as a figure-8 on its side: (I) renewal,
(II) exploitation, (III) conservation, and (IV) creative destruction (Fig. 7). The roman numerals
here correspond more or less to those in the
successional sequence outlined above, and also in
the state-space model sequence discussed below.
Kay (1984) discussed Holling’s model in thermodynamic terms. So did Ulanowicz (1997), and Fig.
7 is a modification of his version which is asymmetric compared to the original due to different
interpretations of what constitutes ‘renewal.’
Ulanowicz (pp. 89–90) writes, ‘‘Holling identified
renewal as the breakdown of biomass by biological and physical agencies that slowly releases nutrients. Renewal in our narrative is assumed to
follow perturbations, like fire, that very suddenly
destroy both organization and biomass, releasing
nutrients in the process.’’ The x-axis in Fig. 7 is
biomass-specific exergy while in Ulanowicz’s presentation it was mutual information of the flow
structure. The basic idea is, however, the same.
The y-axis is biomass in both cases, which (Eqs.
(19) and (21)) is proportional to exergy storage.
The exploitation phase (II) corresponds to rapid
increase in the information component of exergy
(Eqs. (19), (20) and (22)). The conservation phase
(III) is marked by a very slow increase in both
biomass and information. In creative destruction
(phase IV) both the biomass and information
components crash, but thereby new possibilities
arise for resurgent growth. During the renewal
phase (I), biomass and information both increase
rapidly. After each round of the Holling cycle
total-system biomass cannot increase much due to
limiting factors, as discussed above. But the ‘creative’ element in creative destruction introduces
new environmental conditions and altered
genomes which can recombine to accelerate exergy and specific exergy increases more than
would be possible without the Holling cycle. Creative destruction, then, aligns quite nicely with
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Fig. 8. Differences between early and mature stages of an
ecosystem. Young systems reduce reflection of solar radiation
by increasing their stored exergy (structure). Mature ecosystems require more exergy for maintenance due to their more
developed structure. Total exergy storage can only be increased by reducing the amount used for maintenance of the
increasing structure, as the reflected part cannot be reduced
(much) further due to physical constraints.
Schneider–Kay maximum dissipation in being a
necessary antecedent, or at least concomitant, of
‘creative construction’ in the form of Jørgensen–
Mejer maximum exergy storage, the working hypothesis of this paper.
5.4. An editorial aside…
Modern thinking in ecology questions whether
climax systems ever exist. Whether climax states
are reached and persist (in mono-, poly- or disclimax phases at the landscape scale), or communities are reset by perturbation back to earlier
successional stages, is irrelevant to the central
issue of this paper, how ecosystems grow and
develop. They always develop in a continuum of
stages toward a final attractor: initial state (0)“
transient (nonrepeating) states (I, II)“steady (re-
peating) states (III), which the forces of
dissipation then proceed to unravel in longer-term
senescence (IV). The roman numerals here correspond to those used above for ecological succession and the Holling cycle, to show that these
processes conform to formal state-space dynamical theory. They are manifestations, in other
words, of the way energy and matter universally
become organized, and to realize this is to place
empirical observations about ecological change
within the broader body of general scientific understanding rather than have them stand as isolated, disconnected facts. That early ecologists
like Clements and Shelford discerned this pattern
long before there was any system theory to frame
the processes of ecosystem growth in general
terms is eternally to their credit as acute, astute
observers of nature. The climax as a concept and
pattern does not require concrete expression and
realization in order to be understood as exemplifying the end state, or constellation of states,
toward which all dynamical systems trend in their
development. The mathematical concept of attractor applies well to give the ecological concept of
‘climax’ its true significance as the endpoint of an
unfolding standard dynamical process. Whether
the climax is ever or never actually reached or
sustained in nature is irrelevant to the fact of its
existence as an expression of underlying pattern,
that is, as Aristotelian formal (if not final) cause.
5.5. Ecological orientors
Another word for attractors might be the more
ecological concept of orientors, environmental
properties that guide system development and
adaptive responses (Bossel, 1977, 1998). We have
seen that early-stage ecosystems build free-energy
stores by increasing boundary capture, for example through decreasing initially high reflection
(Fig. 8a versus Fig. 8b), and by having high P/R
ratios and thus high net production (Fig. 8a,
showing large change in stored exergy compared
to Fig. 8b). The latter contributes to predominant
growth-to-structure, or Form I. Intermediate
stages build the increasingly complex networks
that take energy and matter around the system.
This is growth-to-throughflow, Form II. Mature
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ecosystems store exergy by minimizing inherently
high maintenance dissipation (Fig. 8b) and increasing information content. This is growth-toorganization, or Form III. Müller and Fath
(1998), fig. 2.1.1, p. 16) diagrammed the role of
orientors in the growth and development of ecological state variables. Kutsch et al. (1998), fig.
2.12.1, p. 210) aligned 20 ecological orientors
along a time line spanning pioneer to mature
stages. In their scheme, divided below into four
categories, development is seen to proceed over
time in the following directions:
“ Organisms: toward more K-selected species,
larger body sizes, longer lifetimes, and more
developed symbioses.
“ Matter: toward higher storage, higher biomass
(B), more biotic nutrient storage, more complex element cycles, longer residence times, and
higher flux densities.
“ Energy:
toward higher exergy storage
(Jørgensen–Mejer; this paper’s hypothesis),
higher total entropy production (Schneider–
Kay), but lower specific entropy production.
“ Systemic organization: higher production/
biomass (P/B) ratios, higher total-system respiration (R), lower metabolic quotient (R/B),
higher total information, higher spatial heterogeneity, more indirect effects, and higher
ascendency.
For organisms, fitness is the singular goal function of evolutionary biology. As organisms compete for resources and living space, they invent
thousands of new and ingenious ways to improve
their survival and distribute their genes to the next
generation (Reeves, 1991). Some species invest in
movement; speed can be a valuable asset both in
capturing prey and avoiding predators. Others use
protective armor or chemical poisons. The innovations are endless. Under state-space organization, each species randomly ‘proposes’ from its
current state the terms under which it would meet
the future conditions of life, and the environment
‘disposes’ in the form of natural selection. The
feedback hones adaptations that buffer environmental uncertainty, and specializations that allow
adaptive radiation into evolving niches. All the
adaptations and specializations are work requiring, and all the accumulated biomass and infor-
271
mation of the ecosystem are work-enabling since
(Eqs. (19), (21) and (22)) they correspond to
stored exergy. The whole ecosystem can, by the
selective pressures it directly and indirectly exerts,
be taken as an attractor or orientor that canalizes
development.
One of the most general organismal expressions
of this is transition from r to K species. Evolution
of many taxonomic groups has been towards
larger body size (Raup and Sepkowski, 1982),
entailing more stored exergy and higher energy
demands per organism, but less degradation relative to storage. Specific exergy dissipation decreases. Organisms of r-type are smaller in their
group, and have higher turnover and resource-exploitation rates; K-type organisms are larger,
slower, and have less specific exergy to support.
Succession from r to K forms occurs in microbial
communities (Gerson and Chet, 1981). In mature
ecosystems, K-type plants produce litter poor in
nutrients and simple sugars but high in lignin in
comparison to r-species (Heal and Dighton,
1986). These differences alter the physicochemical
characteristics of soil, which ripples through all
levels of the ecosystem. Shift from r to K species
in succession is a process with manifold indirect
effects.
Model
systems
reinforce
these
observations.
Cross-scale recursions occur in ecosystems as
reciprocal constructive and destructive relationships (Ulanowicz, 1997). For example, behind
biodiversity is the Schneider–Kay dictum to
break down environmental gradients. Breakdown
agents (organisms—exergy storage units) are produced by performing work (expending exergy) at
biochemical and cellular levels. The constituted
organisms do work in both hierarchical directions, tearing down gradients to build ever steeper
ones as ecosystems on the one hand, and deconstructing and reconstructing ever more biochemicals, cells and cell types on the other. This is
‘adaptive radiation’ fanning out in two directions,
both negentropic: (1) a centrifugal spiral or recursion process from inner analysis (cellular and
biochemical breakdown) to outer synthesis
(ecosystem construction), and (2) a centripetal
spiral or recursion from outer analysis (environmental gradient destruction) to inner synthesis
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(cell and biochemical buildup). The organism
thereby becomes a self-maintaining, self-sustaining, reciprocating autocatalytic and autodegradative system at medial levels within ecosystems.
Parallels with human systems are instructive:
5.5.1. The urban ecosystem
Towns and cities undergo the same four phases
and three forms of growth and development as
outlined above for ecosystems. Early, growth-tostorage (Form I) dominates in the initial laying
out of structures and infrastructure to enable
distribution of goods and services to inhabitants.
Later, growth-to-throughflow (Form II) dominates the middle stages as the channels for human
intercourse expand and reticulate. Growth-to-organization (Form III) is the maturing phase in
which activity becomes increasingly determined
by information. In ecosystems, catabolic demands
represent the free energy needed to maintain distance from thermodynamic equilibrium, and are
proportional to the total biomass and systemic
organization maintained. The same is true for
towns and cities. A large city with many buildings
and infrastructure of diverse kinds requires much
more energy for maintenance and operations per
capita (Fig. 8b) than a small village consisting of
a few similar farm houses requiring only basic
services (Fig. 8a). A skyscraper in a peasant village would be unsupportable and dysfunctional, a
vertical slum, and for the same but inverse rea-
sons simple dwellings such as seen in the slums
and shack-towns of large metropolises exist on the
fringes of the information flow that dominates the
life of the metropolitan mainstream. Urban decay
is all too familiar in the cities of the world as
examples of the fourth senescent phase that, usually for too long, precedes urban renewal (‘creative destruction’). Altogether, the urbanization
of humanity entails parallel processes and orientors to those previously discussed for ecosystems,
and these have similar systemic and thermodynamic requirements as those for natural systems.
5.5.2. Economic systems
Again, the same four developmental phases and
three forms of growth can be recognized in the
typical dynamics of economic systems and cycles.
When a business or country is first under development, it is important to invest in inventory, production facilities, and infrastructure, representing
Form I growth. After establishment, attention
should be turned to expanding sales and purchasing networks and increasing turnover. This means
retarding storage and increasing circulatory flows
(Form II), both boundary and internal, to achieve
the economic equivalent of maximum power.
Turnover is of course dependent on investment
already made. In the long run the enterprise or
nation making the most useful investments for the
circumstances, which are the orientors, will be in
the best position for competition. As maturity
approaches, investment in education and information (Form III) becomes crucial to future viability
in a changing economic environment.
6. Supporting evidence
Fig. 9. Biomass-specific exergy capture as a function of stored
exergy over time. The units (kJ, m and d) are arbitrary.
The essentials of exergy relationships in ecosystem growth and development as presented in the
preceding section and Figs. 5–8 are summarized
in the generalized sketch shown in Fig. 9. It is
difficult to obtain data from a single study or site
to support all the implications, but deductive inferences about likely relationships can be made
from widely spaced observations on ecosystems of
different types in different stages of development,
or at different seasons, and also from models. We
S.E. Jørgensen et al. / Ecological Modelling 126 (2000) 249–284
Table 3
Exergy utilization and storage in a comparative set of ecosystems
Ecosystem
Exergy
utilization (%)
Exergy storage,
MJ/m2
Quarry
Desert
Clearcut forest
Grassland
Fir plantation
Natural forest
Old-growth
deciduous forest
Tropical rain forest
6
2
49
59
70
71
72
0
0.073
0.594
0.940
12.70
26.00
38.00
70
64.00
Fig. 10. Percent exergy capture versus exergy stored (MJ/m2d),
calculated from characteristic compositions of eight focal
ecosystems (Kay and Schneider, 1992. The numbers from
Table 3 are applied to construct this plot.
explore these three avenues in the remainder of
this section.
273
store the most. Recall, from Szargut, et al. (1988),
that the theoretical upper limit for exergy capture
is 93.27%. The eight data points in Table 3 are
plotted in Fig. 10; their relationship to Fig. 9 is
unmistakable. Only, in Fig. 10 the sequence represents a composite assembled from different places
and times over the globe. One can visualize in the
figure an imaginary progression through time
from an ‘initial condition’ (0, the origin), through
‘transient states’ (I, desert and quarry; II, clearcut
and grassland), to several examples of ‘steady
states’ (III, forests). Even ‘senescence’ is hinted at
in the last data point (IV, rainforest). Exergy
utilization rises faster than storage for the first
four points (which represent r-selected systems),
and then approaches and recedes from an upper
asymptote in the last four (K-selected). As previously indicated, after exergy degradation attains a
maximum at around 70% of solar input (i.e.
DExresp + evap + … 0.7DExcapt in the notations of
our equations), storage ( ExbiomdDt) continues
to increase in the sequence from fir plantation to
tropical forest. The 9 70% value of Fig. 10 is
considerably less than the Szargut maximum.
Consider the following rendering of the second
law of thermodynamics and the origin of structure
(exergy storage) by Ulanowicz (1997), p. 147):
[I]t is impossible in any irreversible process to
convert a given amount of energy entirely into
work without rendering some of it useless. The
connotation is that order is contingent, and
dissipation, inevitable. Nothing prevents us,
however, from casting the obverse and noncontradictory statement: ‘‘In any real process, it is
impossible to dissipate a set amount of energy
in finite time without creating any structures in
the process’’… Not only is the appearance of
structure ubiquitous, but, once having arisen it
can function as a cause in its own right.
6.1. The 6iew from space
Data from satellite measurements are encouraging. Table 3 shows the exergy utilization and
storage for a number of different types of ecosystems (Kay and Schneider, 1992). Forests utilize
and store more of the free energy in solar photons
than grasslands or deserts, and tropical rainforests
Comparative analysis of the Table 3 and Fig.
10 data suggests that structure, once created as a
correlate of dissipation which rises quickly to its
maximum, can serve recursively as cause in its
own right and act to further increase exergy storage in the four forest ecosystems. Dissipation-specific storage, in other words, continues to rise
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S.E. Jørgensen et al. / Ecological Modelling 126 (2000) 249–284
after the maximum rate of entropy generation
realizable for the conditions has been attained.
The rapid achievement of a dissipation maximum
in Fig. 10 accords with the Schneider – Kay hypothesis. Then, within the same 9 70% level attained, exergy storage continues to grow
consistently with the Jørgensen – Mejer — and
this paper’s — working hypothesis. Thus, remotely sensed data at the landscape scale suggest
the two hypotheses are conformable as a leastspecific dissipation goal function:
Least turno6er hypothesis. If a system receives
an input of exergy, it will use all means available to degrade this exergy as fully and quickly
as possible (Schneider – Kay) and, recursively
through the work performed and structure created, maximize its storage (Jørgensen – Mejer)
faster than the said dissipation such that its
storage/dissipation ratio, or dissipation-specific
storage or turnover time, will become a maximum also, or inversely, its storage-specific dissipation or turnover rate, a minimum.
Exergy storage has dimensions ML2T − 2 (Eq.
(2)), dissipation ML2T − 3 (power), and the storage/dissipation quotient, or turnover time, T.
Maximizing the storage/dissipation ratio is equivalent to minimizing dissipation/storage, which is
storage-specific dissipation, or turnover rate (dimensioned T − 1). The least exergy turnover hypothesis above is compatible with joint
maximization of both storage and dissipation, and
moreover is the equivalent of a principle from
far-from-equilibrium thermodynamics, namely
that of least storage-specific dissipation (Onsager
1931; Prigogine, 1947).
Based on previous developments, and now the
evidence from satellite imagery, we will adopt this
version of exergy storage (at rates faster than
dissipation) as an amended working hypothesis,
referring to it as the ‘least storage-specific dissipation’, or ‘turnover rate’, hypothesis, or equivalently, the ‘maximum dissipation-specific storage’,
or ‘turnover time’, hypothesis. Turnover rate at
maximum dissipation is minimized, and hence
storage of any realized magnitude is further maximized by extending its tenure through time.
6.2. The 6iew from seasons
In natural history it is often observed, particularly at latitudes where there are winters, that
taxonomically more primitive forms tend to pass
through their nondormant phenological states
earlier in growing seasons and more advanced
forms later. It is as though ecosystems must be
rebuilt after the ‘creative destruction’ of winter,
and until they are reconstituted the active life-history stages of more complex forms of life cannot
be supported. Do the exergy principles of this
paper shed any light on the annual activity cycles
of species and communities?
Phenological fluctuations of biota, in fact the
growth of individual organisms themselves, generally parallel the four stages of succession, and also
the three growth forms of this paper. This is true
for the progression of individual species and their
assemblages, and is best seen at mid to high
latitudes. Toward the tropics a great variety of the
life history stages of the rich assortment of species
is expressed at any given time. At higher latitudes
phenological cycles are more obvioulsy entrained
to seasonal fluctuations. Focusing at mid latitudes, and letting ‘time’ be relative to the unit in
question (i.e. biological time, whether for a species
or whole ecosystem), ‘winter’ represents the initial
condition (Stage 0). During ‘spring’, the growth
forms unfold in quick succession. Form I dominates early (Stage I), Form II later (Stage II), and
Form III in ‘summer’, which advances toward
seasonal maturity (Stage III). Ephemeral species
pass quickly through their own Stage III to seed
set, dispersal, senescence (Stage IV), and often,
disappearance. Permanent species remain more or
less in Stage III until near the end of the growing
season, when they or their parts pass into quasisenescent states (Stage IV), as in leaf fall and
hibernation.
Exergy storage and utilization patterns may be
intuited from the principles laid down previously
for succession (Figs. 5–8 and related text) to
follow these seasonal trends also, in mass (Eqs.
(19) and (21)), throughflow, and informational
(Eqs. (19), (20) and (22)) characteristics. In winter, biomass and information content are at seasonal lows. Referring to Fig. 8a, reflection
S.E. Jørgensen et al. / Ecological Modelling 126 (2000) 249–284
associated with high albedos is high and dissipation low; changes in stored exergy tend generally
to be low for those species which enter dormancy,
but those that remain active experience weight
and population losses so that aggregate system
change in stored exergy may be moderate (Fig.
8a) but negative. In spring, the flush of new
Table 4
A partial list of characteristics of developed ecosystems which
are in accordance with the exergy principles of this paper
Characteristics
Explanation
High biomass
To utilize available nutrients
and water to produce the
highest stored exergy
To maintain the system far
from thermodynamic
equilibrium
The system moves as far as
possible away from
thermodynamic equilibrium
To maximally utilize the flow
of exergy and resources
To utilize spacetime
heterogeneity to gain highest
possible level of exergy
To meet the challenge of
changing forcing functions
A consequence of the first
four characteristics
High respiration,
evapotranspiration and
other catabolic processes
Gradient development
High information content
High level of specialization
and differentiation
High level of adaptation
and buffer capacity
High levels of network
complexity and
organization
Big size of (some)
organisms
Highly developed history
High indirect/direct effect
ratio
Irreversible processes
Both bottom up and top
down regulation
Symbioses developed
Diversity of processes
To minimize specific entropy
production and thereby the
cost of maintenance when
exergy flow becomes limiting
Caused by all developmental
processes
A consequence of the
complex network
A consequence of system
history
To utilize all available
avenues to build as much
dissipative structure as
possible
Two or more species move
simultaneously further from
thermodynamic equilibrium
To utilize all available
avenues to build as much
dissipative structure as
possible
275
growth (dominantly Form I) produces rather
quickly a significant biomass component of exergy
(Fig. 8a), but the information component remains
low by the fact that most active flora, fauna, and
microbiota of this nascent period tend to be lower
phylogenetic forms. These rapidly develop
biomass but make relatively low informational
contributions to the stored exergy. As the growing
season advances, in summer, growth forms II and
III become successively dominant. Following the
expansion of system organization that this represents, involving proliferation of food webs and
interactive networks of all kinds, and all that this
implies, waves of progressively more advanced
taxonomic forms can now be supported to pass
through their phenological and life cycles. Albedo
and reflection are reduced, dissipation increases to
seasonal maxima following developing biomass,
and as seasonal maxima are reached further increments taper to negligible amounts (Fig. 8b). The
biotic production of advancing summer reflects
more and more advanced systemic organization,
manifested as increasing accumulations of both
biomass and information to the exergy stores. In
autumn the whole system begins to unravel and
shut down in preadaptation to winter, the phenological equivalent of senescence. Networks shrink,
and with this all attributes of exergy storage,
throughflow, and information transfer decline as
the system slowly degrades to its winter condition.
Biological activity is returned mainly to the more
primitive life forms as the ecosystem itself returns
to more ‘primitive’ states of exergy organization
required for adaptation to winter.
In summary, phenological progression in
ecosystems, when viewed through the lens of exergy relationships, bears unmistakable resemblances to the growth of organisms, succession of
communities, and evolution of taxa. All these
processes can be seen as proceeding on different
spacetime scales more or less under the exergy
principles of growth as outlined in this paper (see
Table 4 for a partial list). The suggestion from
phenology is that the exergetic principles of organization apply also to the seasonal dynamics of
ecosystems. Thus, it is perhaps not too much of a
leap across scales to suggest that, as in biology
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S.E. Jørgensen et al. / Ecological Modelling 126 (2000) 249–284
where ‘ontogeny recipulates phylogeny’ (biogenetic law), in ecology it may be further observed
from lower organisms functioning in underdevel-
oped ecosystems and more advanced ones in developed systems, that also, phenology recapitulates phylogeny.
Fig. 11. Comparison of energy throughflow (kJ/m2d) and storage (kJ/m2) relationships in two hypothetical networks at steady state,
respectively (a) without cycling and (b) with cycling. The networks can be viewed as food webs in earlier (a) and later (b) stages of
development. It is assumed for purposes of calculating three cases of storages that flows are first-order, donor-determined: Case 1,
all transfer rates equal 0.1 d − 1; Case 2, turnover rates are (0.1)ki d − 1, i =1,…, 4, where ki is the number of outflows from each
compartment; Case 3, turnover rates are (0.1)kl, where l= 1,…, 4 is the number of transfer steps (trophic levels) starting at
compartment 1 (x1). Boundary inputs of z1 = 10 kJ/m2d are derived from a virtual environmental reference storage of x0 =100
kJ/m2, and are equal to outputs. Compartmental throughflows are T1,…, T4, and their sums are total system throughflows. Storages
x1,…, x4 for the three cases are shown in sequence by case number at the top of each rectangle, and storage sums are similarly shown
with total system throughflows. The units (kJ, m and d) are arbitrary.
S.E. Jørgensen et al. / Ecological Modelling 126 (2000) 249–284
6.3. The 6iew from modeling
As used in this paper, Form I growth is growthto-storage and Form II is growth-to-throughflow.
The following quotation from the earlier section
on goal functions referred to the essential reciprocity of these two quantities: ‘‘Throughflow
and storage are inversely related…. One can be
traded for the other…. Rapid turnover decreases
storage and increases throughflow, and vice
versa.’’ Given that one quantity can be locally
converted to the other, it would be surprising if at
a global (whole-system) level the two could be
increased or decreased together. Yet, that is exactly what networks are mysteriously able to
achieve, according to an as yet unpublished new
property of connected systems, network aggradation (Patten et al., in prep.). That property is
briefly described below, referring to Fig. 11.
6.3.1. Aggradation-to-throughflow ( form II)
Fig. 11a shows a hypothetical steady-state energy-flow network with the lineal topology of a
food chain. If one can visualize the transient
dynamics of the compartments filling to steady
states from zero intial conditions (paralleling the
dynamics illustrated in Figs. 6 and 9), then it is
apparent that for the fixed structure shown (Fig.
11a) both Form I and Form II growth have been
concluded at steady state. An energy input of
z1 = 10 kJ/m2d (units arbitrary) enters compartment 1, generates a throughflow of T1 =10 kJ/
m2d, of which f21 =7 units are transferred to
compartment 2 and y1 =3 kJ/m2d are dissipated
to the system’s environment. Of the T2 =7 units,
f32 =4.9 and f43 =2.8 pass to the next two compartments to become T3 and T4, respectively, and
outputs y2 =y3 =2.1 kJ/m2d and y4 =2.8 are generated. The total boundary outflow is Syi =10
kJ/m2d, which balances the input and produces
the steady state. The total system throughflow is
STi =24.7 kJ/m2d, giving a ratio of STi/z1 = 2.47
units of internal throughflow generated for each
unit of boundary inflow. This is Form II network
aggradation. Patten et al. (in prep.) show that a
sufficient condition for it to occur is a single
binary interaction in the interior of a system. That
is, two compartments transferring energy or mat-
277
ter between them are the minimal requirement;
the system of Fig. 11 has four such compartments, so throughflow\inflow (aggradation) is
always assured.
In Fig. 11b four arcs representing low flows
(only 1 or 2 units, totaling 5 in all) are added.
These introduce three nested simple cycles of
lengths 2, 3 and 4 into the network topology:
2“1“ 2, 2“3“ 1“ 2 and 2“ 3“ 4“ 1“ 2.
Boundary inflows and outflows remain unchanged
at 10 kJ/m2d. But throughflows increase: T1 = 14,
T2 = 12, T3 = 8.9, T4 = 4.8, and STi = 39.7 kJ/
m2d, giving an internal-to-boundary flow ratio of
STi/z1 = 3.97 units. Form II network aggradation
is greater in this case than in the acyclic example
of Fig. 11a, as the following ratios of the four
compartmental throughflows and total system
throughflow show: 14/10 = 1.4, 12/7 = 1.7, 8.9/
4.9=1.8, 4.8/2.8 =1.7, and 155.7/137.5 = 1.13.
Clearly, in the comparison of Fig. 11b to Fig. 11a,
cycling even of relatively small quantities increases network aggradation.
6.3.2. Aggradation-to-storage ( form I)
There is also Form I aggradation-to-storage to
consider. Noting the concept of a reference state
in Fig. 2, arbitrarily let, say, ten units of storage
in the exterior environment to which aggradation
can be referenced generate one unit of input.
Then, z1 = 10 kJ/m2d in Fig. 11 implies that the
reference environmental state is x0 = 100 kJ/m2.
This parallels Slobodkin’s ‘10-percent rule’ from
trophic-dynamic theory, where flow rates out of
compartments during nominal time intervals are
10% of the compartments’ contents; in this case
the ‘compartment’ is the system’s environment.
Storages in actual compartments like the four in
1
(in
Fig. 11 can be calculated if turnover rates, t −
i
−1
2
d ), are known. Then, xi (in kJ/m )= Ti (kJ/
1
m2d)/t −
(d − 1). Turnover rates can be coni
structed for illustrative purposes again using the
10 percent rule. Several cases will be illustrative.
For Fig. 11a, without cycling:
Case 1a
All turnover rates of compartments
are 10%: t−1
i = 0.1, i= 1,…, 4.
For this case we have: 3+7 = 0.1·x1,
2.1+4.9 = 0.1x2, 2.1+2.8 = 0.1x3,
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2.8+2.8 = 0.1x4, yielding for the
steady-state storages x1 =100,
x2 =70, x3 =49 and x4 =28, summing to 247.0 kJ/m2.
Case 2a
Case 3a
Turnover rates are k *10%:
t−1
i
i =
(0.1)ki, i= 1,…, 4, where ki is the
number of arcs (arrows) exiting
each compartment. This yields
k1 =k2 =k3 =2, k4 =1, giving
−1
−1
−1
t−1
1 =t 2 =t 3 =0.2, and t 4 =
0.1.
Here we have: 3+7 =0.2x1, 2.1+
4.9= 0.2x2, 2.1+2.8 =0.2x3, 2.8+
2.8= 0.1x4, producing the
steady-state storages x1 =50, x2 =
35, x3 =24.5 and x4 =28, which
sum to 137.5 kJ/m2.
Following the Lindeman prescription
from classical trophic dynamics
that transfer efficiencies increase
at successive trophic levels,
can be
turnover rates of k *10%
l
assumed: t−1
l =(0.1)kl, l= 1,…, 4,
where k1 =1, k2 =2, k3 =3, and
−1
k4 =4, or t−1
1 =0.1, t 2 =0.2,
−1
−1
t 3 =0.3, and t 4 =0.4.
For this case: 3+7 = 0.1x1, 2.1+
4.9= 0.2x2, 2.1+2.8 =0.3x3, 2.8+
2.8= 0.4x4, giving for steady-state
storages x1 =100, x2 =35, x3 =
16.3 and x4 =7, summing to 158.3
kJ/m2.
Referencing the compartmental sums to x0 =
100 kJ/m2, i.e. Sxi/x0, these three cases give
Form I aggradation values of 2.47, 1.38 and
1.58, respectively. In general, though complicated by numerical details even in this
simple network, higher aggradation is associated
with lower turnover rates, reflecting lower
transfer efficiencies and longer retention
(turnover) times. This is consistent with the most
recently stated hypothesis above, pertaining to
minimum exergy turnover (or least specific dissipation).
The storage analysis for Fig. 11b follows along
the same lines:
Case 1b
Case 2b
Case 3b
Turnover rates 10%: t−1
i = 0.1,
i= 1,…, 4.
For this case: 3+11 = 0.1x1,
2.1+8.9+1 =0.1x2, 2.1+4.8+
2= 0.1x3, 2.8+1+1 =0.1x4,
yielding for the steady-state
storages x1 = 140, x2 = 120,
x3 = 89 and x4 = 48, summing
to 397.0 kJ/m2.
Turnover rates k *10%:
t−1
i
i =
(0.1)ki, i= 1,…, 4, where k1 =
k2 = k3 = 2, and k4 = 1, giving
−1
−1
t−1
1 = t 2 = t 3 = 0.2, and
−1
t 4 = 0.1.
Here we have: 3+11 = 0.2x1,
2.1+8.9+1 = 0.2x2, 2.1+4.8+
2= 0.2x3, 2.8+1+1 =0.1x4,
producing the steady-state
storages x1 = 70, x2 = 40, x3 =
29.7 and x4 = 16, which sum
to 155.7 kJ/m2.
Turnover rates k *10%:
t–1
l
l =
(0.1)kl, l= 1,…, 4, where k1 =
1, k2 = 2, k3 = 3, and k4 = 4
−1
such that t−1
1 = 0.1, t 2 = 0.2,
−1
−1
t 3 = 0.3, and t 4 = 0.4.
Here: 3+11 = 0.1x1, 2.1+8.9+
1= 0.2x2, 2.1+4.8+2 = 0.3·x3,
2.8+1+1 = 0.4·x4, giving for
steady-state storages x1 = 140,
x2 = 60, x3 = 29.7 and x4 = 12,
summing to 241.7 kJ/m2.
Again, referencing the compartmental sums to
x0 = 100 kJ/m2, the three cases give Form I aggradation values of 3.97, 1.56, and 2.42, respectively,
which are 1.6, 1.1, and 1.5 times greater than
corresponding values for the Fig. 11a network.
Thus, as for throughflow (Form I) aggradation
above, further enhancement of storage aggradation by cycling is also demonstrated.
These results are informative in relation to the
main themes of this paper. They show clearly that
the growth of order, as reflected in the storage
and throughflow forms of aggradation defined
here, occurs automatically in consequence of coupling components together to form a network. To
impart a dynamic flavor to the analysis, let the
S.E. Jørgensen et al. / Ecological Modelling 126 (2000) 249–284
two systems of Fig. 11a and Fig. 11b represent
earlier (a) and later (b) stages of development.
Both systems are supported by 10 kJ/m2d of
boundary input, and they both dissipate an equal
quantity (10 units) as boundary outputs. The
simpler (earlier) system employs the ten units of
inflow to produce 24.7 kJ/m2d of throughflow and
sustain 247.0, 137.5, and 158.3 kJ/m2 of intrasystem storage in the three cases studied. The more
complex (later) system with a more fully developed network utilizes its ten units of input to
generate 39.7 kJ/m2d of throughflow and, for the
three cases examined, 397.0, 155.7, and 241.7
kJ/m2 of storage. With dissipation constant (and,
say, at a maximum) in both systems, it is apparent, as previously argued, that storage continues
to increase with further maturation (i.e. from Fig.
11a to Fig. 11b) such that the dissipation/storage
ratio (specific dissipation) declines, giving least
exergy turnover, our last-stated hypothesis. For
the Fig. 11a system, storage/dissipation ratios (in
days) for the three cases examined are 247.0/10 =
24.7, 137.5/10 = 13.8 and 158.3/10 =15.8; for Fig.
11b, the corresponding values are 397.0/10 = 37.7,
155.7/10 = 15.6 and 241.7/10 =24.2. For all three
cases, retention (turnover) times are greater for
the (later, more mature) system with cycles.
In addition, this example suggests a further
extension of this hypothesis which allows Lotka’s
maximum power principle to also be accommodated within the present theory. Perhaps the most
surprising finding associated with Fig. 11 is the
relation between storages and throughflows when
viewed holistically. Locally, these two quantities
are reciprocals; one can be converted to the other,
and more of one means less of the other. But in
the whole-system context, as ‘growth’ from the
earlier (Fig. 11a) to the later (Fig. 11b) stage
demonstrates, both throughflow and storage may
increase together. There is no clearly identifiable
single cause for this in the comparison of the two
systems; the causality is a distributed property of
all the flow–storage relations in the entire constituted networks. Thus, paralleling the previous
developments for storage, a throughflow- or
power-specific version of the least turnover (stor-
279
age-specific dissipation) hypothesis can now be
offered:
Least throughflow-specific dissipation hypothesis.
If a system receives an input of exergy, it will
use all means available to degrade this exergy
as fully and quickly as possible (Schneider–
Kay) and, recursively through the work performed and throughflow generated, maximize
its power (Lotka) faster than the said dissipation such that its throughflow (power)/dissipation ratio, or dissipation-specific throughflow,
will become a maximum also, or inversely, its
throughflow (power)-specific dissipation a
minimum.
In Fig. 11a, the throughflow/dissipation ratio is
24.7/10 = 2.47, while in Fig. 11b it is 39.7/10 =
3.97. Therefore, in the transformation from the
(earlier, less mature) acyclic to the (later, more
mature) cyclic system, throughflow-specific dissipation has decreased from 1/2.47 = 0.40 to 1/
3.97= 0.25.
Growth of ecosystems, then, is toward maximization of dissipation-specific storage (Form I)
and throughflow (Form II), or conversely, toward
minimization of storage- and throughflow-specific
dissipation. The storage-based quantities have the
alternative interpretations of turnover—turnover
rate which is to be minimized, and turnover (or
retention) time, to be maximized.
7. Recapitulation and synthesis
We began this paper with a working hypothesis, from Jørgensen and Mejer (1977), that ecosystems self-organize during their growth and
development to maximize their stored exergy.
This came into conflict with a later proposal by
Kay and Schneider (1992) that thermodynamic
systems degrade received exergy as quickly and
fully as possible, by ‘all means available.’ This is a
statement that the second law is overarching and
has priority in any dynamical process. Whence,
then, cometh growth? The Jørgensen–Mejer formulation was motivated by the obvious observation that natural objects and organizations persist
despite the second law, and in fact for biological
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S.E. Jørgensen et al. / Ecological Modelling 126 (2000) 249–284
systems antientropic growth seems of the essence,
‘‘It springs to the eye’’, wrote physicist Bridgman
(1941), ‘‘that the tendency of living organisms is
to organize their surroundings, that is, to produce
‘order’ where formerly there was disorder. Life
then appears in some way to oppose the otherwise
universal drive to disorder’’ (quoted from Morowitz 1968, pp. 2 – 3). I. Prigogine is credited with
resolving the paradox in thermodynamics (Glansdorff and Prigogine, 1971).
To understand the paradox, or rather its solution, in ecologically meaningful terms, the idea
that entropy production varies with the stage of
growth of a process was investigated. Entropy
production starts low, increases during development, attains highest levels during maturity, then
declines with senescence (Aoki 1998). Therefore,
exergy dissipation increases in growing states, is
maximal for mature states, and decreases with
degrading states. Extensive exploration of ecological succession led to the conclusion that the early
rise of dissipation, powered by colonizers, ruderals, and other r-selected species, actually proceeds
quite quickly to a maximum, leaving storage lagging behind to catch up later as K-selected forms
ascend to more and more prominence. As it does
catch up, storage-specific dissipation decreases indefinitely because storage can increase indefinitely
as a limit process. This gives rise to the least
turnover (or least storage-specific dissipation) hypothesis under which both Jørgensen – Mejer storage and Schneider – Kay dissipation are conformed. Then finally, the Fig. 11 results showed
that during growth and development throughflow,
which is nominally reciprocal to storage, can actually grow together with storage. This produced
the final hypothesis in the series, the least
throughflow-specific dissipation hypothesis.
In the growth of ecosystems, therefore, dissipation rises early in any sere to approach quickly its
maximum attainable value. This is accompanied
by Form I growth-to-storage, which produces the
maintenance-requiring biomass whose catabolism
generates the dissipation in proportion to the
mass maintained. The mass maintained is of
course biota, whose own requirements for living
extend the interactions (transactions and relations) between living and nonliving components
of the ecosystem to proliferate connectivity, and
with this Form II growth-to-throughflow. As
Forms I and II growth continue more and more
refined into maturity, both storage- and
throughflow-specific dissipation decrease indefinitely until senescence reduces the storages and
throughflows. Then, increasing specific dissipation
begins to degrade the system, pending a disturbance event of ‘creative destruction’ to restore (by
nutrient regeneration, release from dormancy or
resource limitation, and other processes) the system’s capacity for self renewal. This is the pattern
of ecosystem growth, in thermodynamic terms, as
we have been able to fashion it from available
information and data.
What about Form III growth? This is growthto-organization, and while it necessarily occurs to
some extent in all stages of ecosystem development, we see it mainly as an attribute of refinement in the later maturation stages, after Form I
biomass is in place and continuing to increase but
with dimishing returns, and after the transactional
network has been laid down and Form II
throughflow is expanding, also at diminishing
rates. Then growth-to-organization takes over,
engaging the elusive quantity ‘information’ in the
development of relational connectance. This laterstage evolution of nonconservative relations, in
contradistinction to the prior expansion of conservative transactions, is in fact a principal concern
of the four remaining properties to be discussed in
this series: constraint, differentiation, adaptation,
and coherence. Since it is in the informational
aspects of ecosystems where current knowledge
becomes very sparse, the challenges of making a
plausible theory from this point forward will be
very great indeed. Before entertaining this new
domain, however, we should conclude here by
asking our usual question….
8. What would the world be like without growth?
In the previous papers in this series we have
speculated on what the world would look like
without the conservation principles (Patten et al.,
1997), without the irreversibility of all real pro-
S.E. Jørgensen et al. / Ecological Modelling 126 (2000) 249–284
cesses as formulated in the Second Law of Thermodynamics (Straškraba et al., 1999), and without the characteristic openness of systems
(Jørgensen et al., 1999). It was concluded that the
world would be a very different place without
these basic laws of nature. From conservation, the
stuff of reality could not be accounted; spontaneous generation and disappearance of substance
would be possible. Anything could happen. From
dissipation, inexorable running down would not
occur, irreversibility of processes would be unknown, and even time would not be unidirectional
if indeed there could be any such phenomenon as
time at all. From openness, there would be no
insides or outsides, no environments to engage
and surround, no interactions or communications,
nothing would happen without interchange. There
would be no second law, and probably not a first
law either. They would be pointless. Now we have
come to growth.
Is it possible to imagine a non-growing world,
or ecosystem, population, or organism, or body of
knowledge — anything? Environmentalists wish
that economists could invent a no-growth economics to take the place of the neoclassical prescription that dominates world economies and
ensures that resources will be overexploited, enterprises unsustainable, and resource populations
mismanaged and ultimately driven to extinction.
Grow-or-die is the dictum, and despite the apparent folly no one seems able to come up with a
viable nongrowing alternative. And ecologists
wish that demographers and governments could
figure out a way to bring the earth’s human
population to some steady-state level that would
allow an agreeable quality of life for all the
world’s citizenry. But no one seems to be able to
slow the human juggernaught, the ‘population
bomb’ that in evolutionary biology is termed
fitness. What an irony that a population whose
growth may bring about mass misery, high mortality, and wisespread desecration of the planet
and its member species could be thought of by
science as ‘fit.’ We need a better science, it would
seem, than one that calls unfitness fitness. Why
can science and economics not develop a prescription for unchange? Or local creativity within
global stasis? Or growth in quality with quantity
held constant? Is growth so ingrained to biologi-
281
cal process that it is impossible even to think of
reasonable alternatives?
Without positive growth is it possible to imagine negative growth, the decline and degradation
that are the established domain of the second law?
The world would not make sense locked in universal constancy, no running down, no running
up, nothing moving, nothing changing, nothing
happening, ever, everything frozen forever in
spacetime exactly as it would be if ‘growth’ ever
went out of existence. Suppose a flow of exergy
was not able to move systems away from thermodynamic equilibrium? They would remain there.
The Big Bang would never have happened. No
antientropic processes would ever have been realized; no energy gradients would every have been
generated. The second law would have to be
retired; there would be no work to be done that
could give it expression, no gradients to degrade,
no disequilibria to equilibrate. There would be no
development, and on the longer scale no evolution, biological, cosmic, or other. Energy itself
(and exergy within it) would never have existed.
The only possibility for a system to move away
from thermodynamic equilibrium is by input of
energy from an external source, because energy
conservation dictates that the energy needed for
maintenance and growth of processes must come
from somewhere. So, only by a flow of exergy
through a system after a receipt of it at the
boundary can order and organization be established. This is the only possibility for existence in
a world based on growth. And without growth,
existence itself would vanish for it hinges on it.
And, how would the world look if selection of
particular systems from sets of (virtual) possibilities were not in accordance with the final criteria
of this paper — highest exergy storage/dissipation
and throughflow/dissipation ratios? If these are
not the proper orientators of growth, then at least
growth should stand as evidence that they have
been expressed. For if processes or components
were not so selected, then growth would not be
directional but random. What had been achieved
could not be built upon further. A growing system
would devolve to an amorphous mass of featureless stuff, and growth of chaos, not of order,
would be the reality.
282
S.E. Jørgensen et al. / Ecological Modelling 126 (2000) 249–284
Finally, a statement about growth as a positive
feedback process is in order since we have ignored, with our central attention to thermodynamics, the essential deviation-amplifying nature
of growth, and also the basic growth themes fom
classical ecology. In our original outline for this
series, we saw biological growth as a fundamental
process (a force, almost) that continued unrestricted until bounded by the counterforce of environmental limitations, Leibig’s law of the
minimum, Shelford’s law of tolerance, and the
like. The biotic imperative was expressed
in concepts like Malthusian growth and fitness
adding to populations, and the environmental
one in carrying capacity, logistic growth,
and natural selection. In the thermodynamic view
of growth, antientropic departures from equilibrium are the seed for further exergy
accrual through positive feedback, which structures, guides, and determines rates of growth.
This entire paper could have been constructed
around the feedback perspective, but feedback
comes in two forms, positive and negative. Referenced to classical ecology, positive feedback is the
mechanism underlying biological growth, and
negative is that for environmental limitation. Negative feedback is the basis of cybernetics, the
science of ‘control and communication’ (Wiener,
1948), and this subject will come into greater
prominence in the later chapters of our
script because we consider ecosystems all the
way up to the ‘Gaia’ of Lovelock (1979) to be
patently cybernetic systems (e.g. Patten and
Odum, 1981).
Thus, we are not finished with growth at all, we
have just deferred Form III growth-to-organization with its dominantly informational properties
to later development under the rubric of feedback.
Basically, as ecosystems grow more organized,
their degrees of freedom decrease by commitment
to the previously established order, and their initially broad operation space tends to narrow
even as their numbers and kinds of biota and
niches expand. Increasingly canalized and regular
behavior is the result. Components expand but
behavior contracts — another paradox to begin
to deal with in our next installment — 5, Constraints.
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