e c o l o g i c a l m o d e l l i n g 1 9 6 ( 2 0 0 6 ) 283–288
available at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/ecolmodel
Examination of ecological networks
S.E. Jørgensen a,∗ , B.D. Fath b
a
b
DFU, Institute A, Environmental Chemistry, University Park 2, 2100 Copenhagen Ø, Denmark
Biology Department, Towson University, Towson, MD 21252, USA
a r t i c l e
i n f o
a b s t r a c t
Article history:
Using an ecological food web model, we examine the change in exergy storage and energy
Received 21 July 2005
throughflow (power) as a consequence of eight network changes including (1) increased
Received in revised form 7 February
input, (2) removal of food chain links, (3) addition of new pathways (links) from producers
2006
to herbivores, (4) addition of new pathways (links) from herbivores to carnivores, (5) food
Accepted 8 February 2006
chain prolongation, (6) increased flow rates in the food chains, (7) transfer of energy from
Published on line 5 June 2006
one food chain to another, and, (8) reduced loss as detritus. It has been shown previously
that exergy storage and energy throughflow increase during stages of ecosystem growth
Keywords:
and development. We hypothesis that network changes yielding the highest exergy storage
Food web
and throughflow will have a selective advantage and would be more favorable to the overall
Food chain
system organization. This hypothesis could be used to explain the selective criterion for
Ecosystem
changes that occur in an ecological network. Here, we investigate which changes, in gen-
Exergy
eral, lead to these more favorable conditions. Model results demonstrate the following six
Network changes
rules regarding network effects on exergy and power: I. Increased input gives proportional
increase of exergy and power; II. Additional links only affect power and exergy when they
increase the overall network throughflow, thus the connection placement is important; III.
Food chain prolongation has a positive effect on the power and exergy of the network; IV.
Reduction of loss of exergy to the environment or as detritus (with a ˇ value of 1 only) yields
a higher power and exergy of the network; V. Faster cycling—detritus is decomposed faster
or the transfer rates between two tropic levels are increased—implies higher power and
exergy; and, VI. Input of additional exergy or energy recycling flows has bigger effect the
earlier in the food chain the addition takes place.
© 2006 Elsevier B.V. All rights reserved.
1.
Introduction
Many studies, starting with the work by Lotka (1922) and classic papers by Juday (1940), Lindeman (1942), Odum (1957) and
Teal (1957) have addressed energy flow in ecosystems. More
recent efforts to assemble food web data include Paine (1980),
Cohen et al. (1990), Polis (1991), Goldwasser and Roughgarden
(1993), Townsend et al. (1998), Christian and Luczkovich (1999),
Dunne et al. (2002, 2004) and Pimm (2002). However, there
is a difference between food web analysis and energy flow
∗
Corresponding author.
E-mail address: [email protected] (S.E. Jørgensen).
0304-3800/$ – see front matter © 2006 Elsevier B.V. All rights reserved.
doi:10.1016/j.ecolmodel.2006.02.029
analysis as few of the former include detritus as part of
the food web. This omission is changing as food web ecologists are beginning to recognize the importance of all energy
flow pathways including detrital (e.g., Wetzel, 1995; Sandberg
et al., 2000; Heymans et al., 2002; Leguerrier et al., 2003;
Moore et al., 2004, 2006). One promising way to investigate all the direct and indirect pathways in food webs or
energy flow models is using ecological network analysis (e.g.,
Dame and Patten, 1981; Patten, 1985; Ulanowicz, 1986, 1997;
see Fath and Patten, 1999 for more details). Here, we apply
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e c o l o g i c a l m o d e l l i n g 1 9 6 ( 2 0 0 6 ) 283–288
Table 1 – Model equations (see conceptual diagram;
Fig. 2)
dX1 (plants A)/dt = f10 − f21 − f61 − f91 − f01
dX5 (plants B)/dt = f50 − f65 − f95 − f05
dX2 (herbivores A)/dt = f21 − f32 − f72 − f02
dX3 (carnivores A)/dt = f32 − f43 − f93 − f03
dX4 (top-carnivores A)/dt = f43 − f94 − f04
dX6 (herbivores B)/dt = f61 + f65 + f69 + f6,10 − f76 − f96 − f06
dX7 (carnivores B)/dt = f72 + f76 + f79 − f47 − f87 − f97 − f07
dX8 (top-carnivores B)/dt = f87 − f98 − f08
dX9 (detritus)/dt = f91 + f92 + f93 + f94 + f95 + f96 + f97 + f98 − f79 − f10,9 − f09
dX10 (bacteria)/dt = f10,9 − f6,10
Fig. 1 – The exergy content of an ecological system
(eco-exergy) is calculated for the system relative to a
reference environment at the same temperature and
pressure, but as an inorganic soup with no biological
structure, information, or organic molecules.
network analysis to understand how energetic properties
change during ecosystem growth and development, using
a series of network models representing various stages of
succession.
Using models, empirical data and ecological networks, it
has been shown that ecosystem growth and development
can be described by four growth and development forms
(Jørgensen et al., 2000; Fath et al., 2004): boundary growth,
biomass growth, network growth and information growth.
These growth and development forms provide the sequence
during which the attributes proposed by Odum (1969, 1971)
unfold; see Fath and Patten (2001) and Jørgensen (2001). All
four growth and development forms are associated with
increased throughflow and eco-exergy (Jørgensen, 2002). Ecoexergy, defined as the work that an ecosystem can perform
when it is brought into equilibrium with the same ecosystem
at the same temperature and pressure but at thermodynamic
equilibrium (Fig. 1), expresses the distance from thermodynamic equilibrium where there is no chemical gradient
and no life. According to this definition, the contribution to
eco-exergy arises entirely from the many complex biochemical compounds that the living organisms in ecosystems
possess.
This paper examines a series of networks that have different structures and different parameters to observe how much
the throughflow and eco-exergy change as a result of a series
of general network changes. It is furthermore discussed to
what extent these eco-exergy observations are in accordance
with the abovementioned increase of exergy for all growth
forms because the network changes can be directly or indirectly related to them.
2.
Model examinations
The baseline model consists of two parallel, four-component
food chains each with primary producers, herbivores, carni-
All transfers are first-order donor reactions, fij = cij × xj where
transfers are from j to i. For instance, f05 = c05 × x5 is respiration
of carnivores A = respiration coefficient carnivores A × carnivores
A, or f87 = c87 × x7 is top-predation B = top-predation B coefficient × carnivores B. The baseline coefficient value is cij = 0.25 for
all i, j.
vores and top-carnivores without bacteria (Fig. 2; see Table 1
for model equations). The primary production components
each receive a constant input of 10 detritus equivalents (1
detritus equivalent is 18.7 kJ, which is the average free energy
of 1 g of detritus). A detritus component is added to receive
dead organic matter from all components, and the energy
(exergy) is recycled by utilization of the detritus as food for
some organisms, notably a detritus-feeding bacteria component. Eco-exergy is calculated by the following equation:
Exergy =
n
ˇi Ci
(1)
i=1
where ˇi is a weighting factor that considers the ith species’
information embodied in the amino acid sequence of the
proteins that control the enzymatic life processes and Ci
represents the concentration of the ith species. ˇ-value
estimations for various organisms (Table 2) are taken from
Jørgensen et al. (1995, 2000, 2005) and Jørgensen (1982, 2002).
All flow equations are first-order donor expressions except
the inflow (photosynthetic solar radiation). The baseline,
donor transfer coefficient was constant at 0.25 for all three
pathways (numbered 2 and 3 in the figure). For each network
configuration, the model is run to steady state and the steady
state exergy is calculated. The exergy of the network is
found by summing up the contributions from Eq. (1) for each
compartment X1, X2, X3, . . ., to X10. The sum of throughflows
are found as the sum of all the values for the internal flows
f21 , f32 , f43 and so on at steady state. Exergy values result-
Table 2 – Eco-exergy coefficient
Compartment
Detritus
Bacteria
Plants A and B
Herbivores A and B
Carnivores A and B
Top-carnivores A and B
ˇ-coefficient
1
8
200
400
1000
2000
e c o l o g i c a l m o d e l l i n g 1 9 6 ( 2 0 0 6 ) 283–288
285
Fig. 2 – Diagram of conceptual model. Solid lines indicate baseline model and dotted lines medications that were made
during different scenario analyses. All transfers are first-order donor reactions, fij = cij × xj where transfers are from j to i. The
baseline coefficient value is cij = 0.25 for all i, j.
ing from different network manipulations are compared
in order to determine the overall impact to structural and
functional network changes. We also calculated the total
energy throughflow for each model configuration.
3.
Results
We applied eight different changes to the above baseline
model to observe the impact of boundary biomass, network
and information growth of the model (Table 3). Changes are
shown in Fig. 2 by dotted lines (Table 4). A doubling of the input
to the primary producing components represents biomass
growth; this resulted in a doubling of the exergy storage and
throughflow. All the other changes give a considerably smaller
increase of the exergy and the throughflow except removal of
components and links which implies a decrease in exergy and
throughflow. The other changes all resulted in increases, but
by around one half as much. For example, network growth,
the addition of extra links, typically resulted in greater exergy
and throughflow. However, in some instances, such as when
a transfer of 0.25 herbivores is removed from food chain A to
food chain B, the extra network does not increases the total
exergy.
In addition to the structural network changes, simulation of information growth was accomplished by decreasing, for each compartment, one-by-one the loss to detritus,
the loss to respiration and the growth rates. It is assumed
that increased information results in greater energy efficiency,
which is made possible through improved feedbacks, larger
size, or change from r-strategists to K-strategists. The result
was greater exergy storage and throughflow. Furthermore, we
Table 3 – Network modifications to baseline model
1
2
3
4
5
6
7
8
Doubling input to primary producer
Removing food chain B top-carnivores
Adding a link between plants A and herbivores B
Adding a link from herbivores A to carnivores B
Adding a link from carnivores B to top-carnivores A
Reduction of energy transfer from herbivore A to
carnivores A by 0.25* herbivores and a transfer of
0.25 herbivores A to carnivores B, named transfer of
exergy from A to B
Adding a link from bacteria to herbivores B
Adding links from detritus to herbivores B and carnivores B
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e c o l o g i c a l m o d e l l i n g 1 9 6 ( 2 0 0 6 ) 283–288
Table 4 – Network changes and the corresponding exergy changes at steady state
Change
1
2
3
4
5
6
7
8
9
Exergy in detritus equivalent
Basic model
Doubling of input exergy to 2
Removing top-carnivores
Link plant A to herbivores B (specific rate 0.25)
Link herbivores A to carnivores B
Link carnivores B to topcarnivores A
Transfer of exergy from A to B
Adding bacterial food chain
Detritus to carnivores B instead of to herbivores B
calculated an exergy – sensitivity parameter defined as:
(Exergy/Exergy in)
(Parameter 1/Parameter 2)
(2)
Sensitivity results are shown in Table 5. The impact of
changing all the parameters has been examined, but not
recorded if the numerical results are only changed slightly.
Tables 4 and 5 list only the significant changes.
The results are based upon prescribed changes listed in
Table 4. If, for instance other changes had been applied,
then the results would have differed. Therefore, the results
only cover the possibilities of several scenarios. These scenarios were designed to represent realistic ecosystem changes
but in their limited scope are only interpreted as semiquantitative—see the discussion below.
The results can also be interpreted by the effects of the type
of network changes:
I. Increased input gives a proportional increase of exergy
and power.
II. Additional links will only affect the power and exergy
when it gives additional exergy or energy transfer.
Removal of one energy flow from one food chain to
another has no effect.
III. Prolongation of the food chain has positive effect on the
power and exergy of the network.
IV. Reduction of exergy loss to the environment or as detritus
(with a ˇ-value of 1 only) yields a higher power and exergy
of the network.
Table 5 – Exergy sensitivities of flow changes (at steady
state)
Parameter
Detritus from plants
Detritus from herbivores
Detritus from carnivores
Detritus from top-carnivores
Respiration plants
Respiration herbivores
Respiration carnivores
Respiration top-carnivores
Grazing
Predation
Top-predation
Microorganisms feeding on detritus
Herbivores feeding on microorganisms
Sensitivity
−205
−50.2
−200.8
−752
−287.5
−493.2
−255.7
−126.8
+283.8
+148.9
+3.4
+122.1
+19.3
54463
105636
52818
57424
55567
54652
54463
61938
54762
Throughflow
58.4
90.9
45.4
59.9
59.0
58.7
58.4
65.3
58.9
V. Faster cycling—through either faster detritus decomposition or increased transfer rates between two tropic
levels—yields higher power and exergy.
VI. Input of additional exergy or energy cycling flows has
greater effect the earlier in the food chain the addition
takes place.
4.
Discussion
The model results show that boundary (doubling input),
biomass (increased compartments), network (adding connections) and information (changing transfer rates) growth all
contribute to increase exergy storage and throughflow. These
results are in accordance with the hypothesis regarding exergy
storage and energy throughflow. For example, it has been
proposed that if a system receives an input of exergy, it
will utilize this exergy first to maintain the system far from
thermodynamic equilibrium, and second, to move the system further from thermodynamic equilibrium by increasing
the exergy stored in the system (Jørgensen and Mejer, 1977,
1979; Jørgensen, 2002; Jørgensen et al., 2000; Fath et al., 2004;
Jørgensen and Fath, 2004) and the total system throughflow
(i.e., power; Odum, 1983). As the open ecosystem moves away
from equilibrium, if more than one pathway (i.e., model configuration) is available, then the one yielding the greatest
exergy storage and throughflow under the prevailing conditions (i.e., most ordered structure with largest gradients) will
tend to be selected. This supports the idea that the principles of maximizing power and exergy storage are consistent.
Adding extra links that carry additional exergy transfer will
therefore mean that power is increasing and in accordance
with the hypothesis it should be expected that also the exergy
of the system would increase—as shown in the modelling
results in Table 4. The increase of exergy and throughflow
resulting from a transfer between the food chains is highest for an addition of 0.25* plants A to herbivores B, which
is bigger than the transfer of 0.25 herbivores A to carnivores B,
which in turn is bigger than the transfer of 0.25 carnivores
A to top-carnivores B: plants > herbivores > carnivores > topcarnivores. Since the differences in concentration is minor,
it may be possible to hypthesize that the earlier the exergy
is added in the food chain the more components throughout the food chain can benefit of this transfer of additional exergy and therefore the higher is the gain in total
eco-exergy.
The addition of an extra link to detritus has a particular
effect, although addition of a top-carnivore in one food chain
ecological modelling
also yields a significant increase of exergy and throughflow.
Change of the detritus feeders from the trophic level of herbivores to the trophic levels of carnivores gives a gain in exergy
and throughflow, which may be explained by the increasing
weighting factors through the food chain.
If the species decreases the respiration or the loss of detritus, then the exergy increases. These changes could be caused
by:
(1) an increase in size which according to the allometric principle means that the specific respiration rate and the mortality decreases;
(2) a shift from r-strategists to K-strategists, which implies
that less exergy is lost by high mortality of offspring.
In accordance with Odum (1969, 1971), ecosystems develop
toward larger size of the organisms present in the ecosystem
and toward greater abundance of K-strategists. Therefore, the
system also moves toward an increase in the exergy as shown
in Table 4.
An increase in the growth rates (grazing, predation and toppredation) means that throughflow increases and it should be
expected according to the above hypothesis that exergy also
increases along with throughflow. Therefore, both are augmented simultanesouly and can be viewed as two sides of the
same coin (see also Fath et al., 2004). The results in Table 4
confirm the hypothesis and the close relationship between
exergy and throughflow. Notice that the increase of grazing
has a greater effect (the sensitivity is higher) than an increase
of predation, which in turn has a higher effect than the effect
of top-predation. The explanation is that the earlier in the food
chain the transfer rate increase is realized the more components later in the food chain will be affected. An increase in
the top-predation has only a small effect, which is due to the
high loss of top-carnivores to detritus (the rate is selected for
both food chains to 0.9* top-carnivores). This is not necessarily
the case in realistic food webs. It is easy to demonstrate that
the increase of top-predation would have much higher effect
on the exergy of the system when the transfer to detritus from
top-carnivores is decreased.
Overall, it is clear that the selected parameter values
have—not surprisingly—strong influence on the results presented in Tables 4 and 5. Several relevant parameter changes
were tested and corresponding changes of exergy storage
and energy throughflow were observed. The results discussed
above for several scenarios are consistent but as the scenarios
tested are very limited, the results should only be considered
semi-quantative. Further research is needed to more systematically investigate possible model network configurations.
5.
Conclusion and summary
A baseline network model was used to examine how structural
changes to a model, which represent scenarios of biomass,
network and information growth, affect the overall exergy
storage and energy throughflow within the model. The four
major growth stages were represented accordingly:
(1) boundary growth corresponds to an increase in input;
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( 2 0 0 6 ) 283–288
287
(2) biomass growth corresponds to an increase in the number
of compartments (as well as the size of the existing ones
through more efficient mechanisms);
(3) network growth corresponds to adding additional transfers of energy (exergy) in the network or by increasing the
energy (exergy) flows in the existing network;
(4) information growth corresponds to a decrease of exergy
losses in form of respiration and detritus (i.e., r-strategists
and K-strategists).
All growth forms yield more power and more stored exergy
and are thus in accordance with Odum’s attributes (Odum,
1969, 1971). These conclusions have already been presented
partly in Jørgensen (2002) and more completely in Fath et al.
(2004). Furthermore, the results support the hypothesis that
systems organize to move further away from equilibrium by
storing greater amounts of exergy and transferring greater
amounts of energy.
The presented hypothesis has been supported by several observations (see Jørgensen, 2002; Jørgensen et al., 2000;
Jørgensen and Svirezhev, 2004) and again in this paper by
observing the results of network changes. It would therefore
be a natural development to use the hypothesis to conclude
that certain network changes promote further accumulation
of exergy storage and energy throughflow. If we would apply
the hypothesis in this way, then we can conclude that network changes that add to the exergy or energy transfer are
likely to be selected. Furthermore, linkages lower in the food
chain have greater impact on the total exergy level of the
ecosystem and therefore play an important role in the overall competition among possible linkages. Finally, we conclude
that development that would decrease the loss of exergy to
the environment would be favored.
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