An example: Georgia salt marsh energy flow study using EcoNet

This work is contributed by Gaston Small

We present an eight-compartment model based on John M. Teal's classic study of energy flow in a Georgia salt marsh [19,18]. Followed by the model description, we provide the EcoNet model and go over essential network analysis results.

Model Description

Figure: Energy flow diagram of a Georgia salt marsh, by J. M. Teal [19]

The model represents the energy budget for one square meter of salt marsh. Compartments are measured in $ kcal/m^{2}$ and flows are measured in $ kcal/m^{2}d$. Energy enters the salt marsh through primary production at compartments salt marsh cordgrass Spartina and algae. Much of this energy is lost through respiration by these plants, but the remainder enters the salt marsh food web. Bacteria and insects feed directly on the Spartina, and spiders, in turn, feed on the insects.

A substantial portion of the Spartina dies and enters the detritus pool. Nematodes feed on bacteria and detritus, and mud crabs feed on the nematodes. Every compartment in the model contributes to the detritus pool through fecal material (for the animal compartments) and dead tissue. Every compartment except detritus, the only nonliving compartment in this model, dissipates energy through respiration. One of the surprising findings was that this salt marsh exported substantial amounts of energy through detritus (0.6% of incoming radiation). Detritus export is represented by a loss term in the model.

Figure: EcoNet model of the energy flow study in a Georgia salt marsh
# Energy flow in the salt marsh 
# ecosystem, by G. Small 
# based on model by J. Teal
 
* -> spartina c=94.74  
* -> algae c=4.93  
spartina -> insects c=0.002  
spartina -> detritus c=0.03  
spartina -> bacteria c=0.0001  
algae -> detritus c=0.02  
algae -> nematodes c=0.02  
insects -> detritus c=0.2  
insects -> spiders c=0.05  
detritus -> bacteria c=0.01  
detritus -> nematodes c=0.01  
bacteria -> nematodes c=0.01  
bacteria -> detritus c=0.5  
spiders -> detritus c=0.1  
nematodes -> detritus c=0.6  
nematodes -> mudcrabs c=0.01  
mudcrabs -> detritus c=0.1  
spartina -> * c=0.15  
algae -> * c=0.1  
insects -> * c=.1  
detritus -> * c=0.02  
bacteria -> * c=0.4  
spiders -> * c=0.05  
nematodes -> * c=0.2  
mudcrabs -> * c=0.05
 
spartina=450, algae=20, insects=1  
detritus=250, bacteria= 800,  
spiders=0.18 nematodes=0.5, mudcrabs=0.1
\includegraphics[width=5.5cm]{teal.epsi}

Because energy, rather than carbon or nutrients, is the currency for this model, dissipation rates are high. Energy dissipates rapidly because of respiration losses and detritus export. However, energy does cycle in this ecosystem in the form of detritus. A kilocalorie of energy can make multiple passages through all of the non-plant compartments before exiting the system.

Flow analysis

Table: N and B matrices of Georgia salt marsh model.
B Spartina algae insects detritus bacteria spiders nematodes mudcrabs
Spartina(1) -1 0 0 0 0 0 0 0
algae(2) 0 -1 0 0 0 0 0 0
insects(3) 0.011 0 -1 0 0 0 0 0
detritus(4) 0.164 0.142 0.571 -1 0.549 0.667 0.745 0.667
bacteria(5) 0.005 0 0 0.4 -1 0 0 0
spiders(6) 0 0 0.143 0 0 -1 0 0
nematodes(7) 0 0.143 0 0.2 0.011 0 -1 0
mudcrabs(8) 0 0 0 0 0 0 0.0062 -1

N Spartina algae insects detritus bacteria spiders nematodes mudcrabs
Spartina(1) 1 0 0 0 0 0 0 0
algae(2) 0 1 0 0 0 0 0 0
insects(3) 0.011 0 1 0 0 0 0 0
detritus(4) 0.278 0.399 1.063 1.595 0.889 1.063 1.195 1.063
bacteria(5) 0.117 0.159 0.425 0.638 1.356 0.425 0.478 0.425
spiders(6) 0.001 0 0.142 0 0 1 0 0
nematodes (7) 0.056 0.224 0.217 0.326 0.193 0.217 1.244 0.217
mudcrabs(8) 0.0004 0.0014 0.0013 0.0020 0.0012 0.0013 0.0077 1.0013


In the matrix N given above, $ n_{44}=1.595>1$ represents the fact that a unit of energy in detritus is more likely to cycle through the salt marsh food web and reenter the detritus compartment before being dissipated from the system.

Bacteria, nematodes, and mud crabs are all part of the detritus-based salt marsh food web, and thus have the potential to cycle energy in this ecosystem ( $ n_{55},n_{77},n_{88}>1$). By contrast, a unit of energy that enters the Spartina, algae, insects, or spiders compartment will never again reenter those compartments ( $ n_{11},n_{22},n_{33},n_{66}=1$), because all of their energy is derived from primary production.

The N matrix traces the throughflow generated by inputs into various compartments in our model. The non-zero entries in the first row of N indicates that a unit of energy input into Spartina generates energy flowing through every compartment except algae. Detritus is the largest recipient of energy derived from Spartina, both from the direct movement of Spartina to detritus ( $ b_{41}=0.164$) and from indirect pathways ( $ n_{41}=0.278$). Therefore $ n_{41}-b_{41}=11.4\%$ of this energy travels through the food web before entering the detritus compartment. There is no direct flow from Spartina to mud crabs ($ b_{81}=0$), and the shortest path between them is (See figure):

$\displaystyle Spartina\rightarrow\textrm{detritus}\rightarrow\textrm{nematodes}\rightarrow\textrm{mud crabs}$

Therefore mud crabs receive only $ n_{81}=0.04\%$ of energy that is captured by Spartina photosynthesis.

Similarly, the second row of N indicates that the energy inputs to algae generate throughflows in four of the model compartments. Nearly 40% of this energy will pass through the detritus compartment, and 16% will reach bacteria through consumption of detritus ( $ n_{42}=0.399,\, n_{52}=0.159$). $ n_{12},n_{23},n_{26}=0$, therefore Spartina, insects, and spiders cannot capture energy derived from photosynthesis by algae.

Although energy only enters the salt marsh through photosynthesis by Spartina and algae, the B and N matrices trace flows generated by hypothetical inputs into all compartments in the model. For example, of a unit input of energy in nemotodes, nearly $ b_{47}\approx75\%$ goes directly to detritus and less than 1% is consumed by mud crabs ( $ b_{87}=0.006$), with the remaining 24% lost to respiration.

From the mud crabs, the energy is either lost through respiration or recycled as detritus (see figure). The energy in detritus can reenter the detrital food web or be washed out to sea. Through the detrital food web, a small fraction of this energy ( $ n_{87}-b_{87}=0.15\%$ of the original input) will make at least a second passage through the mud crab compartment.

Storage and Utility Analysis

Table: Storage (S) and Utility (U) analysis matrices of the Georgia salt marsh model.
S
 		Spartina algae insects detritus bacteria spiders nematodes mudcrabs
Spartina(1) 5.46 0 0 0 0 0 0 0
algae(2) 0 7.14 0 0 0 0 0 0
insects(3) 0.031 0 2.86 0 0 0 0 0
detritus(4) 5.56 7.97 21.26 31.89 17.79 21.26 23.91 21.26
bacteria(5) 0.128 0.175 0.467 0.701 1.49 0.467 0.525 0.467
spiders(6) 0.010 0 0.952 0 0 6.67 0 0
nematodes (7) 0.071 0.279 0.270 0.405 0.239 0.270 1.55 0.270
mudcrabs(8) 0.002 0.009 0.009 0.013 0.008 0.009 0.052 6.68


U Spartina algae insects detritus bacteria spiders nematodes mudcrabs
Spartina(1) 0.016 -0.005 -0.090 -0.003 0.219 0.032 0.038 -0.003
algae(2) -0.023 0.187 0.084 -0.001 0.003 -0.037 -0.915 0.045
insects(3) 0.025 -0.012 0.548 -0.006 0.521 -0.243 0.084 -0.007
detritus(4) 0.008 0.001 -0.029 0.0004 -0.063 0.013 -0.005 0.0005
bacteria(5) 0.052 -0.017 -0.202 0.0006 0.785 0.087 -0.031 0.002
spiders(6) 0.019 -0.013 0.559 -0.006 0.556 0.751 0.086 -0.008
nematodes (7) -0.004 0.160 0.012 -0.0002 0.063 -0.006 0.187 -0.009
mudcrabs(8) -0.002 0.042 0.008 -0.0001 0.028 -0.004 0.050 0.997


The storage analysis matrix S traces the storage generated by a constant rate of energy inputs into different compartments in the model. For example, a rate of $ 1kcal/m^{2}d$ energy input into Spartina will generate $ s_{11}=5.46\, kcal/m^{2}$ stored energy in Spartina. Because of recycling in the detritus-based food web, even more energy from this input will be stored in the detritus compartment ( $ s_{41}=5.56\, kcal/m^{2}$). Smaller amounts of energy will be stored in all of the other compartments reachable from Spartina.

The utility analysis matrix U indicates interaction types and strengths among compartments in this network. Some of these relationships are straightforward. For example, insects feed on Spartina, so the addition of a unit of Spartina benefits the insects ( $ s_{31}=0.025>0$), and the addition of a unit of insects is even more detrimental to the Spartina ( $ s_{13}=-0.090<0$). Indirect effects can be traced using the utility analysis matrix. For example, the addition of mud crabs has a negative effect on their prey, nematodes ( $ u_{78}=-0.009<0$), and in turn, benefits algae and bacterial compartments, on which nematodes feed ( $ u_{28}=0.045>0,\, u_{58}=0.002>0$) [15].

Because of multiple branches in the food web, some relationships are more complex, and may be different than what one may derive from the network diagram (figure). For example, even though insects produce detritus, the addition of a unit of insects is detrimental to the detritus compartment ( $ u_{43}=-0.029<0$), because these insects are consuming (and subsequently respiring) additional energy from Spartina that would otherwise go into detritus.

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