1. Introduction
SIM (Stable Isotope Modelling) is a Windows-based program that provides the user with the facility to design food webs and simulate 13 C pulse labelling experiments over a specific duration. This user guide is supplied as a succinct introduction to performing simulations with SIM. The software also comes supplied with a more comprehensive online help facility (see Section 6) which contains more detail on the features of SIM itself.
The basic food web model is based on that described in Hunt et al. (1987) and Berg et al. (2001). To this basic framework has been added the facility to simulate 13 C pulse experiments through the food web, enabling the user to validate the model’s outputs against newly available stable isotope data
(Fitter et al. 2005). The underlying food web model envisages the soil ecosystem as a network of connected boxes, each box corresponding to a species or functional group and the connections representing directed trophic linkages between them. The central assumption is that the biomasses in all functional groups remain constant over time (the default unit of time is one year in the software) so that, for each functional group, one can assert biomass gained = biomass lost. The implementation of this basic principle across the web uniquely defines all the carbon flows. In practice, the situation is more complicated, involving mortality, variable prey preferences, and production and assimilation efficiencies.
The model requires that the first functional group (“box 1”) of any food web is a detritus compartment into which is collected all unassimilated carbon, dead material, and faeces from the other parts of the food web. Thus all functional groups are implicitly linked to the detritus box; these implicit links are not shown graphically because the food webs only show “who eats whom”.
2. Installing the program on a computer running Windows
SIM comes with its own installation program, and will run on Windows 9x, 2000, Me, NT and XP
3. Starting the program
The program can be started by double clicking on the SIM desktop icon, clicking once on the SIM taskbar icon, or using the standard Windows START menu. The program opens and presents the user with the food web dialogue box as shown below:
The choice to create a new food web is automatically selected. If you want to create a new food web, simply click on OK and continue reading Section 4. If you have already created a food web or wish to chose one from the available library, check the appropriate circle and click OK, and then select the file from an existing library or another location (see Section 5). SIM is supplied with two examples of soil food webs which might be helpful to users; “Sourhope” is a complex food web constructed and parameterised where possible with data arising from the NERC Soil Biodiversity programme, with
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additional input from Hunt et al. (1987) and Berg et al. (2001), and a “Simple Example Food web” which reduces the system to three general components.
4. Creating and modelling a new food web
4.1 Adding functional groups to a food web – the food web layout page
After clicking OK, the dialogue box disappears and you are left with a blank food web layout page .
This represents an empty model, allowing you to create your own ecosystem. Note that at the bottom of the screen there are three tabs: food web layout, parameters and feeding preferences, which let you toggle between the food web layout page (this section), the parameters page (section 4.2) and the feeding preferences page (section 4.4). With a blank food web layout, no data is stored on either the parameters or feeding preferences pages.
To begin creating a food web, you use the toolbar at the trop of the screen
The functions of the eight buttons on the toolbar are summarized in Table 1 . Note that the Balance and
Split commands can also be accessed from the Model Drop Down Menu , while the Align and Split commands can also be accessed from the Food web Drop Down Menu .
Table 1. Summary of button functions on the main SIM toolbar. Note that the first six buttons only work on the food web layout page, while the balance and simulation buttons also work on the parameters and feeding preferences pages.
To create a new food web, first use the draw tool to add a new functional group. Click on the draw tool and then click anywhere on the blank page to position the group. A new parameters dialogue box will appear:
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Your new functional group will be given the default name ‘1’ (subsequent groups will be named ‘2’,
‘3’, etc.) but you can choose your own name, e.g. ‘Earthworms’ and type it in the name field. If you know the values of the other parameters, you can set these too, but you may wish to construct the layout of the food web first and add all your functional parameters at a later stage (Section 4.2).
Please note that the first functional group in any food web MUST be detritus; even if your food web contains no detritivores it is necessary to include a detritus functional group (which need not be explicitly linked to other functional groups) into which all unassimilated carbon, faeces, and dead material collects. If detritivores are included in the food web, it is essential (and biologically correct) that their assimilation efficiencies are set to <1 or the calculations will produce misleading results.
Once you have named your functional group and entered any other parameters, click OK (if you have made a mistake and wish to abort the operation, click on Cancel). After clicking OK, the food web layout screen will reappear, and your first functional group will be represented by a turquoise box.
Note that if you have used a long name for your group, not all the letters will be displayed.
To add a second functional group, click somewhere else on the food web layout screen. You do not need to click the draw tool again, as the program will remain in draw mode until the operation is cancelled. Do not worry about aligning the functional groups at this stage, as this can be done automatically later. However, if you wish to move functional groups about on the food web layout, this can be done by clicking on the arrow tool . A single click selects the functional group for movement, which is shown by the appearance of a perimeter of eight black squares (see Bacteria functional group in the image below). Simply drag the functional group to its new position. Double-clicking on a functional group with the arrow tool will open the parameters dialogue box once again (Section 4.2)
Continue adding functional groups until all the groups you need in your food web are present. More can be added at a later stage if necessary. In the example below, five functional groups have been created:
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If you make a mistake and wish to remove one of the functional groups, use the eraser tool . Simply click on the erase button and click once on the functional group to be removed. Note there is no undo tool in this program so the only way to reverse an erasure is to replace the functional group using the draw tool . If you erase a functional group and then replace it, it will not necessarily be given the same number as originally allocated. For example, if the earthworms functional group is erased and then replaced in the example above, its number will be changed from 1 to 5.
4.2 Adding data to functional parameters – the parameters dialogue box and parameters page
There are three ways to modify the parameters of a functional group
Add the data into the functional parameters box when the functional group is created
Add the data into the functional parameters box at a later stage by selecting the arrow tool and double clicking on the appropriate functional group
Use the tabs at the bottom of the screen to navigate to the parameters page. In this mode, you can modify any or all of the functional groups.
The parameters page provides details on the intrinsic ecological features of each functional group (i.e. there is no information about the relationships between groups). The categories listed initially are biomass, death rate, assimilation efficiency, production efficiency, initial 13 C proportion and labile proportion. After the food web has been balanced (Section 4.6) the parameters are updated to include predation mortality, feeding rates, respiration and biomass lost for each functional group.
Please note that the parameters provided as default values when new functional groups are created are not necessarily appropriate, or even plausible, in most cases. In particular the default values of assimilation efficiency and production efficiency are suitable for the first functional group (detritus) but not for higher trophic levels; we suggest that values based on those in the Sourhope food web supplied with SIM (typically production efficiency = 0.05, assimilation efficiency = 0.5) are more appropriate for these levels.
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In some operating systems, particularly Windows 98, the software does not accept its own default values of 13C when simulating a C4 site and displaying 13C signals in delta notation rather than as simple concentrations, due to a rounding error. If this occurs, the user can remedy the problem either by ensuring they work in simple concentrations rather than delta notation (by clicking the appropriate box under File -> Options), or by manually increasing the default 13C value very slightly (e.g. to –
12.0074).
The parameterisation of each functional group is not a trivial matter and is beyond the scope of this
User Guide; Hunt et al. 1987 and Berg et al. 2001 (and references therein) provide helpful details. It should be noted that, because the governing equations for stable isotope dynamics rely on concentrations of labelled carbon, any units of biomass may be used in the parameterisation of the model PROVIDED THESE UNITS ARE CONSISTENT ACROSS ALL FUNCTIONAL GROUPS.
For example, biomasses might all be measured as grams per m 2 , or grams per sampled soil core: provided all units are consistent the pulse simulations will still be valid.
Please note that the “Labile proportion” or each functional group, visible when editing the functional parameters box and also when all parameters are displayed using the parameters tab, is under development and has not been implemented in this release of the software. It is assumed that all biomass within any functional group can be regarded as labile.
4.3 Adding links in the food web – the food web layout page
Once the functional groups and their initial intrinsic parameters have been entered, relationships between the different functional groups can be developed. This is carried out on the food web layout page by adding links between functional groups. The links are unidirectional arrows and represent net carbon flow in the direction of the arrow.
To add a link between two functional groups, select the link tool . Click and hold on the functional group that is to be the source of the carbon (e.g. the prey in predator-prey relationships) and drag the pointer to the sink of the carbon (e.g. the predator in predator-prey relationships). An arrow will appear between the two groups. Further relationships can be set up by repeating this process. Functional groups can be the source and sink for any number of links, as shown in the example below. There is no need to click on the link tool each time you add a link, since the program will remain in link mode until cancelled.
The erase tool can be used to remove links that are added by mistake. Click on the erase button and simply click on the link to be removed. If the food web is complex with many overlapping links, it is best only to remove links which are clearly separated from their neighbours. If necessary, functional groups can be dragged around the screen using the arrow tool in order to separate the links. Always choose a clear line rather than a dense cluster of overlapping lines when you use erase. Alternatively, the user can delete links very easily within the “Feeding preferences” tab, simply by setting the appropriate feeding preference to zero (see below).
4.4 Adding data to feeding relationships – the feeding preferences page
Once relationships have been defined by adding links to the food web layout page, the feeding parameters can be established. This can be done in two ways:
By navigating to the feeding preferences page, values can be entered in the feeding preferences table for all relationships.
By selecting the arrow tool and double-clicking on a particular link on the food web layout page, feeding preferences can be added for individual relationships.
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In SIM, predators feed on their prey in proportion to the body weight of their prey, which in turn influences the feeding rate. On the feeding preferences page, the rows correspond to prey (carbon source) and the columns to predators (carbon sink). Default values are set at either 1 (which indicates a predator-prey relationship) or 0 (which means there is no link). The diagonal of the table shows 0 values because one functional group cannot prey on itself. Increasing the number above 1 increases the feeding preference, i.e. the amount of that prey eaten by that predator is higher than average. Reducing the number below 1 reduces the feeding preference, i.e. the amount of that prey eaten by that predator is lower than average.
4.5 Aligning the food web
When the food web is complete and all data values have been added, clicking the align tool redraws the food web so that functional groups on the same integer trophic level are vertically aligned. The example below shows before and after alignment with our simple example food web. The align command can also be accessed from the Food web Drop Down Menu .
Before After
When, in a particularly complex simulation, a single trophic level contains more than eight functional groups, it is possible that functional groups in the aligned web may “disappear” off the bottom of the screen. If this happens, their properties and links can still be manipulated by editing contents of the
“parameters” and “feeding preferences” pages directly.
4.6 Balancing the food web
Once all the data on functional group parameters and their feeding relationships have been added, the food web must be balanced by applying the balance tool or using the balance command, which can be accessed from the Model Drop Down Menu . The balance tool can be used on any of the three major display pages (food web layout, parameters or feeding preferences) and its function is to assimilate the intrinsic parameters and feeding relationships between the functional groups, and create several new datasets. These are:
Predation mortality
Feeding rate
Respiration
Biomass lost
The new datasets are added automatically to the parameters page.
Balancing also generates a new feeding rate page , which can be accessed using the tabs at the bottom of the screen.
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4.7 Stable isotope modelling
With the food web balanced, stable isotope modelling can now be applied. This is achieved using the simulation tool . Clicking on this tool will bring up the simulation parameters dialogue box , which can be used to select the length of the simulation in days, weeks, months or years, and the length of time between time points on the resulting graph.
Once the desired values have been chosen, click on OK, or click Cancel to abort the simulation.
The simulation is performed and a scale bar shows the progress of the simulation. Once the simulation is complete, three new tabs appear on the status bar at the bottom of the screen. The eigenvalues and eigenvectors page shows the calculated eigenvalues and eigenvectors of the model. Each column shows the eigenvector and below it the corresponding eigenvalue. The carbon fluxes page shows the carbon flux data, which is used to plot the carbon flux graph. The carbon flux graph page shows the proportion of 13 C against time, in the units specified above in the simulation parameters dialogue box.
The plus and minus buttons on each axis can be used to expand and contract the scale. The graphical output in the carbon flux graph page provides a rapid visualisation of pulse dynamics, but may not offer sufficient flexibility in terms of colours for functional groups or upper/lower limits of axes. If more flexibility of required, the data are readily exported in a form suitable for use in specialist graphical and spreadsheet software e.g. Microsoft Excel (see the Export option in Section 5).
5. File management
File management in SIM is carried out using the file menu , although the operator is always prompted with the food web dialogue box and so can choose between new, saved and library files when the program first opens (Section 3).
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From the file menu, the user can choose the following options:
New. Opens the food web dialogue box , allowing the user to choose between new, saved and library files (Section 3).
Open. Allows the user to open a previously saved file, or a file archived in the SIM library. The default source is the library folder. The two example food webs supplied with SIM, “Sourhope” and “Simple
Example Food web”, are accessed using this facility.
Save. Allows the user to save a current file to a specified location. The default location is the library folder.
Export . Exports data into a third party plotting program. The data exported is dependent on the page selected, and details can be found in the SIM help file.
Options. Allows the user to set default values and units used in the model.
Exit. Quits the program.
SIM does not automatically save modified versions of your files. If Exit is selected without the current file being saved, a prompt will appear asking if you really want to lose the current file without first saving it. Note that opening a new file or a previously saved file will remove any food web that is currently open without saving it. Save the current file before opening another.
6. Help
The help menu provides on-the-job help with the use of drop down menus, toolbars, the status bar
(showing the tabs for each page) and the types of data listed on each page. The help menu also provides a keyword search facility and information about the program. There is a print facility, accessed by clicking the printer icon, allowing the user to take a hard copy of any particularly useful pages.
7. References
Berg M, DeRuiter P, Didden W, Jansen M, Schouten T, and Verhoef H (2001) Community food web, decomposition and nitrogen mineralization in a stratified Scots pine forest soil. OIKOS 94, 130-142.
Fitter AH, Gilligan CA, Hollingworth K, Kleczkowski A, Twyman RM, Pitchford JW and the members of the NERC Soil Biodiversity Programme (2005) Biodiversity and ecosystem function in soil Func.
Ecol.
(in press).
Hunt HW, Coleman DC, Ingham ER, Ingham RE, Elliott ET, Moore JC, Rose SL, Reid CPP and
Morley CR (1987) The detrital food web in a shortgrass prairie. Biol. Fert. Soils 3, 57-68.
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Food web model
The basic food web model is based on that described in Hunt et al. (1987) and Berg et al. (2001). To this framework has been added the facility to simulate 13 C pulse experiments through the food web, enabling the user to validate the model’s outputs against newly available stable isotope data (Fitter et al. 2005). The underlying food web model envisages the soil ecosystem as a network of connected boxes, each box corresponding to a species or functional group and the connections representing directed trophic linkages between them (e.g. Figure 1). The central assumption is that the biomasses in all functional groups remain constant over time (the default unit of time is one year in the software) so that, for each functional group, one can assert biomass gained = biomass lost
The implementation of this basic principle across the web uniquely defines all the carbon flows. In practice the situation is more complicated, involving mortality, variable prey preferences, and production and assimilation efficiencies, as explained in detail below.
Modelling 13 C pulses in the food web
Once the feeding rates between functional groups have been calculated as outlined above, the fate of a
13 C pulse through the system can be tracked by employing simple laws of mass action. The model assumes that labelled carbon behaves identically to 12 C (i.e. that there is no significant fractionation on the time scale of the pulse). This results in a system of linear ordinary differential equations (ODEs), which are solved numerically to produce graphs of 13 C concentration against time, for each functional group. The “first order dynamics” implicit in this ODE representation ensures that only rather simple graphs of 13 C against time can emerge; in any given (non-basal) functional group there will always be a period of 13 C increase culminating in a single peak and followed by a slower decay in the signal. Whilst the equations are derived and the calculations undertaken using biomass proportions of 13 C, the software allows the user to opt for output using

13 C notation. In response to comments from users, natural abundance of 13 C is explicitly taken into consideration: the user can opt to choose default natural abundances corresponding to a site dominated by either C3 or C4 plants (with consequent differences in the

13 C of soil organic matter), or can set natural abundance to zero.
Fundamental equations for solving carbon flows through the food web
All notation is based on that in Berg et al. (2001). Each functional group j has associated with it the following parameters, which must be supplied by the user:
B j
- biomass d j
- rate of deaths not due to predation i.e. natural mortality rate p j
- production efficiency a j
- assimilation efficiency w jk
- relative preference for food type k over other foods
One then defines, for each group j ,
F ij
F j
M j
- loss of biomass inflicted on i due to predation by j
- total loss of biomass inflicted on all of j ’s prey due to predation by j
- loss of biomass of j due to predation by j ’s predators
One can calculate the total feeding rate for each functional group j by requiring that biomass lost = biomass gained:
F j a j p j

M j
 d j
B j

F j

M j
 d j
B j a j p j
One can then evaluate the feeding rate F ij of group j on group i by calculating what proportion of group j ’s diet is based on group i and multiplying that by the overall feeding rate of group j :
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F ij
 w ij
B i k n 

1 w kj
B k
F j
F j
 n  i

1
F ij
The SIM software performs these calculations sequentially, starting with the functional groups corresponding to the top predator(s), and working backwards through the food web. The actual algorithm used involves using a “queue”; groups are added to the queue only if all of their out-flows are known, and removed from the queue only when all of their in-flows have been calculated. This allows the software to handle complex food web structures.
The carbon mineralisation rate is the amount of carbon assimilated but not used in the production of new biomass (Berg et al. 2001):
C min
 j n 

1
The software provides the user with values of F ij a j
( 1
 p j
) F j
(in the Feeding Rates tab) and C min
(as Respiration in the Parameters tab) for all food web connections and functional groups respectively.
Fundamental equations for simulating a 13C pulse through the constant biomass food web
Total input into the compartment
F j
Into detritus from assimilation of compartment F j
Total assimilated: a j
F j
Loss from assimilation
(feces etc):
(1-a j
)F j
Total loss:
(1-a j p j
)F j
Total assimilated and used for production: a j p j
F j
Loss from production
(mainly respiration): a j
(1-p j
)F j
Species j: biomass B j
Mineralisation from compartment
F j escapes the system as respiration (CO
2
) dj B j
M j
Into detritus from death from compartment F j
Let z j
= z j
(t) be the proportion of 13 C in functional group j at time t.
During a small time interval
 t the amount of carbon reaching the group from groups in lower trophic levels is
 t
 i
F ij
(see the above diagram) of which a fraction
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 t
 i z F i ij is 13 C. The incoming carbon is then partitioned and (i) transferred to detritus through wastage, (ii) assimilated and respired, and (iii) assimilated and used to produce new biomass (see the above diagram), with appropriate proportions of 13 C associated with each gain or loss term. It is assumed that after the end of each small time period “old” biomass is indistinguishable from “new” biomass. The carbon also leaves the current group by death and predation, and
 t z d B j
 j j
  k
F jk
 is the fraction of this transfer that is 13 C. Thus the proportion of 13 C in group j at time t +
 t consists of the proportion of 13 C in the new biomass, plus the amount of 13 C in the existing biomass, minus the 13 C in the lost biomass to the entire biomass. Allowing
 t to tend to zero allows one to write the set of coupled differential equations
B j dz j 




dt
  i
F z ij i
 a j
  i
F z ij i


 a j

 p j
  i
F ij

 z j
 d B z j j j
  k
F z jk j for each functional group j . The above formula assumes that the respiration reflects 13 C abundance of the respiring species, and is implemented in the SIM. An alternative formula, in which the respiration carbon reflects the prey abundances, has also been considered.
For primary producers, the gain term is replaced by z c
 i
F ij where z c represents a natural abundance of 13 C in the carbon input.
Thus, once the F ij
have been calculated, the progress of a 13 C label through the food web can be followed by solving the above system of linear ordinary differential equations. This can (in theory) be achieved analytically via a diagonalisation process (i.e. by identifying the eigenvalues and eigenvectors of the above system of equations and solving directly), but in the SIM software these equations are solved using an explicit Euler method. An analysis of the dominant eigenvalues, and their corresponding eigenvectors, may in principle be used to identify the key pathways along which carbon flows through the food web. At the time of writing such an analysis has not proved successful when confronted with observational data; the noise in these data (due to spatial and temporal heterogeneity and/or observational error) has been too large to allow any convincing ecological insight to be achieved.
It should be noted that, following the above derivation, a slightly modified equation governs the 13 C signal z
D
in the detritus, since this compartment acts as a sink for all unassimilated carbon and external mortality. Under the assumption of a constant biomass in the detritus compartment we obtain dz
D dt

  i j
( ) ij
(1
 a j
)
  k d B z t
 z t
B
D
 k
F
Dk
It can be shown that unassimilated non-living carbon can accumulate in the detritus (thereby violating one of central assumptions of the Hunt model) and this can cause a slow linear drift in the model’s prediction of 13 C signal across the food web. In the SIM software this possible slow accumulation of detritus is artificially compensated for at each time step (i.e. detrital biomass is artificially constrained to remain constant) so as to ensure that all proportions of 13C tend to natural abundance over long periods of time. This artificial constraint has a negligible effect on the order and timing of 13 C peaks.
Sample application of SIM
The default “Sourhope” food web supplied with SIM provides an example of how the model can be applied to a particular system, and can be readily adjusted when more data or expertise are available.
An early Sourhope model, based on published Soil Biodiversity data where possible but relying on
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Hunt et al. (1987) and Berg et al. (2001) for food web structure and certain key parameters, proved unsatisfactory: overall carbon flux and respiration were unrealistically low, and the order of peak 13 C signal in the various groups was inaccurate. After the active involvement of several more applied scientists, several modifications were made to the model, in particular reduction of detrital feeding preferences and amendment of linkages. This process resulted in a more realistic model, both in terms of overall carbon flux and detailed simulation of 13 C labelling. Figure 1 summarises the Sourhope food web resulting from this process.
Figure 1: Proposed Sourhope food web resulting from July workshop. Dark lines represent the original model linkages, the medium grey lines represent linkages added, and the light grey lines are linkages removed from the model.
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