SIM user guide - NERC Soil Biodiversity Thematic Programme

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SIM user guide
1. Introduction
SIM (Stable Isotope Modelling) is a Windows-based program that provides the user with the facility to
design food webs and simulate 13C 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 13C 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:
2
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 13C 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 m2, 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 13C 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.
8
SIM user guide – Technical Annex
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 13C 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 13C 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 12C (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 13C concentration against time, for each functional
group. The “first order dynamics” implicit in this ODE representation ensures that only rather simple
graphs of 13C against time can emerge; in any given (non-basal) functional group there will always be a
period of 13C 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 13C, the
software allows the user to opt for output using 13C notation. In response to comments from users,
natural abundance of 13C 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 13C 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:
Bj - biomass
dj - rate of deaths not due to predation i.e. natural mortality rate
pj - production efficiency
aj - assimilation efficiency
wjk - relative preference for food type k over other foods
One then defines, for each group j,
Fij - loss of biomass inflicted on i due to predation by j
Fj - total loss of biomass inflicted on all of j’s prey due to predation by j
Mj - 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:
Fj a j p j  M j  d j B j
 Fj 
M j  d jBj
aj pj
One can then evaluate the feeding rate Fij 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:
9
Fij 
wij Bi
n
w
k 1
kj
Fj
Bk
n
F j   Fij
i 1
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):
n
C min   a j (1  p j ) F j
j 1
The software provides the user with values of Fij (in the Feeding Rates tab) and Cmin (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
Into detritus
from assimilation of
compartment Fj
Total input into the compartment
Fj
Loss from assimilation
(feces etc):
(1-aj)Fj
Total assimilated:
ajFj
Total loss:
(1-ajpj)Fj
Loss from production
(mainly respiration):
aj(1-pj)Fj
Total assimilated
and used for production:
ajpjFj
Mineralisation from compartment
Fj
escapes the system as
respiration (CO2)
Species j:
biomass Bj
dj Bj
Into detritus
from death from
compartment Fj
Mj
Let zj = zj(t) be the proportion of 13C 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 Fij
(see the above diagram) of which a fraction
10
 t  i zi Fij
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is 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 13C 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 j  d j B j   k Fjk 
is the fraction of this transfer that is 13C. Thus the proportion of 13C in group j at time t + t consists of
the proportion of 13C in the new biomass, plus the amount of 13C in the existing biomass, minus the 13C
in the lost biomass to the entire biomass. Allowing t to tend to zero allows one to write the set of
coupled differential equations
Bj
dz j
dt
 gain from food  waste  respiration  death  predation


  Fij zi  1  a j   Fij zi   a j 1  p j   Fij  z j  d j B j z j   F jk z j
i
i
i
k


for each functional group j. The above formula assumes that the respiration reflects 13C 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
zc  Fij where zc represents a natural abundance
i
of 13C in the carbon input.
Thus, once the Fij have been calculated, the progress of a 13C 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 13C
signal zD 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
dzD

dt

i
j
zi (t )Fij (1  a j )   k d k Bk zk (t )  zD (t ) k FDk
BD
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 13C 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 13C 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 13C
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 13C 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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