McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
Spatially explicit spreadsheet modelling for optimising the efficiency of
reducing invasive animal density
Clive R. McMahon, Barry W. Brook, Neil Collier, Corey J. A. Bradshaw
Appendix 1. User manual for the Spatio-Temporal Animal Reduction (STAR)
model
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
Overview .......................................................................................................................... 4
Compartmentalisation ................................................................................................... 5
Improving user-interface and model performance ..................................................... 5
General cell-changing rules ........................................................................................... 6
Worksheet layers ............................................................................................................ 7
Inputs ........................................................................................................................... 7
Choosing a species ................................................................................................... 9
Scenario .................................................................................................................... 9
Map ........................................................................................................................... 9
Status ...................................................................................................................... 10
Population dynamics parameters ............................................................................ 10
Maximum rate of population increase (rm) ............................................................. 13
Maximum carrying capacity (Km)........................................................................... 13
Mean carrying capacity (K) .................................................................................... 14
Growth response shape parameter () .................................................................... 16
Starting proportion relative to K – initial fraction of K: D0 ( K) ......................... 16
Minimum density (Minimum D) ............................................................................ 17
Projection interval (Duration)................................................................................. 17
Escarpment K modifier ........................................................................................... 18
Escarpment dispersal modifier ............................................................................... 18
Culling .................................................................................................................... 19
Cell Size.................................................................................................................. 20
Dispersal ................................................................................................................. 20
Logistical costs ....................................................................................................... 22
Hunting efficiency .................................................................................................. 22
Revenue .................................................................................................................. 23
Budget ..................................................................................................................... 24
Run Simulation button ............................................................................................ 24
Habitat area ............................................................................................................. 24
Pre-specified management scenarios ...................................................................... 25
Budget and Density Optimisation........................................................................... 32
Non-spatial / Budget ............................................................................................... 33
Non-spatial / Minimum Density ............................................................................. 35
Spatial / Budget ...................................................................................................... 35
Culling ....................................................................................................................... 36
Distribution ............................................................................................................... 39
Culling Costs ............................................................................................................. 39
Culling Scenario Maps ............................................................................................. 40
Damage ...................................................................................................................... 42
Areas of Vexation ..................................................................................................... 43
Output ........................................................................................................................ 44
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
Output Maps ............................................................................................................. 47
PopSim ....................................................................................................................... 50
PopC........................................................................................................................... 51
Habitat ....................................................................................................................... 51
Elevation .................................................................................................................... 51
Dispersal .................................................................................................................... 52
Bioeconomics ............................................................................................................. 53
References...................................................................................................................... 55
3
McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
Overview
Using Microsoft Excel® worksheets and Visual Basic for Applications (VBA)
programming language, we have chosen to model the population dynamical response to
different culling regimes that have or might be imposed upon the feral animals in
Kakadu National Park (Kakadu). The choice of computer package was based on its ease
of implementation, visual power and ubiquity (almost every PC should be able to run
the model). Thus, it should be easy to distribute among potential users and provides a
clear visual output for the development of management strategies.
The model provides spatial information in the form of grid-based maps that are
linked through the processes of births, deaths, immigration and emigration. The model
is habitat driven in that animal densities are ultimately linked to the habitat quality of
the region of interest. This process necessarily required a simplification of the spatial
grain of investigation and the habitat complexity of the region because finer-scale
outputs would have been too computationally expensive and are limited by data
availability. Therefore, we chose to model the spatial structure of feral animal control
measures on a 10  10 km cell grid of the entire park. Thus, park, district and habitat
boundaries are approximations of the real-world coordinates.
Although there are many feral animal species currently occupying parts of
Kakadu, we have provided explicit, pre-specified information for three of these: pigs
(Sus scrofa), swamp buffalo (Bubalus bubalis) and horses (Equus caballus). Other large
herbivorous feral species such as donkeys (Equus asinus) and cattle (Bos taurus) have
not been included because they are lower in abundance, and furthermore, their
population dynamics resemble species represented specifically by the model.
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
We have designed the model for maximum flexibility while limiting the amount
of complexity or required inputs necessary to run simulations. We expect that users with
various degrees of computer and mathematical training will use the model, so we
prescribe specific components in an attempt to reduce confusion, including a suite of
pre-designed culling scenarios and optimisation routines. It should be noted that this
model should be used as a heuristic tool and not as a predictive tool. In other words, the
results should inform management direction and not be used to predict vast population
changes over the short-term future of the park.
Compartmentalisation
Each named worksheet in the Excel file comprises specific information relating to a
particular spatial layer or group of input variables. Some of these layers are designed for
user modification; others must not be modified during a model run. Other cells are
directly modified by the user and are ‘open’. The following section details how each
layer and input variable should be modified by the user, with particular emphasis on
maximum flexibility.
Improving user-interface and model performance
There are a few things that you need to consider when beginning to use the STAR
model. Different screen resolutions on different computers will inevitably lead to
different magnifications when viewing each worksheet layer. We have attempted to
optimise the screen magnification for a fairly high-resolution screen, but not all users
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
will have access to such a monitor. You can easily adjust the worksheet’s magnification
by adjusting the ‘zoom’ tool in the lower right-hand corner of the Excel window, e.g.,
Try to find a zoom level that maintains figure clarity but brings as much of the
worksheet as possible into view.
Although the STAR model file is relatively small, the optimisation routines (see
more detail below) can make your computer work extremely hard in the background
(with the spatial/budget optimisation taking the longest to run). This can result in Excel
storing unnecessary temporary files if too many optimisations are run sequentially. If
your computer is taking a long time to process an optimisation run, then we suggest you
let the current run finish, shutdown Excel, re-open Excel and re-load the STAR model
file. This will clear Excel’s over-burdened memory and allow for faster processing.
General cell-changing rules
In each spatial layer and especially in the Input worksheet, cell modification capacity
has been colour-coded according to the following key:

Blue cell values – these are cells whose values must be modified directly by the
user prior to running a particular model scenario. In some cases, these cells
cannot take on values outside a particular range (e.g., a probability ranging from
0 to 1). In these cases we have provided a validation check where completely
unrealistic values cannot be entered into the cell. In other cases, blue cell values
will update automatically depending on the choice of species, scenario or map
chosen.
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009

Green cell values – these cells can be modified by the user, but they should only
be modified with a more advanced understanding of model structure. These cells
are also bounded so that overly unrealistic values cannot be entered (although
there is generally more flexibility here than for blue cells). We have
endeavoured to obtain as realistic values as possible for these cells to limit user
confusion, but they can still be modified if deemed inappropriate for a particular
modelling scenario.

Red cell values – these cells should not be modified by the user. They usually
represent the results of formulae or other hard-coded values.
Worksheet layers
The various worksheet layers can be accessed by clicking on the tabs at the bottom of
the screen – these are: Inputs, Culling, Distribution, Culling Costs, Culling Scenario
Maps, Damage, Areas of Vexation, Output, Output Maps, PopSim, PopC, Habitat,
Elevation, Dispersal, and Bioeconomics. The function of each worksheet layer is
described in detail below.
Inputs
This worksheet entails most of the input parameters required for each model simulation
(see Figure A1). This layer also includes two special features of the model: (1) prespecified management scenarios and (2) optimisation for specific budgets and density
target goals. The pre-specified scenarios and the optimisation options are described in
separate sections below following a detailed description of specific input cells. You will
also notice in the lower right-hand corner of this worksheet a series of buttons that allow
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
for quick navigation to some of the more frequently accessed worksheets, specifically
the Output and Output Maps worksheets:
Similar buttons are available in those worksheets that allow for quick and easy
navigation back to the Inputs worksheet.
Figure A1. The Inputs worksheet for the STAR model.
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
Choosing a species
Input the species of interest for the particular simulation. Possible values are ‘Pig’,
‘Buffalo’ or ‘Horse’. Note that these should be in singular form. No other values can be
entered into this cell. If you highlight this cell with the mouse, a drop-down menu will
appear that allows you to pick one of the three species. Some fields update
automatically with each new species entered. These parameter values will be explained
in more detail below.
Scenario
This drop-down menu selects one of the 32 pre-specified scenarios given in the table on
the far right of the Inputs worksheet. See section on Pre-specified management
scenarios below for more details.
Map
This drop-down menu allows the user to select one of 16 pre-defined spatial culling
regime maps that are described in more detail in the Culling scenario maps worksheet
below. These culling maps only define the areas to cull (or not to cull) and do not
specify any other parameters such as cull rate. This field is also updated when a
particular scenario is loaded (e.g., when Scenario 1 is loaded, Map 4 – ‘No cull’ is
loaded into this field).
A pop-up window will appear each time a map is loaded successfully, e.g.,
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
The choice of the ‘Custom’ field in the drop-down menu (last item) is reserved for when
you wish to revert to a user-defined culling map set in a previous run. This option
essentially reloads the current culling map and prevents optimisations from loading
particular maps.
Status
This cell indicates whether a pre-specified management scenario chosen has been
loaded correctly by showing the word Loaded. Any changes to the Inputs worksheet
after loading a scenario will change the cell to say Not Loaded. See section on Prespecified management scenarios below for more details.
Population dynamics parameters
For this exercise we employed one of the more-common population dynamical models
used to describe population trends over time – the -logistic model. The advantage of
using this model to describe populations over time is that it determines the form of
density feedback. In other words, the rate of population increase depends on the number
of animals in the population. For example, when the population is relatively small, the
per capita resources such as food and breeding areas are relatively abundant, so on
average an individual has a higher chance of surviving and producing more offspring.
However, when the population is large, individual resource availability declines and
parameters such as survival and fertility suffer. Most population demonstrate some form
of density feedback, and the -logistic model allows full flexibility to describe this
relationship:
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
Here, Nt = population size at time t, r = realized population growth rate, rm = maximum
intrinsic population growth rate, K = carrying capacity, and θ permits a nonlinear
relationship between rate of increase and abundance (if set to 1, the relationship is
linear). The fundamental aspect of this relationship is generally a declining r with
increasing N (Figure A2).
Figure A2. The theoretical relationship between the population rate of change (r) and
population size (N).
>1
=1
r
<1
N
Here,  (the shape parameter) will determine how r varies with N. This is described in
more detail below. The main component of the r versus N growth response is that when
a population increases, the amount it can increase from one year to the next starts to
decline. This makes a lot of sense when you consider, for example, that the amount of
food per individual starts to decline when populations become large, so that each
individual’s survival and number of offspring produced decline.
The various parameters of the -logistic model have been set and are derived
mainly from the literature. However, we have designed the input page to allow changes
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
to be made to some of these values. Table A1 summarises these parameter estimates and
provides the source used to define them.
Table A1. Base model parameters used to describe feral herbivore population dynamics
in Kakadu. Parameter descriptions follow in subsequent sections. rm is a dimensionless
parameter, but 100× (1- er) is equal to the seasonal percentage increase in the
population. Km is in units of density (individuals per km2). A  value > 1 implies that
density feedback operates most strongly close to carrying capacity, whilst  < 1
indicates a stronger effect of density at low numbers. Habitat types found to harbour the
highest densities for each species in northern Australia are shown as ‘top habitat’. The
final parameters (kill intercept and kill slope) are parameters in the kill efficiency
functional response outlined in more detail below.
Parameter
Pigs
Buffalo
Horses
Reference
rm
0.34
0.17
0.20
Bayliss & Yeomans 1989
Graham et al. 1982; Hone
Km
12.6
25.2
7.2
1986; Bayliss & Yeomans
1989; Freeland 1990

1.3
10.3
wetland /
top habitat
Floodplain
wet
woodland
kill intercept
0.1464
0.102
1.0
open woodland /
floodplain
-1.445
-0.673
Jedrzejewska et al. 1997
Bayliss & Yeomans 1989
NA (assume
Bayliss & Yeomans 1989;
value for
Choquenot, Hone &
buffalo)
Saunders 1999
NA (assume
kill slope
Dublin et al. 1990;
value for
buffalo)
Bayliss & Yeomans 1989;
Choquenot et al. 1999
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
Maximum rate of population increase (rm)
The maximum rate of population increase differs among species and is a function of
survival probability and fertility. For example, pigs have an exceptionally high rm given
their ability to produce multiple large litters annually. The values used here are
estimated from allometric (body size) relationships explained in Bayliss & Yeomans
(1989). rm is a dimensionless parameter, but 100× (1- er) is equal to the seasonal
percentage increase in the population. The model is designed to give population change
seasonally (wet/dry season) because most control efforts would be implemented during
the dry season. For simplicity we have assumed that population growth would be
identical for each season (on average). Therefore, the rm value in red becomes the
maximum rate shown in the table divided by two.
You will notice that there are two cells to the right of the maximum growth rate
cell under the heading ‘sensitivity’. This effectively allows the user to test the sensitivity
of model projections to variation in parameter values. The user can set a desired
uncertainty (under the ‘% var’ subheading) as a percentage (limited to 1 to 50 %), and
then choose whether the parameter is taken from the lower, mean or upper end of this
set uncertainty range (via a drop-down menu under the ‘lo/mn/up’ subheading). This
option is extended to other parameters (described below) such as carrying capacity (K),
theta parameter in the theta-logistic model (), the escarpment K modifier and the
escarpment dispersal modifier.
Maximum carrying capacity (Km)
The concept of maximum carrying capacity should not be taken as the ‘maximum
number of animals the land can support’ because this value will change from year to
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
year depending on a number of environmental factors such as rainfall and fire patterns.
However, Km is a useful guide to what animal densities could achieve under ‘optimal’
conditions and so it is a useful heuristic tool for directing management effort. We have
set Km to the maximum values observed for these feral species from various areas
throughout northern Australia (Graham et al. 1982; Hone 1986; Bayliss & Yeomans
1989; Freeland 1990). Km is expressed in units of density (individuals per km2). These
values are shown in the Base Settings table in the centre of the Inputs worksheet. More
on habitat-specific carrying capacity is given below.
Mean carrying capacity (K)
Obviously, K will not be constant across the landscape because different species have
different habitat requirements. Therefore, habitat type will dictate how many animals
can be supported. The mean K has been calculated within the worksheet using the
following logic:
1. The optimal habitat for a given species has the maximum carrying capacity
(but modified relative to starting K values – see below). The optimal habitats
are assumed to be floodplain for pigs, paperbark forest for buffalo and
savanna-woodland for horses (Bayliss & Yeomans 1989).
2. Given that there are a total of four available habitat complexes in the model,
we assumed that densities would vary among habitat types. Using published
work and anecdotal evidence we assumed that habitat-specific K would
represent approximately 2 3 Km in the next-best habitat type, 1 3 Km in the
following habitat type and 1 6 Km in the least-optimal habitat type. For pigs,
we set this habitat sequence as floodplain – paperbark – savanna/woodland –
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
forest. For buffalo, the sequence was paperbark – floodplain –
savanna/woodland – forest, and for horses it was savanna-woodland –
floodplain – paperbark – forest.
3. The average K was then calculated as the mean over all habitat types for
each species.
These values can, of course, be modified as more information on habitat selection
relative to carrying capacity becomes available. The user does have the immediate
option, however, of modifying habitat-specific carrying capacity and relative habitat
suitability directly.
An examination of the Base Settings table in the centre of the Input worksheet
shows the species-specific values that are used when the choice of target species is
made. The user will notice that the relative carrying capacity for each of the four general
habitat types in Kakadu is given for each species. Below these values is a Relative
suitability score that essentially provides the maximum carrying capacity density for
each habitat type. Assuming that the highest densities indicated in Table 1 are realistic
values for Kakadu, then a value of 1.0 should be placed in the appropriate ‘top’ habitat
type for each species (floodplain for pigs, paperbark swamp for buffalo and savannawoodland for horses). As mentioned above, the default settings start at 1.0 and have
progressively smaller values for progressively sub-optimal habitat types. We
recommend that the user refrains from changing these values until more habitat-specific
densities are measured directly. The habitat-specific densities (maximum carrying
capacity and initial density) for each species’ current run are shown in the Current Run
box at the top centre of the Input worksheet, e.g.,
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
Growth response shape parameter ()
As mentioned above,  is a shape parameter that modifies the relationship between r
and population size (N). There are many theoretical reasons why  should take on a
particular value for a particular species, and it should be much greater than one for longlived herbivores (Fowler 1981; Owen-Smith 2006) given that density feedback does not
seem to be apparent until populations are large. A  value > 1 implies that density
feedback operates most strongly close to carrying capacity, whilst  < 1 indicates a
stronger effect of density at low numbers. We have restricted the cells to accept only 
values greater than 0.
Starting proportion relative to K – initial fraction of K: D0 ( K)
Obviously Kakadu might not be at maximum carrying capacity for each of these
species, even after taking habitat differences and suitability into account. For example,
the extensive culling of buffalo during the Brucellosis and Tuberculosis Eradication
Campaign (BTEC) severely reduced buffalo densities in most of the park (Department
of Environment and Heritage 2004).
The user has the option here of reducing initial carrying capacity (K) by a
particular proportion () for the entire park as the start density to any model simulation.
For example, if buffalo densities are deemed to represent, on average, only 50 % of the
amount of buffalo that could inhabit Kakadu, then this value should be set to 0.5. There
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
is, unfortunately, little information available to prescribe this proportion for each
species given the severe lack of reliable, recent census data. However, the final outcome
of any heuristic modelling exercise should not be affected too greatly by changing this
value erroneously because it will still provide the best combination of control
approaches to reduce population density to target levels. The habitat-specific densities
(maximum carrying capacity and initial density) for each species’ current run are shown
in the Current Run box at the top centre of the Input worksheet.
There are other methods for controlling the densities of individuals within the
park by using some of the options described below such as the escarpment K modifier
and the Distribution worksheet. These items will be outlined in more detail below.
Minimum density (Minimum D)
This cell cannot be changed by the user. It is set to a minimum density relative to K that
would be effectively considered to represent extirpation (near eradication).
Projection interval (Duration)
This value represents the maximum number of years into the future that the user wishes
to project the population within the control (cull) area and the entire park. The longer
the duration the user sets to examine culling effects into the future, the more uncertain
outcomes will be. We suggest limiting projections to between 5 and 20 years into the
future – still well within the budgetary planning constraints of most management
organisations and government departments. All pre-specified scenarios have been set to
project population size over 10 years.
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
Escarpment K modifier
Analogous to the  K modifier described above, this parameter takes into account any
elevation effects on carrying capacity. For example, it is generally believed that there is
a higher density of buffalo in the escarpment country of Kakadu than in the lower areas,
irrespective of habitat type or the effects of the BTEC. Similarly, it is believed that there
are fewer pigs in the higher country than in the lowland areas, irrespective of habitat
type.
We have thus provided a parameter that modifies these escarpment carrying
capacities accordingly. We have arbitrarily set these values to 1.2 for buffalo (i.e., there
are on average 20 % more buffalo per km2 in the escarpment country as there are in the
lowland areas after controlling for habitat type), half as many pigs and half as many
horses. The user can modify these values in the green section of the Base Settings table
on the Input worksheet. The escarpment area is delimited in the Elevation worksheet
described in more detail below.
Escarpment dispersal modifier
As the escarpment K modifier changes the carrying capacity of the escarpment country
relative to the lowland areas, the escarpment dispersal modifier changes the way in
which animals move between cells within each iteration of the model. For example, it is
commonly suggested that the rougher terrain of the escarpment limits the dispersal
capacity of species between adjacent areas (cells). Dispersal itself is described in more
detail below in the Dispersal () parameters and in the Dispersal worksheet. We have
arbitrarily set this value to 0.5 for all species (i.e., dispersal is 50 % less in the
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
escarpment when compared to that in the lowland areas), but if the user wishes to
change the values, they should be updated in the Base Settings table.
Culling
This section of the Input worksheet is the true testing power of the model format. In
addition to setting the spatial arrangement of culling regimes in the Culling worksheet
(see detailed description below), these parameters dictate the temporal flexibility in
culling regimes.
1. Initial Cull – this parameter is the proportion of the initial population that is
culled in the first year of the culling program. Often it is more efficient to
attempt to reduce the target population’s density as much as possible in the first
year of a control program and then maintain the resultant lower density using
reducing culling effort in subsequent years.
2. Maintenance – this parameter is the proportion of the new population that is
culled in years following the Initial Cull. This is often a much lower value than
the Initial Cull.
3. Per cell stopping density – this parameter is set by the user as the maximum per
cell density below which it is no longer deemed efficient to allocate more
resources to continue the reduction in that cell. This value is used by the model
to maximise culling efficiency by allocating effort only to those cells of high
density. This is important from the perspective of the functional response
(described below) that changes the hunting efficiency relative to cell densities.
The value is set in the pre-specified scenarios, and it is estimated in the
optimisation routines (also described below).
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
4. Control area target density – this parameter is set by the user as the maximum
density acceptable under a particular control regime. For example, if it were
deemed that a reduction to 50 % of pre-cull numbers was considered acceptable,
then this value would be set to 0.5.
Cell Size
This value has been hard-coded into the worksheet and indicates the total area of the
cell (10  10 km = 100 km2). It cannot be modified because this would require a
concomitant re-design of the maps.
Dispersal
Dispersal represents the proportion of animals dispersing to and from adjacent cells. For
example, if we take a target cell i, j (Figure A3):
Figure A3. Dispersal of animals among adjacent cells.
i-1,j-1
i-1,j
i-1,j+1
i,j-1
i,j
i,j+1
i+1,j-1
i+1,j
i+1,j+1
Then the dispersal probability dictates the proportion of animals in cell i, j that disperse
out to the eight cells surrounding it. Thus, the dispersal probability for any given cell is
divided by eight to determine how many individuals arrive in each cell. This process is
repeated for each cell in the map of the park.
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
The user has the opportunity to modify the minimum and maximum dispersal
proportions used by the model (min and max). We have defined a simple algorithm that
adjusts the dispersal proportion based on the density of a particular cell. Here, the
dispersal out of a particular cell to its neighbours will increase as the number of animals
in the cell of origin increases. This takes into consideration the observation that animals
are more likely to move out of their home range when per capita resources begin to
decline, or antagonistic interactions between individuals or herds increase.
This simple density-modified dispersal model depends on the maximum and
minimum values set by the user (indicated in green in the Base Settings section on the
Input worksheet). It is unknown what the true proportional dispersal capacity of the
three species modelled is, or how this relates to density, so we have assumed the
following:
1. Dispersal is higher for pigs than for buffalo or horses.
2. Horses demonstrate lower dispersal than buffalo given that anecdotal
information suggests slower rates of spread for horses.
3. Minimum dispersal proportion (the proportion of animals moving out of a focal
cell per year) is 0.01 (i.e., 1 % of the population size, per season).
4. Dispersal is equally likely in wet and dry seasons.
Users can, of course, adjust these values as more information becomes available.
Dispersal is limited to adjacent cells per season; in other words, animals can move no
further than 10 km from their home cell within a given season.
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modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
Logistical costs
This and the subsequent subsections of the Input worksheet incorporate the
bioeconomic components of the model. These parameters are based on the costs
associated with helicopter or ground shooting. Thus, the most-realistic hourly rate for
the hire of helicopters or for the combined salary of ground shooters should be entered
into the first cell (helicopter or ground cost $/hour). The Overhead multiplier is the
additional costs associated with labour, ammunition and other associated costs involved
in the shooting process. These have been estimated as 18 % (i.e., so the modifier should
= 1.18) in the past (Bayliss 1986), but more up-to-date values should be used if
available.
If broad-scale control measures do not avail themselves of helicopter technology
(e.g., on-ground shooting, poisoning, trapping), then the ‘helicopter’ costs can be
downgraded accordingly to an hourly cost of operation for the chosen method.
Therefore, the user would have to express this as the effort equivalent to one hour of
helicopter flight. It should be noted here that although ground-based hunting is likely to
be less expensive than helicopter shooting, more hours of hunting will be required to
achieve the same kill rates. The shape of the function relating animal density to effort
required (see Hunting efficiency below) will remain constant, but the absolute values
(dollar costs) will change according to method.
Hunting efficiency
These values are based on data from various sources for the different species (Bayliss &
Yeomans 1989; Choquenot et al. 1999). The coefficients (intercept and slope) refer to
the following equation:
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
time/kill = intercept  Dslope
where D = animal density (individuals/km2). This is what is known as a functional
response and basically indicates the increasing difficulty of shooting an animal as
population density declines (the relationship in this instance is an exponential one,
whereby culling costs are relatively constant across a wide range of densities but then
become rapidly more expensive as populations are suppressed). These relationships are
shown in the Culling Costs worksheet. The values calculated from this functional
response are multiplied by the cost of helicopter time per hour (set by the user). Values
for pigs and buffalo are available; however, none were found for horses, so we assumed
that the functional response for horses was similar to that of buffalo.
Revenue
If a separate economic analysis can establish that a profit can be made for animals that
are culled (e.g., for the domestic pet meat or international wild meat markets, safari
revenue – e.g., Brook et al. 2006; Bradshaw & Brook 2007), then this value should be
modified accordingly. Alternatively, the ‘benefit’ of eliminating ferals (‘savings’ per
animal removed) with respect to the lessening of damage or cultural/tourist impacts
could be given a pseudo-quantification here for illustrative purposes. Of course for large
culls, not all carcasses will be retrievable (especially if the method of choice is
helicopter shooting), so the profit per individual should be adjusted accordingly.
Similarly, costs involved in retrieval, dressing, refrigeration and shipping should be
reflected in the final per-individual profit value entered.
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
Budget
This cell represents the total budget allocated or required over the entire duration of the
model projection. For example, if $10 million was available over ten years to reduce
animal densities, the user would enter 10000000 into this cell. For a basic run of the
model, this value is not required because each particular run estimates the total cost
associated with particular cull rates and areas. This cell only becomes useful when using
the optimisation routines (described below) when the user is seeking to optimise culling
efficiency for a particular allocated budget. On the other hand, when optimising for a
particular control-area-wide target density, this cell is then modified by the program to
reflect the budget required to achieve the target.
Run Simulation button
Once the user is satisfied that the cell entries are valid, clicking this button
will initiate the model run over the projection interval defined. The user will be taken to
the Output worksheet (described below) at the termination of the model run.
Habitat area
At the top of the Base Settings table in the centre of the Input is a section entitled
Habitat  Area. This table simply sums the total area in Kakadu represented by each of
the four main habitat types (floodplain, paperbark swamp, savanna-woodland and
forest). The total number of 10  10 km cells and the current population size based on
the habitat-specific carrying capacities are also shown here.
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
Pre-specified management scenarios
Inexperienced users or managers with little background in mathematical models used to
direct management decisions can be intimidated to design a particular set of culling
parameters from scratch. In anticipation of this potential problem, we have provided a
series of pre-specified management scenarios that users can examine to become more
familiar with the model’s performance. We have endeavoured to provide realistic
options for feral animal management and have anticipated various possible approaches
useful for cross-scenario comparisons. Although the specific output details and crossscenario comparisons are described in more detail in the main text, here we only
provide a basic guide to their overall structure and how they can implemented.
In general the scenarios we have designed fall into three main categories:
1. A desire to reduce feral animal densities to specified target levels over
large areas.
2. A desire to reduce damage in highly damaged and vexed environments to
specified levels.
3. A desire to maximise profit from feral animal management while
achieving reduction goals.
The 32 scenarios provided are further divided into three main species groups: those
pertaining to (1) pigs, (2) buffalo and (3) horses. Within each of these major categories,
there are several different goals that each scenario attempts to achieve. These can range
from a zero culling rate to examine how populations will change over time with no
management actions, to those that attempt to eradicate a large proportion of the animals
from the park and adjacent areas. Between these extremes are several ‘example’
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
scenarios that have particular final target densities or those that focus on only certain
districts within the park. We have also provided options to examine the effects of
providing ‘refugia’ (areas of zero cull embedded within larger control regions) to
animals, and the consequences of failing to target animals outside of particular control
areas.
Each scenario is described in a table on the right-hand side of the Inputs
worksheet (Figure A4). The first column indicates scenario number, and this is the
number that is loaded in the drop-down menu in the Scenario cell. The second column
indicates the target species; the third describes the scenario’s goals. The next columns
IC, MC, SD, D0, T, and Map refer to Initial cull rate, Maintenance cull rate, Per cell
stopping density, Initial density proportional to K, Duration of the projection and the
map to which the culling regime refers, respectively. The maintenance culling rate and
per cell target density have been set for each scenario based on logic. The initial density
is calculated as the maximum value of either the maintenance cull or 2/3  (1 – stopping
density). We have also set the initial density of pigs to 1.0K due to the ubiquity of this
species within the park, 0.5K for buffalo due to the extensive reductions of density
during the 1980-1990s Brucellosis and Tuberculosis Eradication Campaign (BTEC,
Corbett & Hertog 1996; Skeat, East & Corbett 1996), and 0.75K for horses given their
more-recent invasion of the park. The duration (T) for all scenario projections was set to
10 years.
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
Figure A4. Management scenario table found in the Inputs worksheet.
The parameters have been pre-set in each scenario so that the final population size of
the target species is within 1000 individuals of the target density. The final column in
the Scenarios table refers to a particular culling map defined in the Culling Scenario
Maps worksheet. In this sheet the various spatial arrangements of culling for each
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
scenario are clearly labelled as Map 1, Map 2, etc. For example, Map 1 (Figure A5)
indicates a park-wide cull including a 10-km buffer strip around the park’s boundary.
Figure A5. Map 1: Park-wide culling map. Red denotes cells to be culled.
Map 2 (
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
Figure A6) focuses culling on the high-priority cells (see full description of priority
below),
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
Figure A6. Map 2: Medium & High Priority Areas map. Red denotes cells to be culled.
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
and Map 4 (Figure A7) indicates no culling is to occur during the course of the 10-year
projection.
Figure A7. Map 4: No culling map. Red denotes culling cells (none in this scenario).
To invoke a particular scenario, simply click on the scenario cell, pull down the dropdown menu and select the scenario of interest. This will automatically load the selected
scenario’s parameters. Once loaded, a panel will appear stating that the scenario of
choice has been loaded successfully:
If the user wishes to reload the scenario displayed in the ‘Scenario’ cell, simply click the
Reload scenario button in the lower left-hand corner of the Inputs worksheet:
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
The word Loaded will also then appear in the Status cell.
We have also provided space for eight additional scenarios that the user can enter based
on particular management requirements. It is important that if extra scenarios are
defined, their associated spatial culling maps are also defined in the Culling Scenario
Maps worksheet. These customised culling scenarios have been validated so that they
can only accept realistic values. If the user forgets to enter a value in one of these
custom scenarios (e.g., Initial Cull rate – IC), then a warning message appears:
If this or a similar warning message appears, check to ensure all values are entered for a
particular customised scenario.
For customised scenarios we have provided two blank maps in the Culling
Scenario Maps worksheet as base templates for user modification. If a particular cell is
designated as a cull zone, then a ‘1’ should be placed in the cell. If no cull is planned,
then a ‘0’ should be placed in that cell (see more specific details of culling map design
in the Culling worksheet).
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
Budget and Density Optimisation
This component of the model is probably one of the most important features we have
designed to assist in feral animal management in Kakadu. Although the particulars of
this module are described in more detail in the main text, we outline here some of the
basic features of the optimisation routines.
The term ‘optimisation’ has different implications based on the parameters one
wishes to ‘optimise’ for a particular management scenario. For this reason, we have
provided three different optimisation routines that have different outcomes. For
example, one of the most important components of any broad-scale feral animal
reduction campaign is the normally prohibitive costs associated with culling operations.
The optimisation procedures attempt to find the most effective culling strategies for set
budgets within particular time constraints.
Another optimisation goal is the desire to find the best culling strategies to attain a
particular density. For example, if one wishes to reduce the pig population to 5 % of its
current size, how high should annual culling rates be, and how much will the program
cost? To answer these questions we have provided an optimisation routine that attempts
to find the most inexpensive and effective approach to reduce a population to a target
density. Finally, optimisation of control needs to be considered in space as well as time.
For a given budgetary goal, what is the optimal spatial arrangement of target cells to
cull in the control area of the park?
It is essential to note that the optimisation routines rely principally on the
combination of what the user sets as the damage and areas of vexation layers. The
details of how these two layers are combined into a priority map are outlined below (see
Culling worksheet). This priority map then modifies the cost-benefit scores (see
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
Bioeconomics worksheet) on which the entire optimisation routines are based. Thus, any
changes to the damage and areas of vexation layers will result in different ‘optimal’
budgetary, density and spatial configurations.
We have included a matrix of three optimisation options in the Inputs worksheet
for user interface (Figure A8).
Figure A8. Optimisation routine buttons available on the Input worksheet.
Non-spatial / Budget
The first option (Non-spatial / Budget) requires the user to enter a total budget that will
apply for the intended duration of the culling program (the Budget cell). After setting
the appropriate logistical costs and defining a spatial culling area of interest (i.e., by preloading a particular culling map or designing a custom map in the Culling Scenario
Maps worksheet), clicking the Non-spatial / Budget button finds the most-effective
initial and maintenance culling rates and per cell stopping density for the funds
available. The user will be shown a progress meter each time that an optimisation
routine is run, e.g.
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
One thing that might cause some confusion is that the progress meter is only an
approximation of the optimisation process; therefore, the progress meter might jump
back and forth at times and even go slightly beyond 100 % in certain circumstances.
If the optimisation is successful, a pop-up window like the following will appear:
If the budget is set too low for the spatial configuration chosen to implement (e.g., parkwide or specific area cull), then there might not be an optimum allocation of culling
rates that will fit the insufficient budget. If this occurs, the user will be presented with
the following pop-up window:
If this window appears, the user will either have to increase the budget or reduce the
number of culling cells specified in the Culling worksheet.
Alternatively, if the user specifies a budget that is excessive for the culling area
specified, the following pop-up warning appears:
If this occurs, increase the area to be culled or reduce the budget accordingly.
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
Non-spatial / Minimum Density
If the goal is to achieve a particular density of the feral population within a specified
culling area at the end of the culling program, the Non-spatial / Min D button will
provide the culling rates that achieve this outcome most efficiently. Both of these
options rely on the user specifying a particular control area through either the
customised culling map or one from a particular scenario.
Spatial / Budget
The previous two optimisation routines assume that the user has already identified their
‘optimal’ spatial culling configuration. However, it is often unknown even within
particular jurisdictional units (e.g., Kakadu districts) what the ‘optimal’ spatial
arrangement for maximising culling efficiency should be. The two spatial optimisations
provide some more information in this regard.
As with the non-spatial budget optimisation, this option assumes that there is
some upper limit of allocated funds directed at the culling program. However, the user
starts with a fairly vague idea of the area he/she wishes to cull and would like to know
the optimal allocation of culling effort over the specified area for the given budget. The
routine has an additional level of complexity in that it examines which proportion of the
set culling area gives the biggest return on investment based on the cost-benefit scores.
Once this proportional area is found, then the optimal culling rates are set. The outcome
is a new set of culling rates for a number of cells identified for culling within the
original, pre-defined culling area to achieve the largest reduction in density whilst
staying within budget.
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
Culling
This worksheet is where the user sets the spatial configuration of the cells destined for
culling. The first map (Figure A9) shown is a representation of the number of animals
culled per cell based on the input parameters and the culling map (the second map in
this worksheet).
Figure A9. Density-reduction map.
For the culling map (Figure A10), it is simply a process of entering a ‘1’ in a cell if it is
destined for control measures, or ‘0’ if no control is to occur. For convenience sake, a
rough outline of the Kakadu districts has been provided given that district-based control
scenarios are more likely. Of course, if a particular scenario is loaded in the Inputs page,
then the culling map is updated automatically. By changing cells in the culling map, the
number of animals culled in the density reduction map is updated automatically.
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
Figure A10. Culling map.
The third map (Figure A11) provided is a composite map detailing our best attempts to
define priority areas for culling. This is based on two other spatial layers: the Damage
and Areas of Vexation worksheets (described in more detail below). The priority matrix
to the right of the Priority map indicate combinations of damage and level of vexation
that lead to a hierarchical listing of priority. For instance, if the management vexation of
a cell is low (i.e., it is relatively easy to invoke a particular management strategy within
that cell because the proposed management action is not controversial) and the damage
from feral animals is high, then that cell receives a high-priority rating. This map can
assist users in spatial culling regimes, and it is the basis for the cost-benefit scores used
in the optimisation routines (see the Bioeconomics worksheet for more details on the
cost-benefit scores).
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
Figure A11. Culling priority map.
We anticipate that the user will attempt several different spatial configurations of culls
depending on the budget at hand (if the optimisation routines are not invoked), or
experiment with the various pre-loaded scenarios that reflect a suite of potential
management options. Ideally, the entire park would be targeted for reductions of feral
animal density, but this is most likely restricted by annual budgets and the trade-off
between park-wide, low-level culls or intensive operations on more restricted spatial
scales. The user will be able to allocate the number of cells that could be targeted based
on budgetary restrictions and then allocate these in different patterns to provide the most
cost-effective control configuration. We have provided a single-cell buffer around the
park to include the possibility of achieving ex-park controls to maximise the costeffectiveness of within-park culls.
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
Finally, users can refer to the Habitat worksheet (specifically, the Carrying
Capacity map – see below) to identify the cells with the highest densities of the target
species. This can assist in designing the spatial configuration of the most effective (in
terms of cost-benefit) culling program if the optimisation routines are not invoked.
Distribution
If it is known that a particular species definitely does not occur in a particular map cell,
then the value of that cell in the worksheet entitled Distribution should be changed to a
zero. For example, not all cells within the park contain horses, and if this is known,
those cells can be set to zero. This manipulation does not prevent animals from
immigrating into these cells; rather, it simply indicates that in the starting year, no
animals of the target species are known to occur there. Dispersal into these cells in
subsequent years of the model run will be dictated by the dispersal components
provided by the user in the input.
Once the distribution layer has been modified, all subsequent runs will refer to
this configuration for the initial spatial arrangement of densities. To alleviate some of
the potential problems associated with this, the Distribution layer is always reset to a
map of 1s whenever a pre-defined scenario is loaded.
Culling Costs
This worksheet outlines the functional relationships between per-individual costs and
population density (hunting efficiency – Figure C12). The only values that might require
modification are the green cell values for each species’ slope and intercept in the Base
Settings. We do not anticipate that these will require modification by the user until more
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
species-specific data are obtained. Note that no such relationships for horses have been
calculated, so we assume the empirically-based buffalo functional relationship also
applies to horses.
Figure C12. Functional relationship between the number of hours (and cost) required to kill a
single buffalo and the density of the population for swamp buffalo (Bayliss & Yeomans 1989).
0.6000
$600
0.5000
$500
0.4000
$400
0.3000
$300
0.2000
$200
0.1000
$100
0.0000
Cost ($)
Hours
Buffalo
$0.0
2.0
4.0
6.0
8.0
10.0
Density
Culling Scenario Maps
As defined above, the culling scenario maps are the particular spatial configuration
maps for each pre-specified culling scenario as outlined in the Inputs worksheet. If a
pre-specified management scenario is loaded, then the corresponding map in this
worksheet is copied to the Culling worksheet and used as the basis for that model run.
User-specified culling scenarios can be added to this list of maps and referenced in the
scenario or map selection drop-down menus accordingly.
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
We have also provided a series of maps that do not occur specifically within any of the
pre-defined culling scenarios. We have pre-defined culling maps for each of the Kakadu
districts so that regional managers can easily begin to model their specific districts. The
full list of maps is shown below in Table A2.
Table A2. List of pre-defined maps provided in the Culling scenario maps worksheet.
Number
Name
Description
1
Park-wide
Culling occurs in each cell of Kakadu including a one-cellwide buffer surrounding the park.
2
M/H Priority
Culling occurs in medium and high priority areas only.
3
Nourlangie
Culling occurs in the Nourlangie district only.
4
No cull
No culling occurs in the park.
5
S Al – surrounds
Culling occurs in the South Alligator district and includes a
single-cell buffer around the district (i.e., some culling on the
edges of East Alligator, Nourlangie and Jim Jim districts).
6
S Al – refugia
Culling occurs only within the South Alligator district, but with
some cells experiencing no culling (i.e., animal ‘refugia’).
7
Patchy (ad hoc)
Culling occurs in a random fashion over the entire park. In this
particular map, the same number of culling cells used in the
M/H Priority map (Map 2) is used.
8
High yield (pig)
Culling occurs in cells where pig density is highest. This
culling regime assumes that the goal is to take the maximum
number of pigs from the park, but not necessarily to reduce
pig-related damage.
9
H. yield (buffalo)
Culling occurs in cells where buffalo density is highest. This
culling regime assumes that the goal is to take the maximum
number of buffalo from the park, but not necessarily to reduce
buffalo-related damage.
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
10
H. yield (horse
Culling occurs in cells where horse density is highest. This
culling regime assumes that the goal is to take the maximum
number of horses from the park, but not necessarily to reduce
horse-related damage.
11
East Alligator
Culling occurs in the East Alligator district only.
12
Jim Jim
Culling occurs in the Jim Jim district only.
13
Mary River
Culling occurs in the Mary River district only.
14
South Alligator
Culling occurs in the South Alligator district only.
15
Blank
No culling has been defined. This map can be modified and
pre-set by the user.
16
Blank
No culling has been defined. This map can be modified and
pre-set by the user.
Damage
This layer was compiled from various consultations with Kakadu National Park rangers,
administrators, Aboriginal traditional owners and others familiar with Kakadu. At this
point in time, the layer represents the best, coarse-scale spatial representation of damage
done by feral animals in the park. Each cell in the map can receive one of three values:
0 = no damage, 1 = moderate damage and 2 = high damage. However, this is a highly
dynamic property of the landscape and can be modified by the user accordingly. With
more information (e.g., from aerial surveys, on-site inspections, etc), the map can be
adjusted. However, if no new information is available, we suggest that the map be used
as a first approximation of damage.
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
Figure A13. Land damage layer (darker red indicates a higher damage score).
Areas of Vexation
This layer is a completely user-defined map that can incorporate a relative scale of
‘management vexation’ for each cell in Kakadu. In essence, greater is the vexation of a
cell, greater is the challenge to implement a culling regime due to various sociological
and other factors. This layer is combined with the Damage layer to provide a priority
index for management intervention (see the Culling worksheet for a more detailed
description).
The map is provided initially with no assumption about the level of vexation. The
user can then modify these cells according to their perceptions or measured values of
vexation in the park. Each cell in the map can receive one of three values: 0 = no
vexation, 1 = moderate vexation and 2 = high vexation. For example, the cell
incorporating the Jabiru township might receive a vexation score of '2' for an aerial
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
buffalo shoot given the potential danger to people on the ground. Other possible reasons
to classify a cell as ‘vexed’ is that it might contain sacred sites or areas frequented
commonly by tourists (e.g., campgrounds).
Output
This is the worksheet that provides a season-by-season overview of the results of the
simulation just run through to the final simulation year. This worksheet will be activated
at the end of each run, so if the user wishes to return to the Inputs worksheet, clicking
the
button at the bottom right-hand corner of the worksheet and then clicking on the
Inputs worksheet tab will re-open the Inputs worksheet. Alternatively, clicking the Go
to Inputs button will invoke the same action. There are several elements to this output
sheet:
1. The table on the left-hand side of the worksheet shows (a) the year of the
simulation starting with year ‘0’ (the start year) down to the length of the
simulation (+ 1), (b) the season (wet or dry) of the year in question, (c) the total
number of animals of the target species estimated to occur in the entire park (N),
(d) the total number of animals of the target species estimated to occur in the
control (cull) area, (e) the proportion of individuals in the control area relative to
the initial population size at the end of each season (N0), (f) the total number of
animals culled in each dry season of each year, (g) the total cost of the cull in
each year, (h) the average cost per animal culled for each year, and (i) the total
cost-benefit score for each year of the simulation.
2. For verification purposes, the species being modelled is indicated at the top of
the worksheet and a species icon is placed in the projection chart.
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
3. A second table in the top middle of the worksheet gives some output parameters
for the run. These include:
i. The total cost of the culling program over all years of the
simulation
ii. The total benefit (profit) derived from the culled animals (will be
zero unless quantified via revenue details)
iii. The net gain/loss (in $) over all years of the culling program
(total benefit – total cost)
iv. The average cost per animal over the duration of the culling
program
v. The total number of animals culled over the duration of the
culling program
vi. The average population size of the target species with the park
over the simulation interval
vii. The maximum per cent reduction in population size achieved
within the control (cull) zone over the simulation interval
viii. The target population size for the control zone relative to the
proportion set in the Input worksheet
ix. Whether the control area target density was achieved (i.e., if the
final population was within 1000 individuals of the set target
density).
4. Two quick-navigation buttons that take the user back to the Inputs worksheet or
to the Output Maps worksheet.
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
5. A graph showing the change in average per animal culling costs over the
duration of the simulation and the change in the cost-benefit score over time
(Figure A14).
Figure A14. An example plot of average-per-individual cost of culling and the change in costbenefit over the course of the culling program. Filled circles represent the average cost per
animal culled and open squares indicate the cost-benefit score.
The rounded ‘fitted’ lines to each of the cost/individual and cumulative costbenefit scores are based on a polynomial function that attempts to capture the
general trend of each. However, at times the functions overfit after the final
points in each trajectory, thus creating the illusion that they change markedly
after the final year of the culling program. Therefore, only the trend up to the
last point in each trajectory should be regarded (i.e., ignore information beyond
these points).
6. A graph showing the estimated population trend within the entire park (blue
trajectory, left axis) and within the control (cull) area (red trajectory, right axis -
47
McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
Figure A15). The target population size for the control area is also shown as a
dashed red line on this graph.
Figure A15. An example plot of the estimated population trend within the entire park (blue
line) and within the culling control area (red line).
Ideally, the user will modify the input parameters and culling regime to achieve the
maximum reduction in density within the control region for the lowest cost or use the
optimisation routines to achieve the same result. The summary parameters and the
graphed population trajectories make this assessable quickly.
Output Maps
The maps that appear in this layer are a quick way of assessing visually the relative
success of each culling regime implemented. The maps are automatically generated at
the end of each culling scenario run, so the user will have to click on the worksheet tab
of this worksheet to view them. The first map (Figure A16) shows a colour-coded
48
McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
representation of the initial density distribution for the target species (darker green
indicates higher initial densities).
Figure A16. A colour-coded map indicated the relative distribution of the target species prior to
implementing a culling regimen. Darker colours indicate higher densities per cell.
The second map in this worksheet (Figure A17) indicates the distribution of relative
densities after the implementation of the culling regime. The colour scale is maintained
between this map and the first map so a visual assessment of the relative change in
densities can be made quickly.
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
Figure A17. Spatial distribution of relative animal densities after implementation of a culling
regime.
The final map (Figure A18) in this worksheet indicates the cumulative cost-benefit
scores for each cell in Kakadu. The cost-benefit score is described in more detail below
(see Bioeconomics worksheet), but it essentially indicates where the most cost-effective
effort has been placed during the course of the culling regimen chosen. In this case,
darker squares indicate a lower cost-benefit score (i.e., those cells where you get the
biggest return on investment).
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
Figure A18. Cumulative cost-benefit map indicating the relative cost-efficiency of culling in
each cell in the park. Darker pink colours indicate a lower cost-benefit score.
PopSim
This is the worksheet that calculates the seasonal changes in population density per map
cell during the course of a simulation run and the updating maps for the control area and
the entire park are seen during the process. None of the values should be modified in
these maps. After initialising the model, the maps will update their cell-by-cell values
for each time step. The final results are indicated in the Output worksheet and the
simulation automatically opens that worksheet upon completion.
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
PopC
This worksheet simply reflects the ‘current’ population size for each year of the
simulation. It is used solely to provide the Output numbers, and so should not be
modified by the user.
Habitat
The distribution of the different vegetation layers that provide the four main habitat
types: (1) Floodplain, (2) Paperbark Swamp, (3) Savanna-Woodland, and (4) Closed
Forest have been derived from finer-scale maps and so represent a coarse approximation
of the habitat types available in the park. We have assumed here that the buffering cells
outlining the park have approximately similar habitat types to those lying immediately
adjacent and within the park.
Generally, none of the values in this worksheet should be modified because they
are linked to values set in the Input worksheet. For example, the Carrying Capacities
map to the right of the Habitat map in this worksheet is a function of the habitat-specific
K set in the Input worksheet.
Elevation
This worksheet indicates the approximate location of the Arnhem Land plateau in the
park. It should not require modification (Figure A19).
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
Figure A19. Coarse-scale elevation map showing the approximate position of the Arnhem Land
plateau bisecting the south-eastern corner of the park.
Dispersal
The Dispersal worksheet contains three maps:
1. The number of per-cell outward movements
2. The total number of individuals moving into cells from adjacent cells
3. The dispersal probability that will depend on the per-cell estimates of
population size for each iteration.
No modification of these pages is required.
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
Bioeconomics
The first map in this worksheet calculates the costs (and any associated benefits) in
terms of dollars for each cell within the park. It should not require modification by the
user. The total cost of culling (C) per cell in each year is:
where H is the hourly cost of helicopter (or ground-based) hire, a is the hunting
efficiency intercept, N = the number of animals per cell in a particular season, A = the
area of cell (i.e., 10  10 km = 100 km2), b = the hunting efficiency slope, and V is the
overhead cost of implementing the cull.
The second map (Figure A20) shows the relative cost-benefit (γ) score used to derive the
best culling scenarios in the optimisation routines. The cost-benefit score is calculated
on the basis of the following equation:
where C = the total cost of culling per cell per year, T = the duration of the model run in
years, nc = the total number of cells being culled in the control area, B = the total budget
available for the cull and P = the priority composite score derived from the Damage and
Areas of Vexation maps.
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
Figure A20. Cost-benefit map indicating cost-benefit scores for each year of the simulation run.
Darker blue cells indicate a lower cost-benefit score.
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
References
Bayliss, P. (1986). Operation Howship: a simulated exotic disease controlc exercise,
using buffalo and pigs, in the Arnhem Land escarpment, Unpublished Report to
the Conservation Commission of the Northern Territory, Darwin, Northern
Territory.
Bayliss, P. & Yeomans, K.M. (1989) Distribution and abundance of feral livestock in
the 'Top End' of the Northern Territory (1985-86), and their relation to population
control. Australian Wildlife Research, 16, 651-676.
Bradshaw, C.J.A. & Brook, B.W. (2007) Ecological-economic models of sustainable
harvest for an endangered but exotic megaherbivore in northern Australia. Natural
Resource Modeling, 20, 129-156.
Brook, B.W., Bowman, D.M.J.S., Bradshaw, C.J.A., Campbell, B.M., & Whitehead,
P.J. (2006) Managing an endangered Asian bovid in an Australian national park:
the role and limitations of ecological-economic models in decision-making.
Environmental Management, 38, 463-469.
Choquenot, D., Hone, J., & Saunders, G. (1999) Using aspects of predator-prey theory
to evaluate helicopter shooting for feral pig control. Wildlife Research, 26, 251261.
Corbett, L. & Hertog, A.L. (1996) An experimental study of the impact of feral swamp
buffalo Bubalus bubalis on the breeding habitat and nesting success of magpie
geese Anseranas semipalmata in Kakadu National Park. Biological Conservation,
76, 277-287.
Department of Environment and Heritage (2004). The Feral Buffalo (Bubalus bubalis),
Australian Government, Canberra.
Dublin, H.T., Sinclair, A.R.E., Boutin, S., Anderson, E., Jago, M., & Arcese, P. (1990)
Does competition regulate ungulate populations? Further evidence from Serengeti,
Tanzania. Oecologia, 82, 283-288.
Fowler, C.W. (1981) Density dependence as related to life history strategy. Ecology, 62,
602-610.
Freeland, W.J. (1990) Large herbivorous mammals: exotic species in northern Australia.
Journal of Biogeography, 17, 445-449.
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McMAHON, CR, BW BROOK, N COLLIER, CJA BRADSHAW. 2010. Spatially explicit spreadsheet
modelling for optimising the efficiency of reducing invasive animal density. Methods in Ecology and
Evolution Appendix 1 – User Manual 10.11.2009
Graham, A., Raskin, S., McConnell, M., & Begg, R. (1982). An aerial survey of feral
donkeys in the V.R.D, Conservation Commission of the Northern Territory,
Darwin, Northern Territory, Australia.
Hone, J. (1986). An evaluation of helicopter shooting of feral pigs, Report to the
Conservation Commission of the Northern Territory, Darwin, Northern Territory,
Australia.
Jedrzejewska, B., Jedrzejewski, W., Bunevich, A.N., Milkowski, L., & Krasinski, Z.A.
(1997) Factors shaping population densities and increase rates of ungulates in
Bialowieza Primeval Forest (Poland and Belarus) in the 19th and 20th centuries.
Acta Theriologica, 42, 399-451.
Owen-Smith, N. (2006) Demographic determination of the shape of density dependence
for three African ungulate populations. Ecological Monographs, 76, 93-109.
Skeat, A.J., East, T.J., & Corbett, L.K. (1996). Impact of feral water buffalo. In
Landscape and vegetation ecology of the Kakadu region, Northern Australia (eds
C.M. Finlayson & I.V. Oertzen), pp. 155-177. Kluwer Academic Publishers,
Netherlands.
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