Feral Animal Management Strategy for Kakadu National Park

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 Manual10.11.2009

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

Overview

Compartmentalisation

Improving user-interface and model performance

General cell-changing rules

Worksheet layers

Inputs

Choosing a species

Scenario

Map

Status

Population dynamics parameters

Maximum rate of population increase (rm)

Maximum carrying capacity (Km)

Mean carrying capacity (K)

Growth response shape parameter ()

Starting proportion relative to K – initial fraction of K: D0 (K)

Minimum density (Minimum D)

Projection interval (Duration)

Escarpment K modifier

Escarpment dispersal modifier

Culling

Cell Size

Dispersal

Logistical costs

Hunting efficiency

Revenue

Budget

Run Simulation button

Habitat area

Pre-specified management scenarios

Budget and Density Optimisation

Non-spatial / Budget

Non-spatial / Minimum Density

Spatial / Budget

Culling

Distribution

Culling Costs

Culling Scenario Maps

Damage

Areas of Vexation

Output

Output Maps

PopSim

PopC

Habitat

Elevation

Dispersal

Bioeconomics

References

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 includedbecause they are lower in abundance, and furthermore, their population dynamics resemble species represented specifically by the model.

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 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.
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) pre-specified 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 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.

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.,

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 Pre-specified 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:

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).

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 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. Kmis 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
Km / 12.6 / 25.2 / 7.2 / Graham et al. 1982; Hone 1986; Bayliss & Yeomans 1989; Freeland 1990
 / 1.3 / 10.3 / 1.0 / Dublin et al. 1990; Jedrzejewska et al. 1997
top habitat / Floodplain / wetland / wet woodland / open woodland / floodplain / Bayliss & Yeomans 1989
kill intercept / 0.1464 / 0.102 / NA (assume value for buffalo) / Bayliss & Yeomans 1989; Choquenot, Hone & Saunders 1999
kill slope / -1.445 / -0.673 / NA (assume value for buffalo) / Bayliss & Yeomans 1989; Choquenot et al. 1999

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 year depending on a number of environmental factors such as rainfall and fire patterns. However, Kmis 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 Kmto 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:

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).
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 Km in the next-best habitat type, Km in the following habitat type and Km in the least-optimal habitat type. For pigs, we set this habitat sequence as floodplain – paperbark – savanna/woodland – forest. For buffalo, the sequence was paperbark – floodplain – savanna/woodland – forest, and for horses it was savanna-woodland – floodplain – paperbark – forest.
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.