Map showing how private and other conservation reserves contribute to connections between the Stirling range and Fitzgerald River National Parks. The inset shows the Gondwana Link concept. Map courtesy of Gondwana Link.

tionships between the various variables need to be entered into the software so that model testing can start straightaway, often with the end users of the model taking an active part in the process. Relationships can be entered either as a mathematical equation, a table or a graphical representation. Automated pro- cedures can be used to fit the outputs of the model to given datasets using iterations and a predetermined metric distance between “observed” and “predicted” values. A modeller-friendly interface is available with pull-down menus, a graphic interface, with windows allowing us to enter key parameters for each run. The software has the ability to create a user-friendly interface layer with a range of tools such as explanatory notes, buttons, sliders, dials and graphs, so that end users can be guided through the running of the model and the interpretation of its outputs.

This approach to modelling provides an opportunity for clearly stating the assumptions underpinning the model. Gra- phical relationships behind various model assumptions can be changed in an interactive fashion by the model user, without requiring any intervention of the modeller. A model file can be compiled into a runtime version in such a way that model end users do not need to purchase the full version of the software to use the model, but only download a cheaper runtime version. However, such model users don’t have access to the model development tools that allow the structure of the model to be changed, thus preventing any unauthorised model modifications. Model sharing can also be done over the internet.

The Data

One of the objectives of most rehabilitation plans, including that of Alcoa, is to create a self-sustaining forest ecosystem. An important aspect of this is the re-establishment of nutrient cycl- ing, a process that is mediated by the interaction of micro-or- ganisms and decomposer-associated invertebrates (Swift et al., 1979). Figure 3 provides a conceptual diagram of the links between rehabilitation prescriptions, the climatic zone in which the site is situated and, ultimately, nutrient cycling back to the soil. This is of particular importance since, despite the fact that fertilizers are applied at the time of initial revegetation, in some of Alcoa’s early plots trees ceased to put on girth once the soil nutrients were exhausted (Ward & Pickersgill, 1985). Thus, to be self-sustaining, the site needs to close the nutrient cycling process so that no further fertilizer applications are required (Grant et al., 2007).

Three of the most important inputs to the rehabilitation process are topsoil treatment, diversity of plants in the seed mix and nursery-reared plantings, and also the climatic zone in which the site is situated.

Alcoa’s early revegetation efforts lacked topsoil addition, resulting in poor understorey diversity and plant cover (Koch, 2007b). This approach was soon superseded by the application of topsoil which, in early efforts, had been stored, but more recently involved topsoil freshly stripped from new areas (Koch, 2007a). Since the mid-1980’s, a double-stripping technique was developed which resulted in preservation of the seed bank and nutrient reserves in the upper soil profile. All of these devel- opments have resulted in progressive improvements in plant diversity and plant cover, the stages of which have been quanti- fied in various publications (see papers in Bell & Hobbs, 2007). The outcome is also influenced by the diversity of plants which are applied in the seed mix and in the planted material. Alcoa

Conceptual diagram of the relationships between restoration prescriptions, the climatic zone in which the site is situated, and one of the desired restoration outcomes―The re-establishment of nutrient cycling.

has invested considerable research money in devising ways to grow “recalcitrant” species, which have proved difficult to grow from seed. All of these efforts have resulted in progres- sive improvements in plant diversity and cover (Koch, 2007b). A third governing factor is the climatic zone in which the reha- bilitated area is situated. Using ants as a responding bioindica- tor, Majer (1990) has observed that ecosystems become pro- gressively more resilient as the rainfall increases, particularly if it falls during the warmer parts of the year. With exceptions, there seems to be a linear increase in ecosystem resilience with increasing rainfall. Although this has limited relevance to single minesite studies, it assists in predicting outcomes from one minesite region to another. In other words, since the relation- ship between rainfall (more correctly, growing season) can be quantified, it may be possible to use data from one climatic zone to another, with appropriate adjustments for prevailing climate being made to the model.

The three “inputs” in Figure 3 all influence plant cover and plant diversity in ways which have already been quantified, albeit to a limited extent. It is also known from litter-fall studies, in which collecting funnels or traps have been placed beneath vegetation of different densities and species composition, that both plant cover and diversity influence the quantity and type of litter which drops to the ground (Hatch et al., 1955). The com- position of the litter is of importance, since leaves of some plants, such as nitrogen-rich acacia’s, enhance the decomposi- tion process (Swift et al., 1979; Hingston, 1980), while other species, such as eucalypts, decompose more slowly.

A large amount of data exists on the relationship between rate of litter fall and build-up of leaf litter in Jarrah forest eco- systems in which Alcoa’s bauxite mines are situated. Similarly, the amount of litter has been quantified in a large range of bauxite mined areas that have been rehabilitated by a range of different methods and in ones which represent different rehabil- itation ages (Majer et al., 1984). There should be no problem in combining the data from the bauxite mines with those from the surrounding forest in order to obtain a robust relationship be- tween litter fall and standing litter biomass, with the passage of time being easy to factor in.

The relationship between litter biomass and decomposition has been quantified in a wide range of bauxite mines of differ- ing age and rehabilitation prescription. This was achieved by placing out meshed litter bags containing known amounts of litter for 18-month periods and then measuring weight loss, litter respiration, and losses of nutrients. Strong relationships were found between these decomposition variables and the nature and age of the rehabilitation and its associated leaf litter (Ward et al., 1991).

Concurrently with the decomposition study, Greenslade and Majer (1993) sampled soil and leaf litter Collembola (spring- tails), a group of arthropods that is intimately tied in with the decomposition process. They found strong relationships be- tween the diversity and abundance of springtails from the de- composition guild with the nature of the litter load. Additional- ly, there were similarly strong relationships between this guild of springtails and the degree of litter decomposition taking place in the various areas. There is therefore sufficient data to quantify for the model the relationships between quantity or nature of the leaf litter and the diversity of key decomposer organisms and, following on, with these and the rate of litter decomposition.

There remains one further link that is required to demonstrate how this chain of events leads on to the cycling of nutrients back to the soil, a process so necessary for a self-sustaining ecosystem. Knowing the litter load, the rate of decomposition and the amount of nutrients release per unit area (Hatch, 1955) enables this to be calculated. Additionally, Alcoa has underta- ken a large amount of research into restoration of soil nutrient loads (see Grant et al., 2007), thus enabling this link in the model to be quantified.

The Model

The model (Figure 4) has three input variables. Seed mix diversity and topsoil treatment are key determinants of the rate of change in both plant cover and plant diversity. The third input variable is the climate or, more specifically, the length of growing season for the area in which the rehabilitation takes place. This variable can be altered to simulate the effects of climate change or of the region where the particular minesite is situated.

Both plant diversity and plant cover affect the rate of litter fall, which in turn relates to leaf litter. In addition, these two plant variables also influence the diversity (and abundance) of selected invertebrate groups, in this case the important decom- poser organisms, the springtails. However, rate of change in springtail levels is also influenced by leaf litter, so a third con- nector is added to the rate of change in springtails.

At this point a negative feedback loop is added to represent the influence of litter-decomposing springtails on the rate of litter decomposition. This, in turn, influences the rate of nu- trient release into the soil, which is the ultimate question that the model is designed to answer.

There are several interactions in the model where two or three connectors lead into the same flow rate descriptor. Whe- ther these operate in an additive or synergistic manner is un- known at present, and this probably would need to be investi- gated during the refinement stage of the model.

Conclusions

This model is only in its initial stage. Additional interactions may need to be added in order to provide a more realistic re- presentation of the real-life situation. Furthermore, it represents the pathway leading to the re-establishment of one ecosystem process, nutrient cycling. There are others, such as restoration of soil structure, pollination, seed dispersal, etc., all of which are equally important for the establishment of self-sustaining rehabilitation. Thus, the ultimate model will need to have a series of modules, with some of the relationships (e.g., seed mix diversity with understorey plant diversity) being shared between modules. This adds to the complexity of the task, but Alcoa’s extensive research portfolio should enable a large pro- portion of the required relationships to be quantified.

Some of the relationships may lack data to enable them to be quantified for the model. In itself, knowing this is of value as it points to gaps in the research program which need to be fol- lowed up on. If time or resources do not permit this, previously quantified relationships from other mined areas, or even from other types of disturbance or other native ecosystems may be “borrowed” and incorporated into the model, possibly with adjustments being made to suit the local situation.

The majority of mining situations do not have access to the extensive research history that a large and wealthy mining company such as the one featured in this paper has. Indeed, smaller mining or resource companies could not possibly afford to undertake or fund such an extensive research program. De- spite this, they still need to have an understanding of rehabilita- tion outcomes in order to prepare mine closure plans and/or to meet required completion criteria. One of us (JDM) has per- formed research on invertebrate recolonisation in minesites throughout all climatic regions of Australia, in coastal dune forest in Kwazulu, South Africa, and in both Atlantic and Amazon rain forest of Brazil (Majer, 1990; 1992; 1996; Majer & de Kock, 1992) From these studies it is apparent that the processes involved in the resulting succession of the biota are similar, the major different being in the rate at which change occurs. It therefore seems reasonable to develop a model for one, or a few, rehabilitated areas and then adapt it to other re- gions or situations where a total investigation is not possible. One of the main variables that could be manipulated in the model presented here is “length of growing season”.

The Gondwana Link Spatial Model

Spatial modelling of landscape patterns can be used to aid restoration by considering the effects of landscape heterogenei- ty on ecological function, identifying locations that benefit most from restoration efforts, and predicting the effects of nat- ural and anthropogenic changes on the distributions of plants and animals. Landscape heterogeneity produces a range of ef- fects on the dynamics of an ecosystem (Pickett & Candenasso, 1995; Turner, 1989; Wiens, 1976), including both flora (With, 2002) and fauna (Lindenmayer et al., 2003). Of particular im- portance is the structure of edges (Haddad, 1999; Ims, 1995) and corridors, both of which have potential effects that extend beyond their immediate locations (Levin, 1992). Corridors are considered valuable components of fragmented landscapes because of the way in which they can positively contribute to the maintenance of biodiversity (Beier & Noss, 1998).

On the south coast of Western Australia, the Gondwana Link project seeks to mitigate the risks of anthropogenic influence in the area by rehabilitating tracts of land that improve the con- nectivity between the woodlands of the Stirling Ranges and the Fitzgerald River National Park (Figure 2). In the context of what we are considering here, the aim of spatially explicit modelling and simulation is to determine the importance of individual corridors with regards to seed dispersal (Pearson & Dawson, 2005) and fauna movement (McRae et al., 2008), estimating where restoration efforts are best applied, and pre- dicting the effects of these efforts on the wider system. By identifying specific locations to target for intervention and es- timating the effects of decision-making, the aim is make more efficient use of resources and avoid unintended negative con- sequences. Computational methods, including network analysis

Re-interpretation of the relationships shown in the conceptual diagram in Figure 3 as a systems dynamic model prepared using the STELLA^® modelling package. The box beneath is a key to the symbols used in the model; “clouds” represent the outer limits of the model.

and simulation, are useful for this purpose because large-scale controlled experiments conducted on the ground are typically not feasible and traditional analytical approaches do not expli- citly consider the spatial patterns of landscapes.

A major difficulty in constructing spatially-explicit models of restoration is in capturing the different ways in which organ- isms perceive the landscape structure (Baguette & Van Dyck, 2007). For plants, this perception includes suitable conditions for growth, as well as the presence of vectors that perform seed dispersal (typically wind, water, animals and anthropogenic disturbance) (Jones & Helen, 2008; Nathan & Muller-Landau, 2000). For animals, this may also include predation, food, shel- ter and mating. As a consequence of these differences, a single representation of a landscape is unlikely to be appropriate for a holistic model of restoration because it will not capture the different perceptions of the organisms in the system. It is therefore important to consider a range of data sources describ- ing the landscape to match the range of perceptions held by organisms in the system.

In what follows, we progress through an example of analysis and simulation with increasing complexity, showing how we address the problem to produce more encompassing models of ecological phenomena. As an example in network analysis, we consider how vagility and perception of habitat affect pathways of likely fauna movement (Dunn & Majer, 2009). In simula- tions, we consider the example of multiple vectors of seed dis- persal, which is achieved by linking multiple views of the same landscape (Dunn, 2010b; Dunn & Majer, 2007), showing how the combined effects produce different results, similar to the way in which the “stocks and flows” approach considers feed- back between elements within the system.

Analysing Single-Level Landscape Patterns

The simplest way to represent a fragmented landscape is a binary (habitat or not habitat, rather than levels of habitability) description of the landscape pattern, either as a set of habitat patches separated by a matrix (Forman, 1995), as a regular grid of pixels (for example, McRae et al., 2008; Pinto & Keitt, 2009), or using an irregular grid (Dunn, 2010a; Holland et al., 2007) (see Figure 5). Landscape connectivity metrics use the underlying patterns of habitat in a landscape to define a net- work (also called a graph), in which nodes represent a patch or small area of landscape and connections between nodes re- present how well-connected the nodes are in relation to move- ment or dispersal.

We use irregular cell-based structures to represent the land- scape because they offer a higher resolution of analysis than patch-based representations and avoid the grid-induced bias associated with regular lattices (Dunn, 2010a). In irregular cell-based structures, the landscape is represented by Halton points (Halton & Smith, 1964) and connections between nodes in the network are defined by the Delaunay triangulation (see Okabe et al., 2000).

Spatially explicit metrics (those that give values at each point on the landscape) that may be used to quantify the relative im- portance of locations in a landscape include the conditional minimum transit cost (Pinto & Keitt, 2009), the circuit theory

Three approaches for representing habitat in a landscape are the patch (left), grid (centre) and irregular (right) decompositions applied to a small section of the Peniup-Fitzgerald corridor. The colours in the left sub-figure show 79 internally-contiguous patches (black dots indi- cate centroids), and in the centre and right sub-figures, discrete cells of habitat are represented by grey squares and polygons, respectively.

method (McRae et al., 2008), and the betweenness centrality methods (Figure 6). Therefore, the limitation common to the three metrics discussed above is the need to accurately quantify habitat perception (what values are associated with different habitat and non-habitat areas) and vagility (specifically, over what distances should nodes spanning non-habitat be consi- dered connected) for the organisms in question (Johnson et al., 1992; Wiens, 1976). Validating the accuracy of habitat percep- tion and vagility or dispersal estimates is rarely performed when applying spatially-explicit models and should be incur- porated into future applications.

In applying these methods to restoration, there are two aims. One is to identify and strengthen pathways that are already important in organism movement, which may be done by wi- dening bottlenecks or targeted improvement of quality. The other is to examine how selective restoration can create new pathways, including redundant pathways engineered to reduce the reliance on others. Therefore, from a practical perspective, the approach to restoration using these analyses may involve either: 1) identifying important locations to improve, maintain or monitor; or 2) making changes to the landscape pattern in simulations to examine what the likely effects on connectivity may be if those changes were applied on the ground.

Simulating Single-Vector Dispersal

In the above examples using network analysis, each cell or patch is considered to be a static representation of what is con- tained within a small area of landscape and their spatial ar- rangement defines their importance with respect to providing connectivity. When simulating the behaviour of organisms over a landscape, we are considering changes that happen over time. This is achieved by attaching information to each of the cells that collectively represent the landscape, and creating the rules that allow those states to change over time, in response to ex- ternal stimuli or the state changes of other cells. In this case, the rules are implemented to model propagation.

In this case, we use the same irregular cell representation as in the network analysis above, and allow each cell to hold a value between zero and one, where zero represents the absence of a population of a hypothetical organism, and one represents the presence of that organism. We make the assumption that dispersal may occur through cells representing the matrix, al- beit with a much lower likelihood than through habitat cells. This assumption is consistent with studies examining the quail- ty of the matrix for dispersal of organisms (Fahrig, 2001; Murphy & Lovett-Doust, 2004).

In the previous section, we found that the Peniup-Fitz corri- dor features several important stepping-stone pathways that separate the Fitzgerald River biosphere from Peniup (as well as further west to the Stirling Ranges). We also concluded that stepping-stone pathways may be problematic for some species without the ability to travel easily through non-habitat areas. By simulating dispersal from a single location in the Peniup region, it is possible to watch the spread of a particular species (or in- deed a specific genotype, disease, or invasive species) based on the relative ease of dispersal through habitat and non-habitat regions. By repeating the simulations many times, it is possible to estimate the likelihood of finding a species in a specific loca- tion after a specified amount of time.

In the beginning of each simulation, one cell is assigned a positive state value (i.e. it contains a population of the hypo- thetical plant species), and the rest are set with a zero state val- ue, representing a single population in one location. Simula- tions progress by applying neighbourhood-based rules to each cell―where inactive cells become active as a consequence of having active cells within their neighbourhood. Simulations of propagation are common across a range of disciplines and there are several ways to construct the rules for updating the state of individual cells in a landscape over time. Probabilistic updating is performed by assigning a probability to each connection, which most closely resembles the probabilistic rules used in cellular automata applications (see Chopard & Droz, 1998; Schönfisch, 1997). Other non-deterministic approaches to mod- elling movement over landscapes include approximations and modifications to random walks or Levy flights (see Benhamou, 2007). The results of the simulation show the burst-like spread of the population―as the less likely dispersal through the ma- trix reaches each new patch, the propagation within that patch proceeds quickly (Figure 7).

Seed dispersal curves offer a method for calibrating spatially explicit simulations. Seed dispersal curves are used for model- ling seed dispersal but are rarely used in combination with spa-

The results of analyses using the circuit theory (left), conditional minimum transit cost (centre) and betweenness centrality (right) ap- proaches on the Peniup-Fitzgerald corridor (considering only vegetation as habitat) reveals differences between the methods. Each analysis uses an identical irregular structure and connectivity, and edges through habitat cells are considered 100 times less costly than edges at- tached to non-habitat cells. Points are labelled (black circles) where they are required by the algorithm (see text).

In a single-layer simulation of seed dispersal by fauna, spread is illustrated through areas amenable to growth (red) and across non-habitat (white to blue) at three time steps. In this hypothetical example, areas with vegetation are 100 times more likely to produce seed dispersal, creating burst-like population growth as new vegetation patches are encountered.

tially explicit models (Jones & Helen, 2008; Nathan & Muller- Landau, 2000). Seed dispersal curves can be used to calibrate because it is possible to train the parameters of the simulation to produce the same rate of spread in habitat and across non- habitat areas using dispersal curves derived empirically in a variety of habitat patterns. From a practical perspective, the method for calibrating the seed dispersal curve to the simula- tion relies on taking the empirical information about seed dis- persal in different environments (different proportions of habi- tat and matrix, and different levels of fragmentation) and cali- brating that against the rates of spread in simulations.

Using Multiple-Layer Extensions to Compose Data Sources and Phenomena

To achieve a more holistic model of ecosystem functions and the restoration efforts designed to promote them, it is important to consider interactions. Concepts from hierarchical patch dy- namics (Wu, 1995) may be implemented using a hierarchical extension of the cell-based simulation method described above (Dunn, 2010b; Dunn & Majer, 2007). The aim is to provide the framework for connecting multiple layers of landscape infor- mation “vertically” allowing interaction of different behaviours (in this case, seed dispersal by different vectors) with different types of information at each level.

In an extended version of the simulations described above, the landscape is represented by two layers instead of one. The first layer remains as the vegetation and the second layer is an estimate of anthropogenic disturbance from the locations of roads and towns. Since the model represents two forms of dis- persal, there are separate rules that govern the updating of cell states in each layer. In the vegetation layer, the rules are used to model the dispersal of seeds by frugivores. In the anthropogenic disturbance layer, the rules estimate the effect of anthropogenic disturbance on the spread of the hypothetical plant species. At each time step, the rules are applied for each layer, and the two layers are combined to produce a single estimate of the spatial distribution of the plant at each time step. The result is a model of the combined effects of the two forms of dispersal (Figure 8).

In Figure 8, the distance covered by seed dispersal has in- creased dramatically from the spread seen in the single-layer example. The seed dispersal has easily reached the Fitzgerald River biosphere. In the case of an invasive species, the in- creased spread due to human movement along the roadways is undesirable. The simulations provide targets for which to enact policy (in particular, along Maringarup Road in the south, and Carlawillup Road in the north), to reduce the effects of anthro- pogenic disturbance and mitigate unwanted spread.

While the examples above rely on simple state information to represent the presence or absence of a population of plants, the process of modelling may require more detailed state informa- tion such as seasonal and climate effects, and the more detailed kinds of feedback captured in system dynamics models of an ecological system (see above). However, as with most model- ling (Epstein, 2008), the aim is to produce the simplest model that replicates and predicts the behaviour of the system, pro-

Intermediate steps in a simulation of single-origin dispersal using two levels of information and two forms of dispersal. The two layers in- clude a vegetation layer (green) and an estimate of anthropogenic disturbance along roads (dark grey), which are superimposed to produce a single image. The spread is illustrated through locations amenable to growth (red) and as dispersal across non-habitat (white to blue) at three points in the simulation.

viding decision support for restoration efforts to increase effi- ciency and avoid unintended consequences.

Conclusion

The two case studies provided in this paper serve to illustrate the potential for computer modelling and simulation to contri- bute to the design and implementation of restoration following any type of land use, be it mining, forestry, agriculture or what- ever. The challenges in obtaining the required data are great, although in one regard, they assist those concerned with resto- ration to target their research to where it is most needed. We believe that these procedures offer great potential to enhance the quality of restoration and to enable it to be carried out in the most effective and economical manner.

References