In the previous chapters we have discussed many ecological principles as they apply to landscape ecology. Among those, the ecological consequences of landscape pattern to landscape processes have been a focus of many chapters. We have also identified numerous metrics to assist in the detection and interpretation of pattern. In this chapter we will give examples of the application of landscape ecology principles and tools such as models to the management of landscapes – in other words, taking it from the realm of scientific theory and concepts to applied ecology of landscapes. These landscapes may vary in size, management objectives and temporal scale, and degree of human control and intervention (“naturalness”). The landscapes used in examples vary from those that are dominated by human activity to those that function under more “natural” conditions. The principles still apply although their application will vary.

10.1 Natural Processes and Landscape Management

Understanding landscape patterns, the dynamic nature of the landscapes and the ecological and social processes that drive landscape changes are all very important aspects of Landscape Ecology.

We have discussed how landscape pattern and process is always associated with landscape dynamics. These concepts can also be applied to landscapes where changes are mostly driven by natural processes or are primarily determined by humans in intensively managed landscapes.

In many cases management attempts to use natural processes as much as possible. This is, for example, the concept of Close‐to‐Nature Forestry advocated by PROSILVA, an association of foresters who support strategies that use and adapt ecological processes in forest management as the means for rational, sustainable, and profitable management. This approach has been applied mostly in temperate forests of Western and Central Europe (Figure 10.1) and originates from the knowledge that in the past most of Europe was covered by highly complex forest ecosystems with many plant and animal species and that during the recent millennia man has seriously reduced diversity or modified those forests. Close‐to‐Nature Forestry rejects the treatment of forests as agricultural crops and tries to ensure sustainable and profitable production by imitating the structure and the dynamics of natural forests¹.

However, in many other regions of the world where the impact of man has been more influential and associated with disturbances, the idea of natural forests is much less developed. Possibly one of the best examples in the World of using natural processes to manage landscapes is in Western Australia, where fire has been extensively used by the indigenous people (Figure 10.2).

After the arrival of Europeans in Australia, the historical use of fire by indigenous people was largely abandoned and policies of fire exclusion were established. However, in areas with a Mediterranean climate of hot and dry summers, wildfires (bushfires) were an increasing threat. In 1961, after major wildfires, the Royal Commission recommended the Forests Department to carry out more research into fire control. Foresters in Western Australia, such as McArthur and others, then started developing guidelines for an effective use of prescribed burning^2,3. The technique of aerial ignition was developed to apply low‐intensity prescribed fires for fuel reduction over large forest areas (Figure 10.3).

Under this system of landscape management, using natural processes (fire) similar to what indigenous people had been doing for more than fifty thousand years, landscapes became less homogeneous, composed of patches with various ages after fire, with different fuel loads, therefore making it more difficult for a wildfire to find a percolating patch and making fire‐fighting easier (Figure 10.4).

After fuel reduction by prescribed fire, the wildfire control was much more effective, contrary to what happened in southeastern Australia and Tasmania, where the wildfire threat continued. The differences in the success of wildfire control were rightly attributed to fuel reduction, with burning undertaken much more extensively in Western Australia than in Tasmania⁴.

Two studies⁵ indicate this change from a fire regime dominated by cyclic large wildfires to a system where prescribed fire is applied annually. A 53‐year study⁶ (1937–1990) in the Perup area east of Manjimup shows a sharp decline of wildfires after the introduction of prescribed burning by the Forests Department in the 1950s. Another 50‐year study (1937–1987) in the Collie District of the Department of Conservation and Land Management dominated by jarrah forests (Eucalyptus marginata) indicates that prescribed burning practices increased significantly in the 1960s with aerial burning and remained high (9–15% of the area burned annually by prescribed fire), also resulting in a rapid decline in the area burned by wildfires⁷ (Figure 10.5).

These examples show how landscapes can be managed to achieve specific objectives, in this case the reduction of wildfire burned area, by simulating natural processes and historical disturbance regimes such as fires. In Western Australia, where the Department of Environment and Conservation manages around 2.5 million hectares and targets at burning annually 200 thousand hectares of forests (8% of the total landscape), summer high‐intensity wildfires were being gradually replaced since the 1960s by frequent lower‐intensity prescribed fires in spring and autumn. Ecological studies are the basis for many of the operations. Historical and science‐based management of these ecosystems follow similar rules based on natural processes.

10.2 Transition Matrices as the Mathematical Framework

We saw in the previous chapter how landscape dynamics could be modeled using transition matrices. Here we will see how management can be incorporated in the same framework.

We can look at a landscape as a mosaic composed of different states (classes or habitats) that replace each other in time. If this replacement pattern is such that one state is only replaced by another state then we have a simple structure, as we saw in the previous chapter in the example of rotations.

A simple transition model of this kind was first proposed for forest management by Usher^10,11 and for forest succession by Horn¹². For both cases the transition model approach could give a simplified version of a relative transition matrix (M) of the form:

where e can be seen as the probability that an area that is in a certain class will be replaced by ecological succession by the next class (probability considered equal for all classes) and d as the probability that an area in a certain class is disturbed and is replaced by a pioneer initial state (also considered constant in this example).

This simple formulation has very interesting properties. The parameter e can be seen as a measure of the dynamic stability of the ecological succession system and largely controlled by natural factors (as tree growth or biomass accumulation) whereas the parameter d can be seen as the probability of disturbance, which could be of natural origin (tree mortality due to age, natural stand replacing fires) or caused by humans (by changing the probability of disturbance and by harvesting).

From this simple formulation it can be seen that, without disturbance (d) and without ecological succession (e), the landscape would have the maximum inertia with the diagonal equal to unity. We also saw that we could simulate the dynamics of landscape composition by premultiplying the vector of the initial composition V(t) by the transpose of M to have the landscape composition vector at time t + 1, that is V(t + 1):

Predictions using transition matrices can then be made with the assumptions that the matrix M, that is all the transition probabilities, remains constant over the projection period and that the future state depends only on the current state and not on past history. These are the assumptions of the first‐order Markov chains (Figure 10.6).

Under those assumptions a Markov process of landscape changes would always converge to a certain landscape composition (EQ) that is in equilibrium with that process. In mathematical terms:

In reality, this equilibrium state might never be achieved because of changes in the process (matrix M), but it provides a very good reference for the long‐term perspective.

Using our simplified matrix we can predict what would be the equilibrium matrices for different values of the disturbance parameter (d) and the dynamic stability parameter (e). It becomes clear that, for any given value of e (the dynamic parameter), low disturbance probabilities (low values of d) would make all the landscape converge towards the last state and the equilibrium landscape would be composed of only that state. On the contrary, with higher values of d (higher disturbance probabilities) the landscape would tend to converge towards the initial state and the equilibrium landscape would be again very much dominated by only one state.

It is possible then to compute different diversity values (habitat diversity of the landscape, HDL) for different values of the two parameters d and e. As demonstrated by Horn¹³, the value of the diversity of the equilibrium composition depends on the number of classes, but it has always a maximum value at an intermediate value of disturbance as measured by a disturbance/stability index (DSI):

In the same study, Horn also indicates a simple way to calculate the diversity of a landscape composition based on the disturbance/stability index (DSI), using the modified Simpson index H₂ = 1/∑p_j ²:

From this equation it can be seen that, for a landscape with only two classes (m = 2), the equation reduces to H₂ = (2 – DSI)/(DSI + 2) with a maximum value of 2 when DSI = 0.5, that is, when the disturbance parameter (d) is equal to the dynamic parameter (e). This is exactly equivalent to what was shown in the previous chapter on disturbance and equilibrium in the two-state landscapes.

The above equation also shows that, for the same value of DSI, the diversity of the landscape increases with its number of classes, or its richness (H₀ = m). The equation also shows that with a higher number of classes the maximum diversity is attained with lower values of DSI, showing the importance of disturbance to maintain diversity in landscapes with few classes.

Using our example with four classes we can now calculate two different measures for the diversity of the composition of the equilibrium landscapes, based on either the Shannon or Simpson formulations. The values are plotted in Figure 10.7.

The results of this simple formulation of the problem are in agreement with the intermediate disturbance hypothesis, which indicates that maximum diversity is generally associated with intermediate levels of disturbance^14,15.

10.3 Management of Landscape Composition and the Transition Matrix Model

The transition matrix model was first proposed for animal populations by Leslie in 1945¹⁶ where the composition of the populations was based on age classes.

A similar concept was proposed in 1966 by Usher, to respond to the needs of the manager of the forest who wanted to know which forest structure would give him “the greatest production, but yet conserve his forest”¹⁷. In this case the classes were established in terms of size rather than age and, in the case that the units are single trees, size was generally expressed as diameter at breast height (dbh).

In general for the management of forest landscapes or broad‐scale analysis, it is more convenient to use areas of forest stands (patches) as units. In this case it is more common that the size of the forest is expressed by a measurement that is more readily used by the manager interested in producing timber: the volume per unit area (typically m³/ha). Also, it is generally preferred to assume that the transition parameters are different from class to class¹⁸.

In view of the simplicity of the approach based on age classes and that classes reflect the volume available for harvesting, forest simulators of forest dynamics using matrix models are considered more useful to establish classes based on a combination of age classes and volume classes. This is the approach developed by Sallnäs for Swedish forests¹⁹ and the European Forest Information Scenario model (EFISCEN) developed to project future scenarios for the forests in all of Europe^20,21 (Figure 10.8). Figure 10.8 allows for the understanding that some of the processes will occur largely independent of management (e.g., growth, aging, natural mortality) while others are influenced by management regimes (thinning, harvest, artificial regeneration).

Based on transition matrix models with a five‐year time step, EFISCEN provides predictions on the forest resource structure, stem wood volume, wood harvest, and, by using conversion factors, biomass and carbon stocks.

Recent applications of transition matrix models were proposed and applied using plot data of the Austrian National Forest Inventory²² and also using an area‐based matrix model but with classes defined by combinations of tree density (stem number per hectare) and volume (growing stock in m³/ha). The development of a European Forest Dynamics Model (EFDM) used classes as combinations of age and volume or combinations of stem density and volume with examples from five countries (Austria, France, Sweden, Finland, and Portugal), concluding the feasibility of this modeling approach, especially for tackling issues traditional models have difficulties with, such as uneven‐aged forestry or management under risk²³.

Similar approaches have been used with different objectives, such as optimizing economic returns, tree diversity, or carbon sequestration, and have been applied in many different regions of the world^24,25,26,27. A good overview and outlook of matrix models in forest dynamics was provided in 2013 by Liang and Picard²⁸.

The possible format of a corresponding relative transition matrix (M) could be

where the probability of a tree transition to the first stage (d_i) can include natural regeneration resulting from disturbance and/or artificial regeneration; it is dependent on the class (i) and the probability to change to the next size class (e_i) is dependent on growth and also on harvesting.

10.4 The Use of Transition Matrices to Incorporate Changes in Disturbance Regimes and/or Management Activities

We will use a simple example to illustrate the use of transition matrices to simulate changes in disturbance regimes and to predict future landscape composition resulting from management activities.

As discussed in Chapter 6, in the Owyhee Mountains of southwestern Idaho, USA, a historical quasi‐stable composition of the steady‐state shifting mosaic has been altered by twentieth century direct and indirect fire suppression actions by land managers. This has resulted in an increase in the area dominated by western juniper woodland and a decrease in the area dominated by sagebrush steppe. These landscape composition changes have resulted in a more homogeneous landscape with a loss of the early and mid seral vegetation stages and a loss of the sagebrush steppe habitat that is critical for the conservation of many species. The photos in Figure 10.9 illustrate the composition changes that have been and are occurring on a broad scale.

In the simplest case (baseline) the transition model would be represented by changes of classes according to a replacement sequence along a successional development and a reverse process caused by wildfire setting back succession to the first successional stage. This process can be represented diagrammatically in Figure 10.10.

In this approach the annual probability of a cell in one class to change to the following class is estimated as the inverse of the duration of the previous class. For example, if class A has a duration of 10 years, then each cell in that class has an annual probability of 1/10 = 0.10 to change to class B. The annual probabilities of wildfires are also different for the different classes. Annual probabilities of fire in the different successional stages were estimated for a baseline scenario based on the fire history in the Owyhee Mountains between 1973 and 2014 (Figure 10.11).

Finally, to start the simulations, the initial composition of the landscape provided represents a typical watershed in the area studied. A summary table (Table 10.1) shows the values used for the annual probabilities for each class to advance to the next stage or to be burned and go back to the initial stage, as well as the initial landscape composition. The corresponding relative transition matrix with annual probabilities is shown in Table 10.2.

In Table 10.2, for simplicity, the probability of the initial class to remain in the same class was only considered dependent on the time it takes for succession and the probability that the final class will remain in the same class is only dependent upon the probability of disturbance (as there are no other subsequent classes). In fact, old woodland develops slowly and juniper trees greater than 1000 years old are commonly found.

The transition matrix shown in Table 10.2 provides the baseline scenario “business as usual” that can be used to simulate future landscape composition at different time steps. We can now use the same approach to create new transition matrices with different probabilities to evaluate different scenarios.

Important issues for future landscapes can be made as “what if” questions. One such question is that of the possible influence of changing climate and other factors of global change on fire regimes. It is apparent from statistical data²⁹ that in recent decades the areas burned in wildfires have been increasing in the region (Figure 10.12).

We can now use our transitional model to evaluate the possible outcomes of different scenarios in the change of wildfire regimes. We can use the baseline scenario as the average probabilities for the period 1973–2014 and we can now simulate the changes in landscape composition by applying different scenarios of change.

“What if” wildfire probability increases in all classes by 100%, 200%, or 300%? We can term these scenarios as Wildfire × 2, Wildfire × 3, and Wildfire × 4, and use the same approach multiplying by 2, 3, or 4 the annual probabilities of wildfire determined for the baseline scenario.

Even though it is known that there may be several problems associated with running ecological models for long time periods, there are also good reasons to justify this option. For example, Keane and others³⁰ recommend a simulation timespan long enough for the majority of the landscape units to experience at least 3–5 fires during the simulations. Therefore, we decided to run the models for 1000 years into the future as there are often long‐term effects that may not be readily observed when modeling over shorter time periods such as 100 years. In addition it may be difficult to determine when the landscapes will theoretically achieve a steady‐state shifting mosaic condition. The results of the simulations for the four scenarios are shown in Figure 10.13.

The results shown in Figure 10.13 indicate that, with the current low wildfire probabilities resulting from the current wildfire suppression strategy, the tendency of landscapes’ composition in the Owyhee Mountains will continue to show an increasing dominance by juniper woodland (stages F and G) at the expense of sagebrush steppe (stages B and C). Our modeling output agreed with previous research that indicated that within 100 years our landscape would be dominated by advanced woodland (stage F). Our results indicate that, after 1000 years, the landscapes will tend to be dominated by the last stage (G, old juniper woodland). Major differences from that trend are only found after 1000 years when the proportion of class G is shown to decrease significantly with increased wildfire probability (especially in the scenario Wildfire × 4) allowing for a better representation of the classes of the seral stages.

An equivalent exercise can be made using alternative management strategies. A previous study³¹ on this issue used a distributional dynamic landscape model, the vegetation dynamics development tool (VDDT)³². In that system, the simulated landscape is composed of cells, and the area of each cell and that of the landscape are determined by the user. VDDT moves cells from one vegetation composition to another via deterministic transitions based on time (years), which define the successional pathway. When a cell initially enters a stage along the pathway, it will remain in that composition for a specific number of years, referred to as time steps, unless a disturbance factor affects that cell. Disturbance factors, such as fire, insect and pathogen outbreaks, domestic animal grazing, and forest harvest, are represented by probabilistic transitions. Probabilities can range from 0 to 1, where a 0 means that the disturbance will not occur at all and a 1 means that the disturbance will occur at every time step. A probability of 0.1 means that the probability will occur every 10 time steps on average. The probabilistic transitions lead to predetermined stages along the successional pathway. The model is run for a specific number of time steps. The model output is not spatially explicit but does allow calculation of the landscape metrics that are based on composition, such as diversity, richness, and evenness.

We can use the same transition model to illustrate the efficacy of different management alternatives with the goal of addressing the loss of sagebrush steppe in this ecosystem. Recall that it is known that sagebrush steppe (Figure 10.14) is critical to many organisms and that it has been declining in this area for the past half century. Therefore it is considered that the management of the landscape should meet the goal of maintaining at least 25% of the landscape in sagebrush steppe (classes B and C).

Mature juniper woodland is also critical habitat for many organisms and requires 400–500 years to develop. It is also considered that the management of that landscape should meet the requirement of retaining at least 15% of the landscape in mature juniper woodland (classes F and G).

In order to assume the stability of the transition matrix (Markovian process) it was considered that, although climate varied between years, the mean climate did not change during the model period. The management treatments were superimposed on the baseline scenario.

Similarly to what was done before, four scenarios, now representing management alternatives, were used in the simulations. The diagrammatic picture of the different management options is presented in Figure 10.15, and images of the two types of management treatments (prescribed fire and mechanical) are shown in Figures 10.16 and 10.17.

The four management scenarios used in the simulations were:

1. The baseline scenario (as before only with average wildfire probabilities 1973–2014).
2. The prescribed burning scenario (baseline probabilities with increased probabilities of fire d = 0.02 in classes D and E that result in changes to class A).
3. The mechanical treatment scenario (baseline probabilities with mechanical treatment in class F with d = 0.01 and class G with d = 0.005, resulting in changes to class D).
4. A combination of prescribed burning and mechanical treatment (adding baseline probabilities to those associated with prescribed burning and mechanical treatments).

The successional stages and results of wild and prescribed fires have been described by Bunting and others³³ and the mechanical treatment was added for this illustration. The probabilities for prescribed burning and mechanical treatments were developed by the authors to best achieve the management goals. The initial landscape composition is the same as before. Table 10.3 summarizes the input data for the model.

The relative transition matrix with annual probabilities corresponding to scenario 4 is shown in Table 10.4. The four management scenarios were then used to make simulations of future landscapes for 1000 years. Results are shown in Figure 10.18.

In order to try to achieve our management goals we modeled a prescribed fire program (Scenario 2) that would be applied to vegetation stages D and E, as it has been shown that these stages are more easily burned than later woodland stages (F and G) because of greater amounts of herbaceous and smaller woody fuel components. In addition the vegetation responds more rapidly following a fire³⁴. The annual proportion of burned area was set at 2%.

The results indicate that under that prescribed fire program the sagebrush steppe would decline from its current levels (Scenario 2), but slower than in the wildfire only scenario (Scenario 1). After 100 years class F would dominate the landscape but after 1000 years it would be the final stage G that dominates. The management goal of maintaining an adequate proportion of sagebrush steppe is not achieved in the long run with this level of prescribed burning.

Scenario 3 includes more aggressive mechanical treatments of F and G. These treatments are not effective in retaining adequate levels of sagebrush steppe. After 1000 years it is young juniper woodland (F) that has a higher proportion in the landscape but old woodland (G) is also well represented. This management alternative maintains reasonable proportions of initial and mid woodland development stages (D and E) and mature juniper woodland (F and G). However, it is observed that, in the long run, the initial stages (A, B, and C) are virtually absent from the landscape. The management goal of maintaining adequate levels of sagebrush steppe (classes B and C) are not met in this scenario.

The last management scenario (4), with a combination of prescribed fire and mechanical treatments, results in a more rapid development of landscapes with a more diverse landscape composition, where all the classes are relatively well represented (high evenness). The various indices of diversity and evenness already explained in the previous chapters can be easily applied and confirm this conclusion.

It can be concluded that this management alternative meets the required management goals and rapidly results in a balanced landscape. Therefore the combination of prescribed burning in the younger successional stages and mechanical treatments in more developed woodlands seems to be the most interesting scenario.

This example illustrates the usefulness of the simple approach of transition models in evaluating alternative management scenarios through the simulation of the dynamics of future landscape composition.

These exercises are very useful in contributing to our understanding of the system dynamics. However, they should always be considered as models that simplify reality. Some of the basic assumptions of these models are generally not completely met, as in the assumption of transition matrices being constant through time, a requirement for the use of results originating from Markovian processes. Also, it is important to recall that scales matter. Spatial and temporal scales have to be considered. For a small landscape it is likely that one large wildfire event, for instance, will cover the entire landscape. In this case the behavior of a shifting mosaic where only a small proportion of the landscape is changing can only be observed in larger landscapes.

Relatively rare but broad scale events can result in major changes to large landscapes. For example, the combination of several years of extreme drought combined with pine beetle and other insect epidemics resulted in widespread mortality of native pines including ponderosa pine (Pinus ponderosa) and sugar pine (Pinus lambertiana) trees in the southern Sierra Mountains of California, USA (Figure 10.19). In 2017 it was estimated that more than one hundred million pine trees had died in California³⁵. Pine trees of all size classes were affected. Many trees killed were hundreds of years old. Rare events such as these are nearly impossible to predict in landscape modeling frameworks given their low probability and the brief temporal scale of our data. However, these effects will influence the Sierra Nevada Mountains landscape composition and processes for decades if not hundreds of years into the future.

Despite the indicated limitations of assumptions and of scale, the approach of the transition matrices has been very useful in evaluating landscape changes and planning landscape management by comparing different alternative scenarios.

10.5 Combining Spatial and Temporal Analysis in Transition Models

As described above, transition models are very useful for understanding landscape dynamics and Markov chain processes, and they can be used to project future changes in landscape composition based on the immediately preceding state described in a transition probability matrix. However, this type of analysis does not provide any information about the spatial distribution of classes in the landscape, that is, there is no spatial component in the modeling outcome. Therefore, landscape composition can be modeled with transition matrices, but this approach does not provide information about landscape configuration.

In many cases, as in forest management, the spatial units are already defined in planning, and the management actions are applied to those spatial units. Typically, the size of these units is limited as extensive tree harvesting can have effects on soil protection, biodiversity, and natural regeneration of the forests. In addition to achieving sustained and continuous output of products the harvest unit size may also be determined by the total area of forest managed.

Within this framework the transition matrices presented earlier are fundamental to decide on the proportion of the mature forest to be harvested in each year (Figure 10.20), but the spatial allocation of the harvesting operations is decided by the manager in another step.

However, in the absence of predefined planned spatial units, the map cells are the spatial units used in the analysis and the modeling. In this case, if there is no spatial information in the transition matrices presented, all cells (or patches) of the same class will have the same probability to change to another class irrespective of its location. This would occur in a random neutral process where classes change randomly in the landscape and no interactions between a cell and nearby cells occur. However, as we saw before in real landscapes represented by cells of different classes, cells of the same type tend to occur more frequently in the proximity of similar cells. This can occur because of existing processes of contagion promoting expansion of that class (e.g., seed regeneration from forests creating new forests in the proximity), because of external preexisting factors (e.g., a certain class can only occur in soils of a certain parent material or on a given slope class), because of physical factors associated with the process (e.g., a certain change can only occur if a certain disturbance occurs), or because of social factors (e.g., certain changes can be limited in some areas because of legal restrictions).

In order to add spatial dependence to landscape change modeling, we need to be able to differentiate transition probabilities between cells (or patches) of the same class that are in different locations in the landscape. This can also be done with the use of the concept of conditional probabilities.

A first example can illustrate the concept of spatially explicit conditional probabilities. We can use a simple two‐class landscape and compute, as before, the transition probabilities between the two classes A and B (Figure 10.21).

In the case shown in Figure 10.21 all cells in class B will have a probability of 1 to remain in class B and zero probability to change to class A. In any simulation all cells already in class B are expected to remain in the same class. For cells that are in class A, the probability of remaining in class A is 0.7 and the probability of changing to class B is 0.3. Then, in the simulation of the landscape at the next period, the allocation of any cell to the future class can be performed by generating a random value (between 0.0 and 1.0 from a uniform distribution) and comparing it to the cumulative probabilities of the outcomes. In this case we have, for a cell that is class A:

• Cumulative probability of a cell in class A remaining in the same class: from 0.00 to 0.70
• Cumulative probability of a cell in class A to change to class B: from 0.70 to 1.00

Then, for any given cell in class A, if the random value falls between 0.00 and 0.70 the cell is expected to remain in class A; if the random value falls between >0.70 and 1.00 the cell is expected to change to class B. Table 10.5 illustrates the procedure.

Now we can simulate the landscape dynamics in the following period. From the 14 cells of class A in the second map, 10 cells are predicted to remain in class A in the next period as the random value is below the threshold 0.7. The other 4 cells, where the random value was above 0.7, were predicted to change to class B. The outcome (one of many possible maps representing the landscape composition and configuration in the next period) is shown in Figure 10.22.

This exercise shows how a simulation of future landscapes could be generated with no additional information about the spatial location of the cells.

However, we can look at the same example using an auxiliary map of a certain variable that is known or supposed to have an influence on the transitions between the two classes. As an example we will consider that the variable in question is slope and that we can subdivide our landscape in two categories, the flat terrains (≤5%) and the slopes (>5%). In this case two different relative transition matrices could be computed: one for areas with a flat terrain and another for slopes. Figure 10.23 shows an example to illustrate the procedure.

We now have two different transition matrices applying to different areas of the map. We can also see that some transition probabilities for cells of the same class can be considered to be different, depending on their spatial location. For example, the probability of a cell to change from class A to B is 0.6 on flat terrain whereas the corresponding probability on slopes is 0.0. We can see this situation as expressed as spatially explicit conditional probabilities where the transition probabilities between classes are conditional to the topography (flat terrains or slopes).

The changes in the cells of class A in the landscape can now be simulated and results are presented in Table 10.6, using for comparison the same random values as in Table 10.5.

It is clear from Table 10.6 that cells of class A in flat terrain are likely to change to class B (3 of 4 cells change and only the last one remains unchanged) whereas for slopes all 10 cells of class A remain in the same class. The outcome of this simulation results in the map of Figure 10.24.

By simulating maps of projected changes using conditional probabilities, new cells of class B would only occur on flat terrain and none would be created on slopes. Given the apparent importance of slopes in the process the results of this simulation seem to be more realistic than those obtained earlier without considering slope in the process.

The use of spatially explicit conditional probabilities as a tool to develop more realistic maps of possible future landscapes is not restricted, however, to preexisting factors. As we saw in the preceding chapter, the occurrence of disturbances, such as wildfires, can also be considered an important conditional factor for the transition probabilities of the various landscape classes and can be used in the simulations of future landscapes. In our example we could define the left part of the landscape, considered to be a flat terrain, as representing an area that burned and that changes from class A to class B could result from that disturbance. We could also define the right part of the landscape as given a protection status where no further urban developments were allowed. If class A was an urban area then its development would not occur in the right part of the landscape. These are all examples of conditional transition probabilities arising from external factors that are not included in maps of land classes.

Using only the information provided by the maps of the landscape classes, we can also use the concept of conditional transition probabilities using proximity analysis. One particularly important case of the use of conditional probabilities to deal with spatial proximity is in the use of cellular automata. In the simplest case where the whole landscape is equally suitable for all the changes, these changes may be only a function of the proximity of existing cells of the same class. A patch of cells of a given class will then grow as a contagion process from the existing boundary. In practice, this hybrid spatial and temporal system based on cellular automata and Markov chain analysis has been used in a module known as CA_MARKOV in the GIS analysis tool IDRISI³⁶. A contiguity filter is applied as a spatially explicit weighting factor for the transition probabilities for a given class, weighing more heavily those that are in the proximity of existing cells of the same class. Different contiguity filters using different neighborhood methods can be used (Figure 10.25).

In general, simple contagion models using contiguity filters and proximity analysis are very useful to understand and explain certain phenomena, but in reality landscape changes are often more complex. Also, simple models that explain the changes only by suitability or constraints without taking into account the spatial proximity of cells of the same class are often too limited to adequately represent the reality of landscape changes.

Therefore, in many cases, it is convenient to use both contiguity filters combined with suitability maps to indicate the areas where changes are more likely to occur due to criteria such as proximity to existing classes or to roads, to water bodies, to areas with high population density, or other physical or social factors. A multicriteria evaluation can be used to create specific suitability land use/land cover maps based on the rules that associate these factors with the classes and their dynamics. These suitability maps are then used to assist the spatial allocation of the transitions.

Combinations of spatial and temporal analyses can then benefit from information of physical and social attributes of the landscape. These systems have been applied to various situations resulting in maps that may provide descriptions of possible future landscapes that are in agreement with the processes taken into account. In most cases the importance of the factors is not as strong as was illustrated by our example of dichotomous outcomes (flat terrain versus slopes). In these cases we can use gradients as suitability factors and create suitability maps that indicate the areas where changes are more likely to occur due to physical or social factors.

A multicriteria evaluation can then be used to create specific suitability land use/land cover maps based on the rules that associate these factors with the classes and their dynamics. These suitability maps are then used to assist the spatial allocation of the transitions. Also constraints such as those derived from planning laws can be included as factors. This was the approach initially proposed by J.R. Eastman in the development of the Land Change Modeler, included in the software IDRISI in 2006³⁷.

This system has been applied to various situations resulting in maps that provide descriptions of possible future landscapes that account for numerous processes and other restrictions. This work has continued with the extension of the Land Change Modeler for ArcGIS in 2015 and with the simultaneous development of Modules for Land Use Change Simulations (MOLUSCE) for QGIS.

An example of the land use dynamics of the Portuguese mainland can help to visualize the projected landscape changes (Figure 10.26). This work shows the composition and configuration of the Portuguese landscapes under a scenario of the continuation of the trends observed between 1990 and 2005, including urban growth in coastal areas and replacement of pines by eucalypts in central Portugal.

One major issue for the realistic behavior of the simulations is in the appropriate choice and combination of factors to generate suitability maps. A possible procedure to create suitability maps can be illustrated by the development of a suitability map for urban development for the metropolitan area of Seoul (South Korea)³⁸ (Figure 10.27).

In the next step it is important to consider the legal limitations for urban development. The final result for the analysis of the suitability areas for urban development around Seoul is shown in Figure 10.28.

The example of the definition of suitability classes for urban development in Seoul (Figure 10.29) includes the combination of physical and social factors that should be taken into account when analyzing and predicting landscape changes. From the figures it is apparent that suitability for urban growth tends to be in the proximity of roads, expressways, trains, or subway stations and in the vicinity of already existing urban areas, as in a contagion process.

The two previous examples (for Portugal and Seoul) illustrate the use of suitability maps together with Markov analysis and cellular automata in assisting with forecasts of landscape changes.

However, there are situations where physical or legal constraints are more important in the process of landscape change, there are others where land physical suitability is more relevant, and still others where the contagion processes are more influential.

When major landscape processes are contagious by nature the use of contiguity filters associated with transition matrices is particularly helpful in modeling. It is therefore easy to understand that many successful examples of this approach are found in the literature associated with contagion landscape processes, for example urban sprawl, as illustrated in studies in various areas of the world from the United States³⁹, Australia⁴⁰, and Iran⁴¹.

A popular model that uses the cellular automaton approach for the computational simulation of urban growth and land use changes that are caused by urbanization is SLEUTH. This “detective” model originated in 1993 from work on another contagion process, the propagation of wildfires⁴². The initial application of SLEUTH for urban growth was focused on the San Francisco Bay area⁴³ in 1997 and it has been used in many other cities in the United States since then.

The first application of the SLEUTH model outside the United States was conducted in Portugal, in the Metropolitan areas of Lisbon and Porto⁴⁴, and has been applied in many other cities in the world, especially in rapidly growing cities in fast developing countries such as China.

We will use the example of Changsha⁴⁵, China, to illustrate the process. The first steps in the analysis were to determine the best coefficients to use for transitions by model calibration and validation. After these steps, the model was used to simulate the observed changes in the validation period. Yin and others simulated changes in the landscape around the city of Changsha between 1999 and 2005 and compared them to the actual changes. In spite of some observed differences, especially around the road networks, an importance in the urbanization process that was overemphasized by the model, the simulated and actual landscapes were quite similar.

The validated model was then used to simulate the future urban growth under different scenarios. The planning scenarios used were:

• Scenario 1. Urban areas grow according to the current trend with no consideration of loss of farmland, forestland, and other green areas.
• Scenario 2. Aimed to protect farmland, urban growth occupies the least farmland, forestland, and other green areas with no consideration of current trends.

The results of the simulations for 2015 with the two different scenarios can be compared with the actual landscape image in 2017 (Figure 10.30).

This comparison shows that the projection provided by Scenario 2, where protection of farmland, forests, and green areas was included, was much closer to reality than that of Scenario 1, where the trend observed before 2005 was predicted to continue.

It can easily be concluded from the observation of the images that the explosion of urban growth predicted in Scenario 1 did not occur, possibly because the conservation measures included in Scenario 2 were largely effective. In fact, in 2015 the city of Changsha has been awarded the “2015 China Sustainable City” for achieving high human development while also minimizing damage to the environment (Figure 10.31).

This example shows that we can use the concepts of Landscape Ecology to predict the future landscape composition and configuration also in the context of urban development. We can also use these tools to simulate future scenarios and to evaluate the consequences of legal restrictions of landscape changes and different land use policy and planning alternatives.

In summary, we have seen that, in many different contexts from true wilderness areas to landscapes dominated by urban development, the principles and techniques of Landscape Ecology are useful to inform Landscape Management. This is, after all, a primary objective of Applied Landscape Ecology.

Key Points

• Understanding how natural processes influence landscape dynamics is an important aspect of applied landscape management.
• The use of transition matrices are effective in simulating changes in disturbance regimes and predicting future landscape composition resulting from management activities.
• The use of transition matrices are an effective means to model landscape dynamics to meet management objectives.
• To add spatial character to landscape change modeling, we need to differentiate transition probabilities between cells (or patches) of the same class that are in different locations in the landscape. This can be done with the use of conditional probabilities. Contagion can be modeled by assigning different conditional probabilities to adjacent and faraway pixels or polygons.
• The use of landscape models, both spatially specific and distributional models, are important tools that land planners and land managers can utilize to incorporate the principles of Landscape Ecology into applied landscape management.