Modelling historical deforestation on Mauritius

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Modelling historical

deforestation on

Mauritius

Abstract

The aim of this research was to accurately simulate the historical deforestation on the island of Mauritius. The island has been inhabited since its initial colonisation in the seventeenth century. Because of its shifting ownership and other historical developments, the deforestation rate and predominant land use on the island has changed significantly over the centuries. While there are maps of the forest extent available for several years, a general overview of the spatiotemporal changes and knowledge of the underlying driving forces is missing. In order to generate this overview, a model which can simulate the historical deforestation has been created. The model itself is of the cellular automata type, using historical and current land use data, suitability maps and transition rules based on known historical developments and general processes. The output of the model consists of detailed land use change data and visualisations (both dynamic and static). The created model has an accuracy ranging between 74.9 and 97.7 percent and a fuzzy Kappa ranging between 0.211 and 0.653. In general, the model seems to perform well for the periods of Dutch and English occupation. However, the model might not be accurate for the French and independent periods. The model seems to be sensitive to changing weights and further research is required concerning the used and possible other environmental factors included in the model.

Author: Matthijs Hinkamp Supervisors: dr. ir. E.E. (Emiel) van Loon, dhr. S.J. (Sietze) Norder MSc Bachelorthesis Earth Sciences Future Planet Studies University of Amsterdam 5799 words Date: 20-06-2018

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Introduction

The general history of Mauritius and the effect human occupation has had on its forest and ecosystems is well-known and extensively documented (Brouard, 1963). The introduction of non-endemic species and habitat destruction over several centuries caused the overall ecosystem to degrade severely. In turn, this caused many endemic species to go extinct (Hansen et al., 2002; Cheke & Hume, 2010; Hume, 2006; Safford, 1993).

Overview of the known impacts of human activities

Before the actual colonisation of Mauritius, Arab and Portuguese traders used the island to gather resources for their travels. At some point, these traders introduced rats and cats to the island (Cheke and Hume, 2008; Hume, 2013). These species seem to have had an impact on the environment, but did not immediately cause the extinction of endemic species (Gosling et al., 2017).

Figure 1: The available historical maps of the forest extent on Mauritius. Data retrieved from Norder et al. (2017).

In 1638, the Dutch colonised the island of Mauritius for the first time, introducing new crops (Cheke & Hume, 2010) and domestic animals. The population of settlers was reasonably small and land use change occurred at a slow pace. Deforestation was very localised and was mostly due to the harvesting of a small number of tree species (Moree 1998). During the Dutch occupation, the Dodo, Raven parrot and giant tortoise became extinct (Cheke and Hume, 2008; Hume, 2013).

Sometime later the island was abandoned, only to be colonised again by the French in 1721. The French established a trading post on the island and the settlement became a commercial trading centre. The French also introduced a plantation system, with sugarcane as the most common crop (Allen, 2008). This expansion increased the demand for land and timber and the deforestation rate

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3 increased as well (Grove 1996). The French introduced locusts and the Java sparrow and probably caused the extinction of species such as the fruit bat (Cheke and Hume, 2008; Hume, 2013). Near the end of the French occupation, the island's soil and remaining forests were severely degraded (Brouard, 1963).

The British took Mauritius from the French in 1810, after which the plantation system (and sugarcane cultivation) grew significantly and became the primary economic driver on the island (Alladin, 1986; Allen, 2008). While during the British occupation no iconic endemic species went extinct, the deforestation rate increased again and kept increasing for several decades (Florens, 2013). This caused further degradation of the environment and at the end of the British occupation, only patches of forest were left at several location on the island (Brouard, 1963).

Mauritius became independent in 1968 and by that time the great majority of agricultural land was used for sugarcane cultivation (Meisenhelder, 1997). The decades after its independence, Mauritius became more industrialised and started to attract a great number of tourists (Ramessur, 2002). The demand for land for these new sectors increased and caused more deforestation (Hammond et al., 2015).

Knowledge gaps

While these known historical events seem to provide an accurate overview of the developments on the island of Mauritius, the actual spatiotemporal resolution of the currently available data is low. This resolution is limited by the available historical maps. There are currently six of these maps available (Figure 1), for 360 years of human interactions. This means that while the driving forces and dates of extinctions of the iconic endemic species are known (Cheke and Hume, 2008; Hume, 2013; Gosling et al., 2017), the exact spatial developments leading up to these extinctions are not. In addition, while there is a general overview of human motives behind the historical developments (logging, agriculture etc.) (Brouard, 1963), the accuracy and relative importance of these motives have not been tested using spatial data.

Aim and relevance of this research

As it could be very valuable for understanding multiple complex issues and processes, the main goal of this research was to generate detailed and reproducible spatiotemporal data concerning deforestation on Mauritius and thereby providing an overview of the historical deforestation. This has been done through creating a spatially explicit model and using historical and current data on land use (and cover) as input.

Spatial models have been widely used to simulate various forms of land use change (Stevens & Dragicevic, 2007; Kamusoku et al, 2009; Ménard & Marceau, 2007; Moreno et al., 2007; Soares-Filho et al., 2002; White & Engelen, 1993; Han et al., 2009; Santé et al., 2010). There are also several spatial models for Mauritius, for example for estimating soil loss due to deforestation (Norder et al., 2017; Le Roux et al., 2012). However, no attempt has been made to create a spatially explicit model which provides a complete overview of deforestation on Mauritius.

Such an overview could help contribute to filling the current knowledge gaps concerning the historical deforestation on Mauritius and its driving forces and this could be valuable for research of several scientific disciplines. For example, the many extinctions of endemic species (Hansen et al., 2002; Cheke & Hume, 2010; Hume, 2006; Safford, 1993) on the island and the driving forces behind

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4 them could be better understood by having detailed knowledge of the spatiotemporal changes of forest cover (as it relates to habitat destruction). It could also contribute to investigating the survival of other species on the island (and other isolated islands) and the way land use change has historically influenced certain populations.

This last scientific interest also overlaps with the societal relevance of having detailed spatiotemporal data and an accurate model concerning the deforestation on Mauritius. If the data and the model are shown to be accurate, it could help government agencies and NGOs to formulate effective policies aimed at conserving the current forests and remaining endemic species.

Research questions and content

The main research question for this bachelor thesis is: How can a spatially explicit model be used to accurately simulate the historical deforestation on the island of Mauritius? This main research question can be split up into multiple sub questions:

 Which modelling technique(s) should be used?  What parameters should this model have?

 How accurate is the data generated by the model?

 What conclusions can be drawn based on the results concerning the historical driving forces? In the following chapters, each of these research questions will be answered. First, the data and methods chapter explains the data which was used as input for the model and the overall structure of the model. This chapter is followed by the results chapter, which compares the results of the model with the available historical maps of the forest extent. The final chapters are the discussion and conclusion, which deal with the interpretation, limits and future use of this research.

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Data and Methods

Due to the spatially explicit nature of this research, the most suitable models would be cellular automata and agent-based models (Agarwal et al., 2002). A purely statistical model is not an option because of the limited amount of historical data (Yang et al., 2014).

Cellular automata

For this research, a cellular automata approach chosen. A big advantage of these models is that they have been applied to a wide range of studies (Clarke & Gaydos, 1998; Verburg et al., 2002; Pontius et al., 2001). In addition, cellular automata models have been applied successfully when making land use decisions on the national and international (Verburg et al., 2008; Uthes et al., 2010), regional (Claggett et al., 2004) and local level (van Berkel & Verburg, 2012). According to the National Research Council (2013), cellular automata models have been so successful due to their relative simplicity and availability. However, cellular automata models can also be expanded and can become more complex if necessary (Lazrak et al., 2010; Santé et al., 2010). Cellular automata models also have some drawbacks, which are mainly due to the difficulties in translating known processes accurately into the transition rules cellular automata models use (National Research Council, 2013).

Input and calibration data

The input data used for the model was retrieved from various sources (Appendix 1, Figure 2). The spatial data consists of digitised historical maps of the forest extent for the years 1638, 1685, 1773, 1835, 1872, 1935 and 1997, an agricultural suitability map, a digital elevation model (DEM), five historical maps and a current topographic map of the island. The maps with the historical forest extent were originally retrieved from Vaughan and Wiehe (1937) and Page and D’Argent (1997). These maps have been used as data for the calibration and validation of the model. From now on, these maps are therefore referred to as calibration maps and the years these maps were made for as the calibration years.

In addition to this spatial data, qualitative and quantitative data concerning deforestation (Appendix 1), population growth and locations of human activities was retrieved and used as input data or in order to calibrate the model.

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Figure 2: The overall structure of the cellular automata model used for this research.

Model structure

Modules and periods

The model has three modules: the suitability module, the regrowth module and the deforestation rate module (Figure 2, the green rectangles). The deforestation rate module and the regrowth module determine the amount of land which is cleared and reforested and the suitability module determines which cells are deforested.

The model has been split up into six time periods due to the availability of six historical maps: Dutch, French, Early English, Middle English, Late English and Independent. Each of these periods has its own suitability calculation and its own weights.

Suitability module

The suitability module uses several factors in order to determine the overall suitability (Figure 2, red rectangles). The module takes the elevation, slope angle, distance to settlements/coast/rivers and the agricultural suitability into account. Soares-Filho et al. (2002) and the reviewed models in Santé et al. (2010) used similar factors and achieved accurate results when modelling deforestation in the Amazon and urban sprawl. These articles cite more factors, but not all of them are suitable for this research.

Deforestation rate module

In order to create a realistic simulation of the historical deforestation, it is imperative that the rate of deforestation in the model mirrors that of known historical developments. Instead of altering the rules under which the model operates, a module has been included which restricts the maximum number of transitions per time step. This was done by calculating the number of cells which have been deforested in the calibration maps (Figure 3, the red line). The gaps in between these points

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7 were filled in (Figure 3, the blue line) with data from Brouard (1963) for the Dutch period and relative population growth based on the population data for Mauritius for the other periods (Appendix 2).

Brouard (1963) describes in which areas deforestation took place during various time slots of the Dutch period. Based on this information it could be determined how many years it took to reach the deforestation extent of the calibration map of 1685 in the various areas of the island, which meant that the deforestation rate for these different areas could be calculated (assuming the deforestation rate for each area did not change over time). Combining the deforestation rates for all areas resulted in the general reconstructed deforestation rate for the Dutch period.

The reconstruction based on the population data (Appendix 2) was done by calculating the relative increases in population within each period and calculating the deforestation rate based on those relative increases and the deforestation extent on the calibration maps. The precision of the reconstructed deforestation rate is limited by the population data itself and the overall deforestation for each period was still determined by the deforestation extent of the calibration maps.

Such restricted rate modules are relatively common in cellular automata models (Santé et al., 2010; National Research Council, 2013). For example, Soares-Filho et al. (2002) successfully implemented a similar module in a comparable model.

Figure 3: the reconstructed deforestation rate (blue) and the deforestation rate when assuming linear changes between the calibration years (red).

Regrowth module

The regrowth module determines the regrowth of secondary forest (Figure 2). The time it takes for secondary forest to grow has been retrieved from Soares-Filho et al. (2002). The regrowth module keeps track of the amount of time steps a certain cell has been deforested and when the threshold value is reached (20 years), the cells are reforested.

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Parameter estimation

The results of a model describing natural processes are often not accurate enough when using apriori parameter values and most models will therefore have to be calibrated. The calibration process for this model had three steps and the main data source that was used for calibration were the calibration maps (Figure 2).

Accuracy of the deforestation rate

Firstly, the accuracy of the rate of deforestation is calculated (Figure 2). This is done by comparing the number of deforested cells for the calibration years with the extent of deforestation on the calibration maps. This ensures the accuracy of the deforestation rate module and prevents excessive and insufficient deforestation. If the amount of deforestation for the calibration years is not correct, the deforestation rate has to be adjusted manually.

Calibration phase 1

Secondly, when the deforestation rate was correct the weights of each factor have been switched on and off (Figure 2). The best combination of factors was recorded and used for calibration phase 2. Calibration phase 1 was a manual process and can be done by adjusting the initial settings in the model.

Calibration phase 2

The third calibration step consisted of testing different weights for all factors for all time periods (Figure 2). This was done by running the model with weights varying from zero to 100 (the initial weights were 50). Firstly the factors that were switched off were tested, followed by the factors which had been switched on. After the ideal weight for each factor was determined, this ideal weight was put in the model and the new setup was used to test the next weight. When this process was finished, the model had all weights at their ideal value.

Output

The output of the model consists of several aspects (Figure 2). First of all, the model can produce a dynamic overview of the deforestation. This means that, when running the model, a visualisation is generated which is updated with each time step.

As the dynamic visualisation consists of a series updated static visualisations (belonging to each time step), it is also possible to view and save visualisations of certain time steps. This allows the user to easily compare the model output for certain time steps to other data or to draw conclusions based on that output if this is necessary.

The model output also consists of maps for the calibration years. These maps have been used for the calibration ad validation processes.

Validation

In order to validate the final results of the model, the method of Hagen et al. (2003) is used. This method involves calculating the Model Fuzzy Kappa statistic (MFK). The way this statistic is calculated, is very similar to a regular Kappa statistic (Formula 1, retrieved from Hagen-Zanker, Straatman & Uljee, 2005):

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9 'S' represents the overall similarity and 'E' the expected similarity. The main difference with a regular Kappa statistic is that the neighbourhood for each cell is taken into account, which means that a cell can still be partly in agreement with the same cell on the reference map if its location is close to a cell with the same category. Based on this method and the work of Power et al. (2001), the Map Comparison Kit was built (Visser & Nijs, 2006), which is a programme that was used to automatically calculate a Fuzzy Kappa statistic.

As the Fuzzy Kappa takes the neighbourhood of cells into account, it requires a set maximum acceptable deviation. In other words, it has to be determined how far can a cell be removed from the location of a cell on the reference map with the same category for it to be categorised as similar. This maximum acceptable deviation value depends (in this case) on the accuracy of the calibration maps. The accuracy of these maps is unknown and therefore the accuracy of other available historical maps (Appendix 5) has been used as a proxy. In order to calculate the accuracy of these reference maps, the programme MapAnalyst was used, which can calculate the distortion of old maps when comparing them to current maps (Jenny et al., 2007). This is done through georeferencing and in the case of this research the coastline of the island was used to do so. In addition to the distortion, the programme also calculates the standard deviation of the georeferenced points (Formula 2, retrieved from Jenny & Hurni, 2011):

The numerator represents the distances between the georeferenced points and 'np' is the number of

points. This value was used as the acceptable deviation limit (the neighbourhood which is used in the Fuzzy Kappa statistic calculation) (Appendix 5). As the accuracy of historical maps can vary with different purposes and authors, the highest accuracy for each period was used (Appendix 5). This ensures that the accuracy was not overestimated.

In addition to using the Map Comparison Kit to validate the results, two different validation methods have been used. Firstly, a sensitivity analysis was performed to check the influence of changing the weights of the factors. In this case, the sensitivity analysis was of the Monte Carlo type, with margins of ten. Not only has this provided some insights into the sensitivity of the model, but it might have also revealed some interaction effects (something which the calibration method did not take into account) (Demaria, Nijssen & Wagener, 2007).

Secondly, a worst case scenario analysis was performed. This means letting the model run without splitting it up into different periods and determining the difference in accuracy the model with a single time period (and therefore a single set of weights) and having multiple sets of weights and multiple time periods. This shed some light on why the model is useful for generating data and information that was previously lacking.

Modelling steps and choices

This section contains a brief overview of the steps the model takes during a full run and the choices that can be made when running the model. This process is visualised in Figure 4.

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Initialisation

The initialisation phase of the model consists of loading the data and transforming it to a useful format (generating the suitability maps). The user can decide whether the model calculates a static suitability map (this will be used for all periods) or recalculates the suitability for each period. In addition, the user must determine the initial weights. The default weights of the current model (Appendix 6) are the optimal weights as determined during the calibration phases 1 and 2. The user can also choose whether the model should use the reconstructed deforestation rate or a simple linear deforestation rate based on the calibration maps.

Simulation

After the initialisation is completed, the model starts its simulation phase. During this phase, the actual results are generated. This is a dynamic part of the model and it goes through this part once for each model time step of one year. If the static suitability is turned off, the model will first calculate the new suitability each time it enters a new time period. After that, it checks the current forest extent, determines how many cells need to transition based on the deforestation rate and the forest extent. The actual rate is the rate which takes the regrowth during the previous iteration into account. The last step of the simulation part is reforesting cells when cells have been deforested for over 20 years (based on the model of Soares-Filho et al., 2002). The forest extent array which is generated during one iteration is input for the next iteration.

Calibration

The built-in calibration phase is only used when performing calibration phase 2. If activated, the model runs the simulation part for as many times as indicated by the user, while each time altering the weight of a specific factor by a certain amount. During each of these calibration iterations, the model calculates and records the accuracy. When finished, the model returns a vector with accuracies and the weight with the highest accuracy is used from that point on.

Figure 4: The steps the model uses during a full run to simulate the historical deforestation. This includes the automated

functions of the model script, which is why only calibration phase 2 is included. Calibration phase 1 is a manual process and therefore not included in this figure.

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Results

In this section, the results of this research are shown. These results include the optimal settings (derived from the calibration process), the generated maps, overall accuracy for the calibration years, sensitivity analysis and worst case scenario comparison.

Optimal weights

The optimal weights for all factors in all periods have been determined using the second phase of the calibration process. An overview of the importance of the factors for each period can be viewed in Table 1. The changes of relative importance over time show that different environmental and human factors may have been important for the inhabitants during the different periods. This could be used to corroborate theories concerning historical developments and this is further discussed in the discussion section.

Period Dutch French Early

English Middle English Late English Independent Important

factors Distance to settlements

Distance to rivers Distance to settlements Elevation Agricultural suitability Elevation Agricultural suitability Elevation Elevation Minor

factors N.A. Agricultural suitability

Slope angle Distance to the coast

Distance to the coast

Slope angle Agricultural suitability Negligible factors Elevation Slope angle Agricultural suitability Elevation Slope angle Agricultural suitability

Slope angle Distance to the coast

Table 1: The relative importance of the different factors during the various periods, based on the results of the calibration phases. The exact weights can be found in Appendix 3.2.

As the weights in Table 1 and Appendix 3 provide the overall highest accuracy, these weights have also been used to create visualisations of the data for the calibration years (Figure 5). When performing a visual analysis, it becomes clear that the model performs best for the calibration years 1685, 1872, 1935 and 1997. However, the model seems to not be able to accurately recreate the historical maps of 1773 and 1835.

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Figure 5: Visualisations of the historical and generated data for the calibration years.

Accuracy

The overall accuracy and kappa statistic for all calibration years can be seen in Table 2. The kappa statistics indicate almost the opposite of the quick visual comparison (Figure 5). However, this method only compares cells with the exact same location and does not take closeness and approximate correctness into account. Therefore, a fuzzy Kappa statistic was also calculated using the Map Comparison Kit. The maximum acceptable deviation used to calculate the Fuzzy Kappa can be viewed in Appendix 5. According to the guidelines of Landis and Koch (1977), only the data for 1685 has a substantial degree of agreement, while the data for 1997 only has a slight degree of agreement. Year 1685 1773 1835 1872 1935 1997 Overall accuracy 97.7% 82.3% 74.9% 79.1% 91.0% 95.1% Kappa statistic 0.650 0.409 0.497 0.446 0.368 0.2076 Fuzzy Kappa 0.653 0.411 0.498 0.448 0.374 0.211 Degree of agreement

Substantial Moderate Moderate Moderate Fair Fair

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Sensitivity

As mentioned in the methods section, the sensitivity analysis is a Monte Carlo sensitivity analysis. The results of this analysis can be seen in Figure 6. Three of the distributions are unimodal, while during the Dutch, Late English and Independent periods there seem to be two peaks (which might indicate interaction between the factors). The sensitivity ranges from one to three percent, depending on the length of the period and the ratio of forest and non-forest cells.

Figure 6: The results of the sensitivity analysis for all periods.

Worst case scenario

Besides a sensitivity analysis, a worst case scenario analysis was performed. The results of this analysis can be viewed in Table 3. The accuracy decreases for all calibration years, however the difference is negligible for 1997. The kappa statistic also shows an overall decrease, except for 1835, for which this scenario actually performs better. All in all, it can be concluded that the intermediate periods increase the accuracy.

Year 1685 1773 1835 1872 1935 1997

Accuracy worst case scenario

95.6% 71.7% 73.9% 76.8% 88.3% 95.06%

Kappa statistic 0.331 0.056 0.476 0.385 0.181 0.205

Fuzzy Kappa 0.336 0.056 0.478 0.387 0.183 0.210

Difference with full model (Fuzzy Kappa)

-0.317 -0.355 -0.020 -0.061 -0.191 -0.001

Degree of agreement Fair Equivalent to

chance

Moderate Fair Slight Fair

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Discussion

Model parameters and accuracy

Parameters and accuracy of this model

The model seems to perform best for the Dutch period, which is the only period it for which reaches a substantial degree of agreement. The main factor for this period is the distance to the settlements. This makes sense, because the Dutch seem to have been mostly interested in exporting timber from a few species on the island (Brouard, 1963; Moree, 1998). The Dutch have probably cultivated some crops, but mostly for their own use. This means that agricultural suitability probably did not play a huge role in the location of deforestation (Brouard, 1963). In addition, the deforested area is not that big. This means that near most of the settlements and logging camps, the Dutch stayed relatively close to the coast and remained in quite flat and low-lying areas.

As mentioned before, the model performs less well for the French period. The most important factors are distance to the rivers that might have been used and the distance to the known locations of settlements. However, even with these factors the results are not impressive. There are several possible reasons for this relatively poor performance. The areas that have been deforested seem to resemble rivers, but perhaps it indicates some sort of infrastructure. During the French period the plantation system was introduced and sugarcane was produced in large quantities (Brouard, 1963; Allen, 2008). This makes the assumption of the implementation of infrastructure reasonable. However, there is no spatial data available to back this theory up. Another option might be that the map is rather inaccurate. However, as shown by the results of the accuracy tests of old reference maps (Appendix 5), there were quite accurate maps available. A third option might be that the locations were chose somewhat arbitrarily or that the deforested locations had some other environmental factor that was not included in the model. This theory is corroborated by the fact that agricultural suitability seems not to have played a significant role. In addition, there were some environmental policies (such as protected areas) in place during the French occupation (Brouard, 1963), but because of missing spatial specifications this was not included in the model.

Deforestation during the English period seems to not have been based on the settlement location, but rather on the elevation and agricultural suitability. While the Fuzzy Kappa is not that much better during the English occupation than during the French occupation, it is clear that the generated maps resemble the historical maps a lot more. The plantation system was greatly expanded and the population grew significantly (Allen, 2008; Appendix 2), which means that it makes sense that deforestation did not only take place near several settlements, but all along the coast. The main feature the model does not predict well during this period is the large deforested patch in the centre of the island. This patch seems to correspond with the boundary of the preceding French deforestation, which makes it more likely that there is some environmental factor which is either not correctly represented or not included at all.

According to the Fuzzy Kappa statistics, the model performs worst for the Independent period. This seems rather strange, as the main factor seems to be the elevation. This is reasonable, as it is likely that the most inaccessible and highest areas are deforested last. The patch on the south-eastern part of the island seems to be correctly placed at first sight, but this patch does not correspond to the patch which is indicated in the historical map. The independent Mauritian

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15 government embraced globalisation and industrialisation and tried to stimulate tourism (Lincoln, 2006). This also means that the government might have implemented policies to protect certain forests which were still left.

The sensitivity analysis indicates that the model is quite sensitive to changing the weights. Even though the periods span only a certain number of years, the accuracy can change up to three percent when altering the weights by a relatively small amount.

The worst case scenario also indicates the sensitivity of the model. In fact, the degree of agreement for the French period is reduced to equivalent to chance. On the other hand, the model without multiple periods performs reasonably well for the English and Independent period. This seems to go against the idea of relatively high sensitivity, but the weights for the worst case scenario are quite similar to the weights used in the full model for these periods.

Similar models

As this research is unique in several aspects, it is difficult to compare the results of this model to those of other studies. However, it is possible to look at studies with similar approaches and determine rough standards accordingly. The overall accuracy of cellular automata models in predicting urban growth is quite high (Santé et al., 2010). The overall accuracy of such models ranges from 55 to 94 percent, with the average being about 75 percent. The Kappa index ranges between 0.48 and 1, with the average being about 0.64. When only the transitioned area is taken into account, the accuracy drops significantly (Santé et al., 2010; Jantz et al., 2003). Soarers-Filho et al. (2002), who created a cellular automata model for deforestation in the Amazon, achieved an accuracy of 99.15 percent when performing randomised validation. In addition, Kamusoko et al. (2009) reached an accuracy of 88 percent when modelling agricultural land use change, with a Kappa index ranging from 0.83 to 0.88. The performance of the model created for this research varies per period. However, all of the results seem to be worse than the average results of other cellular automata models.

The fact that the results are worse than those of most other studies indicates that more research is needed concerning several aspects. First of all, the model could possibly perform much better if the factors which have been used would be adjusted or replaced. As mentioned before, it is likely that some factors are either not properly represented or that there are other environmental factors which not have been included. This research is based on the available (spatial) data and it was impossible to confirm anything through for example field experiments. This means that it is also impossible to validate much of this spatial data. Research which is aimed at investigating potential other factors might therefore also include field tests. This could for example shed some light on certain aspects of agricultural suitability which have not been included in the FAO map used for this research.

In addition, certain data which had no spatial component was excluded. This mainly included policies. As mentioned before, there were certain protected areas during the French, English and Independent periods and these have not been included. However, it is reasonable to assume that these sorts of policies have had a great impact on the overall spatial developments. Another example of spatial policies which could have had an effect on the developments is the land allotment system used by the French (Brouard, 1963). If the colonial government allotted land based on certain criteria, a model which just uses environmental factors will not generate very accurate results.

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Modelling techniques

While the results are worse than those of other studies with similar models, a constrained cellular automata model seems to be the best approach for a study like this one. The main advantages of this type of model are that they have been used in many other studies (Clarke & Gaydos, 1998; Verburg et al., 2002; Pontius et al., 2001), and that they have been used successfully when modelling land use change (and policies) (Verburg et al., 2008; Uthes et al., 2010; Claggett et al., 2004; van Berkel & Verburg, 2012). In addition, cellular automata are often quite simple, but can be expanded to deal with complex situations (Lazrak et al., 2010; Santé et al., 2010). Constraining a such a model (as has been done for this research) reduces the number of assumptions and allows for the incorporation of available historical data (National Research Council, 2013; Soares-Filho et al., 2002).

A major drawback of cellular automata is that the theoretical link between the transition rules and reality can be difficult to establish (National Research Council, 2013). This might also have been one of the reasons why the model did not perform that well for the different periods. The land use changes are based on environmental and historical factors, but indirectly on the assumption that rational decision making is the basis behind land use change. For example, the agricultural suitability factor implies that even the early colonists had extensive knowledge of the agricultural suitability of the whole island.

An alternative modelling approach could have been a agent-based model. Such a model might have worked, but it is unlikely that it would have generated more accurate data. Agent-based models require a lot of historical data and/or assumptions to function properly (National Research Council, 2013). Given that not that much data is available, the lacking data would have to be replaced with assumptions concerning historical processes. The same drawbacks apply to a purely statistical model (Agarwal et al., 2002; Yang et al., 2014) and most other types of models are not suitable to generate spatially explicit data (National Research Council, 2013; Agarwal et al., 2002).

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Conclusion

The overall results of the model are decent. The Fuzzy Kappa statistic for the calibration years ranges from 0.653 to 0.211 and the degree of agreement from substantial to fair. The model only reaches a substantial degree of agreement during the Dutch period, mainly because the only factor seems to be the distance to the settlements and logging camps (Brouard, 1963). The deforestation during the French period is less well predicted, with the main factors being the distance to the rivers which might have been used and the distance to the known locations of settlements. Contrary to the previous periods, the deforestation during the English occupation mainly occurs near the coastline all around the island. While the Fuzzy Kappa is not much higher than that of the French period, it is clear from the generated maps that the model predicts the deforestation for this period much better. The model performs worst for the Independent period. This seems strange and the exact reason is unclear. One possibility is that it is related to implemented policies.

A sensitivity analysis was performed to test the sensitivity to changing weights. It indicated that the model is relatively sensitive to these changes in weights as relatively small changes can alter the accuracy by up to three percent.

In addition, a worst case scenario was performed to test the added value of including the intermediate period. Besides corroborating the results of the sensitivity analysis, it indicated that the intermediate period adds a significant amount of accuracy to most periods, except for the Independent period (for which it is calibrated).

Unfortunately, the accuracy of the model created for this research seems to worse than the average accuracy of other (similar) models (Santé et al., 2010; Santé et al., 2010; Jantz et al., 2003; Soarers-Filho et al., 2002; Kamusoko et al., 2009). This indicates that more research is needed concerning the factors used to predict deforestation in the current model and possible other factors which were left out (such as policies).

Even though the results are not as accurate as expected, a constrained cellular automata model seems to be the best approach for a study like this one (Clarke & Gaydos, 1998; Verburg et al., 2002; Pontius et al., 2001). Alternative modelling approaches are possible, but these often require more data (which is not available) and/or are not able to handle the spatial nature of the research (Agarwal et al., 2002; Yang et al., 2014; National Research Council, 2013).

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Appendix

Appendix 1: Input and calibration data

Name Type of data Author Date of publicati on Link of publication Data usage Topographi c map in French of Mauritius Island Map created in

GIS Eric Gaba 2008

https://commons.wi kimedia.org/wiki/Fil e:Mauritius_Island_ topographic_map-fr.jpg Reconstruction of rivers used by the French Isle de France Scanned map Rigobert Bonne 1791 https://commons.wi kimedia.org/wiki/Fil e:Bonne_-_Isle_de_France_( Detail).jpg Reconstruction of rivers used by the French, determining the accuracy of historical maps Carte de I'Île Maurice Scanned map Bellin 1763 https://commons.wi kimedia.org/wiki/Fil e:Isle_de_France_-_carte.jpg Reconstruction of rivers used by the French, determining the accuracy of historical maps Charte von Île de France oder der Insel Frankreich Scanned map Bory de Saint-Vincent & Jean-Baptiste Genevieve Marcellin 1811 http://digitool.is.cu ni.cz:1801/view/act ion/nmets.do?DOC CHOICE=853791.x ml&dvs=15294209 87383~199&locale =nl&search_terms= &adjacency=&VIE WER_URL=/view/a ction/nmets.do?& DELIVERY_RULE_ID =3&divType= Determining the accuracy of historical maps Map of the island of Mauritius Scanned map A. Descubes 1880 https://commons. wikimedia.org/wiki /File:Mauritius_188 0_map_by_Descub es.jpg Determining the accuracy of historical maps Mauritius Scanned map Unknown 1910 https://commons. wikimedia.org/wiki /File:Mauritius_Wa terlow_map_1910.j pg Determining the accuracy of historical maps Land Resources and Agricultural Suitability Scanned map FAO 1970 http://ref.data.fao.or g/map?entryId=86d 13433-159e-4351- bc42-e3ee73fce163&tab =about Agricultural suitability map DEM100x10 0_Resample

.img Raster file

Norder et al., 2017 2017 https://www.ecolog yandsociety.org/vol 22/iss1/art29/ Height suitability map, slope suitability map forest_1638 Shapefile Norder et al., 2017 2017 https://www.ecolog yandsociety.org/vol Reconstruction of the historical

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23 22/iss1/art29/ deforestation rate,

calibration and validation forest_1773 Shapefile Norder et al., 2017 2017 https://www.ecolog yandsociety.org/vol 22/iss1/art29/ Reconstruction of the historical deforestation rate, calibration and validation forest_1835 Shapefile Norder et al., 2017 2017 https://www.ecolog yandsociety.org/vol 22/iss1/art29/ Reconstruction of the historical deforestation rate, calibration and validation forest_1872 Shapefile Norder et al., 2017 2017 https://www.ecolog yandsociety.org/vol 22/iss1/art29/ Reconstruction of the historical deforestation rate, calibration and validation forest_1935 Shapefile Norder et al., 2017 2017 https://www.ecolog yandsociety.org/vol 22/iss1/art29/ Reconstruction of the historical deforestation rate, calibration and validation forest_1997 Shapefile Norder et al., 2017 2017 https://www.ecolog yandsociety.org/vol 22/iss1/art29/ Reconstruction of the historical deforestation rate, calibration and validation Population Mauritius Table Norder et al., 2017 2017 https://www.ecolog yandsociety.org/vol 22/iss1/art29/ Reconstruction of the historical deforestation rate A History of Woods and Forests in Mauritius Text N.R. Brouard 1963 N.A. reconstruction of settlement locations, reconstruction of the historical deforestation rate

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Appendix 2: Population graph

Figure 7: Graph of the population of Mauritius during the modelled time period. The data was retrieved from Norder et al. (2017).

Appendix 3: Calibration results

Appendix 3.1: Calibration phase 1 - accuracy of combinations of factors

This appendix contains all of the results from the first phase of calibration. This phase consisted of finding the best combination of factors using equal weights. The first table for each period contains the standard accuracy (with all factors) and the accuracies with all combinations of three factors. The second table for each period contains the accuracy of all other possible combinations of factors. For the French period, the first table contains the accuracy of the rivers and settlements factors.

Dutch period Calibration year Standard accuracy Agricultural suitability removed Slope removed DEM removed Settlements removed 1685 95.45% 96.54% 95.71% 95.44% 95.28%

Table 5: Part 1 of calibration phase 1 for the Dutch period.

Agricultural suitability

Slope DEM Settlements

Agricultural suitability 95.45% 93.88% 95.68% 95.85% Slope 93.88% 93.63% 94.48% 96.65% DEM 95.68% 94.48% 94.57% 97.22% Settlements 95.85% 96.65% 97.22% 97.72%

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French period

Rivers only Settlements only

Rivers and settlements

79.54% 73.31% 81.88%

Table 7: Accuracy of the rivers and settlements factors.

Calibration year Standard accuracy Agricultural suitability removed Slope removed DEM removed Rivers and settlements removed 1773 76.63% 77.32% 77.32% 77.57% 73.71%

Table 8: Part 1 of calibration phase 1 for the French period.

Slope DEM Rivers and settlements

Agricultural suitability 74.59% 74.27% 73.76% 78.56% Slope 74.27% 71.53% 69.14% 79.75% DEM 73.76% 69.14% 69.36% 79.01% Rivers and settlements 78.56% 79.75% 79.01% 81.88%

Table 9: Part 2 of calibration phase 1 for the French period.

Early English period Calibration year Standard accuracy Agricultural suitability removed Slope removed DEM removed Coast distance removed 1835 71.36% 72.30% 72.45% 69.64% 69.07%

Table 10: Part 1 of calibration phase 1 for the Early English period.

Slope DEM Coast distance

Agricultural suitability 54.69% 51.35% 68.68% 70.54% Slope 51.35% 61.70% 73.22% 71.50% DEM 68.68% 73.22% 74.63% 73.41% Coast distance 70.54% 71.50% 73.41% 70.90%

Table 11: Part 2 of calibration phase 1 for the Early English period.

Middle English period

Year Standard accuracy Agricultural suitability removed Slope removed DEM removed Coast distance removed 1872 77.55% 75.18% 78.22% 75.78% 75.70%

Table 12: Part 1 of calibration phase 1 for the Middle English period.

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Late English period

Year Standard accuracy Agricultural suitability removed Slope removed DEM removed Coast distance removed 1935 87.19% 85.13% 86.72% 86.63% 88.73%

Table 14: Part 1 of calibration phase 1 for the Late English period.

Table 15: Part 2 of calibration phase 1 for the Late English period.

Independent period Year Standard accuracy Agricultural suitability removed Slope removed DEM removed Coast distance removed 1997 94.15% 93.68% 93.99% 93.77% 94.49%

Table 16: Part 1 of calibration phase 1 for the independent period.

Table 17: Part 2 of calibration phase 1 for the independent period.

Appendix 3.2: Calibration phase 2 - testing all weights in order to find optimal values

This appendix contains all results of the second calibration phase. This phase consisted calculating the accuracy when assigning weights ranging from 0 to 100 to all individual factors. The results of calibration phase 1 were used as input. The test was performed for all factors consecutively in the order as shown in the tables. This means that for each test the optimal situation up to that point (based on the previous tests) was used. The optimal weight is the weight which resulted in the maximum accuracy and the worst weight is the weight which resulted in the minimum accuracy.

Dutch period Optimal weight Maximum accuracy Worst weight Minimum accuracy

DEM 0 97.72% 100 96.94%

Slope 0 97.72% 100 96.15%

0 97.72% 22 95.85%

Table 18: Calibration phase 2 results for the Dutch period.

French period Optimal weight Maximum accuracy Worst weight Minimum accuracy

DEM 0 81.88% 100 77.21%

Slope 0 81.88% 100 78.56%

Agriculture 3 82.06% 100 76.68%

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Settlements 53 82.28% 0 79.66%

Table 19: Calibration phase 2 results for the French period.

Early English period

Optimal weight Maximum accuracy Worst weight Minimum accuracy

Slope 7 74.77% 15 72.98%

Coast distance 6 74.65% 100 72.42%

Agriculture 0 74.77% 100 59.25%

DEM 75 74.95% 0 61.71%

Table 20: Calibration phase 2 results for the early English period.

Middle English period

Slope 0 78.88% 100 75.60%

Coast distance 7 79.07% 100 77.15%

Agriculture 58 79.11% 0 75.39%

DEM 57 79.09% 0 73.38%

Table 21: Calibration phase 2 results for the Middle English period.

Late English period Optimal weight Maximum accuracy Worst weight Minimum accuracy

Slope 22 90.67% 100 87.60%

Coast distance 0 90.64% 100 84.88%

Agriculture 73 91.01% 0 88.37%

DEM 53 91.01% 1 89.56%

Table 22: Calibration phase 2 results for the Late English period.

Independent period

Slope 1 94.86% 91 93.65%

Coast distance 0 94.86% 100 93.58%

Agriculture 15 95.06% 82 94.75%

DEM 83 95.07% 0 94.48%

Table 23: Calibration phase 2 results for the Independent period.

Appendix 4: Worst case scenario

For the worst case scenario all intermediate periods were removed. Consequently, the same calibration procedure as with the full model was used.

Calibration year Standard accuracy Agricultural suitability removed

Slope removed DEM removed Coast distance removed

1997 94.15% 93.68% 93.99% 93.77% 94.49%

Table 24: Part 1 of calibration phase 1 for the worst case scenario analysis.

Agricultural suitability Slope DEM Coast distance

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Table 25: Part 2 of calibration phase 1 for the worst case scenario analysis.

Optimal value Maximum accuracy Worst value Minimum accuracy

Slope 1 94.86% 100 93.65%

Coast distance 0 94.86% 100 93.58%

Agriculture 15 95.06% 80 94.74%

DEM 89 95.07% 0 94.49%

Table 26: Calibration phase 2 results for the worst case scenario analysis.

Appendix 5: Accuracy of reference historical maps.

Map & Author Year Standard deviation

(m) Max acceptable deviation (m) Used for which period?

Carte de I'Île

Maurice, Bellin 1763 421.046 692.621 Dutch, French, _{Early English,}

Middle English Isle de France,

Rigobert Bonne 1791 790.711 1300.720 N.A.

Charte von Île de France oder der Insel Frankreich, Bory de Saint-Vincent & Jean-Baptiste Genevieve Marcellin

1811 492.916 810.847 N.A.

Map of the island of Mauritius, A. Descubes

1880 648.511 1066.801 N.A.

Mauritius,

Unknown 1910 301.794 496.451 Late English, _Independent

Table 27: Results of testing the accuracy of the reference historical maps.

Appendix 6: Full model script and data

The full model script and all of the used data can be downloaded from GitHub: https://github.com/M-Hinkamp/Deforestation-Mauritius

Modelling historical deforestation on Mauritius