Modelling of deforestation

The ongoing destruction of forests is a threat to biodiversity, climate, and the provision of forest goods and services such as timber production, soil and water retention, and recreation. The problem is concentrated in developing countries, which collectively lost 9.4 million hectares of forest during the 1990s (FAO 2001). The factors leading to destruction of forests (Figure 1) are complex and interrelated, making it difficult to anticipate future trends or to evaluate the likely impact of policy measures aimed at promoting conservation and sustainable forest use. Here I review some of the models of deforestation have been developed in an attempt to shed light on this issue.

Figure 1: Factors involved in deforestation (based on Geist & Lambin 2002).


Overview of model types

Quantitative models of deforestation fall into three general categories (Angelsen & Kaimowitz 1999). Analytical models use theoretical constructions of the interrelationships between the factors involved in deforestation to explore the implications of different economic and behavioural assumptions. In simulation models, observed or conjectured parameter values are put into a theoretical model to investigate the outcome of different scenarios. Empirical models begin with a large amount of real data and attempt to deduce from it the theoretical relationships between factors, using statistical techniques such as multiple regression analysis. Simulation and empirical models are able to make use of actual observed data, but their conclusions have limited validity outside the region for which the model was constructed, and correlations obtained from statistical analyses do not establish causal relationships between variables (Lambin et al 2000). Analytical models produce results that are more general in nature and can shed light on the mechanisms underlying observed trends.

Models can also be classified by their spatial scale, with microeconomic models investigating forest clearance at the level of the individual farm or settlement, while macroeconomic models aggregate data at a regional, national or global level. Models that focus on a particular region are often able to use good-quality data obtained through household surveys or remote sensing (Sills & Pattanayak 2006). Global models, by contrast, typically rely on national statistics of deforestation and land use, which contain notorious degrees of error (Achard et al 2002). Meta-analyses incorporating the results of many individual local studies may be a better way of drawing global conclusions (Geist & Lambin 2002). Global models have also been criticised for making the dubious assumption that the variables involved in deforestation interact in the same way across different regions (e.g. Grainger 1999).
Despite their strengths, a major limitation of microeconomic models is that many of their variables must be set exogenously, limiting the models' ability to capture a full range of economic effects. For example, in reality the degree of forest exploitation is likely to depend on the price of forest products, which reflects their supply and the state of the overall economy, which in turn is affected by the degree of forest exploitation. By taking prices as given, microeconomic models typically fail to capture this feedback process. By making such variables endogenous (determined within the model), macroeconomic models are better able to study the interactions between forestry and other sectors of the economy (Kaimowitz & Angelsen 1998). Another factor that is commonly treated as exogenous in microeconomic models is a region's population, even though deforestation may be closely interlinked with migration (e.g. Harrison 1991).

A distinction can also be made between time-series models, which explore trends in the area of forest cover over a period of time, and cross-sectional models, which compare the rate of forest loss in different regions or situations at a given point in time. Empirical time-series models have only been constructed for a few countries due to a lack of suitable data (Grainger 1999).

Models also differ in their ability to capture forest degradation - partial losses of biomass or biodiversity from a forest - rather than simply deforestation, which is generally defined as permanent and near-total loss of tree cover (e.g. FAO 2001). Taking into account degradation is particularly important when modelling regions in which tree cover comprises open woodland and the land has multiple, overlapping uses - for example, being exploited both for grazing of animals and for collection of fuelwood (Namaalwa et al 2007). In contrast, models involving dense rainforests such as the Amazon generally make the assumption that land uses are mutually exclusive at a given point in time. In such areas, changes in land use may proceed sequentially, with an area of forest first subjected to degradation (through selective logging) and then total clearance, with the former facilitating the latter (Grainger 1999). In models of these areas, changes may be expressed in terms of transition probabilities between one land use and another (Soares-Filho et al 2001).

Quantitative models of deforestation have some general limitations: they do not capture institutional factors, or broad issues which cannot easily be quantified, such as market failure. However, since these influences tend to be beyond the control of decision-makers, their omission may not diminish the usefulness of models as a planning tool (Angelsen & Kaimowitz 1999).


Case studies

Below are three studies that not only illustrate the application of different types of modelling but have contributed to the general development of modelling techniques.

An analytical model

Angelsen (1996) used an analytical model of deforestation to explore the implications of different assumptions about household behaviour and economic structure. Four sets of assumptions were examined. In the subsistence approach, rural householders seek to satisfy a basic level of needs with minimal labour. In the Chayanovian approach, householders use their land in a way that maximises private utility, balancing leisure and consumption. In the open economy / private property approach, householders seek to maximise their income, obtained both through land exploitation and off-farm employment. In the open economy / open access approach, householders have the additional motivation of being able to assert property rights over land by clearing it. (These sets of assumptions represent idealised cases: many models fall somewhere in between these categories - for example, incorporating markets for labour and agricultural produce that are limited in scale and operate imperfectly.)

In the model, forest clearing was assumed to proceed outwards from a settlement, with expansion limited by the cost of travel to and from the frontier. It was assumed that the available area was heterogeneous and divided equitably between households; the effect of factors such as road-building was thus beyond the scope of the model. Equations were formulated linking the size of the cleared area of land with various input parameters, and the qualitative effect of varying these parameters was shown algebraically for each of the four approaches. A quantitative illustration of these effects was then provided by inputting parameter values based on data obtained from a household survey in Sumatra.

This model highlights the fact that differing behavioural assumptions may fundamentally alter the conclusions obtained from a model. For example, in an open economy, for example, higher agricultural prices increase deforestation, while in the subsistence case they do not. This finding makes sense of the apparent contradiction between simulations that show higher agricultural prices reducing deforestation (Ruben et al 1994, cited by Kaimowitz & Angelsen 1998), and empirical studies of regions such as Mexico (Barbier & Burgess 1996) and Sudan (Elnagheeb & Bromley 1994) that show the opposite effect. The model also shows the impact of policy decisions that qualitatively alter land users' behaviour, such as the granting of land rights to those who clear it.

A simulation model

Namaalwa et al (2007) simulate the effect of different management options on open woodlands in the Masindi district of Uganda, using a bio-economic model that integrates biophysical processes (the growth of vegetation) with socio-economic ones (Figure 2). In Uganda's woodlands, exploitation often takes the form of degradation rather than outright clearance, and the model incorporates this by quantifying the reduction in biomass at different vegetation levels (such as trees, shrubs, and grasses). However, this fails to explicitly capture the effect of degradation on factors such as species diversity. A matrix growth model allows the rate of regeneration of biomass to be determined endogenously, an improvement on previous models in which yields were input as an exogenous parameter.

Like in many other models of tropical deforestation (e.g. Sankhayan & Hofstad 2001), decision-making is regarded as taking place at the village level. Land is treated as homogeneous, and clearance proceeds outwards from a settlement. 'Off-farm' employment is available but at low wage rates, reflecting the typical situation in the region. Villages are assumed to maximise their utility, derived from a combination of income from forest products, agricultural income, off-farm income and leisure. The model thus combines aspects of the Chayanovian and open economy approaches described by Angelsen (above).

Figure 2: A simplified outline of the model framework used by Namaalwa et al (2007).

Data for input into the model were obtained by a variety of methods, including land cover mapping, household interviews and group discussions. (Data collection encompassed only two villages in the region, necessitating caution when extrapolating from the model results.) Results were simulated for a base scenario ('business-as-usual'), and for five alternative scenarios: increased charcoal prices, increased crop yields, increased charcoal taxes, the imposition of quotas on wood extraction, and the imposition of quotas on charcoal production. In all of the scenarios there was reduction in forest area (deforestation) and reduction in biomass density (degradation), although taxes and quotas reduced the extent of forest losses relative to the base scenario. Some changes improved one outcome at the expense of the other: higher agricultural yields, for example, reduced degradation but increased deforestation.

Simulations of this kind can be characterised as multi-agent models, whose purpose is to elucidate the overall trends that emerge from the aggregate behaviour of many agents (Verburg et al 2004). In this case, it shows how 'rational' utility-maximising behaviour by village communities leads to deforestation and degradation. The model highlights both the need for intervention to ensure sustainable use of Uganda's woodlands, and the difficultly of devising intervention measures that succeed in this goal. Its authors point out additional difficulties not encompassed by their model, such the fact that corruption may prevent taxes and quotas from being properly implemented: the model merely provides "a hint as to what can be achieved". The model also demonstrates the importance of taking into account both deforestation and degradation when assessing natural resource use.

An empirical model

Mertens & Lambin (1997) used an empirical model to investigate spatial patterns in deforestation in southern Cameroon. Decreases in forest density were estimated by comparing infrared satellite images taken in 1973 and 1986 (more recent images were unusable because of cloud cover). This method allows partial degradation of a forest to be measured, although Mertens & Lambin considered only deforestation, with patches classified either as 'forested' or 'non-forested' depending on whether or not they exceeded a certain threshold of vegetation thinning. Field survey results and aerial photos were used to validate the satellite imaging data. A regression analysis was performed in which deforestation rates (the dependent variable) were compared with four independent variables: proximity to roads, proximity to towns, proximity to the forest edge, and forest fragmentation. Across the study area as a whole, the relationships discovered are sketched in Figure 3. These factors were then used to predict the areas most at risk from future deforestation.

Figure 3: Sketch of relationships between variables discovered by Mertens & Lambin (1997).

Although the discovery of relationships between variables is useful for predictive purposes, but it does not tell us anything directly about the mechanisms involved. The fact that deforestation is greater in close proximity to roads, for example, does not prove that road construction causes deforestation.

Perhaps the most insightful aspect of this study consists of an attempt to break the study area down into regions according to the type of deforestation taking place, judged on the basis of observed patterns of forest clearance: roadside deforestation characterised by 'corridors' of forest clearance, periurban deforestation characterised by large 'islands' of forest clearance, and deforestation for subsistence agriculture where forest clearance was diffuse. The factors predicting deforestation were found to be different in each case, with proximity to roads and the forest edge the main predictors of roadside deforestation, proximity to roads and towns the main predictors of periurban deforestation, and forest fragmentation the strongest predictor of deforestation in areas of subsistence agriculture. These findings provide quantitative empirical support for the widely-repeated observation that the causes of deforestation differ between regions, and demonstrate a means of taking account of such differences when aggregating results over a wider area. Mertens & Lambin's approach has since been used by other modellers such as McConnell et al (2004), who identified different deforestation patterns within a region of Madagascar and ascribed these different patterns to institutional factors such as the effectiveness of law enforcement.



Deforestation takes many forms, and when analysing its causes or predicting its extent, the choice of approach depends partly upon the type of scenario being modelled. For example, the analysis of deforestation on rainforest frontiers, where land clearance represents an investment decision by settlers, will differ from the analysis used for areas such as Uganda's woodlands where existing landowners seek to obtain the greatest utility from their land. In the light of such differences, conclusions drawn from analysis of one forest area should not be extrapolated to another without great caution.
Within a particular area, there are different types of model that may be applied, and to some extent their results are complementary to one another. Empirical models can be used to derive the relationships between variables which form the basis of simulation models (Sills & Pattanayak 2006), whilst analytical models can be used to explore the implications of the assumptions upon which the results of simulation models depend. By combining the results of different model types it should be possible both to draw conclusions with a firm empirical basis and to establish the boundaries within which these conclusions can validly be applied.



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This was originally written as an essay for MSc Ecological Economics at the University of Edinburgh

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© Andrew Gray, 2010