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Keywords:

  • climate change;
  • conceptual modeling;
  • forest–savanna boundary;
  • natural fires;
  • South America

Summary

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information
  • We used a climate–vegetation–natural fire (CVNF) conceptual model to evaluate the sensitivity and vulnerability of forest, savanna, and the forest–savanna transition to environmental changes in tropical South America.
  • Initially, under current environmental conditions, CVNF model results suggested that, in the absence of fires, tropical forests would extend c. 200 km into the presently observed savanna domain.
  • Environmental changes were then imposed upon the model in temperature, precipitation and lightning strikes. These changes ranged from 2 to 6°C warming, +10 to −20% precipitation change and 0 to 15% increase in lightning frequency, which, in aggregate form, represent expected future climatic changes in response to global warming and deforestation.
  • The most critical vegetation changes are projected to take place over the easternmost portions of the basin, with a widening of the forest–savanna transition. The transition width would increase from 150 to c. 300 km, with tree cover losses ranging from 20 to 85%. This means that c. 6% of the areas currently covered by forests could potentially turn into grass-dominated savanna landscapes. The mechanism driving tree cover reduction consists of the combination of less favorable climate conditions for trees and more fire activity. In addition, this sensitivity analysis predicts that the current dry shrubland vegetation of northeast Brazil could potentially turn into a bare soil landscape.

Introduction

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

In the last two decades, many modeling studies have explored vegetation–climate interactions in the Amazon tropical forest. On the one hand, these studies show that drier and warmer climate conditions could disturb the vegetation–climate system and lead to a potential ‘savannization’ of eastern and even central areas of the Amazon basin (e.g. Salazar et al., 2007; Lapola et al., 2009; among others). On the other hand, land cover change due to cropland expansion, grazing, and other anthropogenic activities (Morton et al., 2006) could also contribute to the ‘savannization’ process, through feedback mechanisms that could negatively affect the amount of local precipitation and thus weaken the entire hydrological cycle, favoring droughts (Nobre et al., 1991; Hahmann & Dickinson, 1997; Costa et al., 2007; Sampaio et al., 2007; among many others). Although large-scale studies, using dynamical global vegetation models (DGVMs), have also considered a more realistic simulation with climate and land cover disturbances occurring concurrently (e.g. Costa & Foley, 2000), Amazon ‘savannization’ remains an open scientific issue (Nobre & Borma, 2009), particularly in relation to the search for specific thresholds (‘tipping points’) related to a breakdown of the climate–vegetation equilibrium and an abrupt ecosystem shift (Scheffer & Carpenter, 2003).

In this context, conceptual models are expected to be an important tool for simulating complex system behavior and evaluate its ‘tipping points’ in more understandable and tractable ways. Although their parameterizations may be limited, conceptual models have in many cases produced successful results for nonlinear complex systems, particularly those models focusing on the resilience and adaptability of social-ecological systems (Anderies et al., 2002; Walker et al., 2004; Folke, 2006). However, they have also been applied as a first-order approach to represent biome boundary shifts in the Sahara/Sahel region in Africa (e.g. Zeng et al., 2005) and in the forest/savanna region in the tropics (Sternberg, 2001). Most of these investigations using conceptual models have been carried out considering climate and vegetation as the main state variables. This is reasonable for the Sahara/Sahel transition, in spite of the contrast between desert and savanna climatic conditions. However, although climate is one of the major drivers in controlling vegetation distribution in tropical South America, climate gradients are not as marked as in the arid African transitional zone (Coutinho, 1990), and natural fires are reported also to be very important in maintaining the savanna biome and, thus, delimiting the forest–savanna transition. Unlike humid tropical forests, which are quite impenetrable to natural fires, mainly because of their high humidity, tropical savannas are naturally influenced by fires triggered by lightning activity (Mistry, 1998; Ramos-Neto & Pivello, 2000; Miranda et al., 2002).

In light of the ecological relevance of natural fires, some large-scale DGVMs include, with varying levels of complexity, fire ignition and its effects on vegetation in their fire modules (e.g. Thonicke et al., 2001; Arora & Boer, 2005; Cardoso et al., 2007). In simulations of the world without fire, for example, an important expansion of forest areas is likely to occur (Bond et al., 2005; Scheiter & Higgins, 2009). Some landscape-scale demographic-bottleneck models have also been developed to investigate in detail tree–grass coexistence exclusively within the savanna biome (e.g. Higgins et al., 2000; Gardner, 2006; Hanan et al., 2008). These models essentially consider that the impacts of disturbances, particularly fires, are different depending on the life history stages of trees; that is, disturbances affect tree germination, mortality and demographic transition in different ways (Sankaran et al., 2004).

Despite quite accurate parameterizations to represent real-life biophysical processes, DGVMs and demographic-bottleneck models usually produce outputs that are difficult to disentangle to further quantify under which conditions (‘tipping points’) the system may abruptly shift towards other equilibrium states (Holling, 1973; Scheffer et al., 2001). For instance, for South America, it has been suggested that there are two potential stable vegetation–climate states (Oyama & Nobre, 2003): one showing the current forest and savanna distribution, and a second with savannas covering most of eastern and southeastern Amazonia. A thorough review of the literature on potential tipping points of the Amazon forest is presented by Nobre & Borma (2009), highlighting the insufficient quantitative understanding on the role of natural fires in determining the location and extent of tropical forest–savanna boundaries.

Therefore, inspired by the conceptual approaches described above (e.g. Sternberg, 2001) and by the lack of climate–vegetation–natural fire (CVNF) modeling in South America (Nobre & Borma, 2009), we have developed a simplified CVNF model which has three main benefits: good representation and quantification of the forest–savanna boundary in tropical South America in response to the combination of climate and lightning-triggered natural fires; investigation of vegetation-cover sensitivity to environmental changes in precipitation (P), temperature (T) and lightning activity (R); and evaluation of environmental tipping points, which could displace the forest-savanna transition and lead to a potential shift into another equilibrium state.

Materials and Methods

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

The study region

Ecological observations have indicated that there is an enormous variety of arboreal and herbaceous cover types constituting the vegetation gradient between forest and savanna (also referred to as cerrado) biomes within tropical South America. The high degree of complexity of the floral diversity in this tropical continuum is determined and affected by many natural factors such as climate, fires, soil types, topography and geological history, either primarily or secondarily depending on the spatial and temporal scale (Furley et al., 1992).

In this study, we performed assessments on a coarse spatial scale, in which climate and fire drivers overcome other finer-scale factors such as soil fertility and drainage. While the latter factors influence structural, compositional and physiognomic variations within a biome (e.g. waterlogged vs terra firme forests; distrophic vs mesotrophic woodland savannas), they are not sufficient by themselves to explain the forest–savanna transition we are expecting to represent (e.g. Janssen et al., 2008).

The coarse-scale mapping of the study region requires simplifications according to the degree of representation we expect to characterize in this work. For instance, the natural vegetation map proposed by Lapola et al. (2008) (hereafter referred to as ‘LONS08’) represents the vegetation distribution for climate studies with particular improvements on the representation of South American vegetation distribution, and uses biome types to classify vegetation cover (Fig. 1a). While focusing on the natural vegetation distribution over South America, the LONS08 map will be used as a general guide to compare model outputs and the locations of forest, savanna and the forest–savanna transition.

image

Figure 1.  (a) The location of the selected domain of the study within tropical South America according to the LONS08 natural vegetation map; (b) the study domain (15–5°S, 71–42°W) in greater detail; (c) the one-dimensional biome distribution map derived from (b), showing the forest, the savanna and a range of forest–savanna edges (the LONS08 map does not indicate forest–savanna transitions directly).

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As the LONS08 map was designed to provide approximate locations of biome types according to the dominant vegetation species, it does not separate vegetation cover by type of tree (evergreen, deciduous, etc.) or grass (perennial or seasonal). Because vegetation cover in the proposed model is composed basically of trees and grasses over the tropical area defined in Fig. 1a, we assume that tree type is represented by a generic-evergreen-forest species, which supports climate seasonality and is very sensitive to fire disturbance (Nepstad et al., 2004). Grasses, in contrast, are parameterized to represent the cerrado herbaceous species, which means that, although climatic seasonality and fire disturbance may promote death of the above-ground herbaceous biomass, grasses recover rapidly because the root zone is preserved (Batmanian & Haridasan, 1985). Moreover, the model uses fractional coverage areas for each vegetation type rather than individual elements or the whole biome (see Model description section), and thus tropical forest corresponds to a fractional coverage area dominated by generic (evergreen) forest trees (close to 100%), with low grass population development (close to 0). In this simplified scheme, the forest–savanna boundary begins whenever tree cover is < 100%, and continues when a mixture of grasses and trees is present. Finally, only grass-dominated areas, which would be linked to the most open savanna physiognomies, correspond to the savanna biome for the model outputs.

As we propose a one-dimensional model (see Model description section) and adopt a two-dimensional gridded map for comparison, we use the selected region in the LONS08 map (Figs 1a,b) to create a correspondent one-dimensional map of biome locations (Fig. 1c). This simplification results in three regions: the tropical forest (dark green color) is defined as the area from 71°W to 50°W, as this is an area mostly covered by the forest biome, except where the LONS08 map indicates portions of the savanna biome in the southeastern boundary of the Amazon forest (from 60°W to 50°W); the forest–savanna transitional zone (light yellow) is defined according to a range of possible locations whose selection is based on forest–savanna edges (the map does not indicate forest–savanna transitions directly); and the savanna (light pink) is defined as the remaining area to the east.

Model description

We used the CVNF model to simulate the simplified dynamics of the climate–vegetation–natural fire system in the tropical South American zone. The CVNF is a one-dimensional model covering the longitudinal domain 71–42°W, with a 0.5° longitudinal spatial grid and an averaged latitudinal band ranging from 5 to 15°S (Fig. 1a).

The complete model description can be found in Supporting Information Notes S1. In the following paragraphs, we provide a brief overview of the main features of the model, particularly the two novel aspects that differentiate the CVNF from the classical set of Lotka–Volterra (LV) competition equations: plant growth parameters, β, are functions of climatic conditions (Table 1), and lightning-triggered fire effects on vegetation are incorporated. Although LV equations usually fail to simulate species coexistence and need adjustments to correctly model this (Bampfylde et al., 2005; Arora & Boer, 2006), we build the model based on these equations for two main reasons: first, we do not aim to model competition between species that are expected to coexist within the same biome types, that is, to represent biome diversity (as done by Bampfylde et al., 2005); and secondly, the inclusion of natural fire mortality should provide a different sort of competition advantage from one species over another, which would lead to the tree-grass coexistence that characterizes the forest-savanna transition defined in the previous Model description section. The set of modified LV competition equations to simulate the time evolution of grass (g) and tree (a) fractional coverage areas (%) is:

Table 1.   Description of the entire set of parameters and variables used in the climate–vegetation–natural fire (CVNF) model
SymbolDefinitionValue
  1. LV, Lotka–Volterra.

Classical parameters of LV equations
 aFractional coverage area of treesModel output
 gFractional coverage area of grassesModel output
 IVegetation typei = g, a
 a*, g*Carrying capacities for a and ga* = 1.0; g* = 1.0
 cgaCompetition coefficient of a over gcga = 0.9 (Cox, 2001)
 νNatural grass mortalityν = 0.1 (Hughes et al., 2006)
 βiPlant growth parameterinline image
 γiTime-scale of establishment (area)inline image
 TiIdem (individual)inline image
 Vs, VfInitial and final fractional areasinline image
 fiClimate-dependent functioninline image
 inline imageLower and upper bounds of HI for ainline image
inline imageLower and upper bounds of HI for ginline image
 HIHumidity indexinline image
Time series generation
 PPrecipitationModel input
 TTemperatureModel input
 RNumber of flashesModel input
 μP,T,RMean annual valueMonthly variation for each grid
 σP,T,RAnnual standard deviationMonthly variation for each grid
 ΔRandom number ∼N(0,1)
 τPeriod of the annual cycle12 months
 AP,T,RAmplitude of the annual cycleMonthly variation for each grid
 φP,T,RPhase of the annual cycleMonthly variation for each grid
 inline imageMonth of maximum variable valueGrid variation
Fire submodel – fire mortality in LV equations
 diMaximum population deathda = 0.1; dg = 0.3 (Gardner, 2006)
 HImaxFire ignition threshold for HI1.2
 LLitter pools from natural dead grassν·g; ν = 0.1
 LminFire ignition threshold for L0.45
 PRFire probabilityinline image
 inline imageLower and upper bounds of RRl = 25; Ru = 65 flashes month−1
 PR,minFire ignition threshold for PR0.55
 RfNumber of flashes to fire ignitionRf = 0.25R (Correia & Saba, 2008)
 IFire intensityinline image
 wSoil memory indexinline image
 inline imageLower and upper bounds of wwl = 110; wu = 200 mm month−1
 hFire intensity dependence on Linline image
 kL, bLParameters used in function h for LkL = 0.7; bL = 2.0
 firiFire effects on vegetation iinline image)
 ka, baParameters used in function h for aka = 0.7; ba = 8.0
 kg, bgParameters used in function h for gkg = 0.3; bg = 2.0
  • image(Eqn 1)
  • image(Eqn 2)

The three basic LV processes represented for trees and grasses are: the vegetation source term, which is driven by the plant growth parameter β; and intra-specific (quadratic term II, inline imageor inline image) and inter-specific (crossed term III, inline image) competition terms (Table 1), where g* and a* correspond to grass- and tree-carrying capacities, that is, the maximum values that the vegetation population may reach, and are set to 1 for general purposes. The inter-specific term should represent the ecological advantage of one vegetation type over another depending on the magnitude of the competition coefficient (cga or cag; Table 1). For grasses, this parameter represents the negative shading effect that favors the growth and development of trees rather than grasses within an area (Cox, 2001). Because there are no general advantages of grasses over trees, inter-specific competition is negligible (cag∼ 0) for tree dynamics.

Climatic monthly time series (for precipitation (P) and temperature (T)) used to calculate plant growth parameters (β) are generated synthetically based on D’Andrea et al. (2006) and A. J. Dolman et al. (unpublished). Time series generation takes into account the annual mean values of P and T; the random behavior of the atmosphere, through the product of the standard deviation of the annual mean values and a random number with a normal standard distribution; and the co-sinusoidal annual cycle, defined according to a calculated amplitude, the period of 12 months and the phase, which depends on the maximum monthly value of P or T (see Fig. S2). All of this statistical information is taken from the Climate Research Unit’s (CRU) high-resolution data set (1901–2002) (New et al., 1999; Mitchell et al., 2003). As the CRU data set contains two-dimensional gridded information and the CVNF model requires one-dimensional statistical inputs, it is necessary to calculate an average between tropical latitudes 15°S and 5°S for each longitudinal point.

In addition to source elements, there is a sink term for grasses that allows the representation of their natural mortality at a constant rate (term IV in Eqn 1). In contrast, according to 14C isotope measurements, trees in central portions of the Amazon forest may be very old, with ages ranging from 200 to 1400 yr depending on tree species (Chambers et al., 1998). We assume, for simplicity, an average age of 800 yr. As this is relatively close to the total simulation period, natural tree mortality is not computed in the CVNF model.

A second sink term is introduced in the classical LV system to reproduce the effect of natural fires on the vegetation death rate. This term is an output of the fire submodel which proposes a simplified and empirical representation of fire triggering, intensity and effects on vegetation (term V in Eqns 1 and 2).

The starting of natural fires depends on three major factors: fuel availability and flammability, and the ignition source (Whelan, 1995). In this context, based on the approach suggested by Arora & Boer (2005), we explicitly include lightning flashes as the ignition source. To represent the occurrence of these flashes, a lightning time series is generated similarly to precipitation and temperature generation (Fig. S2). Therefore, a random component is explicitly incorporated in the lightning time series to represent the highly stochastic nature of lightning strikes. The statistics used for the time series generation is extracted from a combined data set produced by two lightning-detection satellite sensors named Lightning Imaging Sensor and Optical Transient Detector (LIS/OTD) from the Global Hydrology Resource Center–NASA (http://thunder.nsstc.nasa.gov). In the CVNF model, in addition to the lightning ignition source, the other two variables, fuel availability and flammability, must also reach threshold values to start a fire event (for an example, see Fig. S1). Fuel available to burn is composed of dead grass (from natural mortality) which is accumulated within litter pools on the ground (L). These litter pools, in turn, become more flammable as the air over them becomes drier. Litter pool flammability is represented in the CVNF model based on the conceptual assumption that litter pools may be split into two layers. The upper (lower) layer is highly influenced by air humidity (soil moisture). Thus, in order to start a fire, only the top layer needs to be sufficiently dry.

After a fire starts, fire effects depend on the fire intensity, which is a function of a soil moisture index and the amount of litter available to burn. The soil moisture index varies with mean annual precipitation (Fig. S1c). The concept behind the dependence between the fire intensity and the soil moisture index relies on the lower layer of the idealized two-layer litter pools. After a fire starts, whether it keeps burning will depend on the bottom layer moisture content, which is directly related to soil moisture. That, in turn, is associated with mean annual precipitation (Table 1).

Depending on its intensity, fire affects vegetation types in different ways. Grass vegetation cover begins to burn as soon as a fire starts, and after grass is burnt, it regrows much more rapidly than trees. Trees are more resistant to low fire intensities; however, when the fire intensity is high enough, trees are strongly affected and need more time to recover (Fig. S3) (Anderies et al., 2002). Table 1 summarizes all the parameters and constants used in the model.

Simulations

The dynamics of the current forest–savanna boundary within tropical South America is evaluated using the results of two 1000-yr numerical experiments, designated ‘fire-on’ and ‘fire-off’; that is, with and without including the effects of natural fires. Explicit time integration is used to solve the simple set of differential Eqns 1–2 for a 1-month time step.

In the set of environmental change experiments, a fire-on experiment, in turn, is defined as the control run (CTL) to test the sensitivity of tree and grass populations to changes in precipitation (P), temperature (T) and lightning flashes (R). As the CVNF model is composed of a very simple set of first-order ordinary differential equations (ODEs), the impacts of steep or gradual external perturbations on this system are expected to be mathematically similar (Edelstein-Keshet, 1988). For simplicity, these environmental changes are steeply rather than gradually inserted. Because the CVNF model generally takes c. 500 yr to reach an equilibrium state (the time of tree establishment is set as c. 340 yr; Table 1), steep environmental changes are set to occur after the 500th year of simulation by modifying annual mean values of P, T and R in time series generation. Precipitation variations (ΔP) are defined as −20, −10, −5, +5 and +10% of the mean annual value, μP (Table 1); that is, after 500 yr, μP = μP ± ΔP. Similarly, ΔT = +2, +4 and +6°C, and ΔR = +5, +10 and +15%. The assumption that the frequency of lightning strikes will increase with global warming is based on Price & Rind (1994) and Reeve & Toumi (1999).

Results

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

Effects of natural fires on the forest–savanna boundary

Fig. 2 shows the equilibrium vegetation after running the model under ‘fire-on’ and ‘fire-off’ conditions. The simulation without fire, that is, driven solely by climate, leads to an equilibrium solution that does not fit the distribution of natural biomes (the one-dimensional map of Fig. 1c). In this case, the forest, which in our simplified scheme is defined as a tree-dominated fractional coverage area, extends further east (Fig. 2) in comparison to the position indicated in Fig. 1c for the forest–savanna boundary, where trees and grasses are assumed to coexist. Tree cover starts to decrease and to coexist with grasses at c. 44–43°W, which corresponds in the one-dimensional map to a savanna area; that is, an area covered solely by herbaceous-generic type vegetation according to our simplified definition. This result is supported by ecological theories which postulate that, if fire did not exist and the system dynamics was only climate-driven, tropical forest areas would expand into areas that are currently covered by savannas; that is, the forest–savanna boundary would move southeastwards in southern Amazonia (Desjardins et al., 1996; Pessenda et al., 2001).

image

Figure 2.  Comparison between the one-dimensional map of Fig. 1c (created in Section 2) and the one-dimensional model results for grass/tree distribution after 1000 yr of simulation, for fire-off (thinner dotted-continuous lines) and fire-on (thicker continuous lines) experiments. The region encircled by ellipses crudely represents the model-calculated forest–savanna boundary (‘ecotone’) for the fire-on (black) and fire-off (gray) experiments.

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When fire is switched on in the model, the forest–savanna boundary moves westward and its location compares more realistically with the one-dimensional map (Figs 1c and 2). However, the forest–savanna transition starts at c. 50°W in the one-dimensional map, while the CVNF model outputs indicate that it is located at c. 47°W. This may be a consequence of our simplified assumptions in representing the forest–savanna transition and the forest and savanna biomes. For example, the Amazon forest and tropical savannas are supposed to present a variety of mixtures of tree–grass physiognomies, particularly within South America, where, depending on climatic conditions, woodlands composed of c. 15-m tall trees may be found close to the Amazon forest edge (Oliveira-Fillho & Ratter, 2002). Our simplified scheme, however, takes into account only a generic (evergreen) tree, which in this case encompasses all types of tree. Nevertheless, the displacement caused by fire is remarkable and corresponds to c. 200 km; in other words, this means that, instead of a forest region 100% covered by generic trees across 200 km, the tree population declines to 98% at 47°W and to c. 30% at 46°W, and becomes 0% at 45°W (see black ellipse in Fig. 2), while the grass fractional area increases and ends up dominating the area.

Three longitudes are chosen to illustrate the effect of fire on the model-calculated transient behavior of tree and grass populations between 47°W and 45°W (Fig. 3). For all of these longitudes, tree and grass populations evolve quite similarly in the fire-off experiment. At the beginning of the simulation period, grasses grow much more rapidly than trees and dominate the area. However, as they are progressively affected by a tree shading effect (competition), the grass cover area decreases and tends to 0 as the tree cover area tends to 1 (thin dotted lines on the three panels of Fig. 3). Thus, climatic conditions determine tree dominance after c. 400 yr. Note that this time of tree establishment (γa in Table 1 and Notes S1, Eqn 4) exceeds the defined 340 yr because, at this specific location, there are probably less favorable climatic conditions for trees than further west (not shown). In addition, natural grass mortality (ν in Table 1 and Eqn 1) causes periodic increase–decrease variations (up and down movements) in the time evolution of the grass population.

image

Figure 3.  Time evolution of tree (green) and grass (orange) vegetation cover area (%) for three contiguous longitudinal model points located at c. 47–45°W. At the end of the simulation period (1000 yr), the equilibrium fractional vegetation cover is shown for the fire-on experiment (thick solid lines): (a) mostly covered by trees; (b) a mix of trees and grasses; and (c) mostly covered by grass. For comparison, the fire-off experiment is also shown (thin dotted lines), indicating that the final equilibrium vegetation would be trees for that longitudinal range.

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Results from the fire-on experiment at the first selected longitude (located at 47°W) clearly show the point where natural fires begin to influence tree and grass equilibria (thick solid lines in Fig. 3a). In other words, moving eastwards from this point, natural fires and climate act concurrently to affect vegetation cover, and tree coverage starts to decline, to be replaced by a mixture of trees and grasses. At this specific location, although tree dominance prevails at the end of the simulation period, there is a delay in the time of tree establishment from 400 to c. 900 yr. Fire also causes random tree fraction decreases in the tree-evolution line, which is not as smooth as in the fire-off experiment. The (up and down) variations in the grass population mentioned above increase as grass mortality increases with fire activity. Fire in the model is acting to enhance unfavorable conditions for trees and thus causes an increase in the delay of tree establishment, while adding a significant competitive edge for grasses over trees (e.g. Anderies et al., 2002; Scheiter & Higgins, 2009). In the CVNF model, this competitive factor is caused by an inter-dependent relationship between grasses and fire. On the one hand, a grassy litter pool is an enabling factor for fire to start as fire only ignites if grasses exist and die. These pools are equally important for fire intensity: the larger the amount of such litter pools, the higher the fire intensity. On the other hand, tree death, caused by high fire intensity, means a reduced shading effect, favoring grass growth.

The second longitudinal point – located at approximately 46°W – (Fig. 3b) is in a transitional region (we might call it a forest–savanna ‘ecotone’ in our simplified representation), with coexistence of the two vegetation types for the fire-on experiment (see Materials and Methods for further details of the forest–savanna transition definition). The next contiguous point to the east, between 46°W and 45°W (Fig. 3c), represents a region where the final state is grass-dominated in the fire-on experiment, but tree-dominated in the fire-off experiment. Note that, despite the up and down variations, the average population value for grasses may be estimated at c. 75% at this location, which implies c. 25% bare ground, as tree coverage tends to approximately zero.

In summary, depending on its effects, fire may promote the coexistence of trees and grasses (Fig. 3b), the dominance of grasses over trees (Fig. 3c), or the continuing dominance of the tree population, although in this case there is a marked increase in the time required for trees to establish (Fig. 3a). Therefore, fire has the effect of modifying the fractional coverage areas of grasses and trees by favoring grass dominance over trees through the inter-dependent relationship between grasses and fire described in the previous paragraphs. (Anderies et al., 2002).

CVNF sensitivity study on the forest–savanna boundary

The CVNF equilibrium outcome for the most extreme scenario (hereafter ‘EXT’) of precipitation, temperature and lightning activity changes, with ΔP = −20%, Δ= 6°C and Δ= +15%, is compared to the vegetation distribution of the CTL run (Fig. 4).

image

Figure 4.  Longitudinal vegetation distribution resulting from the control (CTL) run (dotted-continuous lines) and from the experiment with extreme environmental conditions (continuous lines; ΔP = −20%, ΔT = +6°C and ΔR = +15%, where P is precipitation, T is temperature and R is lightning activity). Tree and grass evolution is depicted using black and gray lines, respectively. Numbers 1, 2, 3 and 4 indicate regions where changes in environmental conditions affect the final equilibrium in Amazonia (1), the forest–savanna transition zone (2 and 3) and open savannas (4), after 1000 yr of simulation.

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Four regions are selected for detailed analyses in experiment EXT. The first region (indicated by number 1 in Fig. 4), located in the western Amazon forest (at c. 65°W; see Fig. 1a for a guide to the biome distribution), shows a decrease in the tree fractional cover area. This decrease could cause an increase in the grass population as the tree shading effect diminishes. However, grasses remain constantly absent, which in this simplified model means that tree coverage may be replaced by bare soil in this area. A fixed point within area 1 is chosen at 66°W to evaluate interactions between changes in environmental conditions and vegetation.

At this point, when combined with precipitation variation, an increment of 2°C in temperature results in tree cover reduction (Δa), as expected, with the highest (lowest) decrease in tree population c. 11% (c. 3%) for Δ= −20% (Δ= +10%) (Fig. 5a). The maximum Δa occurs with a temperature increment of 4°C, when tree cover reaches values of c. 0.8 (or 80%) independently of ΔP effects. This value remains unchanged for Δ= 6°C and all precipitation variations. Thus, for ΔT ≥ 4°C, tree cover seems to reach a new stable tree cover value of 80% for the entire set of ΔP and ΔT variation.

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Figure 5.  Tree fractional coverage area changes (%) at 66°W as a function of (a) precipitation (P) and temperature (T) variations (ΔP = −20, −10, −5, +5 and +10%; ΔT = +2, +4 and +6°C), (b) T and lightning strike number (R) variations (ΔR = +5, +10 and +15%), and (c) P and R variations.

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However, for this case, instead of having a negative effect on tree cover, variations in the number of lightning strikes (R) do not affect the tree population itself, even when combined with ΔT or ΔP, and may be considered negligible as tree cover reduction is mostly a result of either precipitation or temperature decreases (Figs 5b,c). However, the number of fire events increases up to Δ= 4°C at this location (Fig. 6a). This means that, overall, environmental changes increase the frequency of fire, but fire intensity does not significantly affect tree cover reduction (Figs 5b,c). Fire intensity depends on the amount and dryness of litter pools. Although, on the one hand, a drier climate would promote high fire intensities, on the other hand, because of the competitive effect of tree shading, the grass fractional area would be very low, leading to low litter accumulation and thus low fire intensities. In this case, the litter accumulation effect overcomes the impact of drier climate conditions, and trees are not affected by such low-intensity fires. Conversely, the grass population, which is damaged even by low-intensity fires, is not allowed to grow and remains constantly null at the equilibrium solution (Fig. 4).

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Figure 6.  Number of fire events after the 500th year of simulation, as a function of precipitation (P) and temperature (T) variations (ΔP = −20, −10 and −5%; ΔT = +2, +4 and +6°C) at (a) 66°W and (b) 47°W.

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An unexpected result is the absence of fire events for Δ= 6°C. In this case, fire start is not even occurring; that is, it is inhibited by at least one of the three factors described in Materials and Methods. As fire ignition and flammability conditions are apparently satisfied, the only condition that might not be met is a sufficient amount of fuel available to burn. In fact, the grass population equilibrium solution is zero at 66°W for the EXT experiment (Fig. 4), because, even with a tree cover reduction, the shadow competitive effect of trees on grasses still inhibits grass development. This implies no litter pool accumulation and less fire triggering. Thus, the system reaches a new equilibrium with 20% less tree cover, mostly as a result of the combination of climatic condition variations and the lack of a sufficient grass population to start a fire or to increase fire intensities.

The second region (region 2 in Fig. 4) marks the westward displacement of the transition zone, and is characterized by a decrease in tree cover. According to the CVNF model, the beginning of the forest–savanna transition is located at 47°W under current environmental conditions. The anomalous tree cover reduction at 48.5°W indicates that this boundary moves westward in the EXT experiment, which means a retreat of the forest of c. 150 km. However, grass population growth is displaced westwards only by 50 km (from 47°W in the CTL run to 47.5°W in the EXT experiment; Fig. 4), mainly because tree cover is sufficient to dominate the area and inhibit grass population development over the 48.5–47.5°W longitudinal range. With the lack of available fuel, only one fire episode is recorded at this point after the 500th year of the simulation (not shown). Fuel availability should be lower than at 66°W, where the number of fire events is larger and the tree population is smaller (Fig. 6a). Without a direct effect of fires at this location, the tree cover reduction of 2% at 48.5°W seems to be caused mainly by weaker climate change impacts than at 66°W, where these modifications affect 20% of the tree population.

The third region (region 3 in Fig. 4) shows a steep decrease in tree cover from 47.5°W to 47°W, after a smoother reduction within the first 100 km of the transitional zone (from 48.5°W to 47.5°W). We select longitude 47°W to evaluate the interactions between P, T and R (Fig. 7) within this area. Unlike the other two longitudinal points, there is an abrupt change in tree population at this point. The magnitude of the impact is much larger than in the previous cases: fractional tree cover falls from c. 100% to c. 15% (Figs. 7a,b). If temperature rises by 2°C, tree cover reduces to 0.7 (0.3) in the most positive (negative) scenario of precipitation variation. The range of tree cover reduction diminishes as temperature increases by 4°C, and practically disappears for Δ= 6°C. Under the latter temperature variation, tree cover decrease converges to a single value for the entire precipitation variation interval (Fig. 7a). Unlike the other two cases, the reduction in the tree population (and thus in the tree shading effect) is enough to allow grass vegetation to increase. This, in turn, promotes grass natural mortality and litter accumulation, and the number of fire events increases, particularly for precipitation decreases of 10 and 20% (Δ= 2°C; Fig. 6b). For Δ= 4°C, the number of fire events reaches its maximum value (500), which represents, on average, a frequency of one fire event per year (Fig. 6b). Fire episodes become less frequent when Δ= 6°C, because the grass population is negatively affected by this temperature increase and grows more slowly; thus it takes a longer time to recover litter pools available to burn. Although the illustration in Fig. 7c is not as conclusive as Fig. 5c, it supports the above conclusions by showing that, for Δ= −20%, ΔR contributes to a greater reduction in tree cover, particularly when Δ= +5%. Thus, the larger grass cover area, larger litter pools and greater number of fire events are interrelated. In addition, larger litter pools contribute to higher fire intensities (Notes S1, Eqn 12); more intense fires cause more damage to tree cover, which takes longer to recover than does the grass population.

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Figure 7.  Tree fractional coverage area changes (%) at 47°W as a function of (a) precipitation (P) and temperature (T) variations (ΔP = −20, −10, −5, +5 and +10%; ΔT = +2, +4 and +6°C), (b) T and lightning number (R) variations (ΔR = +5, +10 and +15%), and (c) P and R variations.

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The last region (region 4 in Fig. 4) refers to longitude 42°W. According to the LONS08 map (Fig. 1a), this area covers the eastern boundary of the Brazilian savannas plus the western border of northeastern Brazil’s dry shrubland (caatinga), which has been suggested to be a potential location for replacement by semi-desert or desert biomes under drier and warmer climate conditions (Oyama & Nobre, 2003). Experiment EXT (Fig. 4) supports this suggestion and shows a bare ground configuration in region 4, with a decrease in both tree and grass populations. Moreover, according to our results, not only is the dry shrubland of northeastern Brazil potentially vulnerable to changes to the vegetation types of drier climates, but eastern portions of the Brazilian savannas may equally be affected by similar changes in the case of the extreme environmental changes represented by the EXT numerical experiment.

Discussion

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

Following previous conceptual and theoretical approaches to represent the forest–savanna transition within the tropics (e.g. Sternberg, 2001), we propose a CVNF model to elucidate the dynamic behavior of this boundary in response to changes in climate conditions and naturally triggered fires, and to quantify the impacts of environmental changes on vegetation in the tropical South American zone. The model is composed of a simple set of equations that describe tree and grass time evolution, accounting for vegetation growth, competition and mortality of vegetation. Two novel aspects of the model are a climate-dependent growth function instead of a constant growth parameter, and fire mortality for trees and grasses. These modifications, particularly the inclusion of a fire effect, allow for new vegetation equilibria with tree–grass coexistence. In addition, although it does not represent the carbon cycle and complex ecological features, which would provide more realistic parameterizations, the CVNF model is able to capture mechanisms described by more complex models, such as the inter-dependent grass–fire relationship, supporting a competitive advantage of grasses over trees (e.g. Higgins et al., 2000; Scheiter & Higgins, 2009 among others).

In addition, natural fires force a 200-km retreat of the forest, which means that 8% of regions climatically predicted to be forest would potentially be replaced by a mixture of trees and grasses. This westward displacement of the boundary is more realistic in comparison with the LONS08 natural biome distribution. It should be noted that 8% is a much lower value than that obtained by Bond et al. (2005) in their fire suppression experiment which, although it uses a more complex vegetation representation (DGVM), does not have a reasonable representation of biome boundaries and tree–grass coexistence in the tropics (Scheiter & Higgins, 2009). Conversely, the value is closer to that obtained in the continental-scale fire suppression experiment conducted by Scheiter & Higgins (2009) using an adaptive DGVM with more accurate tree–grass competition modeling for Africa. Thus, despite using much simpler parameterizations, the CVNF model may provide a reasonable first approach to climate–vegetation–natural fire interactions within South America in comparison to other models.

For all locations evaluated, climate change effects or a combination of climate and lightning change effects on vegetation gradually increase up to a temperature increment of 4°C, and remain approximately constant as the temperature change reaches 6°C. Thus, Δ= 4°C is a threshold value for the CVNF model, above which the tree coverage area decreases and reaches another stable equilibrium. This equilibrium may depict either a tree-dominated population (as observed at 66°W and 48.5°W) or grass dominance (as at 47°W) depending on the impact of concurrent variations on precipitation and lightning activity. This temperature control observed in the CVNF outputs may be related to the plant growth parameterization defined as a function of the ratio between precipitation (P) and potential evapotranspiration (PET) (fi; see Notes S1 and Eqns 3, 5 and 6 for further details). The reason why vegetation seems to be more sensitive to temperature may be linked to Thornthwaite’s parameterization (Thornthwaite, 1948) used to calculate PET (Hulme et al., 1992). While plant growth is linearly modified by precipitation variations, temperature increases result in exponential increases in PET. Hence, small differences in temperature could lead to large differences in PET values, which would result in large differences in the ratio between precipitation and potential evapotranspiration which controls plant growth functions (fi; Table 1).

In particular, the central-western portion of the Amazon (c. 66°W), where changes to a warmer and drier climate drive a potential reduction in tree cover, is predicted to be less resilient to climate change than eastern portions of the basin (c. 48.5°W). This is a consequence of the high sensitivity of plant growth parameterizations to small temperature variations as described above. The amplitude of the annual temperature cycle at 66°W is slightly larger than at 48.5°W. Thornthwaite’s method amplifies this difference and produces much larger PET values. This, in turn, results in a sufficient reduction in humidity index values (HI; Table 1 and Notes S1) for longitude 66°W to impose a greater restriction on tree population growth at this location than at 48.5°W. Thornthwaite’s parameterization is configured as a model limitation, and more accurate PET calculations (e.g. the simple correction proposed by Hulme et al., 1992) should be tested in future to confirm the tree cover reduction values predicted by the CVNF model. Therefore, rather than quantitatively assuring the decrease in tree cover, the higher sensitivity of the central-western region of the Amazon only indicates a potential location in which models should also concentrate future analyses. In addition, the CNVF model results should encourage further investigations of potential tree cover reduction and resilience within the central areas of the Amazon basin under drier and warmer climatic conditions, as a high fire risk is projected for this area in the 21st century, according to climate change simulations (Golding & Betts, 2008).

In contrast, when an increase in the frequency of lightning strikes promotes significant increases in fire frequency/intensity at the beginning of the actual forest–savanna transition (47°W), the combination of all environmental conditions (precipitation, temperature and lightning) results in an 85% reduction in tree cover. Whenever the number and intensity of fire events are sufficiently increased as a result of grass population growth, the easternmost edges of the Amazon (100 km before the actual transitional zone) become more vulnerable, and thus the system collapses and there is a change in the vegetation type dominance. The vulnerability of eastern portions of the Amazon basin has also been assessed for drought conditions (Hutyra et al., 2005), future climate change scenarios (Salazar et al., 2007; Lapola et al., 2009; Malhi et al., 2009), and regional climate changes in response to deforestation (Sampaio et al., 2007). Particularly, Sampaio et al. (2007) also suggested that a tree cover reduction of 40% would lead to an abrupt shift towards another stable equilibrium with dominance of low-biomass vegetation. Although the CVNF model does not confirm this, it supports this threshold by showing tree–grass coexistence, that is, forest replacement, only when tree cover reduction is c. 85%, and maintenance of tree dominance when the reduction is 20%. In addition to experiencing water stress caused by higher temperatures, the easternmost parts of the basin are likely to be more vulnerable to natural fires under the most extreme scenario of environmental changes (Malhi et al., 2009). Therefore, these easternmost forest regions, characterized by tree-dominated areas, would undergo a reduction in tree cover of c. 6.4% in response to extreme environmental changes, and the width of the forest–savanna transition (a mixture of trees and grasses) would expand from 150 to 300 km.

The CVNF model also indicates that environmental changes could lead to a bare-ground configuration within an area which corresponds to northeastern Brazil, and thus supports a potential transition to the second stable climate–vegetation equilibrium suggested by Oyama & Nobre (2003).

The interactions between fine-scale processes not represented by the CVNF model and the coarse-scale model forcing features may be relevant to understanding of the whole-ecosystem dynamics over time (Scheffer et al., 2005; Janssen et al., 2008). In addition, the distinction between C4 and C3 grass functional type responses to future CO2 increases could enhance the advantage of trees over C4 grasses (Ehleringer et al., 1997; Bond, 2008), which would result in a lower tree cover reduction than the CVNF model predicts. Thus, the dynamics of a real forest–savanna transition zone is expected to be much more complex than the CVNF model suggests (e.g. Scheiter & Higgins, 2009).

Nonetheless, this conceptual modeling provides a first-order approximation of the forest–savanna transition within tropical South America, and potential thresholds from which it may suddenly shift in response to future environmental changes. In summary, under current environmental conditions, the effect of lightning-triggered fires may result in an overall displacement of this transition by several hundred kilometers. Our results also agree with those of other studies of the sensitivity of the easternmost Amazon forest to future increases in temperature and decreases in precipitation, and add the significant effect of increases in the frequency of lightning strikes as an amplifier of climate-driven changes within this region. In addition, the present work encourages more complex modeling studies to quantify ‘tipping points’ for possible biome boundary changes within this zone, which is crucially important in ecological, climatological, social and economic terms.

To improve the CVNF model predictions, a complete analytical and theoretical analysis should be conducted to investigate the whole set of equilibrium states that can be found by the model. In addition, the CVNF approach does not yet include vegetation–climate feedbacks as a result of deforestation activities/land use change, and human-triggered fires. These features could increase and accelerate tree cover reduction (Golding & Betts, 2008), and also alter climatic threshold values. The inclusion of these improvements in a higher spatial resolution model, which would also take into consideration more detailed soil hydrology, is under way and the results obtained will be discussed in future papers.

Acknowledgements

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

This study is part of the first author’s doctoral thesis under the guidance of the second and third authors and was supported by the National Council for Scientific and Technological Development of Brazil (CNPq). The authors would like to thank Dr Osmar Pinto Jr and Dr Marcelo M. F. Saba for their useful comments on lightning modeling. We also thank Dr. Patrick Meir and the two anonymous reviewers for their valuable suggestions on a draft of the manuscript.

References

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

Supporting Information

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

Fig. S1 Piecewise linear functions for plant growth (fi, g, a - with g and a representing grasses and trees respectively), fire probability (PR) and soil moisture index (w); and an illustration of the thresholds defining a fire event.

Fig. S2 Annual cycle of generated precipitation, temperature and lightning flashes at four different locations.

Fig. S3 Variations of function h defined in Table 1 used in the model, depending on the empirical parameters k and b (see Table 1).

Notes S1 Complete description of the climate–vegetation–natural fire (CVNF) model.

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