Deforestation is a worldwide problem that is particularly acute in tropical regions. Causes include urbanization, conversion to farmland, or even fuel insecurity which causes a population to turn to wood as the primary means of cooking and heating. Meanwhile, negative effects include soil erosion, desertification, and changes to climactic conditions. In the case of Amazon deforestation, biosequestration of atmospheric carbon dioxide is significantly hampered.
Gaining a proper understanding of the mechanism by which deforestation affects the forest is central to addressing the problem.
Bert Wuyts, a fourth-year PhD candidate at the University of Bristol, has studied the effects of deforestation, particularly in the Amazon. He recently published a paper exploring the bistability hypothesis of tropical vegetation and addresses specific shortcomings in previous research. He took the time to explain his research to Scinq.
SCIENTIFIC INQUIRER: Can you discuss the notion of bistability in context of the Amazon forest? How does it come about?
Bistability and bimodality
Multistability, the possibility of coexistence of multiple stable states of a variable of interest x under the same conditions is common in nonlinear dynamical systems. As most processes in nature are nonlinear, multistability is omnipresent and applicable to problems in any field of study including physics, chemistry, biology, ecology, geography and social science. When there are two possible alternative stable states, we speak of ‘bistability’. Between the stable states, there is always an unstable state, a precarious state above which a positive feedback leads to a rapid increase of x, and below which the positive feedback works in the opposite direction and leads to a rapid decrease of x. A graphical metaphor for bistable systems is a ball rolling in a landscape (solid line in Figure 1) with two wells (the stable states; a and c in Figure 1) and a hill in the middle (the intermediate unstable state; b in Figure 1). The dynamics of x (horizontal axis) when starting from a value of x= x0 can be imagined by thinking that the ball is placed at point x0 in the landscape and released. If it is released left of b, the ball will roll into the left well and the system settles in state x=a. If the ball is released right of b, it will roll into the right well and the system settles in state x=c. If we now imagine releasing many balls at the same time with many initial conditions and additionally let the wind blow randomly left and right, we will see that the deeper potential well will collect more balls. This is so because the wind will blow balls more easily from a to c than the other way round . Hence, the eventual probability distribution of x (dashed line in Figure 1) has a mirrored shape compared to that of the landscape. Instead of two wells, it has two peaks, also modes – we say that the distribution of x is ‘bimodal’.
Figure 1 Potential energy landscape V(x) and steady state distribution p(x) of a bistable variable x as a function of x. a and b are the stable states and c the intermediate unstable state.
Tropical tree cover bistability and hysteresis
Previous researchers found from satellite-retrieved data that tropical tree cover has such a bimodal distribution, with savanna as low mode (point a in Figure 1, 20% tree cover) and forest as high mode (point c in Figure 1, 80% tree cover) (Hirota et al., 2011; Staver et al., 2011). Moreover, they found that with increasing mean annual rainfall the inferred probability of being in the forest state increases whereas the probability of being in the savanna state decreases. This can be seen in a plot of tree cover versus rainfall (Figure 2) by observing that the density of the points changes with rainfall, with higher density around the forest state (80%) for high rainfall and higher density around the savanna state (20%) for low rainfall. Higher density around a value of tree cover means that more areas are observed to have this tree cover value, and hence the researchers inferred that they are more stable.
Figure 2 Scatterplot of tree cover versus rainfall for the Amazon region.
This was interpreted as a bistable system having a shifting relative stability of the two states with rainfall. Forest and savanna were inferred to be bistable over a wide range of rainfall (700-3400mm). According to the rolling ball model, the forest well deepens and the savanna well gets shallower with increasing rainfall. Such dependence of stability and dynamics on external conditions is a typical characteristic of bistable systems and allows for the possibility of jumps and ‘hysteresis’ (Strogatz, 2014). Let us say we start in the savanna state at low rainfall – the ball is hence in the savanna well (Figure 3a). If we let rainfall increase, the savanna well gets shallower and the forest well deeper while the hill between them shifts towards the savanna well (Figure 3b). A further increase makes the savanna state unstable, causing the ball to roll into the forest well, leading to a sudden jump of the tree cover value (Figure 3c). When rainfall decreases from here, the ball will stay in the forest well until rainfall becomes low enough to destabilise the forests state (Figure 3f). This lack of reversibility and dependence on recent history is what is called hysteresis. Moreover, the sudden changes associated with transitions between the states have been observed in many complex systems with examples ranging from asthma attacks and epileptic seizures in medicine, market crashes in global finance, shifts of ocean circulation in earth systems and population crashes in ecological systems (Scheffer et al., 2009).
Figure 3 Increasing stability of forest and decreasing stability of savanna with increasing rainfall (left to right) leads to hysteresis (figure adapted from https://www.univ-orleans.fr/mapmo/membres/berglund/hystabt.html).
The hypothesised theoretical mechanism behind bistability of forest and savanna is a spatial process known as percolation, which leads to a positive feedback between grass layer continuity and fire spread (Staver et al., 2011; Hirota et al., 2011). Fire requires a grassy fuel layer, but it can only spread if this grassy layer is sufficiently connected, i.e. when it is not too often interrupted by patches of forest. Below a rainfall-dependent tree cover threshold (point b in Figure 1), patches of grass between the trees are well connected and losses of tree cover are self-reinforcing due to a positive feedback between grass layer continuity and fire spread. Above this threshold, the grass layer is too frequently dammed by trees and fires cannot reach the sizes required to inflict unrecoverable damage to the tree layer.
Bistability means that shocks such as forest clearance or drought could lead to a dramatic increase of fire occurrence and tip an area of rainforest into savanna. Hysteresis means that areas that have experienced this transition would then remain locked into this savanna state until large enough increases of rainfall and release of human pressures allow forests to grow back faster than they are lost by intermittent fires.
Shortcomings previous research
Although previous work recognised the importance of seasonality, soils and human impact on forest-savanna bistability, it focused too heavily on rainfall alone to interpret the dynamics from the data. In addition, models were largely non-spatial, they did not take into account edge effects on forest.
SI: Describe what your objectives were at the start, how you designed the study, and how you progressed.
BW: I was already familiar with the bistability hypothesis of tropical vegetation and was determined to work on it from before I started my PhD in complexity sciences. In September 2013, after the end of the taught component of the PhD, I proposed the project with the objective of analysing and modelling human impact on tropical vegetation and teamed up with Alan Champneys, a theorist in applied mathematics. Because I enjoy applying mathematics, I wanted to start with modelling as soon as possible. However, Alan warned me by quoting the proverb “If all you have is a hammer, everything looks like a nail”. Hence, I first focused on the data analysis and decided to do the modelling later. The objectives weren’t very specific at the start but they became increasingly refined as more information became available, either due to new findings or due to new insights.
The eventual design of the study consisted of a data analysis that compared bimodality as a function of natural variables for areas close to human cultivations versus bimodality for areas far from human cultivations. A difference between these analyses would suggest an effect of human impact. Then, model building was done by first setting up a stochastic partial differential equation model for natural tree cover dynamics. In this model, we took into account interactions between neighbouring areas due to fire spread. Then a deforestation term was added to the model to capture human impact.
By September 2015, we had submitted our data analysis and first simple model for publication but it took many rounds of review to take into account the reviewers’ comments, which helped greatly to add detail and nuance, but the main story and conclusions did not change.
SI: What did you discover about Amazon tree cover bistability and how does deforestation affect it? There is an alternative route to Amazon bistability. Can you briefly discuss it and how it relates to your findings?
BW: Taking into account in our data analysis all other factors than rainfall that affect the relative stability of forest and savanna – rainfall seasonality, soils and human impact – shows that the wide overlap of forest and savanna states in tree cover versus rainfall plots is to a great extent due to the confounding effect of these other factors and far less due to bistability. Bimodality occurs especially in places close to human influence (Figure 4). This is confirmed by our model. The spatial interaction in the model is crucial. It causes the less stable state (in the shallower well) to destabilise such that the system will always occupy the most stable state (in the deeper well). Only when both states are equally stable (having equal well depth) will bistability still be possible. This point of equal stability is called the Maxwell point and it defines the boundary in space between forest and savanna. At the drier side of the Maxwell point, there is only savanna whereas at the wetter side there is only forest. As the relative stability of the two states is affected by rainfall averages, rainfall seasonality, soils and human impact, the Maxwell point is a function of each of these factors. Therefore, when plotting tree cover against rainfall alone, the variation of the Maxwell point – the boundary between forest and savanna – due to the other factors will give the impression of wide ranges of bistability. In particular, close to human cultivations, there is high variability of human impact on small spatial scales, causing high variability of the Maxwell point and a wide range of overlap in plots of tree cover versus rainfall that cannot be explained by natural factors alone.
Figure 4 Our data analysis comparing a scatterplot of tree cover versus natural forest suitability, a variable that combines all natural influences on forest stability, for areas far from human cultivation with the same plot for areas close to human cultivation [adapted from Wuyts et al. (2017a)].
Nonetheless, there is still some remaining overlap of forest and savanna states in the data that is not reproduced by the model (Figure 4a). If this remaining overlap is not a consequence of confounding factors that we did not take into account, it is due to bistability occurring on a smaller scale than thought previously. Figure 5 shows a classification of the Amazon region into stability zones before and after removing confounding effects. The inferred region with bistability (yellow) is much larger when only considering average rainfall (Figure 5b) compared to when we also take into account rainfall seasonality and soils (Figure 5d). Moreover, the area of forest that lies in this bistable zone (black dots in the yellow areas) is much more limited in the latter case.
Figure 5 Predicted stability zones in the Amazon region (forest, savanna, or bistable) before (a-b) and after (c-d) removing confounding effects. a. Tree cover versus rainfall in natural+transition areas (similar to previous studies). Below 1000mm of rain per y year, there are only savannas (green). Above 2200mm of annual rain, there are only forests (brown). Between 1000 and 2200mm of yearly rain, both savannas and forests occur (yellow). b. Stability zones in the Amazon region based on the rainfall ranges in (a). Dots indicate where forest exists currently. The yellow zones, which receive between 1000 and 2200 mm rainfall per year, both savanna and forest are possible, as shown by (a). When the yellow zones have dots, they are currently forest. When they do not have dots, they are currently savannas. c-d. The same plots as in (a-b) but without the confounding effect of seasonality and soils, based on data in natural areas. Bistability still occurs in natural areas but the improved analysis shows that far less of the currently forested area is bistable and at risk of being locked into a savanna state (Wuyts et al., 2017b).
The good news is that as long as there is some forest left, shocks like deforestation or drought will not lock currently forested areas into a savanna state. This means that recovery of the forest in human-impacted areas close to cultivations should happen as soon as these areas are released from human pressures. We have to emphasise though that this concerns the degraded forests that are close to human cultivations, which are impacted by selective logging and fires creeping into the forest while not being used for agriculture. Those areas that have been converted to croplands and pastures may have experienced too much soil degradation to experience such rapid recovery, and this effect of soil degradation is subject of further research.
Moreover, there exist other mechanisms that could lead to bistability of Amazonian forest cover, which were not taken into account in this research. The first one works on larger scales than the ones we considered and is called the hydrological feedback [see e.g. Zemp et al. (2017)]. Previous research has shown via simulations that there may be a positive feedback between forest cover and regional rainfall in the Amazon basin due to intensification of the monsoon and increased recycling of rainfall. This means that a larger Amazon forest will attract and recycle more rain, leading to an increase of the forest size. This feedback can also work the other way round; forest loss may lead to decreased rainfall causing further forest loss. Whether climate change or deforestation may still permanently transform the Amazon forest into a savanna depends on the importance of the hydrological feedback and is subject of further research. The third potential mechanism for bistability works on smaller scales than the ones we considered and is called scale-dependent feedback. This occurs when forest facilitates growth of other forest on short ranges, e.g. due to increased nutrient availability, while it competes with other forest on long ranges, e.g. due to competition for soil water. The scale-dependent feedback leads to a bistability range around the Maxwell point in which patterned vegetation can be observed. This has been extensively studied in pattern formation theory and in models of semi-arid vegetation [see a.g. Meron (2015)]. However, as the facilitation works on ranges shorter than the spatial resolution of our data, the resulting bimodality may either not be visible or appear smoothed in our data.
While hydrological feedbacks are an alternative cause of bistability, we do not think that they can explain the remaining bimodality. This is because hydrological feedbacks cause bistability of rainfall for a range of moisture input in the system, not vegetation in a range of rainfall. Hence, if the remaining bimodality in the tree cover data is caused by smaller-scale bistability, it may be explained by the scale-dependent feedback or by another yet unknown feedback.
SI: What role did your collaborators play in the study?
BW: Alan, my main supervisor, has been always there to support me with the theory, at which he is very able and experienced. I keep on being impressed with how quickly he spots errors in my mathematical derivations. Jo, who joined later, helped at times with the applied side. Both have helped extensively with writing and proofreading the paper during its long review period. I usually prefer exploring my ideas freely but as I am very interested in a wide array of subjects, I sometimes end up reading and studying things that are not most relevant to my PhD. Alan kept me focused and motivated while still allowing me to work with great freedom and independence. Jo’s main contribution was to keep things real and practical, as both I and Alan tend to think more in theoretical terms.
SI: What is next for you, in terms of research, and professionally?
BW: I am near the end of my PhD so I am keeping my eyes open for postdocs. Generally, I would like to keep on working in the area of complex systems, ideally focusing on a variety of applications. I remain interested in ecological applications but would be at least as keen to analyse and model problems in other application areas of complex systems.
SI: Has work on your doctorate been what you expected? What was the most difficult aspect?
BW: I expected it to be interesting and engaging and it definitely was. Being someone with wide interests, it hasn’t always been easy to stay focused on the same subject. Thankfully, I was able to do some tutoring in engineering mathematics and in complexity. When it was still hard to focus, I decided to learn a new skill or do an online course in something different but still loosely related to my research.
SI: How did you come to a life and science? Have you always wanted to be a scientist? How did you come to choose this subject?
BW: I developed an interest for the natural world from an early age, mainly due to the influence of my late father, who had extensive knowledge about plants and animals, but it was not until my late teens that I got properly acquainted with and interested in mathematics and physics. Once at the university, I chose to combine physical geography and environmental sciences with units from physics and mathematics, which was made possible by the multi-disciplinary approach to science education at the University of Leuven in Belgium. This is when I first got familiarised with statistical physics, which captivated me both in its elegance and in its potential to be applied on environmental systems. During an exchange program in my masters, where I studied for one year in the Swiss Federal Institute of Technology, I learnt a lot from their systems approach to environmental sciences and took a course in complex adaptive systems. From then, I knew that this is what I wanted to do. After graduating and travelling several times to South America, where I was most impressed by the Amazon forest, I started my PhD in complexity sciences and started my project on the Amazon forest one year later.
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