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Pronounced loss of Amazon rainforest resilience since the
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early 2000s
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Chris A. Boulton1*, Timothy M. Lenton1 & Niklas Boers1,2,3,4
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1Global Systems Institute, University of Exeter, Exeter, UK.
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2Department of Mathematics, University of Exeter, UK
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3Department of Mathematics, Free University of Berlin, Germany
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4Potsdam Institute for Climate Impact Research, Potsdam, Germany
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*Corresponding author: c.a.boulton@exeter.ac.uk
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The resilience of the Amazon rainforest to climate and land-use change is of critical
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importance for biodiversity, regional climate, and the global carbon cycle. Some
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models project future climate-driven Amazon rainforest dieback and transition to
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savanna1. Deforestation and climate change, via increasing dry-season length2,3 and
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drought frequency – with three 1-in-100-year droughts since 20054-6 – may already
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have pushed the Amazon close to a critical threshold of rainforest dieback7,8.
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However, others argue that CO2 fertilization should make the forest more resilient9,10.
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Here we quantify Amazon resilience by applying established indicators11 to remotely-
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sensed vegetation data with focus on vegetation optical depth (1991-2016), which
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correlates well with broadleaf tree coverage. We find that the Amazon rainforest has
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been losing resilience since 2003, consistent with the approach to a critical transition.
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Resilience is being lost faster in regions with less rainfall, and in parts of the
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rainforest that are closer to human activity. Given observed increases in dry-season
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length2,3 and drought frequency4-6, and expanding areas of land use change, loss of
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resilience is likely to continue. We provide direct empirical evidence that the Amazon
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rainforest is losing stability, risking dieback with profound implications for
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biodiversity, carbon storage and climate change at a global scale.
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There is widespread concern about the resilience of the Amazon rainforest to land-use
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change and climate change. The Amazon is recognised as a potential tipping element in the
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Earth’s climate system12, is a crucible of biodiversity13, and usually acts as a large terrestrial
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carbon sink14. The net ecosystem productivity (carbon uptake flux) of the Amazon has,
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however, been declining over the last four decades and during two major droughts in 2005
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and 2010, the Amazon temporarily turned into a carbon source, due to increased tree
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mortality15-17. Several studies have suggested that deforestation18 and anthropogenic global
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warming1,5, especially in combination, could push the Amazon rainforest past critical
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thresholds7,8 where positive feedbacks propel abrupt and substantial further forest loss. Two
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types of positive feedback are particularly important. First, localised fire feedbacks amplify
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drought and associated forest loss by destroying trees19, and the fire regime itself may ‘tip’
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from localised to ‘mega-fires’20. Second, deforestation and forest degradation, whether due
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to direct human intervention or droughts, reduce evapotranspiration and hence the moisture
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transported further westward, reducing rainfall and forest viability there21 and establishing a
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large-scale moisture recycling feedback. Net rainfall reduction may in turn reduce latent
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heating over the Amazon to the extent that it weakens the low-level circulation of the South
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American monsoon18. Model projections of future changes in the Amazon rainforest differ
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widely1,9,10,22. Early studies showed that the Amazon rainforest may exhibit strong dieback by
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the end of the 21st century1,23. Both pronounced drying in tropical South America and a weak
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CO2 fertilisation effect9 contributed to this result, with dieback also more common under
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stronger greenhouse gas emission scenarios10. Other studies based on varying general
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circulation and vegetation model components show a wider range of results24,25.
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Nevertheless, the forest may be ‘committed’ to dieback despite appearing stable at the end
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of model runs26. This highlights the importance of measuring the changing dynamical
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stability of the forest alongside its mean state. Given the uncertainty in model projections, we
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directly analyse observational data for signs of resilience loss in the Amazon.
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The mean state of a system is not usually informative of changes in resilience; either can
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change whilst the other remains constant. Thus, higher-order statistical characteristics that
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respond more sensitively to destabilisation than the mean need to be considered to quantify
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resilience. To measure the changing resilience of the Amazon rainforest, we use a stability
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indicator used to predict the approach of a dynamical system towards a bifurcation-induced
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critical transition. The predictability arises from the phenomenon of critical slowing down27,28
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(CSD): as the currently occupied equilibrium state of a system becomes less stable, it
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responds more sluggishly to short-term perturbations (e.g. weather variability for the
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Amazon). This loss of resilience (defined29 as return rate from perturbation) reflects a
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weakening of negative feedbacks that maintain stability. The behaviour can be detected by
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an increase in lag-1 autocorrelation (AR(1)) in time series capturing the system
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dynamics30,31. It may also manifest as an increase in variance over time, but variance can
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also be easily influenced by changing variability of the perturbations driving the system32.
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Increasing AR(1) has been used to detect critical slowing down prior to bifurcation-induced
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state transitions in a number of systems, including but not limited to climate30,33 and
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ecology34. A caveat, highlighted by analysis of model projections prior to Amazon dieback32,
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is that a system should be forced slower than its intrinsic response timescale for CSD to
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occur (see Methods). Hence, the absence of CSD may not rule out the possibility of a
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forthcoming critical transition. Conversely, increasing AR(1) can sometimes occur for other
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physical reasons. A space-for-time substitution has previously revealed that tropical forest
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resilience as measured by mean AR(1) (on a grid point basis) is lower for less annual rainfall
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sums11, but changes of Amazon resilience over time have not been investigated so far.
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We investigate controls on the resilience of the Amazon vegetation system and how its
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resilience has changed over the last three decades, in terms of a changing AR(1) coefficient
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as estimated from satellite-derived vegetation data. The main dataset we use is from the
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Vegetation Optical Depth Climate Archive (VODCA)35, but we also analyse the NOAA
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Advanced Very-High-Resolution Radiometer’s (AVHRR) normalized difference vegetation
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index NDVI36 for comparison. Vegetation Optical Depth (VOD) has been previously used to
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estimate changes in vegetation biomass37, whereas NDVI is more commonly used to
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measure the greenness of vegetation, i.e. photosynthetic activity38. We use the Ku-band
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product from VODCA, which has a resolution of 0.25°x0.25°, and for direct comparison we
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rescale the NDVI data to the same resolution. We focus on two stressors of the Amazon
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that may cause resilience changes – precipitation and human influence.
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We use the Amazon basin as our study region and focus on those grid boxes which have a
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broadleaf fraction greater than or equal to 80% evergreen broadleaf (BL) fraction according
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to the MODIS Land Cover Type product in 200139 (See Methods). Figure 1 shows that when
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comparing BL fraction in 2001 to mean annual precipitation (MAP) from 2001-2016 (from
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CHIRPS40; see Methods), there is a clear bimodal region visible between approximately
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1500-2250mm, which has been reported previously41-43 (Fig.1a). Bi-stability, where a
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forested or non-forested area can exist under the same MAP, suggests the potential for
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bifurcation- and noise-induced transitions, the latter potentially triggered by single
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perturbations such as droughts or fires. Over most of the region, BL fraction has not
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changed significantly between 2001 and 2016 (Fig. 1b). However, deforestation has
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occurred along parts of the southern and eastern edges of the rainforest, along parts of the
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Amazon river, and in some northern parts of the basin.
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With a very similar spatial pattern as the change in BL fraction (Fig. 1b), we find decreases
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in VOD around the south-eastern edges of the forest (Fig. 1c). Averaged across the Amazon
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study region we find overall decreasing VOD, which matches with the observed decrease in
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the number of grid boxes that have BL >= 80% each year (Fig. 1d). NDVI, in contrast, does
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not agree spatially with the changes in BL fraction – rather, NDVI increases in the south-
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eastern parts of the Amazon where deforestation rates are known to be high (Supplementary
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Fig. 1). Changes in BL fraction from 2001-2016 are strongly correlated with changes in VOD
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over the same period (Fig. 1e), whereas changes in NDVI are not (Fig. 1f), echoing previous
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in-situ comparisons between VOD and NDVI44. Hence, we focus our analysis on VOD in the
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following, with results for NDVI in the Supplementary Figures.
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We begin our resilience analysis by focusing on the temporal changes of AR(1), computed in
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sliding windows from the nonlinearly detrended and de-seasonalised VOD time series (see
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Fig. 2, and Methods). The time series calculated from the mean AR(1) value across our
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study area each month shows a substantial increase over time, particularly from ~2003 (Fig.
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2a). The spatial distribution of the AR(1) tendency, measured by the Kendall rank correlation
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coefficient t (see Methods) at each grid box, shows that decreases in AR(1) (increases in
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resilience) are mostly restricted to parts of the region with higher mean annual precipitation
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(MAP) (Fig. 2b). We also observe stable or decreasing AR(1) values around the tributaries of
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the Amazon river, where vegetation growth will be less dependent on precipitation for water
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availability. Overall, the majority (74.6%) of grid boxes show increasing AR(1) values and
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hence, loss of resilience (Fig. 2c). Using alternative methods of detrending the VOD time
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series (see Methods) yields similar results (Supplementary Fig. 2). A predominance of
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increasing AR(1) trends is also found for the NDVI time series since 2003 (Supplementary
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Fig. 3).
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To further explore the relationship between MAP and AR(1) trend, we create mean AR(1)
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time series on a moving MAP-band of 500mm (see Methods). These bands show broadly
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the same behaviour as the region overall (Fig. 3a), with all bands showing a significant
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decrease in resilience post-2003 (p<0.001). The increase in AR(1) post-2003 appears least
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pronounced for the highest rainfall band (3500-4000mm). Sure enough, the intensity of
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resilience loss increases as the MAP-band decreases below 3500-4000mm (Fig. 3b). For
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NDVI, the same relationship is also observed (Supplementary Fig. 4a,b). However, due to a
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large decrease in NDVI AR(1) pre-2003 across the region, analysing the full AR(1) time
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series yield decreasing AR(1) Kendall t coefficients for the higher MAP-bands.
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It has previously been suggested that the forest near human land-use areas is less
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resilient42. To determine if this is shown by VOD, we measure the distance of each grid box
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from human land use in 2016 (see Methods, Supplementary Fig. 5). Calculating mean AR(1)
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time series on 50km distance bands, shows increases in AR(1) post-2003 are stronger for
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grid boxes closer to human land use (Fig. 4a). Grid boxes that are in more remote locations
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still show a loss of resilience but the AR(1) time series for these are more variable – likely
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because the area they are averaged over shrinks and becomes more disconnected (Fig. 4a).
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Above 200-250km away from human land use the signal of loss of resilience becomes less
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pronounced (Fig. 4b). NDVI time series also show there is a loss of resilience from 2003, in
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grid boxes that are closer than 200km from human land use (Supplementary Fig. 4c,d).
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Our results suggest that the loss of resilience of the Amazon rainforest that is especially
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pronounced since 2003 (Fig. 2), could be due to a combination of changing precipitation
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patterns (Fig. 3) and changing human interference in the region (Fig. 4). Here we reason that
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as lower baseline MAP and greater proximity to human interference are both associated with
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greater loss of resilience, declining MAP and/or increasing human interference may be
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expected to cause increased resilience loss. We find increases in human land use areas
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using the MODIS Land Cover data over the time period, both in reach and intensity
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(Supplementary Fig. 6). However, although there are large parts of the study region with
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decreasing MAP, by comparing the spatial pattern of MAP decreases to the AR(1) increases
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(Supplementary Fig. 7), it is unlikely that the changes in MAP are the dominant driver of
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Amazon rainforest resilience loss. Rather, increases in dry-season length as reported in
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several recent studies2,3,45,46 may explain the loss in vegetation resilience since the early
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2000s detected here. With a longer study period to measure trends in MAP, it is possible
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that a stronger correlation between MAP changes and changes in resilience over time may
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be found.
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The changes in forest resilience observed as increasing AR(1) in both vegetation indices are
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supported by another indicator of critical slowing down, namely increasing variance33 – of
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both VOD (Supplementary Figure 8) and NDVI (Supplementary Figure 9). We note that
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variance is more strongly affected by changes in the frequency and amplitude of the forcing
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of a system, and as such results could be biased towards individual events. This, along with
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other issues, has led AR(1) to be considered a more robust indicator47.
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As emphasized above, changes in BL fraction do not directly relate to changes in resilience.
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Indeed, we infer a marked loss of resilience in terms of increasing AR(1) in vast areas where
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the BL fraction does not strongly decrease (compare Figs. 1b and 2b). One possible
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interpretation of this from model behaviour is that part of the Amazon rainforest might
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already be committed to dieback26 despite not yet showing a strong change in mean state.
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Our results suggest that the overall loss of Amazon resilience we find since the early 2000s
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is attenuated in regions with higher rainfall and amplified in areas closer to human land use
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change. This suggests that reducing deforestation will not just protect the parts of the forest
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that are directly threatened but also benefit Amazon rainforest resilience over a much larger
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area.
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Figure 1: Relationships between different vegetation and rainfall data for the Amazon
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basin. (a) The relationship between 2001-2016 mean annual precipitation (MAP) from
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CHIRPS40 and 2001 MODIS Land Cover Evergreen Broadleaf (BL) fraction39. Points
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coloured black are where 2001 BL >= 80%. (b) Change in the BL fraction from 2001 to 2016
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for grid points where BL > 80% in 2001. Points that are predominantly BL in 2001 according
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to the MODIS 2001 dataset, but <80% are shown in grey. (c,d) Change in Vegetation Optical
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Depth (VOD) Climate Archive Ku-Band product35 from 1991-2016 (difference between the
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2012-2016 and 1991-1995 means) for the grid points where BL > 80% in 2001, along with
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the median time series in these points. Also shown in blue on (d) is the annual percentage of
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grid boxes that have BL > 80%, from those that have BL > 80% in 2001. Sharp decreases in
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BL fraction and VOD could be directly attributed to deforestation. In these cases of externally
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forced forest loss, we may not see changes in AR(1) unless there was an underlying loss of
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resilience beforehand.
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Figure 2: Changes in Amazon vegetation resilience since the early 1990s and from
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2003. (a) Mean VOD AR(1) time series created from grid points that have >= 80% BL
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fraction in the Amazon basin. The full AR(1) time series from 1991 (grey) has a Kendall t
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value of 0.584 (p = 0.007) and from 2003 (black), a value of 0.913 (p < 0.001). (b) A map of
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the Kendall t values of individual grid boxes from 2003, shown alongside contours of MAP
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(mm/year) over the same time period. (c) A histogram of the Kendall t values from the map.
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Figure 3: The relationship between annual rainfall sums and vegetation resilience. (a)
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Example VOD AR(1) time series for 500mm MAP-bands from 1991 (dotted lines) and from
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2003 (solid lines). (b) Full VOD AR(1) Kendall t series for a sliding MAP-band, from 1991
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(grey) and from 2003 (black). Red circles show the results from panel (a) and are closed if
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the Kendall t value is significantly positive (p < 0.05) and open otherwise. The tendency of
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the relationships in (b) are t = -0.423 (grey) and t = -0.553 (black), confirming there is a
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more severe decrease in resilience with lower rainfall values.
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Figure 4: The relationship between human activity and vegetation resilience. (a)
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Example VOD AR(1) time series for 25km bands measuring the distance a forested grid box
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is from a human land use grid box (defined in the Methods from the MODIS Land Cover
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product39 and shown in Supplementary Fig. 6), from 1991 (dotted lines) and from 2003 (solid
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lines). (b) Full VOD AR(1) Kendall t series for a sliding distance-band, from 1991 (grey) and
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from 2003 (black). Red circles show the results from panel (a) and are closed if the Kendall t
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value is significantly positive (p < 0.05) and open otherwise. The tendency of these
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relationships are t = -0.553 (grey) and t = -0.857 (black), showing there is a more severe
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decrease in resilience with increasing proximity to human land use.
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Methods
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Datasets. We use the Amazon basin
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(http://worldmap.harvard.edu/data/geonode:amapoly_ivb) as our region of study. The main
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dataset used to determine forest health is from the Vegetation Optical Depth Climate Archive
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(VODCA)35, of which we use the Ku-band product. This data is available at 0.25°x0.25° at a
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monthly resolution from January 1988 to December 2016. We also use NOAA AVHRR
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NDVI36. For precipitation data, we use the CHIRPS dataset40 downloaded from Google Earth
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Engine (GEE) at a monthly resolution. Finally, to determine land cover types, we used the
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IGBP MODIS land cover dataset MCD12C139. All of these datasets are at a higher spatial
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resolution than the VODCA dataset and thus we linearly interpolate them to match the lower
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resolution.
363
For the vegetation datasets that we measure the resilience indicators on (see below), we
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use STL decomposition48 using the stl() function in R. This splits time series in each grid box
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into an overall trend, a repeating annual cycle (by using the ‘periodic’ option for the seasonal
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window), and a residual component. We use the residual component in our resilience
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analysis. Finding the first 3 years had large jumps in VOD which were seen when testing
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other regions of the world as well as in the Amazon region, we restrict our analysis to
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January 1991 to December 2016.
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To test the robustness of the detrending, we also vary the size of the trend window in the
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stl() function. The results from these alternatively detrended time series are shown
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Supplementary Figure 2.
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Grid box selection. We use the IGBP MODIS land cover dataset at the resolution described
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above to determine which grid boxes to use in our analysis. The dataset is at an annual
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resolution from 2001 to 2018 (but we only use the time series up to 2016 to match the time
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span of our VOD and NDVI datasets). To focus on changes in forest resilience, we use grid
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boxes where the evergreen broadleaf fraction is greater than or equal to 80% in 2001. Grid
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boxes are treated as human land use area if the built-up, croplands, or vegetation mosaics
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fraction is greater than 0% in 2016. to We believe using these years to determine these
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factors is the most cautious and least biased way to choose which grid boxes to use.
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We measure the minimum distance between forested Amazon basin grid boxes and human
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land use grid boxes using the latitude and longitude of each grid point. We do not restrict
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human land use grid boxes to the Amazon basin region when determining the forested grid
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boxes distance from them. This ensures that human land use grid boxes just outside the
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region which could be the closest, are not ignored.
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To ensure that the pattern of changes in resilience is not a consequence of more settlements
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being in the south east of the region combined with the gradient of rainfall from northwest to
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southeast typical of the rainforest, we measure the correlation between MAP and the
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distances from the urban grid boxes. Although this is statistically significant, it is relatively
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weak (Spearman’s r=0.109, p<0.001) and as such we are confident that there are separate
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processes that causes these relationships.
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Resilience indicator AR(1). We measure our resilience indicator on the residual component
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of the decomposed vegetation time series. We focus on lag-1 autocorrelation (AR(1)), which
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provides the most robust indicator for critical slowing down prior to bifurcation-induced
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transitions and has been widely used for this purpose11,28,30. We measure it on a sliding
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window length equal to 5 years (60 months). The sliding window creates a time series of the
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AR(1) coefficient in each location.
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From linearization and the analogy to the Ornstein-Uhlenbeck process, it holds
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approximately that for discrete time steps of width
Δ𝑡
(one month in the case at hand):
400
𝐴𝑅
(
1
)
= 𝑒!"#$
,
401
where k is the linear recovery rate. A decreasing recovery rate k implies that the system’s
402
capability to recover from perturbations is progressively lost, corresponding to diminishing
403
stability or resilience of the attained equilibrium state. From the above equation it is clear that
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the AR(1) increases with decreasing k. The point at which stability is lost and the system will
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undergo a critical transition to shift to a new equilibrium state, corresponds to k = 0 and
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AR(1) = 1, respectively.
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Measuring AR(1) across the whole time series provides information about the characteristic
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timescales of the two vegetation datasets we use31. Inverting k gives the characteristic time
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scale of the system; for the VOD, we find 1/k = 1.240 months, whereas for the NDVI, we find
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1/k = 0.838 months when using the mean AR(1) value across the region. This suggests that,
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in accordance with our interpretation of the two satellite-derived variables, the NDVI is more
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sensitive to shorter-term vegetation changes such as leaf greenness, while the VOD’s Ku
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band is sensitive to longer-term changes such as variability in the thickness of forest stems.
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Creation and tendency of AR(1) and variance time series. For analysis where either
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MAP- or distance-bands are used to create an AR(1) or variance series, we calculate the
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mean AR(1) or variance value in each month for forested Amazon basin grid boxes, from
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which the tendency of this mean series can be calculated. Alternatively, the Kendall t for
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each band can be calculated by taking the mean Kendall t for each individual grid box that is
419
within the band. Results from this method are shown in Supplementary Figure 10 for AR(1).
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The tendency of the indicator is determined in terms of Kendall’s t. This is a rank correlation
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coefficient with one variable taken to be time. Kendall’s tau values of 1 imply that the time
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series is always increasing, -1 always decreasing, and 0 no overall trend. Following previous
423
work30,49,50, we test the statistical significance of positive tendencies using a test based on
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phase surrogates that preserve both the variance and the serial correlations of the time
425
series from which the surrogates are constructed. Specifically, we compute the Fourier
426
transform of each time series for which we want to the significance of Kendal’s t, then
427
randomly permute the phases and finally apply in inverse Fourier transform. Since this
428
preserves the power spectral density, it also preserves the autocorrelation function due to
429
the Wiener-Khinchin theorem. For each time series this procedure is repeated 100,000 times
430
to obtain the surrogates. Kendall’s t is computed for each surrogate to obtain the null model
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distribution (corresponding to the assumption of the same variance and autocorrelation but
432
no underlying trend), from which the significance thresholds are computed as the 95th
433
percentiles.
434
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Data and code availability
436
Data is available from the sources listed. R code is available on request.
437
Methods references
438
48 Cleveland, R. B., Cleveland, W. S. & Terpenning, I. STL: A Seasonal-Trend
439
Decomposition Procedure Based on Loess. Journal of Official Statistics 6, 3 (1990).
440
49 Rypdal, M. Early-Warning Signals for the Onsets of Greenland Interstadials and the
441
Younger Dryas–Preboreal Transition. Journal of Climate 29, 4047-4056,
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doi:10.1175/jcli-d-15-0828.1 (2016).
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50 Boers, N. Early-warning signals for Dansgaard-Oeschger events in a high-resolution
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ice core record. Nature Communications 9, doi:10.1038/s41467-018-04881-7 (2018).
445
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Acknowledgements. NB acknowledges funding by the Volskwagen foundation. This is
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TiPES contribution #X. The TiPES project (‘Tipping Points in the Earth System’) has
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received funding from the European Union’s Horizon 2020 research and innovation
449
programme under grant agreement No. 820970. CAB and TML were supported by the
450
Leverhulme Trust (RPG-2018-046). TML was also supported by a Turing Fellowship.
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Author contributions. NB and CAB conceived and designed the study with input from TML.
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CAB performed the numerical analysis with contributions from NB. All authors discussed
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results and drew conclusions. CAB wrote the paper with contributions from NB and TML.
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Competing interests. The authors declare no competing interests.
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Additional Information
456
Supplementary Information accompanies the paper.
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Correspondence should be addressed to CAB (c.a.boulton@exeter.ac.uk)
458
