Supplement

www.sciencemag.org/content/343/6170/548/suppl/DC1
Supplementary Materials for
Savanna Vegetation-Fire-Climate Relationships Differ Among
Continents
Caroline E. R. Lehmann,* T. Michael Anderson, Mahesh Sankaran, Steven I. Higgins,
Sally Archibald, William A. Hoffmann, Niall P. Hanan, Richard J. Williams, Roderick J.
Fensham, Jeanine Felfili, Lindsay B. Hutley, Jayashree Ratnam, Jose San Jose, Ruben
Montes, Don Franklin, Jeremy Russell-Smith, Casey M. Ryan, Giselda Durigan, Pierre
Hiernaux, Ricardo Haidar, David M. J. S. Bowman, William J. Bond
*Corresponding author. E-mail: [email protected]
Published 31 January 2014, Science 343, 548 (2014)
DOI: 10.1126/science.1247355
This PDF file includes:
Materials and Methods
Figs. S1 to S4
Tables S1 to S5
References (27–188)
Captions for Data Sets S1 and S2
Other Supporting Online Material for this manuscript includes the following:
(available at www.sciencemag.org/content/343/6170/548/suppl/DC1)
Data Sets S1 and S2 as zipped archives:
Data Set S1: Tree Basal Area
Data Set S2: East Africa Stand Structures
Materials and Methods
Dataset
We analyzed 2154 field collected estimates of tree basal area data (m2 ha-1) in relation to
environmental correlates. Data on environmental correlates were collected from a globally
available climatology, soils data and satellite derived information on fire frequency.
Compilation of tree basal area observations
With respect to defining data for this study, we followed the definition of savanna provided by
(7). The presence of an herbaceous layer of C4 grasses is a key indicator of the contemporary
extent of the savanna biome. Savanna is a tropical/sub-tropical biome with C4 grasses
dominating the ground layer, usually to the exclusion of C3 grasses (7, 10). However, the C3
grass species, Echinolaena inflexa, is a common dominant in the ground layer in the savannas of
the cerrado region of Brazil (27).
C4 grasses themselves are a key indicator of the antiquity of the biome as indicated by carbon
isotope signals in palaeosols and animal bones (22). Current modelling and palaeo-evidence
suggests that the strength of the C4 grass – fire feedback was instrumental in driving the
expansion of the biome 8 – 12 Mya (22). The differences in photosynthetic response to low
atmospheric CO2 concentrations remains the most widely accepted explanation for the evolution
of C4 grasses from their C3 ancestors (22).
Both trees and grasses are important in driving the vegetation dynamics of tropical savanna, but
here we focus on woody vegetation. A similar analysis based on grass cover would indeed be
1
valuable; however, we found a lack of the requisite data spanning continents at significant spatial
scales.
We compiled tree basal area data from a wide variety of sources (28 - 136). The dataset includes
records for which basal area was sampled at a sufficient spatial scale (> 0.1 ha for plot
measurements). Data from sites considered to be located in either riparian areas or net water runon areas were excluded. Further, we excluded data from sites that had been cleared for other land
uses (e.g., agriculture and pastoralism). Sites were generally in conservation and protected areas.
Further, in assembling the TBA dataset we used Cook’s distance, where data points that had a
Cook’s D value > 4/n, to class points as outliers and these were not included.
Previous continent wide assessments of savanna vegetation have been based on woody cover,
either via ground-based observations (8), or remotely sensed (15, 137-139). Working across
continents, however, when seeking to understand the relative importance of environmental
controls in determining structure, woody cover can be a difficult metric to use due to regional
differences in the phenology (23) and allometry of dominant species (17). For example, African
savannas are dominated by deciduous species from the Vachellia, Senegalia and Terminalia
genera while the vast majority of Australian savannas are dominated by evergreen Eucalyptus
spp (23).
We seek insight to the degree of equivalence in the processes that govern savanna woody
vegetation structure. For example, how much biomass does a single fire remove in Australia
versus Africa? What is the capacity of each system to regain biomass lost to fire in a single
2
growing season? And, do these relationships vary similarly with rainfall? Such questions have
implications for calculating carbon stocks, the estimation of fire emissions and inferring the
response of savannas to climate change. However, answers to these questions require working in
equivalent biological units. One option is aboveground woody biomass (kg ha-1) or carbon.
However, detailed stand level data is difficult to acquire at continental scales and is usually
derived (140).
We considered field collected estimates of stand tree basal area (TBA, m2·ha-1). Our analysis can
thus examine whether (i) the mean and limits of TBA relative to climate varies among
continents, (ii) the relative role of resources (moisture availability and nutrients), climatic
growing conditions (temperature) and disturbance (fire) changes in its effects on TBA among
continents.
Environmental Correlates
Based on the extensive history of theoretical and empirical work in savannas we determined, a
priori, eight key environmental controls important in structuring savanna vegetation and that
could be estimated consistently at a global scale and for which there were reasonable proxies
(descriptions below). Due to the disparate sources of the tree basal area data used in this study,
and that there was no consistent collection of information amongst sites, we relied on
environmental information available as global data from WorldClim (141), the Food and
Agriculture Organization of the United Nations (FAO) Harmonized World Soils Database (142),
Consultative Group on International Agricultural Research, and MODIS derived estimates of fire
frequency over 2000 – 2010 (http://modis.gsfc.nasa.gov/). WorldClim data are available at:
3
http://www.worldclim.org/download. The FAO Harmonized World Soils Database is available
at: http://www.iiasa.ac.at/Research/LUC/External-World-soil-database/HTML/. Potential
Evapotranspiration data are available at:
http://csi.cgiar.org/aridity/Global_Aridity_PET_Methodolgy.asp. We used these data on
environmental controls to analyze patterns of tree basal area using Structural Equation Models as
outlined below.
Our dataset, aimed to cover the known range of climatic and edaphic conditions found in
savanna (Figure S2 – S3). Consequently, the results presented are not a spurious product of an
incomplete representation of the climatic and edaphic domain occupied by the modern savanna
biome.
Effective Rainfall (ER)
The amount of biomass at a site is largely controlled by the productivity of the system (143).
Globally, productivity is strongly related to available moisture, which in turn is related to rainfall
and the evaporative demand of the system (143). While, various measures of plant available
moisture exist, we chose to use effective rainfall (ER) due to its logical nature and wide spread
use in the literature. ER is defined as the difference between mean annual precipitation (MAP)
and mean annual potential evapotranspiration (PET), which gives a value in mm ranging from
approximately -2000 to 2000. Values less than zero represent environments where the average
evaporative demand exceeds the average incoming precipitation across the entire year. This
index of moisture availability has been previously determined as a correlate of the limits of
savanna (14). Mean annual precipitation was calculated from WorldClim. Information on
4
Potential Evapotranspiration was accessed through the CGIAR Consortium for Spatial
information.
Rainfall Seasonality
Rainfall seasonality was first mooted as important for the determination of the distribution of
savanna by Schimper (144) and is known as a key correlate of the distribution of savanna across
the tropics (14). Rainfall is distributed differently within the year across the globe, and some
regions have much more seasonal rainfall. In systems which experience regular drying and
wetting periods the availability of flammable conditions is high (3) and the number of growing
days reduced (1). WorldClim monthly rainfall data provided at a 0.5 degree resolution were used
to calculate rainfall seasonality, and were defined using an index which gives an indication of
how evenly dispersed rainfall is throughout the year. The index ranges from 0 (all months
contribute equally to total annual rainfall) to 100 (all rainfall fell in one month) and is
independent of the total amount of rainfall that falls within a year. Markham (145) provides a
definition of this index.
Foley’s Drought Index
Drought-induced tree death has long been considered an important factor for maintaining open
canopies in seasonally dry environments (146). However, species that colonize seasonally dry
environments occupied by savanna are generally either facultatively deciduous or evergreen with
high water-use efficiencies (23), and as such the hypothesis that drought is important in
structuring savanna vegetation is controversial (1, 10, 146). It is likely the case that some
savanna regions are more drought prone than others, and that regional differences in climate and
5
drought severity are the foundation to the controversy. Foley’s Drought Index was used in (146)
to examine the relationship between drought and tree mortality. Foley’s Drought Index was
chosen over other drought indices (147) because it can be calculated for any period, only requires
rainfall data and allows for comparison between rainfall zones because it is standardized by
MAP. To investigate drought at global scales, monthly rainfall values at 0.5 degree scale were
used. For each grid cell, the FDI was calculated describing the most substantial rainfall deficit
between 1901 and 2002. FDI is calculated for each month of each year as actual annual rainfall
for three years before every month less the expected (long-term average) rainfall for that period,
divided by the MAP.
Mean Annual Temperature and Annual Temperature Range
C4 grasses are adapted to dry, seasonal and hot environments (4, 5, 148). There is however
significant variation among continents in mean annual temperature (MAT) and the annual
temperature range (ATR). Previously, these have been considered as factors in explaining
variation in the dominant phenology strategies of the woody species of each region (23). Further,
the relationship between the distribution of C4 grasses and MAT and ATR is relatively wellparameterized (148), and we would expect that MAT and ATR will have a strong effect on grass
abundance, and thereby the competitive relationships between trees and grasses. High MAT and
ATR are expected to be causally related to fire frequency, via influencing the curing and
availability of grassy fuels (3, 149).
Soil fertility and drainage
6
Soil fertility has been inferred by a number of studies as a determinant of the presence of
savanna (21, 150-152). Soil fertility affects both the productivity of trees and grasses and, where
there are mega-herbivores, the extent of grazing and browsing (153). We used Percent Soil
Organic Carbon (% SOC) as a proxy for soil fertility, as this is one of the more reliable datasets
available from the Harmonized World Soils (HWS) Database. This dataset nominally has a
resolution of 1 km and where high values of % SOC correspond to high soil fertility. From this
same dataset we also used % Sand as an indicator of drainage conditions. Previously, % Sand has
been found to be strongly correlated with tree basal area (69) and woody cover (8). The HWS
database is a coarse dataset and soils are undoubtedly important in understanding fine scale
variation in woody biomass, and hence these data are unlikely to capture the nuance of the local
scale role of soil fertility and drainage. Developing improved regional scale datasets on soil
types, depth, fertility and drainage should be considered a priority for future work.
Fire frequency
Extensive local scale demographic studies and several modelling studies demonstrate fire affects
savanna vegetation dynamics (1, 8, 9, 10, 14, 15, 18, 19). There is, however, a very limited
understanding of the extent to which fire-vegetation-climate interactions may be equivalent
across savanna regions. Due to the feedbacks between vegetation and fire that are theoretically
involved in maintaining savanna (particularly in high rainfall regions) (14, 15), minor differences
could aggregate to have large ecosystem level differences. Such lack of understanding prohibits
the development of an integrated understanding of vegetation dynamics across the biome.
7
While we compiled data on tree basal area across regions it was generally the case that fire data
were either not available or recorded or not collected consistently among plots and regions.
Hence, we resorted to the available satellite derived fire histories for each region and used the
monthly data layers from 2000 to 2010 from the MODIS (MCD45A1) fire product. These data
are produced at 500-m resolution using a view-direction-corrected change detection procedure to
identify pixels that burned and the approximate day of burning (accurate to within 8 days) (154).
When insufficient input data are available to run the algorithm owing to excessive cloud cover or
sensor problems, pixels are flagged as ‘no data’. A southern African accuracy assessment
indicates that the product can identify about 75% of the burnt area (155). This accuracy is
expected to decrease with increasing tree cover (156). Improved spatial resolution (500m instead
of 1 km) and the availability of quality flag information are a major improvement over previous
burnt area products.
Monthly burned area data layers were combined to calculate the number of times a pixel burned
(fire frequency). Because we sought accurate representation of fire frequency, we were
conservative in our approach to invalid data: we excluded all pixels that had invalid data more
than two times a year on average (14% of the dataset). Savanna fires are grass-fuelled, with
average return periods ranging from 1 to 6 years (3), such that the MODIS dataset can capture a
great deal of the variation in fire frequency across the biome. The result was a map at 500-m
resolution of the number of burns a pixel experienced in 11 years. For each TBA data point we
summarized the MODIS fire data over 5 x 5 pixels, roughly a 6.25 km2 area, by taking the
majority value of the number of fires recorded over the 11 year period. Where two values were
equally prevalent and a majority value could not be determined we used the median number of
8
fires recorded and this represented about 2% of the total dataset. We would expect that the
majority value is indicative of the predominant fire return interval experienced at a location (3).
Herbivores
Herbivores play an important role in determining savanna structure, especially in Africa.
Globally, data availability on herbivore abundance is sparse and unreliable and, as a result, we
could not justify including herbivore abundance as a predictor in our models. A large body of
empirical evidence and theory suggests that herbivore effects on vegetation dynamics are largely
of two types: (i) grazers primarily act to reduce fuel loads, thereby reducing fire frequency and
increasing tree growth, recruitment and biomass (9, 153) and (ii) browsers reduce the size,
growth rate, fecundity and recruitment of woody plants thereby directly reducing tree basal area
(157). Therefore, excluding herbivores from our analysis may exclude relatively little of the
grazer impact, as much of their effect is vectored through fire, but may result in missing direct
negative effects of browsing mammals on tree basal area. We expect some of the unexplained
variance in tree basal area or biomass (i.e. 1 – r2) in our models to be attributed to these missing
effects.
Analytical methods
Quantile analysis
We calculated the upper and lower quantiles of both tree basal area and our estimates of
aboveground woody biomass via the quantreg package in R (http://cran.rproject.org/web/packages/quantreg/index.html). We sought to represent the form of the envelope
of these metrics of vegetation structure relative to effective rainfall. We used a non-parametric
9
piecewise quantile regression using the qss function with the default smoothing parameter
(lambda = 1) and specified the function as convex increasing. In Figure 1 and Figure S1, the 95th
quantile is a proxy for the limits to woody biomass accumulation.
Structural Equation Modelling
Structural equation modelling (SEM) is a framework for analyzing systems, drawing upon
several statistical tools, such as path analysis, regression, correlation, factor analysis and latent
variable modelling, among others (158). The goal of SEM is to understand causal relationships
in systems by evaluating the statistical fit between abstract theories and empirical data. First
generation SEM, in which analyses focused on decomposition of correlations (159), was later
improved by including maximum likelihood estimation of complex model structures based on
the covariance matrix (160). Recently, SEM has seen major improvements in parameter
estimation and evaluation of the fit between models and data, including the use of Bayesian
estimation techniques (161).
We choose the SEM approach because it has proven insightful for testing hypotheses
about causal interactions in ecological systems (162-166) and because we sought to evaluate
direct and indirect relationships among variables which could translate into general theory
relating to the controls of savanna vegetation structure. The focus on causal relationships by
analyzing direct and indirect relationships is one aspect that sets SEM apart from other
multivariate methods. For example, SEM provides a way to evaluate the direct effect of savanna
fires on woody plant abundance after controlling for the joint effects of environmental drivers on
fire and woody plant abundance. For these reasons SEM has distinct advantages over univariate
10
regression approaches, such as GAM’s and GLM’s, which do not allow for the specification of
indirect effects, such as the vectoring of climatic impacts, through fire, on the productivity of
ecosystems.
At the core of our SEM analysis is an a priori conceptual model which describes,
schematically, how our eight environmental drivers may interact to determine TBA (Fig 2). The
eight environmental drivers were grouped into several conceptual entities, called ‘constructs’,
represented by dashed boxes in Fig 2: moisture availability, soil fertility, plant growing
conditions and disturbance. These constructs are composed of observed variables (i.e.
measured), called ‘indicators’, which represent empirical measures of the construct (158, 167).
Indicators are represented by rectangles inside the dashed boxes (Fig 2). Some constructs are
associated with multiple indicators, each representing different, but related, dimensions of the
construct (e.g. the average and the range are two different, but related, indicators of temperature
and growing conditions). Arrows in the diagram represent direct causal influences of one
variable on another, without specifying the directionality (i.e. positive or negative) or the shape
(e.g. degree of linearity) of the relationship. While we acknowledge the potential for non-linear
effects in savannas (168-169), our approach was to seek a simple, multivariate model based on
linear relationships. In addition to parsimony, this approach has the advantage of enabling
general comparisons across global savanna systems.
Our first step in the modelling process was to create a structural equation model which
included all possible effects of the predictors on fire frequency and tree biomass plus the direct
effect of fire frequency on tree biomass. Models were analyzed separately for each continent and
in a single global analysis using the Bayesian module of AMOS version 20.0 and the default
burn-in value of 500. In contrast to standard SEM, which relies on maximum likelihood (ML),
11
Bayesian SEM uses a Markov Chain Monte-Carlo (MCMC) estimation procedure. A path
pruning strategy was utilized to arrive at the final accepted model: paths with a 95% credible
parameter interval that included zero after 105 iterations were declared non-significant and
eliminated until only significant paths remained. Final models were estimated retrospectively
with standard ML procedures to obtain χ2 values based on expected versus observed covariance
matrices, which are standard goodness-of-fit measures in SEM. Additionally, model fit was
assessed in the Bayesian module after 2.5x105 iterations with the deviance information criterion
(DIC), in which competing models with lower DIC values are preferred, and the posterior
predictive P, which is deemed acceptable when the value is near 0.5 (161).
Subsequent to arriving at the final acceptable models (Tables S1 – S4), we followed the
two-stage approach of (170) to create composite variables, shown as ovals in Fig 2. Composite
variables allow for the quantitative measurement of the relative effect strength of multiple
conceptually similar indicators on a response variable. Composite variables are closely related to
latent variables, except that they are associated with a zero error variance term so that the latent
variable is completely determined by its indicator variables (170-171). In order to achieve model
identification, one of the indicator values is set equal to 1.0, so that the composite has the scale
of that indicator (170). Here we use composites to facilitate the comparison of conceptually
simplified, general models of savanna vegetation structure across continents. The resulting path
coefficients from a composite to a response variable depict the combined standardized relative
effect of the indicators on the response variable. Note that the standardized path coefficients in a
composite model show effect strength, not directionality, so that negative path coefficients in the
full models (Tables S1-S4) translated into composite effects will be positive. There is one
exception in our model results: the composite variable ‘Fire’ has only one indicator (fire
12
frequency) and therefore the path coefficient in the composite model is equal to that in the full
model (Tables S1-S4). As a result, we represent the standardized direct effects of fire on TBA
with their negative signs in Fig 2. For all three continents the composite models from Fig 2
converged successfully (convergence criterion > 1.002) and the tree basal area data showed a
very close fit to the model according to goodness of fit statistics (Africa: χ2 = 4.531, df = 6, P =
0.605, n = 365; Australia: χ2 = 4.032, df = 5, P = 0.545, n = 1487; South America: χ2 = 5.344, df
= 8, P = 0.72, n = 302).
Estimation of aboveground woody biomass from tree basal area
To convert from TBA to aboveground woody biomass (AWB kg ha-1), and in the absence of
structural information for each site used in this analysis, we undertook of two data compilations:
(i) biomass – stem diameter relationships for dominant tree species and (ii) tree size class
distributions. We integrated this information to convert our dataset of TBA to estimates of AWB.
Our resulting estimates of aboveground woody biomass are just that, estimates. These analyses
also represent means of accounting for ecologically and structurally important variation in
vegetation structure across thousands of sites. Such variation has been shown to be important in
understanding variation in carbon accumulation across tropical forests (140). The conversion
from TBA to AWB was likely to propagate errors of different descriptions, and hence, our key
analysis in this paper rests on the robust field collected TBA data. The conversion of TBA to
AWB is used to aid interpretation of our analysis (Fig S1), create a map of the predicted
distribution of aboveground woody biomass across savannas (Fig S4) and to consider how
13
woody plant traits and structural variation within the biome could impact trajectories of
vegetation change (Fig 4).
Analysis of woody biomass – stem diameter allometry
Species level characteristics of height – diameter relationships, woody density and architecture
largely determine the woody biomass contained within a single tree and consequently a stand.
How differences in the structural traits of woody species affects estimates of woody biomass has
long been investigated and accounted for across tropical forest systems (140, 172). However, we
found limited published data of studies examining relationships between stem diameter and
above ground stem biomass in savanna species. The original data were in most cases not
available. We therefore restrict ourselves to comparing published biomass - stem diameter
relationships (30, 173-179). We convert these relationships into the form
ln(B) = c + ln(D)a
where B is biomass (kg) and D is stem diameter (m). After conversion, we used the modal
estimates of c and a for each continent and used these to create continent specific diameter biomass regression equations. Below are the equations that we used for each continent.
Africa: ln(B) = 8.99 + ln(D)2.58
Australia: ln(B) = 9.13 + ln(D)2.52
South America: ln(B) = 1.52 + ln(D)2.47
14
Analysis of tree size class distributions
We compiled data on tree size class distributions from some available studies (38, 181-188) to
account for the structural variation in savanna vegetation (Table S5) and in order to transform
tree basal area to aboveground woody biomass.
In Africa, we identified four bio-regions based on known differences in dominant woody species
and regional variation in rainfall. These four regions were: Southern Africa, West Africa, East
Africa and Miombo Woodlands. Australian savannas are consistently dominated by species from
the genus Eucalyptus and hence, we classified two regions in Australia based on climatic
information. There were: mesic Eucalyptus savanna (MAP > 900 mm yr-1) and semi-arid
Eucalyptus savanna (MAP < 900 mm yr-1). We found minimal structural information describing
tree size class distribution in Brazil and Venezuela. Hence, we compiled data for the region as a
single averaged tree size class distribution as we had found insufficient evidence to make a
robust distinction between the structure of Brazilian and Venezuelan savanna, where both
regions receive relatively high rainfall (Fig 2).
For each region data were compiled in 5cm DBH (diameter at breast height) size classes and
used to calculate the proportion of total basal area that each 5cm DBH size class contributed to
the total tree basal area (PROPsc) (Table S5).
To convert each record of total basal area (BAT), to an estimate of aboveground woody biomass
(AWBT), for each record, we derived an estimate of the mean number of stems per size class
15
(STEMSsc) for a given value of BAT based on the regional stand structures (Table S5), where
BAi is the basal area of an average individual tree in a given size class.
STEMSsc = (BAT*PROPsc)/BAi
Via the DBH – biomass allometry information we estimated the aboveground woody biomass of
an average individual tree in a given size class (AWBi). Hence, to derive an estimate of
aboveground woody biomass per size class (AWBsc) we multiplied STEMSsc by AWBi.
AWBsc = STEMSsc*AWBi
For each record of BAT, AWBsc was then summed across relevant size classes to calculate
AWBT for each value of BAT.
AWBT = Sum of AWBsc across all size classes
16
Figure S1. The relationships between estimated Aboveground woody biomass (AWB) and
Effective rainfall (mm) across Africa (r2 = 0.199, F(1, 363) = 90.08, p-value: < 0.001); Australia
(r2 = 0.393, F(1, 1485) = 960.7, p-value: < 0.001); and, South America (r2 = 0.008, F(1, 300) =
2.56, p-value: = 0.111). Also depicted are the piecewise quantile fits of the 5th and 95th quantiles
of TBA relative to effective rainfall. Effective rainfall (ER) is calculated as the difference in
millimetres per year between mean annual rainfall and potential evapotranspiration. Data for
each continent is shown separately, along with piecewise quantile fits of the 5th and 95th quantiles
of AWB relative to ER. The 95th quantile is used as a proxy for the limits to woody biomass
accumulation.
17
Figure S2. Frequency distribution for each of Effective rainfall, Foley’s Drought Index, Rainfall
Seasonality and fire frequency for each continent based on known savanna extent as per (14).
Data for each of these environmental correlates relating to the field observations used in this
study are shown as a rug of grey points at the base of each frequency distribution.
18
Figure S3. Frequency distribution for each of Mean Annual Temperature, Annual Temperature
Range, % Soil Organic Carbon and % Sand for each continent based on known savanna extent as
per (14). Data for each of these environmental correlates relating to the field observations used in
this study are shown as a rug of grey points at the base of each frequency distribution.
19
Figure S4. Predicted aboveground woody biomass (tonnes per hectare) estimated for the
savannas of Africa, Australia and South America. AWB under current climate and fire
conditions are derived from the most parsimonious structural equation model for each continent
(model coefficients presented in Table S1-S3) and presented at a 0.5 degree resolution. Savanna
limits for each continent are from (14).
20
Coefficients derived from Structural Equation Modelling
Standardized
TBA (m2/ha)
Std. Err.
AWB (kg/ha)
Std. Err.
Effective Rainfall
0.5716
0.0080
0.00004
36.9552
0.1719
Drought Index
0.2874
4.7916
0.0332
20370.7339
138.9624
AFRICA
Effects on TBA/AWB
Moisture
Availability
Rainfall Seasonality
n/a
n/a
n/a
n/a
n/a
Growing
Mean Annual Temp.
0.329
0.0523
0.0005
268.9595
2.0180
Conditions
Annual Temp. Range
n/a
n/a
n/a
n/a
n/a
% Sand
n/a
n/a
n/a
n/a
n/a
Soils
% Organic Caron
n/a
n/a
n/a
n/a
n/a
Fire
Fire Frequency
-0.1931
-0.5210
0.0052
-2419.5535
17.7429
Effective Rainfall
0.8252
0.0043
0.00002
0.0043
0.00002
Drought Index
-0.2396
-1.4812
0.0129
-1.5050
0.0135
Availability
Rainfall Seasonality
-0.3338
-0.0478
0.0005
-0.0467
0.0004
Growing
Annual Temp. Range
0.3074
0.0183
0.0002
0.0183
0.0002
Conditions
Mean Annual Temp.
0.7250
0.0428
0.0002
0.0429
0.0002
% Sand
0.3240
0.0295
0.0002
0.0290
0.0003
% Organic Carbon
0.2830
1.1914
0.0114
1.1790
0.0123
Effects on Fire Frequency
Moisture
Soils
Table S1. Standardized path coefficients, unstandardized path coefficients and standard errors (Std. Err.) from the final, accepted,
structural equation models (SEMs) predicting fire frequency and woody plant abundance in Africa savannas. Paths eliminated during
the model pruning steps (see methods) are represented by ‘n/a’. Woody plant abundance is represented as both tree basal area (m2 ha1
) and tree biomass (kg ha-1). The data for tree basal area and tree biomass showed a close fit to the model as judged by goodness of
fit statistics (tree basal area: posterior predictive = 0.51, χ2 = 4.99, df = 6, P = 0.5456, n = 365; tree biomass: posterior predictive =
0.51, χ2 = 5.47, df = 6, P = 0.4847, n = 365).
1
Coefficients derived from Structural Equation Modelling
Standardized
TBA(m2/ha)
Std.Err.
AWB (kg/ha)
Std. Err.
Effective Rainfall
0.2764
0.0025
0.00003
17.4768
0.1209
Drought Index
0.2091
4.2738
0.0271
25225.1523
173.8937
Rainfall Seasonality
n/a
n/a
n/a
n/a
n/a
Mean Annual Temp.
-0.1750
-0.0506
0.00001
-276.7589
1.6353
Annual Temp. Range
-0.2266
-0.0237
0.0002
-113.2386
1.2216
% Sand
n/a
n/a
n/a
n/a
n/a
% Organic Caron
n/a
n/a
n/a
n/a
n/a
Fire Frequency
-0.0663
-0.1546
0.0022
-970.6142
14.7189
Effective Rainfall
0.6301
0.0024
0.00001
0.0024
0.00001
n/a
n/a
n/a
n/a
n/a
Rainfall Seasonality
0.1916
0.0463
0.0002
0.0453
0.0005
Annual Temp. Range
0.7526
0.0325
0.0002
0.0323
0.0002
Mean Annual Temp.
0.3840
0.0472
0.0002
0.0473
0.0002
% Sand
0.1300
0.0141
0.0001
0.0143
00001.
% Organic Carbon
0.0860
0.3668
0.0036
0.3719
0.0040
AUSTRALIA
Effects on TBA/AWB
Moisture Availability
Growing Conditions
Soils
Fire
Effects on Fire Frequency
Moisture Availability
Growing Conditions
Drought Index
Soils
Table S2. Standardized path coefficients, unstandardized path coefficients and standard errors (Std. Err.) from the final, accepted,
structural equation models (SEMs) predicting fire frequency and woody plant abundance in Australian savannas. Paths eliminated
during the model pruning steps (see methods) are represented by ‘n/a’. Woody plant abundance is represented as both tree basal area
(m2 ha-1) and tree biomass (kg ha-1). The data for tree basal area and tree biomass showed a close fit to the model as judged by
goodness of fit statistics (tree basal area: posterior predictive = 0.49, χ2 = 4.03, df = 5, P = 0.5448, n = 1487; tree biomass: posterior
predictive = 0.54, χ2 = 3.98, df = 5, P = 0.5524, n = 1487).
2
Coefficients derived from Structural Equation Modelling
TBA
Standardized
(m2/ha)
Std. Err.
AWB (kg/ha)
Std. Err.
n/a
n/a
n/a
n/a
n/a
0.2742
9.6891
0.0526
50780.34
303.821
Rainfall Seasonality
n/a
n/a
n/a
n/a
n/a
Mean Annual Temp.
-0.2031
-0.0458
0.0003
-240.772
1.8106
Annual Temp. Range
n/a
n/a
n/a
n/a
n/a
0.1621
0.0394
0.0003
207.5575
1.4916
n/a
n/a
n/a
n/a
n/a
Fire Frequency
-0.1141
-1.0512
0.0103
-5504.01
50.7165
Effective Rainfall
0.3187
0.0006
0.00001
0.0006
0.00001
n/a
n/a
n/a
n/a
n/a
Rainfall Seasonality
0.1867
0.0156
0.0001
0.01551
0.0001
Annual Temp. Range
n/a
n/a
n/a
n/a
n/a
Mean Annual Temp.
n/a
n/a
n/a
n/a
n/a
% Sand
n/a
n/a
n/a
n/a
n/a
% Organic Caron
n/a
n/a
n/a
n/a
n/a
SOUTH AMERICA
Effects on TBA/AWB
Effective Rainfall
Moisture Availability
Growing Conditions
Soils
Fire
Drought Index
% Sand
% Organic Caron
Effects on Fire Frequency
Moisture Availability
Growing Conditions
Drought Index
Soils
Table S3. Standardized path coefficients, unstandardized path coefficients and standard errors (Std. Err.) from the final, accepted,
structural equation models (SEMs) predicting fire frequency and woody plant abundance in South American savannas. Paths
eliminated during the model pruning steps (see methods) are represented by ‘n/a’. Woody plant abundance is represented as both tree
basal area (m2 ha-1) and tree biomass (kg ha-1). The data for tree basal area and tree biomass showed a close fit to the model as judged
by goodness of fit statistics (tree basal area: posterior predictive = 0.56, χ2 = 5.34, df = 8, P = 0.7203, n = 302; tree biomass: posterior
predictive = 0.57, χ2 = 5.34, df = 8, P = 0.7203, n = 302).
3
Coefficients derived from Structural Equation Modelling
Standardized
2
Unstandardized
2
Std.
Standardized
Unstandardized
TBA (m /ha)
TBA (m /ha)
Err.
AWB(kg/ha)
AWB (kg/ha)
Std. Err.
Effective Rainfall
0.3806
0.0037
0.00001
0.5413
29.4701
0.0857
Drought Index
0.2097
3.6226
0.0201
0.1318
12636.8382
72.0796
Rainfall Seasonality
0.0520
0.0240
0.0005
0.0765
196.3434
1.9769
Mean Annual Temp.
-0.0736
-0.0148
0.0003
n/a
n/a
n/a
Annual Temp. Range
n/a
n/a
n/a
0.0736
44.1225
0.8295
0.0500
0.0120
0.0002
0.0582
77.3000
20.9947
n/a
n/a
n/a
n/a
n/a
n/a
ALL CONTINENTS
Effects on TBA/AWB
Moisture Availability
Growing Conditions
% Sand
Soils
% Organic Caron
Fire
Fire Frequency
-0.0778
-0.1983
0.0026
-0.1024
-1445.5702
10.2564
Effective Rainfall
0.3925
0.0015
0.00001
0.3948
0.0015
0.00001
Drought Index
n/a
n/a
n/a
n/a
n/a
n/a
Rainfall Seasonality
n/a
n/a
n/a
n/a
n/a
n/a
Annual Temp. Range
0.4472
0.0190
0.00008
0.4516
0.0192
0.00009
Mean Annual Temp.
0.4120
0.0325
0.00008
0.4144
0.0327
0.00006
% Sand
0.1166
0.0109
0.0001
0.1167
0.0110
0.0001
% Organic Caron
0.1398
0.5793
0.0040
0.1402
0.5819
0.0036
Effects on Fire Frequency
Moisture Availability
Growing Conditions
Soils
Table S4. Standardized path coefficients, unstandardized path coefficients and standard errors (Std. Err.) from the final, accepted,
structural equation models (SEMs) predicting fire frequency and woody plant abundance in global savannas. Paths eliminated during
the model pruning steps (see methods) are represented by ‘n/a’. Woody plant abundance is represented as both tree basal area (m2 ha1
) and tree biomass (kg ha-1). The data for tree basal area and tree biomass showed appropriate fit to the model as judged by goodness
of fit statistics (tree basal area: posterior predictive = 0.55; χ2 = 5.59, df = 7, P = 0.5887, n = 2154; posterior predictive = 0.48; tree
biomass: χ2 = 8.0278, df = 7, P = 0.3301, n = 2154).
4
DBH size class
(cm)
0.1 5
5.1 10
10.1 15
15.1 20
20.1 25
25.1 30
30.1 35
35.1 40
40.1 45
45.1 50
50.1 55
55.1 60
60.1 65
65.1 70
Africa
South
n/a
0.262
0.217
0.165
0.092
0.074
0.031
0.062
0.024
0.029
0.012
0.013
0.019
n/a
West
n/a
0.066
0.133
0.132
0.191
0.108
0.145
0.160
0.030
0.036
n/a
n/a
n/a
n/a
East
n/a
0.082
0.273
0.257
0.192
0.101
0.055
0.017
0.023
n/a
n/a
n/a
n/a
n/a
Miombo
n/a
0.112
0.179
0.152
0.138
0.108
0.072
0.049
0.190
n/a
n/a
n/a
n/a
n/a
Australia
Mesic
0.018
0.073
0.063
0.077
0.114
0.142
0.159
0.126
0.096
0.058
0.059
0.012
0.001
0.002
Semi-arid
0.023
0.074
0.125
0.158
0.157
0.139
0.112
0.065
0.060
0.043
0.026
0.007
0.006
0.005
South America
Brazil/Venezuela
0.010
0.015
0.202
0.178
0.187
0.147
0.108
0.091
0.030
0.031
n/a
n/a
n/a
n/a
Table S5. For each region, we show the estimated contribution to TBA by stems in 5cm DBH (diameter at breast height) size classes
based on an estimated tree size class distribution for that region. Note that we could not find consistent information on the 0.1 – 5cm
DBH size class across Africa.
5
Additional Database S1 (separate file)
Tree basal area data used in this analysis showing the latitude, longitude, and
environmental correlates of the record and tree basal area in m2 ha-1.
Additional Database S2 (separate file)
Stand structures used for East Africa, as stem counts in 5cm size classes along with the
contributor, and the source of the data.
1
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