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Mapping tree density at a global scale

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Mapping tree density at a global scale

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The global extent and distribution of forest trees is central to our understanding of the terrestrial biosphere. We provide the first spatially continuous map of forest tree density at a global scale. This map reveals that the global number of trees is approximately 3.04 trillion, an order of magnitude higher than the previous estimate. Of these trees, approximately 1.39 trillion exist in tropical and subtropical forests, with 0.74 trillion in boreal regions and 0.61 trillion in temperate regions. Biome-level trends in tree density demonstrate the importance of climate and topography in controlling local tree densities at finer scales, as well as the overwhelming effect of humans across most of the world. Based on our projected tree densities, we estimate that over 15 billion trees are cut down each year, and the global number of trees has fallen by approximately 46% since the start of human civilization.
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ARTICLE
doi:10.1038/nature14967
Mapping tree density at a global scale
T. W. Crowther
1
, H. B. Glick
1
, K. R. Covey
1
, C. Bettigole
1
, D. S. Maynard
1
, S. M. Thomas
2
, J. R. Smith
1
, G. Hintler
1
, M. C. Duguid
1
,
G. Amatulli
3
, M.-N. Tuanmu
3
, W. Jetz
1,3,4
, C. Salas
5
, C. Stam
6
, D. Piotto
7
, R. Tavani
8
, S. Green
9,10
, G. Bruce
9
, S. J. Williams
11
,
S. K. Wiser
12
, M. O. Huber
13
, G. M. Hengeveld
14
, G.-J. Nabuurs
14
, E. Tikhonova
15
, P. Borchardt
16
, C.-F. Li
17
, L. W. Powrie
18
,
M. Fischer
19,20
, A. Hemp
21
, J. Homeier
22
, P. Cho
23
, A. C. Vibrans
24
, P. M. Umunay
1
, S. L. Piao
25
, C. W. Rowe
1
, M. S. Ashton
1
,
P. R. Crane
1
& M. A. Bradford
1
The global extent and distribution of forest trees is central to our understanding of the terrestrial biosphere. We provide
the first spatially continuous map of forest tree density at a global scale. This map reveals that the global number of trees is
approximately 3.04 trillion, an order of magnitude higher than the previous estimate. Of these trees, approximately
1.39 trillion exist in tropical and subtropical forests, with 0.74 trillion in boreal regions and 0.61 trillion in temperate
regions. Biome-level trends in tree density demonstrate the importance of climate and topography in controlling local
tree densities at finer scales, as well as the overwhelming effect of humans across most of the world. Based on our
projected tree densities, we estimate that over 15 billion trees are cut down each year, and the global number of trees has
fallen by approximately 46% since the start of human civilization.
Forest ecosystems harbour a large proportion of global biodiversity,
contribute extensively to biogeochemical c ycles, and provide count-
less ecosystem services, including water quality control, timber
stocks and carbon sequestration
1–4
. Our cu rrent understanding of
the global forest extent has been generated using remote sensing
approaches that provide spatially explicit values relating to forest
area and canopy cover
3,5,6
. Used in a wide variety of global models,
these maps have enhanced our understan ding of t he Earth sys-
tem
3,5,6
, but they do not currently address population numbers,
densities or timber stocks. These variablesarevaluableforthemod-
elling of broad-scale biological and biogeochemical processes
7–9
because tree density is a prominent component of ecosystem struc-
ture, governing elemental processing and retention rates
7,9,10
,aswell
as compet itive dynamics and habitat suitability for many plant an d
animal species
11–13
.
The number of trees in a given area can also be a meaning-
ful metric to guide forest management practices and inform
decision-making in public and non-governmental sectors
14,15
.For
example, international afforestation efforts such as the ‘Billion
Trees Campaign’, and city-wide projects including the numerous
‘Million Tree’ initiatives around the world have motivated civil
society and political leaders to promote environmental stewardship
and sustainable land management by p lanting large numbers of
trees
14,16,17
. Establishing targets and evaluating the proportional
contribution of such projects requires a sound basel ine understand-
ing of current and potential tree population numbers at regional
and global scales
16,17
.
The current estimate of global tree number is approximately
400.25 billion
18
. Generated using satellite imagery and scaled based
on global forest area, this estimate engaged policy makers and envir-
onmental practitioners worldwide by suggesting that the ratio of
trees-to-people is 61:1. This has, however, been thrown into doubt
by a recent broad-scale inventory that used 1,170 ground-truthed
measurements of tree density to estimate that there are 390 billion
trees in the Amazon basin alone
19
.
Mapping tree density
Here, we use 429,775 ground-sourced measurements of tree density
from every continent on Earth except Antarctica to generate a global
map of forest trees. Forested areas are found in most of Earth’s
biomes, even those as counterintuitive as desert, tundra, and grassland
(Fig. 1a, b). We generated predictive regression models for the
forested areas in each of the 14 biomes as defined by The Nature
Conservancy (http://www.nature.org). These models link tree density
to spatially explicit remote sensing and geographic information sys-
tems (GIS) layers of climate, topography, vegetation characteristics
and anthropogenic land use (see Extended Data Table 1). Following
almost all of the collected data sources, we define a tree as a plant with
woody stems larger than 10 cm diameter at breast height (DBH)
19
.
Incorporating plot-level measurements from more than 50 coun-
tries, the measured tree density values were inherently variable within
and among biomes (Figs 1 and 2). However, the large number of tree
density measurements ensured that the confidence in our mean (and
total) estimates is high (Fig. 3). Furthermore, the scale of these data
1
Yale School of Forestry and Environmental Studies, Yale University, New Haven, Connecticut 06511, USA.
2
Department of Environmental Sciences, University of Helsinki, Helsinki 00014, Finland.
3
Department of Ecology and Evolutionary Biology, Yale University, New Haven, Connecticut 06511, USA.
4
Department of Life Sciences, Silwood Park, Imperial College, London SL5 7PY, UK.
5
Departamento
de Ciencias Forestales, Universidad de La Frontera, Temuco 4811230, Chile.
6
RedCastle Resources, Salt Lake City, Utah 84103, USA.
7
Universidade Federal do Sul da Bahia, Ferradas, Itabuna 45613-204,
Brazil.
8
Forestry Department, Food and Agriculture Organization of the United Nations, Rome 00153, Italy.
9
Operation Wallacea, Spilbsy, Lincolnshire PE23 4EX, UK.
10
Durrell Institute of Conservation
and Ecology (DICE), School of Anthropology and Conservation (SAC), University of Kent, Canterbury ME4 4AG, UK.
11
Molecular Imaging Research Center MIRCen/CEA, CNRS URA 2210, 91401 Orsay
Cedex, France.
12
Landcare Research, Lincoln7640, New Zealand.
13
WSL, Swiss Federal Institute for Forest, Snow and Landscape Research, 8903 Birmensdorf, Switzerland.
14
Environmental Science Group,
Wageningen University & Research Centre, 6708 PB, The Netherlands.
15
Center for Forest Ecology and Productivity RAS, Moscow 117997, Russia.
16
CEN Center for Earth System Research and
Sustainability, Institute of Geography, University of Hamburg, Hamburg 20146, Germany.
17
Department of Botany and Zoology, Masaryk University, Brno 61137, Czech Republic.
18
South African National
Biodiversity Institute, Kirstenbosch Research Centre, Claremont 7735, South Africa.
19
Institute of Plant Sciences, Botanical Garden, and Oeschger Centre for Climate Change Research, University of Bern,
3013 Bern, Switzerland.
20
Senckenberg Gesellschaft fu
¨
r Naturforschung, Biodiversity and Climate Research Centre (BIK-F), 60325 Frankfurt, Germany.
21
Department of Plant Systematics, University of
Bayreuth, 95447 Bayreuth, Germany.
22
Albrecht von Haller Institute of Plant Sciences, Georg August University of Go
¨
ttingen, 37073 Go
¨
ttingen, Germany.
23
Tropical Ecology Research Group, Lancaster
Environment Centre, Lancaster University, Lancaster LA1 4YQ, UK.
24
Universidade Regional de Blumenau, Departamento de Engenharia Florestal, Blumenau/Santa Catarina 89030-000, Brazil.
25
Sino-
French Institute for Earth System Science, College of Urban and Environmental Sciences, Peking University, Beijing 100871, China.
G
2015 Macmillan Publishers Limited. All rights reserved
00 MONTH 2015 | VOL 000 | NATURE | 1
ensures that our modelled estimates are unlikely to be influenced
significantly by recent forest loss, reforestation or natural forest regen-
eration, which are responsible for a net global change of ,1% of the
global forest area each year
3
. Biome-level validation estimates indicate
that our models have high precision when predicting the mean tree
densities of omitted validation plots (Fig. 3a). Although the accuracy
Tree density (stems per ha)
Tropical moist
Tropical dry
Temperate broadleaf
Temperate coniferous
Boreal
Tropical grasslands
Temperate grasslands
Flooded grasslands
Montane grasslands
Tundra
Mediterranean forest
Deserts
Mangroves
0500
b
a
3,0002,5002,0001,5001,000
1 Density plot
91,000 Density plots
Global tree cover
Figure 1
|
Map of data points and raw biome-level forest density data.
a, Image highlighting the ecoregions (shapefiles provided by The Nature
Conservancy (http://www.nature.org)) from which the 429,775 ground-
sourced measurements of tree density were collected. Shading indicates the
total number of plot measurements collected in each ecoregion. A global forest
map was overlaid in green to highlight that collected data span the majority
of forest ecosystems on a global scale. b, The median and interquartile range of
tree density values collected in the forested areas of each biome.
Boreal Deserts Flooded grasslands Mediterranean forests
Montane grasslands Temperate broadleaf Temperate coniferous Temperate grasslands
Tropical dry
10
2
10
4
10
6
10
2
10
4
10
6
10
2
10
4
10
6
10
2
10
4
10
6
10
2
10
4
10
6
10
2
10
4
10
6
10
2
10
4
10
6
Tropical grasslands Tropical moist Tundra
0
0.2
0.4
0.6
0.8
1.0
abcd
efgh
ijkl
Predicted (trees per km
2
)
Measured (trees per km
2
)
Relative
frequency
Figure 2
|
Heat plots showing the relationships
between predicted and measured tree density
data. al, Predictions were generated using
generalized linear models (n 5 429,775). Diagonal
lines indicate 1:1 lines (perfect correspondence)
between predicted and observed points, scaled to
the kilometre level. Colours indicate the proportion
of data points from that biome that fall within each
pixel. Biomes with a greater number of plot
measurements have greater variability but higher
confidence in the mean estimates, highlighting the
trade-off between broad-scale precision and fine-
scale accuracy. Axes are log-transformed to
account for exceptionally high variability in tree
density.
RESEARCH ARTICLE
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2015 Macmillan Publishers Limited. All rights reserved
2 | NATURE | VOL 000 | 00 MONTH 2015
of our models is limited at the level of an individual hectare, the
precision of the mean density estimates is high (640 trees ha
21
)
beyond a threshold of ,200 plots (Fig. 3b).
Global-level and biome-level patterns
Together, the biome-level models provide the first spatially continuous
map of global tree densities at a 1-km
2
(30 arc-seconds) resolution
(Fig. 4a). Based on this map, we estimate that the global number of trees
is approximately 3.04 trillion (60.096 trillion, 95% confidence intervals
(CI)). An order of magnitude higher than the previous global estimate
18
,
the scale of our projection is consistent with recent large-scale inventories
in Europe, North America and the Amazon basin
19
(Fig.4d).Witha
human population of 7.2 billion, our estimate of global tree density
revises the ratio of trees per person from 61:1 to 422:1.
At the biome-level, the highest tree densities exist in forested
regions of the Boreal and Tundra zones (Fig. 1b). In these northern
latitudes, limited temperature and moisture lead to the establishment
of stress-tolerant coniferous tree species that can reach the highest
densities on Earth (Fig. 1). However, the tropical regions contain a
greater proportion of the world’s forested land. A total of 42.8% of the
planet’s trees exist in tropical and subtropical regions, with another
24.2% and 21.8% in boreal and temperate biomes, respectively
(Fig. 4a).
Within-biome trends
Our models also provide mechanis tic insights in to potential con-
trols o n t ree density wit hin biomes (Fi g. 5) . For example, various
climatic parameters correlate with mean forest density within all
ecosystem types. Tree density generally increases with temperature
(mean annua l tempe rature and temperature seasonality) and moi s-
ture availability (precipitation regimes , evapotranspira tion or arid-
ity). These patterns are consistent with previous broad-scale tree
inventory studies and support the idea that, within ecosystem
types, moist, warm conditions are generally optimal for tree
growth
11,12
.
Given the generally positive ef fects of m oisture availability and
war mth on tree density wi thin biomes, the negative relationships
observed in some regions may seem surprising (Fig. 5). Th is high-
lights the complex suite of population- and community-level selec-
tio n pressures that can obscure th e expected effects of climate across
landscapes. For example, in colder (boreal or tundra) biomes,
increasing moisture lev els can cause hydric and permafrost condi-
tio ns in lower lying topographi es, which then limit nutrient avai l-
ability for t ree development
20
. In addition, current and historical
anthropogenic land use decisions have the potential to drive these
relationships in several regions. The negative relationships between
tree density and moisture availability in flooded grasslands and trop-
ical dry forests are, for example, likely to be driven by preferential use
of moist, productive land for agriculture
21
. As a result, forest ecosys-
tems are often relegated to drier regions, reversing the expected
within-biome relationships between moisture availability and tree
density. Such effects will vary among countries, depending on
human population densities, alternative resource availability and
socio-economic status
22,23
.
Along with these indirect effects of human act ivity, the direct
effect of human development (percentage devel oped and managed
land)
6
on tree density represented the only common mechanism
across all biomes (Fig. 5). The negative relationships between tree
density and anthropogenic land use exemplify how humans contend
directly with natural forest ecosystem s for space. Whereas t he nega-
tive effect of human activit y on tree numbers is highly apparent at
local scales, the present study provides a new measure of the scale of
anthropogenic effects, relative to other environmental variables.
Current rates of global forest cover loss are approximately
192,000 km
2
each year
3
. By combining our tree density information
wit h the most recent spatially explicit map of fores t cover loss over
the past 12 years
3
, we estimate that deforestation, forest manage-
ment, disturbances and land use change are currently responsible
for a gross loss of approximately 15.3 billion trees on an annual basis.
Alt houg h thes e rates of for est loss are curre ntly highest in tropical
regions
3
, the scale and consistency of this negative human effect
across all forested biomes highlights how historical land
use decisions have shaped natural ecosystems on a global scale.
Using the projected maps of current and historic forest cover provided
by the United Nations Environment Programme (http://geodata.
grid.unep.ch), our map reveals that the global number of trees has fallen
400 600 800 1,000 1,200
200
400
600
800
1,000
1,200
Observed mean tree density (trees per ha)
Predicted mean tree density (trees per ha)
0 50 100 150 200 250 300
0
50
100
150
200
Sam
p
le size
Standard deviation (trees per ha)
Boreal
Deserts
Flooded grasslands
Mediterranean forest
Montane grasslands
Temperate broadleaf
Temperate coniferous
Temperate grasslands
Tropical dry
Tropical grasslands
Tropical moist
Tundra
a
b
200
Figure 3
|
Validation plots for biome-level predictions. a,Biome-level
regression models predict the mean values of the omitted v alidation plot
measurements in 12 biomes. Overall, the models underestimated mean tree
dens ity by ,3% (slope 5 0.97) but this difference was not statistica lly
significant (P 5 0.51). Bars show 6 one sta ndard deviation for the predict ed
mean and the grey area represents the 95% confidence interval f or the mean.
The values plotted here represent mean densities for the plot measurements
(that is, for forested ecosystems), rather than those predicted for each entire
biome. b, The stan dard deviation of the predicted mean va lues as a function
of sample size. As sample size increases, the variability of th e predicted mean
tree density reaches a thresh old, beyond whi ch an increase in sam ple size
results in a minimal increase in precis ion. Standard deviations were
calc ulated using a bootstrap ping approach (see Metho ds), and smooth curves
were modelled using standard linear regression with a log–log
transformation.
ARTICLE RESEARCH
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00 MONTH 2015 | VOL 000 | NATURE | 3
by approximately 45.8% since the onset of human civilization (post-
Pleistocene).
Discussion
The global map of tree density can facilitate ongoing efforts to under-
stand biogeochemical Earth system dynamics
3,6,7,9
by incorporating
ecosystem features that relate to elemental cycling rates
9,10
. For
example, tree abundance can help to explain some of the variation
in carbon storage and productivity within ecosystem types
7,9
, but the
strength of these effects remain untested across biomes
8
. We assessed
the relationship between tree density and plant carbon storage at a
global scale by regressing our plot-level tree counts against modelled
estimates of plant biomass carbon in those sites
24
. This revealed a
positive effect of tree density on plant carbon storage (P , 0.001).
However, the strength of the relationship is weak (r
2
5 0.14), reflect-
ing the vast array of local ecological forces that can obscure such
global trends. For example, the effect of tree density is likely to interact
strongly with tree size. Larger trees contain the greatest proportion of
carbon in woodlands
25
, but the highest tree densities within a given
ecosystem type are often associated with young or recovering forests
characterized by many small trees
13,20
. A thorough understanding of
total vegetative carbon storage requires information about both the
size and the number of individual trees.
A dense forest environment is a fundamentally different ecosystem
from a sparse one and this influences a vast array of biotic and abiotic
processes
10–12
. Current remote sensing tools capture some, but not all
of this information. The tree density layer that we provide can there-
fore augment the currently available layers by providing unique
insights into ecological dynamics that are not represented by esti-
mates of forest cover or biomass
3,5,6
. It can inform biodiversity esti-
mates and species distribution models by capturing perceivable
environmental characteristics that determine habitat suitability for
a wide variety of plants and animals
11–13
. Baseline estimates of tree
populations are also critical for projecting population- and commun-
ity-level tree demographics under current and future climate change
scenarios
26
, and for guiding local, national, and international refor-
estation/afforestation efforts
14–17
. Finally, by allowing us to compre-
hend the global forest extent in terms of tree numbers, this map
contributes to our fundamental understanding of the Earth’s terrest-
rial system.
High: >1,000,000
Low: 0
Terrestrial biome (number of ground-
sourced density estimates)
Total trees
(billions) ± 95% CI
Boreal forests (n = 8,688) 749.3 (± 50.1)
Deserts (n = 14,637) 53.0 (± 2.9)
Flooded grasslands (n = 271) 64.6 (± 14.2)
Mangroves (n = 21) 8.2 (± 0.3)
Mediterranean forests (n = 16,727) 53.4 (± 1.2)
Montane grasslands (n = 138) 60.3 (± 24.0)
Temperate broadleaf (n = 278,395) 362.6 (± 2.9)
Temperate conifer (n = 85,144) 150.6 (± 1.3)
Temperate grasslands (n = 17,051) 148.3 (± 4.9)
Tropical coniferous (n = 0) 22.2 (± 0.4)
Tropical dry (n = 115) 156.4 (± 63.4)
Tropical grasslands (n = 999) 318.0 (± 35.5)
Tropical moist (n = 5,321) 799.4 (± 24.0)
Tundra (n = 2,268) 94.9 (± 6.3)
n = 429,775
3,041.2 (± 96.1)
a
b
c
0
100
200
Kilometres
d
10
9
10
9
10
10
10
10
10
11
10
11
10
12
10
12
Predicted tree totals
Reported tree totals
Amazon basin
United States
Sweden
UK
R
2
=0.97
Austria
Spain
Germany
Figure 4
|
The global map of tree density at the 1-km
2
pixel (30 arc-seconds)
scale. a, The scale refers to the number of trees in each pixel. b, c, We highlight
the map predictions for two areas (South American Andes (b) and Sardinia
(c)) and include the corresponding images for visual comparison. All maps and
images were generated using ESRI basemap imagery. d, A scatterplot as
validation for our broad-scale estimates of total tree number. This shows the
relationship between our predicted tree estimates and reported totals for
regions with previous broad-scale tree inventories (see Methods for details).
The straight line and the dotted line are the predicted best fit line and the 1:1
line, respectively.
RESEARCH ARTICLE
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2015 Macmillan Publishers Limited. All rights reserved
4 | NATURE | VOL 000 | 00 MONTH 2015
Online Content Methods, along with any additional Extended Data display items
and Source Data, are available in the online version of the paper; references unique
to these sections appear only in the online paper.
Received 6 May; accepted 23 July 2015.
Published online 2 September 2015.
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Supplementary Information is available in the online version of the paper.
Acknowledgements We thank P. Peterkins for her support throughout the study. We
also thank Plant for the Planet for initial discussions and for collaboration during the
study. The main project was funded by grants to T.W.C. from the Yale Climate and
Energy Institute and the British Ecological Society. We acknowledge various sources for
tree density measurements and estimates: the Canadian National Forest Inventory
(https://nfi.nfis.org/index.php), the US Department of Agriculture Forest Service for
their National Forest Inventory and Analysis (http://fia.fs.fed.us/), the Taiwan Forestry
Bureau (which provided the National Vegetation Database of Taiwan), the DFG
(German Research Foundation), BMBF (Federal Ministry of Education and Science of
Germany), the Floristic and Forest Inventory of Santa Catarina (IFFSC), the National
Vegetation Database of South Africa, and the Chilean research grants FONDECYT no.
1151495. For Europe NFI plot data were brought together with input from J. Rondeux
and M. Waterinckx, Belgium, T. Be
´
louard, France, H. Polley, Germany, W. Daamen and
H. Schoonderwoerd, Netherlands, S. Tomter, Norway, J. Villanueva and A. Trasobares,
Spain, G. Kempe, Sweden. New Zealand Natural Forest plot data were collected by the
LUCAS programme for the Ministry for the Environment (New Zealand) and sourced
from the National Vegetation Survey Databank (New Zealand) (http://
nvs.landcareresearch.co.nz). We also acknowledge the BCI forest dynamics research
project, which was funded by National Science Foundation grants to S. P. Hubbell,
support from the Center for Tropical Forest Science, the Smithsonian Tropical
Research Institute, the John D. and Catherine T. MacArthur Foundation, the Mellon
Foundation, the Small World Institute Fund, numerous private individuals, the Ucross
High Plains Stewardship Initiative, and the hard work of hundreds of people from 51
countries over the past two decades. The plot project is part of the Center for Tropical
Forest Science, a global network of large-scale demographic tree plots.
Author Contributions The study was conceived by T.W.C and G.H. and designed by
T.W.C., K.C. and M.A.B. Statistical analyses and mapping were conducted by H.B.G.,
S.M.T., J.R.S., C.B., D.S.M. and T.W.C. The manuscript was written by T.W.C. with input
from M.A.B., P.C., and D.S.M. Tree density measurements or geospatial data from all
over the world were contributed by K.R.C., S.M.T., M.C.D., G.A., M.N.T., W.J., C.Sa., C.St.,
D.P., T.T., S.G., G.B., S.J.W., S.K.W., M.O.H., G.M.H., G.J.N., E.T., P.B., C.F.L., L.W.P., M.F., A.H.,
J.H., P.C., A.C.V., P.M.U., S.L.P., C.W.R. and M.S.A.
Author Information Reprints and permissions information is available at
www.nature.com/reprints. The authors declare no competing financial interests.
Readers are welcome to comment on the online version of the paper.
Correspondence and requests for materials should be addressed to T.W.C.
(thomas.crowther11@gmail.com).
EVI: dissimilarity
EVI: contrast
EVI: ASM
EVI
LAI
Evapotranspiration
Aridity
Precip: seasonality
Precip: driest month
Precip: driest quarter
Annual precip.
Mean annual temp.
Temp. seasonality
Roughness
Northness
Eastness
Elevation
Slope
Latitude
Human development
Boreal
Deserts
Flooded grasslands
Mangroves
Mediterranean forests
Montane grasslands
Temperate broadleaf
Temperate coniferous
Temperate grasslands
Tropical coniferous
Tropical dry
Topical grasslands
Tropical moist
Tundra
Vegetative
Climatic
Topographic
(%)
60
30
10
5
1
0.1
–0.1
–1
–5
–10
–30
–60
Figure 5
|
Standardized coefficients for the variables included in final
biome-level regression models. Coefficients represent relative per cent
change in tree density for one standard deviation increase in the variable. Red
and blue circles indicate negative and positive effects on tree density,
respectively. Circle size indicates the magnitude of effects. All layers are
available at the global scale. Human development 5 per cent developed and
managed land; LAI 5 leaf area index; EVI 5 enhanced vegetation index; EVI:
ASM 5 angular second moment of EVI; EVI: contrast 5 contrast of EVI; and
EVI: dissimilarity 5 dissimilarity of EVI (see Extended Data Table 1).
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00 MONTH 2015 | VOL 000 | NATURE | 5
METHODS
Data collection and standardisation. Plot-level data were collected from inter-
national forestry databases, including the Global Index of Vegetation-Plot
Database (GIVD http://www.givd.info), the Smithsonian Tropical Research
Institute (http://www.stri.si.edu), ICP-Level-I plot data which covers most of
Europe (http://www.icp-forests.org), and National Forest Inventory (NFI) ana-
lyses from 21 countries, including the USA (http://fia.fs.fed.us/) and Canada
(https://nfi.nfis.org/index.php). This information was supplemented with data
from peer-reviewed studies reporting large international inventories published
in the last 10 years (collected using ISI Web of Knowledge, Google Scholar and
secondary references)
19,27,28
.
We only included density estimates where individual trees met the criterion of
$10 cm diameter at breast height (DBH). Although NFI databases can vary
slightly in their definition of a mature tree (for example, the US Forest Service
Forest Inventory and Analysis (FIA)
29
defines a tree as a plant with woody stems
larger than 12.7 DBH) the vast majority of sources use 10 cm as the DBH cut-off.
Indeed, this was the only size class provided by all broad-scale inventories
(including the FIA), so density estimates at other DBH values were excluded.
This provided a total of 429,775 measurements of forest tree density (each
generated at the hectare scale) that were then linked to spatially explicit
remote-sensing data and GIS variables to explore the patterns in forest tree
density at a global scale. The scale of our plot data (in terms of number and
distribution of plots) ensured that any plot location uncertainty or minor
changes in global forest area are unlikely to alter mean values or modelled
estimates.
Acquisition and preprocessing of spatial data. For predictive model develop-
ment, we selected 20 geospatial covariates from a larger pool of potential covari-
ates based on uniqueness, spatial resolution and ecological relevance (Extended
Data Table 1). Covariates were derived through satellite-based remote sensing
and ground-based weather stations, and can be loosely grouped into one of four
categories: topographic, climatic, vegetative or anthropogenic. Topographic cov-
ariates included elevation, slope, aspect (as northness and eastness), latitude (as
absolute value of latitude) and a terrain roughness index (TRI). Climatic covari-
ates included annual mean temperature, temperature annual range, annual pre-
cipitation, precipitation of driest month, precipitation seasonality (coefficient of
variation), precipitation of driest quarter, potential evapotranspiration per hec-
tare per year, and indexed annual aridity. Vegetative covariates included,
enhanced vegetation index (EVI), leaf area index (LAI), dissimilarity, contrast,
and angular second moment. We also included a single anthropogenic covariate:
proportion of urban and/or developed land cover (see Extended Data Table 1).
Several covariates bear special mention. Moving-window analyses were applied
to an EVI derived from a multi-year composite of moderate resolution imaging
spectroradiometer (MODIS) imagery. From the result, we extracted three sec-
ond-order textural covariates that reflect the heterogeneity of vegetation, inten-
ded to capture difference in vegetative structure. These include angular second
moment (the orderliness of EVI among adjacent pixels), contrast (the exponen-
tially weighted difference in EVI between adjacent pixels: see http://earthenv.org
for details), and dissimilarity (difference in EVI between adjacent pixels). Terrain
roughness index (the mean of absolute differences between a cell and its adjacent
neighbours) was derived from aggregated Global Multi-Resolution Terrain
Elevation Data of 2010. Terrain roughness index was computed using the eight
neighbouring pixels, while the others were computed using the four neighbouring
pixels located at 0u,45u,90u, 135u (see http://earthenv.org and ref. 36 for details).
We preprocessed all spatial covariates using ArcMap 10.1 (ESRI, Redlands,
CA, 2012) and RStudio 0.97.551 (RStudio, 2012). All covariates were reprojected
to the interrupted Goode Homolosine equal-area coordinate system (which max-
imises spatial precision by amalgamating numerous region-specific equal-area
projections) to optimize the areal accuracy of our final figures
30
. These were then
resampled to match the coarsest resolution used during analysis (nominal 1 km
2
pixels), and spatially coregistered using nearest neighbour resampling where
necessary.
To account for broad-scale differences in vegetation types, we developed spatial
models at the biome scale. Individual predictive models were generated within
each of 14 broad ecosystem types (delineated by the Nature Conservancy http://
www.nature.org) to improve the accuracy of estimates.
Statistical modelling. We used generalized linear models to generate predictive
maps of tree numbers within forested ecosystems for each biome. This approach
also enabled us to explore the mechanisms potentially governing patterns in
forest tree density within regions (Fig. 5). Due to the inherently interactive nature
of climate, soil and human impact factors across the globe, we predicted that there
would be pronounced non-independence within the full suite of biophysical
variables extracted from the compiled GIS layers. To account for this colinearity,
we performed ascendant hierarchical clustering using the hclustvar function in
R’s ClustOfVar package
31
in each biome-level model. This analysis splits the
variables into different clusters (similar to principal components) in which all
variables correlate with one another. A single best ‘indicator’ variable is then
selected from each cluster, based on squared loading values representing the
correlation with the central synthetic variable of each cluster (that is, the first
principal component of a PCAmix analysis). This set of ‘best’ indicator variables
for each biome was then included in all subsequent models used to estimate
controls on forest tree density.
Using the resulting set of variables, we constructed generalized linear models
with a negative binomial error structure (to account for count data that could not
extend below zero) for each biome (Extended Data Figs 1, 2 and 3) and performed
a multi-model dredging using the dredge function in R’s MuMIn package
32
. This
function constructs all possible candidate sub-models nested within the global
model, identifies the most plausible subset of models for each data set, and then
ranks them according to corrected Akaike Information Criterion (AICc) values
and AIC likelihood weights (AICcw). We derived covariates, coefficients, and
variance-covariance matrices for biome-level models through weighted model
averaging the dredged model results with cumulative AIC weights at least equal to
0.95 (ref. 33). Given the inherent sampling bias present in our plot data (tree
density estimates were only collected in forested ecosystems and non-forested
regions are under-represented), our modelling approach was used to generate
predictive estimates of forest tree density, and these estimates were subsequently
scaled based on the total area of forested land in each pixel (see spatial modelling
for details).
Model validation and testing. We assessed the model fit by investigating the
bias and precision present when predicting mean tree density across an
aggregatenumberofplots.Thisapproachallowedustotesthowmany
plots are required to ensure that the predicted mea n (or total) forest density
has reasonable bias and precision. 20% of the p lots within each biome were
randomly omitted before model fitting to serve as an independent data set for
model testing. Initial model validation was conducted using the biome-spe-
cific regression models (obtained from the remaining 80% of t he data ) to
predict the tree density for each omitted plot. Th e mean p redicted tree den-
sity of the omitted data was then regre ssed a gainst the mean observed tree
density of the omit ted data f or each bi ome (Fig. 2). In addition, a bootstrap-
ping algorithm was used to quantify the standard deviation of the mean
prediction as a f unction of sample size following ref. 34. For eac h biome,
we generated empirica l bootstrap estimates of the standard deviation of the
predicted mea n using random samples drawn from the withheld validation
plots. Specifically, f or each bi ome a bootstra p sample of size n was selected,
with re placement, from the omitted data in that biome. The fitted regression
model for that biome (based on th e 80% retained data) was used to predict th e
tree density of each point, and the mean of the n samples was calculated. This
process was repeate d 10,000 times for each sample size (n 5 10, 20, …, 500)
and in each case the empirical s tandard deviation of the 10,000 sample mean
was calculated and plotte d (Fig. 2). Where the number of plot records in a
biome fell below the sample size threshold identifi ed through bootstrapping,
we used models from the most similar biome available (in terms of phylo-
genetic relatedne ss of the dominant tree species and mean tree d ensity from
the few plot values collected). This was the case for the two smallest biomes:
‘mangroves’ (0.23% of land surface) a nd ‘tropical coniferous’ (0.46% of land
surface) forests, which used models from ‘ tropical moist’ and ‘temperate
coniferous’, respectively.
Spatial modelling. Following model averaging and bootstrapping, we applied the
final negative binomial regression equations used in bootstrapping to pixel-level
spatial data at the biome level. Regressions were run in a map algebra framework
wherein equation intercepts and coefficients were applied independently to each
pixel of our coregistered global covariates to produce a single map of forest tree
density on a per-hectare scale. We then scaled our per-hectare forest density
estimates to the 1-km
2
scale based on the total area of forested land within each
pixel, as estimated by the global 1-km consensus land cover data set for 2014
(ref. 6). This process was then validated using an older (2013) data set that used
fine-scale (30 m) forest cover information
3
, which revealed equivalent total tree
counts. By multiplying our predicted forest density by the area of forest, we
ensured that we did not overestimate tree densities in non-forested sites. From
the resulting maps, summary statistics (mean tree density, total tree number)
were derived for each polygonal area of interest. The variances of the global and
biome-specific totals were calculated using a Taylor series approximation to
account for the log-link negative binomial regression function and correlation
among the regression-based predicted values
35
.
By generating models at the biome-level, we were able to account for broad-
scale differences in vegetation types between biomes, while maintaining high
precision of our mean (and total) estimates at the global scale (due to the high
RESEARCH ARTICLE
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2015 Macmillan Publishers Limited. All rights reserved
number of plot measurements within biomes). However, biome-level models are
limited in their accuracy when predicting tree density at fine-scales, which might
ultimately have the potential to alter final numbers. We therefore constructed
models within each of 813 global ecoregions (delineated by the Nature
Conservancy http://www.nature.org) as a validation for the first biome-level
approach. We generated models and estimated tree numbers using exactly the
same approach as for the biome-level models. Total, and biome-level, tree esti-
mates did not differ significantly (P , 0.05) from those generated using the
biome-level models (Extended Data Fig. 4).
27. Lewis, S. L. et al. Above-ground biomass and structure of 260 African tropical
forests. Phil. Trans. R. Soc. Lond. B 368, 20120295 (2013).
28. Brus, D. J. et al. Statistical mapping of tree species over Europe. Eur. J. For. Res. 131,
145–157 (2011).
29. USDA Forest Service. Forest Inventory and Analysis National Program http://
fia.fs.fed.us/ (2010).
30. Steinwand, R. S., Hutchinson, J. A. & Snyder, J. P. Map projections for global and
continental data sets and an analysis of pixel distortion caused by reprojection.
Photogramm. Eng. Remote Sensing 61, 1487–1499 (1995).
31. Chavent, M., Kuentz, V., Liquet, B. & Saracco, J. ClustOfVar: an R package for the
clustering of variables. J. Stat. Softw. 50, 1–16, http://www.jstatsoft.org/v50/i13/
(2012).
32. Barton
´
, K. MuMIn: Model selection and model averaging based on information
criteria (AICc and alike). (https://cran.r-project.org/web/packages/MuMIn/
index.html) (2015).
33. MacKenzie, D. I. et al. Occupancy Estimation and Modeling (Academic Press, 2005).
34. MacLean, M. G. et al. Requirements for labelling forest polygons in an object-based
image analysis classification. Int. J. Remote Sens. 34, 2531–2547 (2013).
35. Sta
˚
hl, G. et al. Model-based inference for biomass estimation in a LiDAR sample
survey in Hedmark County, Norway. Can. J. For. Res. 41, 96–107 (2011).
36. Tuanmu, M.-N. & Jetz, W. A global, remote sensing-based characterization of
terrestrial habitat heterogeneity for biodiversity and ecosystem modelling. Glob.
Ecol. Biogeogr. http://dx.doi.org/10.1111/geb.12365 (2015).
ARTICLE RESEARCH
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2015 Macmillan Publishers Limited. All rights reserved
Extended Data Figure 1
|
Histogram of the collected measurements of forest tree density in each biome around the world (
n 5
429,775). The red line and the
blue dotted lines indicate the mean and median for the collected data, respectively. Data in each biome fitted a negative binomial error structure.
RESEARCH ARTICLE
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2015 Macmillan Publishers Limited. All rights reserved
Extended Data Figure 2
|
Histogram of the predicted forest tree density
values for the locations that density measurements were collected in each
biome around the world (
n 5
429,775). The red line and the blue dotted lines
indicate the mean and median for the collected data, respectively. As our
models were based on mean values, the majority of points fall on or close to the
mean values in each biome.
ARTICLE RESEARCH
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Extended Data Figure 3
|
Histogram of the total predicted forest tree
density values for each pixel within each biome around the world
(
n
5 429,775). This illustrates the spread of pixels throughout each biome, and
highlights that our map accounts for the sampling bias in tree density plots
(for example, although we had no zero values in our desert plots, the vast
majority of desert pixels contain no trees).
RESEARCH ARTICLE
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2015 Macmillan Publishers Limited. All rights reserved
Extended Data Figure 4
|
Comparison between approaches to generate
the global tree density map. The initial map was generated using 14 biome-
level models (biomes delineated by The Nature Conservancy http://
www.nature.org) to account for broad-scale variations in terrestrial vegetation
types. With several thousand plot-level density measurements in most
biomes, this approach provided highly accurate estimates at the global scale.
However, to improve precision at the local scale, we also generated a map using
ecoregion-scale models. Separate models were generated within each of 813
global ecoregions (also delineated by The Nature Conservancy to reflect
smaller-scale vegetation types) using exactly the same statistical approach (see
Methods). The same 429,775 data points were used to construct each map.
Biome-level and ecoregion-level maps provide total tree estimates of 3.041 and
3.253 trillion trees, respectively.
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Extended Data Table 1
|
Estimates of the total tree number for each of the biomes that contain forested land, as delineated by The Nature
Conservancy (http://www.nature.org)
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