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\begin{document}

\title{Positive biodiversity-productivity relationship predominant in global
forests\\}


 \author{}



\date{}

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Jingjing~ Liang\textsuperscript{1}*, Thomas W.
Crowther\textsuperscript{2}, Nicolas Picard\textsuperscript{3}, Susan
Wiser\textsuperscript{4}, Mo Zhou\textsuperscript{1}, Giorgio
Alberti\textsuperscript{5}, Ernst-Detlef Schulze\textsuperscript{6}, A.
David McGuire\textsuperscript{7}, Fabio Bozzato\textsuperscript{8}, Hans
Pretzsch\textsuperscript{9}, Sergio de-Miguel\textsuperscript{10,11},
Alain Paquette\textsuperscript{12}, Bruno H\selectlanguage{ngerman}érault\textsuperscript{13},
Michael Scherer-Lorenzen\textsuperscript{14}, Christopher B.
Barrett\textsuperscript{15}, Henry B. Glick\textsuperscript{16}, Geerten
M. Hengeveld\textsuperscript{17,17.5}, Gert-Jan
Nabuurs\textsuperscript{17,17.6}, Sebastian
Pfautsch\textsuperscript{18}, Helder Viana\textsuperscript{19,20},
Alexander C. Vibrans\textsuperscript{21}, Christian
Ammer\textsuperscript{22}, Peter Schall\textsuperscript{22}, David
Verbyla\textsuperscript{23}, Nadja Tchebakova\textsuperscript{24},
Markus Fischer\textsuperscript{25,26}, James V.
Watson\textsuperscript{1}, Han Y.H. Chen\textsuperscript{27}, Xiangdong~
Lei\textsuperscript{28}, Mart-Jan Schelhaas\textsuperscript{17}, Huicui
Lu\textsuperscript{29}, Damiano Gianelle\textsuperscript{30,31}, Elena
I. Parfenova\textsuperscript{24}, Christian Salas\textsuperscript{32},
Eungul Lee\textsuperscript{33}, Boknam Lee\textsuperscript{34}, Hyun
Seok Kim\textsuperscript{34,35,36,37}, Helge
Bruelheide\textsuperscript{38,39}, David A. Coomes\textsuperscript{40},
Daniel Piotto\textsuperscript{41}, Terry
Sunderland\textsuperscript{42,43}, Bernhard Schmid\textsuperscript{44},
Sylvie Gourlet-Fleury\textsuperscript{45}, Bonaventure
Sonké\textsuperscript{46}, Rebecca Tavani\textsuperscript{47}, Jun
Zhu\textsuperscript{48,49}, Susanne Brandl\textsuperscript{9,49.5},
Jordi Vayreda\textsuperscript{50,51}, Fumiaki
Kitahara\textsuperscript{52}, Eric B. Searle\textsuperscript{27}, Victor
J. Neldner\textsuperscript{53}, Michael R. Ngugi\textsuperscript{53},
Christopher Baraloto\textsuperscript{54}, Lorenzo
Frizzera\textsuperscript{30}, Radomir Ba\selectlanguage{polish}ł\selectlanguage{english}azy\textsuperscript{55}, Jacek
Oleksyn\textsuperscript{56}, Tomasz
Zawi\selectlanguage{polish}ł\selectlanguage{english}a-Nied\selectlanguage{polish}ź\selectlanguage{english}wiecki\textsuperscript{57}, Olivier
Bouriaud\textsuperscript{58,58.5}, Filippo Bussotti\textsuperscript{59},
Leena Fin\selectlanguage{ngerman}ér\textsuperscript{60}, Bogdan Jaroszewicz\textsuperscript{61},
Tommaso Jucker\textsuperscript{40}, Fernando
Valladares\textsuperscript{62}, Andrzej M.
Jagodzinski\textsuperscript{56,63}, Pablo L.
Peri\textsuperscript{64,65,66}, Christelle
Gonmadje\textsuperscript{46,67},William Marthy\textsuperscript{68},
Timothy O'Brien\textsuperscript{68}, Emanuel H.
Martin\textsuperscript{69}, Andrew R. Marshall\textsuperscript{70,70.5},
Francesco Rovero\textsuperscript{71}, Robert~
Bitariho\textsuperscript{72}, Pascal A. Niklaus\textsuperscript{73,74},
Patricia Alvarez-Loayza\textsuperscript{75}, Nurdin
Chamuya\textsuperscript{76}, Renato Valencia\textsuperscript{77},
Frédéric Mortier\textsuperscript{78}, Verginia
Wortel\textsuperscript{79}, Nestor L. Engone-Obiang\textsuperscript{80},
Leandro V. Ferreira\textsuperscript{81}, David E.
Odeke\textsuperscript{82}, Rodolfo M. Vasquez\textsuperscript{83}, Simon
L. Lewis\textsuperscript{84,85}, Peter B. Reich\textsuperscript{18,86}\\

\textbf{Affiliations:}\\

\textsuperscript{1}School of Natural Resources, West Virginia
University, Morgantown, WV 26505, USA.\\

\textsuperscript{2}Netherlands Institute of Ecology, 6700 AB~Wageningen,
the Netherlands.\\

\textsuperscript{3}Forestry Department, Food and Agriculture
Organization of the United Nations, Rome, Italy.\\

\textsuperscript{4}Landcare Research, Lincoln 7640, New Zealand.\\

\textsuperscript{5}Department of Agri-Food, Environmental and Animal
Sciences, University of Udine via delle Scienze 206, Udine 33100,
Italy.\\

\textsuperscript{6}Max-Planck Institut f\selectlanguage{ngerman}ür Biogeochemie,
Hans-Knoell-Strasse 10, 07745 Jena, Germany.\\

\textsuperscript{7}U.S. Geological Survey, Alaska Cooperative Fish and
Wildlife Research Unit, University of Alaska Fairbanks, Fairbanks, AK
99775 USA.\\

\textsuperscript{8}Architecture \& Environment Dept., Italcementi Group,
24100 Bergamo, Italy.\\

\textsuperscript{9}Chair for Forest Growth and Yield Science, TUM School
of Life Sciences Weihenstephan, Technical University of Munich,\\

Hans-Carl-von-Carlowitz-Platz 2, 85354 Freising, Germany.\\

\textsuperscript{10}Departament de Producci\selectlanguage{ngerman}ó Vegetal i Ciència Forestal,
Universitat de Lleida-Agrotecnio Center (UdL-Agrotecnio), Av. Rovira
Roure, 191, E-25198 Lleida, Spain.\\

\textsuperscript{11}Centre Tecnol\selectlanguage{ngerman}ògic Forestal de Catalunya (CTFC),
Ctra. De St. Llorenç de Morunys, km. 2. E-25280 Solsona, Spain.\\

\textsuperscript{12}Centre d'\selectlanguage{ngerman}étude de la forêt (CEF), Université du
Québec à Montréal, Montréal, QC H3C 3P8, Canada.\\

\textsuperscript{13}Cirad, UMR EcoFoG (AgroParisTech, CNRS, INRA,
Universit\selectlanguage{ngerman}é des Antilles, Université de la Guyane), Kourou, French
Guiana.\\

\textsuperscript{14}University of Freiburg, Faculty of Biology,
Geobotany, D-79104 Freiburg, Germany.\\

\textsuperscript{15}CH Dyson School of Applied Economics and Management,
Cornell University, Ithaca, NY 14853 USA.\\

\textsuperscript{16}Yale School of Forestry and Environmental Studies,
New Haven, CT 06511, USA.\\

\textsuperscript{17}Team Vegetation, Forest \& Landscape Ecology,
Alterra -- 6700 AA Wageningen UR, Netherlands.~~\\

\textsuperscript{17.5}Forest and Nature Conservation Policy group,
Wageningen University, 6700 AA Wageningen UR, Netherlands.~~\\

\textsuperscript{17.6}Forest Ecology and Management group, Wageningen
University, 6700 AA Wageningen UR, Netherlands.~~\\

\textsuperscript{18}Hawkesbury Institute for the Environment, Western
Sydney University, Richmond NSW 2753, Australia.\\

\textsuperscript{19}CI\&DETS Research Centre / DEAS-ESAV, Polytechnic
Institute of Viseu, Portugal.\\

\textsuperscript{20}Centre for the Research and Technology of
Agro-Environmental and Biological Sciences, CITAB, University of
Tr\selectlanguage{ngerman}ás-os-Montes and Alto Douro, UTAD, Quinta de Prados, 5000-801 Vila
Real, Portugal.\\

\textsuperscript{21}Departamento de Engenharia Florestal, Universidade
Regional de Blumenau, Rua S\selectlanguage{ngerman}ão Paulo, 3250, 89030-000 Blumenau-Santa
Catarina, Brazil.\\

\textsuperscript{22}Department of Silviculture and Forest Ecology of the
Temperate Zones, Georg-August University G\selectlanguage{ngerman}öttingen, Büsgenweg 1, D-37077
Göttingen, Germany.\\

\textsuperscript{23}School of Natural Resources and Extension,
University of Alaska Fairbanks, Fairbanks, AK 99709, USA.\\

\textsuperscript{24}V.N. Sukachev Institute of Forests, Siberian Branch,
Russian Academy of Sciences, Academgorodok, 50/28, 660036 Krasnoyarsk,
Russia.\\

\textsuperscript{25}Institute of Plant Sciences, Botanical Garden, and
Oeschger Centre for Climate Change Research, University of Bern, 3013
Bern, Switzerland.\\

\textsuperscript{26}Senckenberg Gesellschaft f\selectlanguage{ngerman}ür Naturforschung,
Biodiversity and Climate Research Centre (BIK-F), 60325 Frankfurt,
Germany.\\

\textsuperscript{27}Faculty of Natural Resources Management, Lakehead
University, Thunder Bay, ON P7B 5E1 Canada.\\

\textsuperscript{28}Research Institute of Forest Resource Information
Techniques, Chinese Academy of Forestry, Beijing 100091, China.\\

\textsuperscript{29}Forest Ecology and Forest Management Group,
Wageningen University, Netherlands.\\

\textsuperscript{30}Sustainable Agro-Ecosystems and Bioresources
Department, Research and Innovation Centre - Fondazione Edmund, Mach,
Via E. Mach 1, 38010 - S. Michele all'Adige (TN), Italy.\\

\textsuperscript{31}Foxlab Joint CNR-FEM Initiative, Via E. Mach 1,
38010 - S.Michele ~all'Adige; Adige (TN), Italy.\\

\textsuperscript{32}Departamento de Ciencias Forestales, Universidad de
La Frontera, Temuco, Chile.\\

\textsuperscript{33}Department of Geology and Geography, West Virginia
University, Morgantown, WV 26505, USA.\\

\textsuperscript{34}Research Institute of Agriculture and Life Sciences,
Seoul National University, Seoul, Republic of Korea.\\

\textsuperscript{35}Department of Forest Sciences, Seoul National
University, Seoul 151-921, Republic of Korea.\\

\textsuperscript{36}Interdisciplinary Program in Agricultural and Forest
Meteorology, Seoul National University, Seoul 151-744, Republic of
Korea.\\

\textsuperscript{37}National Center for AgroMeteorology, Seoul National
University, Seoul 151-744, Republic of Korea.\\

\textsuperscript{38}Institute of Biology / Geobotany and Botanical
Garden, Martin Luther University Halle-Wittenberg, Am Kirchtor 1, 06108
Halle (Saale), Germany.\\

\textsuperscript{39}German Centre for Integrative Biodiversity Research
(iDiv) Halle-Jena-Leipzig, Deutscher Platz 5e, 04103 Leipzig, Germany.\\

\textsuperscript{40}Forest Ecology and Conservation, Department of Plant
Sciences, University of Cambridge, Cambridge CB2 3EA, UK.\\

\textsuperscript{41}Universidade Federal do Sul da Bahia, Ferradas,
Itabuna 45613-204, Brazil.\\

\textsuperscript{42}Sustainable Landscapes and Food Systems, Centre for
International Forestry Research, Bogor, Indonesia.\\

\textsuperscript{43}School of Marine and Environmental Studies, James
Cook University, Australia.\\

\textsuperscript{44}Department of Evolutionary Biology and Environmental
Studies, University of Zurich, CH-8057 Zurich, Switzerland.\\

\textsuperscript{45}D\selectlanguage{ngerman}épartement Environnements et Sociétés du CIRAD,
34398 Montpellier Cedex 5, France.\\

\textsuperscript{46}Plant Systematic and Ecology Laboratory, Department
of Biology, Higher Teachers' Training College, University of Yaounde I,
P.O. Box 047 Yaounde Cameroon.\\

\textsuperscript{47}Forestry Department, Food and Agriculture
Organization of the United Nations, Rome 00153, Italy.\\

\textsuperscript{48}Department of Statistics, University of
Wisconsin-Madison, Madison, WI 53706 USA.\\

\textsuperscript{49}Department of Entomology, University of
Wisconsin-Madison, Madison, WI 53706 USA.\\

\textsuperscript{49.5}Bavarian State Institute of Forestry,
Hans-Carl-von-Carlowitz-Platz 1, Freising 85354, Germany.\\

\textsuperscript{50}Center for Ecological Research and Forestry
Applications(CREAF), Cerdanyola del Vall\selectlanguage{ngerman}ès 08193, Spain.\\

\textsuperscript{51}Univ Aut\selectlanguage{ngerman}ònoma Barcelona, Cerdanyola del Vallés
08193, Spain.\\

\textsuperscript{52}Shikoku Research Center, Forestry and Forest
Products Research Institute, Kochi 780-8077, Japan.\\

\textsuperscript{53}Ecological Sciences Unit at Queensland Herbarium,
Department of Science, Information Technology and Innovation, Queensland
government, Toowong, Qld, 4066, Australia.\\

\textsuperscript{54}International Center for Tropical Botany, Department
of Biological Sciences, Florida International University, Miami, FL
33199, USA.\\

\textsuperscript{55}Forest Research Institute, Sekocin Stary Braci
Lesnej 3 Street, 05-090 Raszyn, Poland.\\

\textsuperscript{56}Institute of Dendrology of the Polish Academy of
Sciences, Parkowa 5, PL-62-035 Kornik, Poland.\\

\textsuperscript{57}Warsaw University of Life Sciences (SGGW), Faculty
of Forestry, ul. Nowoursynowska 159, 02-776 Warszawa, Poland.\\

\textsuperscript{58}Forestry Faculty, University Stefan Cel Mare of
Suceava, 13 Strada Universita\selectlanguage{romanian}ții,720229 Suceava, Romania.\\

\textsuperscript{58.5}Institutul Na\selectlanguage{polish}ţ\selectlanguage{english}ional de Cercetare-Dezvoltare \selectlanguage{ngerman}în
Silvicultur\selectlanguage{polish}ă, \selectlanguage{english}128 Bd Eroilor, 077190 Voluntari, Romania.\\

\textsuperscript{59}Department of Agri-Food Production and Environmental
Science, University of Florence, P.le Cascine 28, 51044 Florence,
Italy.\\

\textsuperscript{60}Natural Resources Institute Finland, 80101 Joensuu,
Finland.\\

\textsuperscript{61}Bia\selectlanguage{polish}ł\selectlanguage{english}owie\selectlanguage{polish}ż\selectlanguage{english}a Geobotanical Station, Faculty of Biology,
University of Warsaw, Sportowa 19, 17-230 Bia\selectlanguage{polish}ł\selectlanguage{english}owie\selectlanguage{polish}ż\selectlanguage{english}a, Poland.\\

\textsuperscript{62}Museo Nacional de Ciencias Naturales, CSIC Serrano
115 dpdo, E-28006 Madrid, Spain.\\

\textsuperscript{63}Poznan University of Life Sciences, Department of
Game Management and Forest Protection, Wojska Polskiego 71c, PL-60-625
Poznan, Poland.\\

\textsuperscript{64}Consejo Nacional de Investigaciones Cient\selectlanguage{ngerman}íficas y
Tecnicas (CONICET), Rivadavia 1917 (1033) Ciudad de Buenos Aires, Buenos
Aires, Argentina.\\

\textsuperscript{65}INTA EEA Santa Cruz, Mahatma Ghandi 1322 (9400) R\selectlanguage{ngerman}ío
Gallegos, Santa Cruz, Argentina.\\

\textsuperscript{66}Universidad Nacional de la Patagonia Austral (UNPA),
Lisandro de la Torre 1070 (9400) R\selectlanguage{ngerman}ío Gallegos, Santa Cruz, Argentina.\\

\textsuperscript{67}National Herbarium, P.O BOX 1601, Yaound\selectlanguage{ngerman}é,
Cameroon.\\

\textsuperscript{68}Wildlife Conservation Society, Bronx NY 10460,
USA.\\

\textsuperscript{69}College of African Wildlife Management, Department
of Wildlife Management, P.O. Box 3031, Moshi, Tanzania.\\

\textsuperscript{70}Environment Department, University of York,
Heslington, York, YO10 5NG, UK.\\

\textsuperscript{70.5}Flamingo Land Ltd., Malton, North Yorkshire, YO10
6UX.\\

\textsuperscript{71}Tropical Biodiversity Section, MUSE-Museo delle
Scienze, Trento, Italy.\\

\textsuperscript{72}Institute of Tropical Forest Conservation, Kabale,
Uganda.\\

\textsuperscript{73}Department of Evolutionary Biology an Environmental
Studies, University of Zurich, Zurich, Switzerland.\\

\textsuperscript{75}Center for Tropical Conservation, Durham, NC 27705,
USA.\\

\textsuperscript{76}Ministry of Natural resources and Tourism, Forestry
and Beekeeping Division, Dar es Salaam, Tanzania.\\

\textsuperscript{77}Escuela de Ciencias Biol\selectlanguage{ngerman}ógicas, Pontificia
Universidad Católica del Ecuador, Aptdo. 1701-2184, Quito, Ecuador.\\

\textsuperscript{78}CIRAD,UPR Bsef, Montpellier, 34398, France.\\

\textsuperscript{79}~Forest Management Department, CELOS, Paramaribo,
Suriname\\

\textsuperscript{80}Institut de Recherche Ecologie Tropicale
(IRET/CENAREST), B.P. 13354, Libreville, Gabon\\

\textsuperscript{81}Museu Paraense Emilio Goeldi, Coordenacao de
Botanica, Belem, PA, Brasil.\\

\textsuperscript{82}National Forest Authority, Kampala, Uganda.\\

\textsuperscript{83}Prog. Bolognesi Mz-E-6, Oxapampa Pasco, Peru.\\

\textsuperscript{84}Department of Geography, University College London,
United Kingdom.\\

\textsuperscript{85}School of Geography, University of Leeds, United
Kingdom.\\

\textsuperscript{86}Department of Forest Resources, University of
Minnesota, St. Paul, MN 55108, USA.\\

*Correspondence to:~
\href{mailto:albeca.liang@gmail.com}{\nolinkurl{albeca.liang@gmail.com}}.\\

\subsection*{Acknowledgments}\label{acknowledgments}

We are grateful to all the people and agencies that helped in collection
and compilation of the field data, including but not limited to T.
Malone, J. Crowe, M. Sutton, J. Lovett, P. Munishi, R. Miina, staff
members from Seoul National University Forest, and all persons who made
the two Spanish Forest Inventories possible especially the main
coordinators, R. Villaescusa (IFN2) and J.A. Villanueva (IFN3). This
work was supported in parts by West Virginia University under the USDA
McIntire-Stennis Funds WVA00104 and WVA00105; the Architecture and
Environment Department of Italcementi Group, Bergamo (Italy); a~Marie
Sk\selectlanguage{polish}ł\selectlanguage{english}odowska Curie fellowship; Polish National Science Center Grant
2011/02/A/NZ9/00108, the French ANR (CEBA: ANR-10-LABX-0025) and the
General Directory of State Forest National Holding DB; General
Directorate of State Forests, Warsaw, Poland; the 12th Five-Year Science
and Technology Support Project (Grant No. 2012BAD22B02) of China; the
U.S. Geological Survey and the Bonanza Creek Long Term Ecological
Research Program funded by the National Science Foundation and the U.S.
Forest Service (any use of trade, firm, or product names is for
descriptive purposes only and does not imply endorsement by the U.S.
Government); National Research Foundation of Korea
(NRF-2015R1C1A1A02037721), Korea Forest Service (S111215L020110,
S211315L020120 and S111415L080120) and Promising-Pioneering Researcher
Program through Seoul National University (SNU) in 2015; Core funding
for Crown Research Institutes from the New Zealand Ministry of Business,
Innovation and Employment's Science and Innovation Group; the DFG
Priority Program 1374 Biodiversity Exploratories; Chilean research
grants FONDECYT No. 1151495 and 11110270; Natural Sciences and
Engineering Research Council of Canada (RGPIN-2014-04181); Brazilian
Research grants CNPq 312075/2013 and FAPESC 2013/TR441 supporting Santa
Catarina State Forest Inventory (IFFSC); General Directorate of State
Forests, Warsaw, Poland; Bavarian State Ministry for Nutrition,
Agriculture, and Forestry project W07; Bavarian State Forest Enterprise
(Bayerische Staatsforsten A\selectlanguage{ngerman}öR); German Science Foundation for project PR
292/12-1; European Union for funding the COST Action FP1206 EuMIXFOR;
FEDER/COMPETE/POCI under Project POCI-01-0145-FEDER-006958 and FCT -
Portuguese Foundation for Science and Technology under the project
UID/AGR/04033/2013; Swiss National Science Foundation Grant
310030B\_147092; and the European Union's Horizon 2020 research and
innovation programme within the framework of the MultiFUNGtionality
Marie Sk\selectlanguage{polish}ł\selectlanguage{english}odowska-Curie Individual Fellowship (IF-EF) under grant
agreement No 655815.

\par\null

We thank the following agencies and organization for providing the data:
the Minist\selectlanguage{ngerman}ère des Forêts, de la Faune et des Parcs du Québec (Canada);
the Alberta Department of Agriculture and Forestry, the Saskatchewan
Ministry of the Environment, and Manitoba Conservation and Water
Stewardship (Canada); the LUCAS programme for the Ministry the
Environment (NZ); Italian and Friuli Venezia Giulia Forest Services; the
Thünen Institute of Forest Ecosystems (Germany); Bavarian State Forest
Enterprise (Bayerische Staatsforsten AöR); Queensland Herbarium
(Australia); Forestry Commission of New South Wales (Australia);
Instituto de Conservação da Natureza e das Florestas (Portugal). All
TEAM data were provided by the Tropical Ecology Assessment and
Monitoring (TEAM) Network, a collaboration between Conservation
International, the Smithsonian Institute and the Wildlife Conservation
Society, and partially funded by these institutions, the Gordon and
Betty Moore Foundation, and other donors; The Exploratory plots of
FunDivEUROPE received funding from the European Union Seventh Framework
Programme (FP7/2007-2013) under grant agreement no. 265171. The Chinese
Comparative Study Plots (CSPs) were established in the framework of
BEF-China, funded by the German Research Foundation (DFG FOR891); Data
collection in Middle Eastern countries was supported by the Spanish
Agency for International Development Cooperation (Agencia Española de
Cooperación Internacional para el Desarrollo, AECID) and Fundación
Biodiversidad, in cooperation with the governments of Syria and Lebanon.

\par\null

Finally, we would like to extend our thanks to the editor and two
reviewers who provided constructive and helpful comments to help us
further improve this paper.

\par\null\par\null\par\null\par\null\par\null

\section*{}\label{section}

\section*{Abstract}\label{abstract}

The biodiversity--productivity relationship (BPR) is foundational to our
understanding of the global extinction crisis and its impacts on
ecosystem functioning. Understanding BPR is critical for the accurate
valuation and effective conservation of biodiversity. Using
ground-sourced data from 777,126 permanent plots, comprising over thirty
million trees from 8,737 species and spanning 44 countries and most
terrestrial biomes, we reveal a globally consistent \emph{positive
concave-down} BPR, whereby biodiversity loss would correspond to an
accelerating decline in forest productivity. On average, a 10\%
reduction in tree species richness would result in a 2.1--3.1\% decrease
in productivity worldwide, and the rate of this decline would increase
exponentially with further reduction of biodiversity. We estimate the
economic value of biodiversity in maintaining global forest productivity
to be US\$396--579 billion per year, and the total global value of
biodiversity would far exceed this estimation. This highlights the need
for a worldwide re-assessment of biodiversity values, forest management
strategies, and conservation priorities.\\



\section*{Introduction}\label{introduction}

The biodiversity--productivity relationship (BPR) has been a major
ecological focus over recent decades. The need to understand this
relationship is becoming increasingly urgent in light of the global
extinction crisis, as species loss affects the functioning and services
of natural ecosystems(\emph{\protect\hyperlink{_ENREF_1_1}{1},
\protect\hyperlink{_ENREF_1_2}{2}}). Alarmed by an emerging body of
evidence which suggests that the productivity and functioning of natural
ecosystems may be significantly impaired by the loss of biodiversity
(\emph{\protect\hyperlink{_ENREF_1_3}{3-10}}), international society has
made substantial efforts to strengthen the conservation and sustainable
use of biodiversity(\emph{\protect\hyperlink{_ENREF_1_2}{2},
\protect\hyperlink{_ENREF_1_11}{11}}). Successful international
collaboration, however, requires a systematic assessment of the value of
biodiversity(\emph{\protect\hyperlink{_ENREF_1_11}{11}}), and
quantification of BPR at a global scale is thus urgently needed to
facilitate the accurate valuation of
biodiversity(\emph{\protect\hyperlink{_ENREF_1_12}{12}}) and accurate
forecast of future changes in ecosystem services
worldwide(\emph{\protect\hyperlink{_ENREF_1_11}{11}}), and to underpin
the integration of biological conservation into international
socio-economic development
strategies(\emph{\protect\hyperlink{_ENREF_1_13}{13}}).\\

The evidence of a positive BPR stems primarily from studies of
herbaceous plant
communities(\emph{\protect\hyperlink{_ENREF_1_14}{14}}). In contrast,
the forest BPR has only been explored at regional scales(see
\emph{\protect\hyperlink{_ENREF_1_3}{3},
\protect\hyperlink{_ENREF_1_7}{7}, \protect\hyperlink{_ENREF_1_15}{15,
and references therein}}) and remains unclear at the global scale.
Forests are the most important global repositories of terrestrial
biodiversity(\emph{\protect\hyperlink{_ENREF_1_16}{16}}), but
deforestation and climate change are threatening a considerable
proportion of tree species
worldwide(\emph{\protect\hyperlink{_ENREF_1_17}{17},
\protect\hyperlink{_ENREF_1_18}{18}}), and the consequences of this
diversity loss pose a critical uncertainty for ongoing international
forest management and conservation efforts. However, forest management
that converts monocultures to mixed-species stands across Europe has
seen a considerably positive effect on productivity(e.g.
\emph{\protect\hyperlink{_ENREF_1_19}{19},
\protect\hyperlink{_ENREF_1_20}{20}}), highlighting the potential of
forest management in strengthening the conservation and sustainable use
of biodiversity worldwide.\\

Here, we compiled \emph{in situ} remeasurement data (i.e. data taken at
two consecutive inventories from the same localities) from 777,126
permanent sample plots (hereafter, global forest biodiversity or GFB
plots) across 44 countries/territories and 13 ecoregions to explore the
forest BPR at a global scale (Fig.1). GFB plots encompass forests of
various origins (from naturally regenerated to planted) and successional
stages (from stand initiation to old-growth). A total of over thirty
million trees across 8,737 species were tallied and measured on two or
more consecutive inventories from the GFB plots. Sampling intensity was
greater in developed countries, where nationwide forest inventories have
been fully or partially funded by governments. In most other countries,
national forest inventories were lacking and most ground-sourced data
were collected by individuals and organizations (Table S1).\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Fig.2/Fig.2}
\caption{\selectlanguage{ngerman}{\textbf{Fig.1. Global forest biodiversity (GFB) ground-sourced data were
collected from \emph{in situ} re-measurement of 777,126 permanent sample
plots consisting of over \emph{thirty million} trees across 8,737
species}. GFB plots extend across 13 ecoregions (vertical axis,
\textbf{} delineated by the World Wildlife Fund where extensive forests
occur within all the ecoregions
(\emph{\protect\hyperlink{_ENREF_1_63}{63}})), and 44 countries and
territories. Ecoregions are named for their dominant vegetation types,
but all contain some forested areas. GFB plots cover a significant
portion of the global forest extent (white), including some of the most
unique forest conditions: (\emph{a}) the northernmost (73°N, Central
Siberia, Russia), (\emph{b}) southernmost (52°S, Patagonia, Argentina),
(\emph{c}) coldest (-17°C annual mean temperature, Oimyakon, Russia),
(\emph{d}) warmest (28°C annual mean temperature, Palau, USA) plots, and
(\emph{e}) most diverse (405 tree species on the 1-ha plot, Bahia,
Brazil). Plots in war-torn regions (e.g. \emph{f}) were assigned fuzzed
coordinates to protect the identity of the plots and collaborators. The
box plots show the mean and interquartile range of tree species richness
and primary site productivity (both on a common logarithmic scale)
derived from ground-measured tree- and plot-level records. The complete
list of species was presented in Table S2.%
}}
\end{center}
\end{figure}\selectlanguage{ngerman}

Based on ground-sourced GFB data, we quantified BPR at the global scale
using a data-driven ensemble learning approach (see §Geospatial random
forest in Materials and Methods). Our quantification of BPR involved
characterizing the shape and strength of the dependency function,
through the elasticity of substitution (\selectlanguage{greek}\emph{θ}\selectlanguage{english}), which represents the
degree to which species can substitute for each other in contributing to
stand productivity. \selectlanguage{greek}\emph{θ} \selectlanguage{english}measures the marginal productivity-- the
change in productivity resulting from one unit decline of species
richness, and reflects the strength of the effect of tree diversity on
tree productivity, after accounting for climatic, soil, and plot
specific covariates. A higher \selectlanguage{greek}\emph{θ} \selectlanguage{english}corresponds to a greater decline
in productivity due to one unit loss in biodiversity. The
niche--efficiency (N--E) model(\emph{\protect\hyperlink{_ENREF_1_3}{3}})
and several preceding
studies(\emph{\protect\hyperlink{_ENREF_1_21}{21-24}}) provide a
framework for interpreting the elasticity of substitution \emph{} and
approximating BPR with the Dixit-Stiglitz-Ethier power function. We
characterized the BPR function with the following model:\\

\(P=\alpha\cdot f\left(X\right)\cdot S^{\theta}\)~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~ (1)\\

where \emph{P} and \emph{S} signify primary site productivity (derived
from two consecutive inventories) and tree species richness (observed on
a 400-m\textsuperscript{2} area basis on average, see Materials and
Methods), respectively,~ \emph{f}(\textbf{X}) a function of a vector of
control variables \textbf{X (}selected from stand basal area and 14
climatic, soil, and topographic covariates, see Materials and Methods),
and \selectlanguage{greek}\emph{α} \selectlanguage{english}a constant. This model is capable of representing a variety
of potential patterns of BPR. 0\textless{}\selectlanguage{greek}\emph{θ}\selectlanguage{english}\textless{}1
represents a \emph{positive and concave down} pattern (a degressively
increasing curve) consistent with the N--E model and preceding
studies(\emph{\protect\hyperlink{_ENREF_1_21}{21},
\protect\hyperlink{_ENREF_1_22}{22}}), whereas other \selectlanguage{greek}\emph{θ} \selectlanguage{english}values can
represent alternative BPR patterns, including decreasing or no effect
(\selectlanguage{greek}\emph{θ}\selectlanguage{english}[?]\selectlanguage{english}0)(\emph{\protect\hyperlink{_ENREF_1_25}{e.g. 25}}), and
linear (\selectlanguage{greek}\emph{θ}\selectlanguage{english}=1) or convex
(\selectlanguage{greek}\emph{θ}\selectlanguage{english}\textgreater{}1)(\emph{\protect\hyperlink{_ENREF_1_14}{e.g.
14}}) (Fig.2). The model (Eq.1) was estimated using the geospatial
random forest technique based on GFB data and covariates acquired from
ground-measured and remote sensing data (Materials and Methods).\\\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Fig.3/Fig.3}
\caption{{\textbf{Fig.2. Theoretical positive and concave-down
biodiversity--productivity relationship supported by empirical evidence
drawn from the GFB data. The diagram (left)} demonstrates that under the
theoretical \emph{positive and concave-down} (i.e. monotonically and
degressively increasing) BPR(\emph{\protect\hyperlink{_ENREF_1_3}{3},
\protect\hyperlink{_ENREF_1_21}{21},
\protect\hyperlink{_ENREF_1_22}{22}}), loss in tree species richness may
reduce forest productivity(\emph{\protect\hyperlink{_ENREF_1_64}{64}}).~
\textbf{Functional curves in the center} represent different BPR under
different values of elasticity of substitution (\emph{\selectlanguage{greek}θ}\selectlanguage{english}). \emph{\selectlanguage{greek}θ}
\selectlanguage{english}values between 0 and 1 correspond to the positive and concave-down BPR
(blue curve). \textbf{The 3D scatter plot (right)} shows \emph{\selectlanguage{greek}θ} \selectlanguage{english}values
estimated from observed productivity (\emph{P}), species richness
(\emph{S}), and other covariates. Out of 5,000,000 estimates of \emph{\selectlanguage{greek}θ}
\selectlanguage{english}(mean=0.27, SD=0.09), 4,993,500 fell between 0 and 1 (blue), whereas
only 6500 were negative (red), and none was equal to zero, or was
greater than or equal to 1. In other words, the positive and
concave-down BPR was supported by 99.9\% of our estimates.%
}}
\end{center}
\end{figure}

We found that a positive biodiversity-productivity relationship (BPR)
predominated forests worldwide. Out of 10,000 randomly selected
subsamples (each consisting of 500 GFB plots), 99.87\% had a
\emph{positive concave-down relationship}
(0\textless{}\selectlanguage{greek}\emph{θ}\selectlanguage{english}\textless{}1), whereas only 0.13\% show negative
trends, and none was equal to zero, or was greater than or equal to 1
(Fig.2). Overall, the global forest productivity increased degressively
from 2.7 to 11.8
m\textsuperscript{3}ha\textsuperscript{-1}yr\textsuperscript{-1} as tree
species richness increased from the minimum to the maximum value, which
corresponds to a \selectlanguage{greek}\emph{θ} \selectlanguage{english}value of 0.26 (Fig.3A).~\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Fig.4/Fig.4}
\caption{\selectlanguage{polish}{Fig.3. Estimated global effect of biodiversity on forest productivity
was \emph{positive and concave-down} (A) and had considerable geospatial
variation across forest ecosystems worldwide(B). (A) Global effect of
biodiversity on forest productivity (red line with pink bands
representing 95 percent confidence interval) corresponds to a global
average elasticity of substitution (\emph{\selectlanguage{greek}θ}\selectlanguage{english}) value of 0.26, with
climatic, soil, and other plot covariates being accounted for and kept
constant at sample mean. Relative species richness (\emph{Š}) is in the
horizontal axis, and productivity (\emph{P},
m\textsuperscript{3}ha\textsuperscript{-1}yr\textsuperscript{-1}) in the
vertical axis (histograms of the two variables on top and right in the
logarithm scale). (B) \emph{\selectlanguage{greek}θ} \selectlanguage{english}represents the strength of the effect of
tree diversity on tree productivity. Spatially explicit values of
\emph{\selectlanguage{greek}θ} \selectlanguage{english}were estimated using universal kriging (see Materials and
Methods) across the current global forest extent (effect sizes of the
estimates were shown in Fig.5), whereas blank terrestrial areas were
non-forested.%
}\selectlanguage{english}}
\end{center}
\end{figure}

At the global-scale, we mapped the magnitude of BPR (as expressed by
\selectlanguage{greek}\emph{θ}\selectlanguage{english}) using geospatial random forest and universal kriging. Plotting
values of \selectlanguage{greek}\emph{θ}\selectlanguage{english}~onto a global map shows considerable geospatial
variation across the world (Fig.3B). The highest elasticity of
substitution (0.29--0.30) occurred in the boreal and temperate forests
in North America, Europe, and Asia, Mediterranean forests, and tropical
and subtropical forests in Southcentral Africa, Southeastern China, and
the Oceania region. In these areas of the highest elasticity of
substitution(\emph{\protect\hyperlink{_ENREF_1_26}{26}}), the same
percentage biodiversity loss would lead to greater percentage reduction
in forest productivity (Fig.4A). In terms of absolute productivity, the
same percentage biodiversity loss would lead to the greatest
productivity decline in equatorial regions, Southern China, Northern
India, Japan, Southeastern Australia, Central Europe, Mediterranean
region, and Southern United States (Fig.4B). Due to a rather narrow
range of the elasticity of
substitution(\emph{\protect\hyperlink{_ENREF_1_26}{26}}) estimated from
the global-level analysis (0.2--0.3), the regions of the greatest
productivity decline under the same percentage biodiversity loss largely
matched the regions of the greatest current productivity (Fig.S1).
Globally, a 10 percent decrease of tree species richness (from 100\% to
90\%) would cause a 2--3 percent decline in productivity, and with a 99
percent decrease of tree species richness, this decline would escalate
to 62--78 percent (Fig.4A).\\\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Fig5/Fig5}
\caption{{Fig.4. Estimated percentage(A) and absolute(B) decline in forest
productivity under 10 and 99 percent decline in tree species richness
(values in parentheses correspond to 99 percent). (A) Percent decline in
productivity was calculated based on the general BPR model (Eq.1) and
estimated worldwide spatially explicit values of the elasticity of
substitution (Fig.3B). (B)Absolute decline in productivity, was derived
from the estimated elasticity of substitution (Fig.3B) and estimates of
global forest productivity (Fig.S1). The first 10 percent reduction in
tree species richness would lead to 0.001--1.138
m\textsuperscript{2}ha\textsuperscript{-1}yr\textsuperscript{-1} decline
in periodic annual increment, which accounts for 2--3 percent of current
forest productivity.%
}}
\end{center}
\end{figure}

\subsection*{\texorpdfstring{Discussion\\
}{Discussion }}\label{discussion}

Results from our global analysis provide strong and consistent evidence
that productivity of forests worldwide would decrease at an accelerating
rate with the loss of biodiversity. The positive concave-down pattern we
discovered across forest ecosystems worldwide corresponds well with
recent theoretical advances in
BPR(\emph{\protect\hyperlink{_ENREF_1_3}{3},
\protect\hyperlink{_ENREF_1_22}{22-24}}), as well as
experimental(\emph{\protect\hyperlink{_ENREF_1_21}{e.g. 21}}) and
observational(\emph{\protect\hyperlink{_ENREF_1_14}{e.g. 14}}) studies
from other forest and non-forest ecosystems. It is especially noteworthy
that the elasticity of
substitution(\emph{\protect\hyperlink{_ENREF_1_26}{26}}) estimated in
this study (ranged between 0.2 and 0.3) largely overlaps the range of
values of the same exponent term (0.1-- 0.5) from previous theoretical
and experimental studies(\protect\hyperlink{_ENREF_1_10}{see \emph{10,}
and references therein}). Furthermore, our findings are consistent with
the global magnitude of the biodiversity-dependent ecosystem service
debt estimated under distinct assumptions based on previous theoretical
and experimental results(\emph{\protect\hyperlink{_ENREF_1_10}{10}}),
and with recent reports of the diminishing marginal benefits of adding a
species as species richness increases, based on long-term forest
experiments that date back to 1870\emph{(see
\protect\hyperlink{_ENREF_1_15}{15}, \protect\hyperlink{_ENREF_1_27}{27,
and references therein})}.\\

Our analysis relied on stands ranging from unmanaged to extensively
managed forests, i.e. managed forests with low operating and investment
costs per unit area, excluding managed forests with harvests exceeding
50 percent of the stocking volume. Because species manipulation can
weaken the mechanisms underlying biodiversity effects
(\emph{\protect\hyperlink{_ENREF_1_3}{3}}), the positive concave-down
BPR may not be applicable to intensively managed forests (Fig.S2), and
this limitation should be taken into account in developing biological
conservation and forest management strategies (see \selectlanguage{ngerman}§Natural vs. Managed
Forests in Materials and Methods). Nevertheless, as intensively managed
forests only account for a minor (\textless{}7\%) portion of global
forests(\emph{\protect\hyperlink{_ENREF_1_16}{16}}), our estimated BPR
would be minimally affected by such manipulations and thus should
reflect the inherent processes governing the vast majority of global
forest ecosystems.~\\

\par\null

\section*{Discussion}\label{discussion}

We focused on the effect of biodiversity on ecosystem functioning and
productivity. Recent studies on the opposite causal direction (i.e.
productivity-biodiversity relationship, cf.
\emph{\protect\hyperlink{_ENREF_1_14}{14},
\protect\hyperlink{_ENREF_1_28}{28},
\protect\hyperlink{_ENREF_1_29}{29}}) suggest that there may be a
potential two-way causality between biodiversity and productivity. It is
admittedly difficult to use correlative data to detect and attribute
causal effects. Fortunately, substantial progress has been made to tease
BPR causal relationship from other potentially confounding environmental
variables(\emph{\protect\hyperlink{_ENREF_1_14}{14},
\protect\hyperlink{_ENREF_1_30}{30},
\protect\hyperlink{_ENREF_1_31}{31}}), and this study made considerable
efforts to account for these otherwise potentially confounding
environmental covariates to assess causal effects of biodiversity on
productivity. Another feature that contributes to the detection of the
causal effects in this study was the fact that \emph{S} reflects tree
species richness of the first inventory, whereas \emph{P} reflects
average annual productivity between the two inventories. This temporal
order reflects the BPR causality which requires the cause \emph{S} to
precede or coincide with the effect \emph{P} in time. The greater
uncertainty in our results for the developing countries (Fig.5) reflects
the well documented geographic bias in forest sampling including
repeated measurements; strong commitments are needed towards improving
sampling in the poorest regions of the world.\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Fig7/Fig7}
\caption{{Fig.5. Standard error (A) and generalized \emph{R\textsuperscript{2}}
(B) of the spatially explicit estimates of elasticity of substitution
(\selectlanguage{greek}θ\selectlanguage{english}) across the current global forest extent.~ Standard error increased
as a location was farther from those sampled. The generalized
\emph{R\textsuperscript{2}} values were derived with a geostatistical
nonlinear mixed-effects model for GFB sample locations, and thus (B)
only cover a subset of the current global forest extent.%
}}
\end{center}
\end{figure}

Because taxonomic diversity indirectly incorporates functional,
phylogenetic and genomic diversity, our results that focus on tree
species richness are likely applicable to these other elements of
biodiversity, all of which have been found to influence plant
productivity (\emph{\protect\hyperlink{_ENREF_1_1}{1}}). Such a
straightforward analysis also makes it easier to understand the
taxonomic contribution to forest ecosystem productivity and functioning,
and the importance of preserving species diversity to biological
conservation and forest management.

\par\null\par\null

Our findings highlight the necessity to re-assess biodiversity valuation
and re-evaluate forest management strategies and conservation priorities
in forests worldwide. We estimate that the economic value of
biodiversity in maintaining forest productivity is \$396--579 billion
per year (\$3.96--5.79\selectlanguage{ngerman}×10\textsuperscript{11} in 2015 US\$, see
§Economics Analysis in Materials and Methods), which is over five times
higher than the estimated total annual cost of effective global
conservation (\$76.1 billion per
year(\emph{\protect\hyperlink{_ENREF_1_32}{32}})). This estimation only
reflects the monetary value of biodiversity in maintaining forest
productivity, and the total global value of biodiversity would far
exceed this estimation, prompting a re-evaluation of forest management
and conservation strategies. In tropical and subtropical regions, many
areas of high elasticity of
substitution(\emph{\protect\hyperlink{_ENREF_1_26}{26}}) overlapped with
biodiversity hotspots(\emph{\protect\hyperlink{_ENREF_1_33}{33}}),
including Eastern Himalaya and Nepal, Mountains of Southwest China,
Eastern Afromontane, Madrean pine-oak woodlands, Tropical Andes, and
Cerrado. For these areas, only a few species of commercial value are
targeted by logging, hence the risk of losing species through
deforestation would far exceed the risk through
harvesting(\emph{\protect\hyperlink{_ENREF_1_34}{34}}). Deforestation
and other anthropogenic drivers of biodiversity loss in these
biodiversity hotspots may have high impacts on the productivity of
forest ecosystems.\\

Amid the struggle to combat biodiversity loss, the relationship between
biological conservation and poverty is gaining increasing global
attention(\emph{\protect\hyperlink{_ENREF_1_13}{13},
\protect\hyperlink{_ENREF_1_35}{35}}), especially in rural areas where
livelihoods depend most directly on ecosystem products. Due to the
substantial geographic overlaps between severe, multifaceted poverty and
key areas of global biodiversity
hotspots(\emph{\protect\hyperlink{_ENREF_1_36}{36}}), biodiversity loss
in these hotspots can aggravate local poverty situation by diminishing
forest productivity and related ecosystem services, reinforcing the
poverty trap for tens of millions of local
residents(\emph{\protect\hyperlink{_ENREF_1_35}{35}}).\\

Our study demonstrates the combined strength of large-scale integration
and synthesis of ecological data and modern machine learning methods in
advancing understanding and quantification of a long-standing ecological
issue. We have accounted for physiographic, climatic, and soil
attributes in estimating the BPR to ensure that our estimates were not
an artifact of potential confounding factors. Our resultsimprove the
understanding of the consequences of global biodiversity loss, and
should be useful for efforts to accurately forecast future changes in
ecosystem services worldwide--- a goal of the Intergovernmental Platform
on Biodiversity and Ecosystem Services (UN IPBES). Our findings can also
be used as an indicator, or as a tool for baseline information for the
UNCBD Aichi targets, for the UNFCCC REDD+ goal, and for the UNCCD land
degradation neutrality goal.\\

\subsection*{\texorpdfstring{Materials and Methods\\
}{Materials and Methods }}\label{materials-and-methods}

\textbf{\emph{Data collection and standardization}}\\

Our current study used ground-sourced forest measurement data from 45
forest inventories collected from 44 countries and territories (Fig.1).
The measurements were collected in the field from predesignated sample
area units, i.e. GFB plots. For the calculation of primary site
productivity, Global Forest Biodiversity permanent sample plots
(hereafter, GFB plots) can be categorized into two tiers. Plots
designated as `Tier 1' have been measured at two or more points in time
with a minimum time interval between measurements of two years or more
(global mean time interval is 9 years, see Table 1). `Tier 2' plots were
only measured once and primary site productivity can be estimated from
known stand age or dendrochronological records. Overall, our study was
based on 777,126 GFB plots, of which 597,179 (77\%) were Tier 1, and
179,798 (23\%) were Tier 2. GFB plots primarily measured natural forests
ranging from unmanaged to extensively managed forests, i.e. managed
forests with low operating and investment costs per unit area.
Intensively managed forests with harvests exceeding 50 percent of the
stocking volume were excluded from this study. GFB plots represent
forests of various origins (from naturally regenerated to planted) and
successional stages (from stand initiation to old-growth).\\

For each GFB plot, we derived three key attributes from measurements of
individual trees--- tree species richness (\emph{S}), stand basal area
(\emph{G}), and primary site productivity (\emph{P}). Because for each
of all the GFB plot samples, \emph{S} and \emph{P} were derived from the
measurements of the same trees, the sampling issues commonly associated
with biodiversity
estimation(\emph{\protect\hyperlink{_ENREF_1_37}{37}})~ had little
influence on the \emph{S}--\emph{P} relationship (i.e. BPR) in this
study.\\

Species richness, \emph{S}, represents the number of different tree
species alive at the time of inventory within the perimeter of a GFB
plot with an average size of [?]400 m\textsuperscript{2}. 95 percent of
all plots fall within a range of plot size between 100 and 1,100
m\textsuperscript{2}. To minimize the species-area
effect(\emph{\protect\hyperlink{_ENREF_1_38}{e.g. 38}}), we studied the
BPR here using a geospatial random forest model in which observations
from nearby GFB plots would be more influential than plots that are
farther away (see \selectlanguage{ngerman}§Geospatial random forest). Because nearby plots are
most likely from the same forest inventory data set, and there was no or
little variation of plot area within each data set, the BPR derived from
this model largely reflected patterns under the same plot area basis.
Furthermore, because plot size \emph{I}\textsubscript{2} had the second
lowest (0.8\%) importance
score(\emph{\protect\hyperlink{_ENREF_1_39}{39}}) among all the
covariates (Fig.6), the influence of plot size on our results was
negligible. Across all the GFB plots there were 8,737 species in 1,862
genera and 231 families, and \emph{S} values ranged from 1 to 405 per
plot. We verified all the species names against 60 taxonomic databases,
including NCBI, GRIN Taxonomy for Plants, Tropicos - Missouri Botanical
Garden, and the International Plant Names Index, using the `taxize'
package in R(\emph{\protect\hyperlink{_ENREF_1_40}{40}}). Out of 8,737
species recorded in the GFB database, 7,425 had verified taxonomic
information with a matching
score(\emph{\protect\hyperlink{_ENREF_1_40}{40}}) of 0.988 or higher,
whereas 1,312 species names partially matched existing taxonomic
databases with a matching score between 0.50 and 0.75, indicating that
these species have not been documented in the 60 taxonomic databases. To
facilitate inter-biome comparison, we further developed relative species
richness (\selectlanguage{polish}\emph{Š}\selectlanguage{english}), a continuous percentage score converted from
species richness (\emph{S}) and the local maximal species richness
(\emph{S}\textsuperscript{*}) using\\

\(S=\frac{S}{S*}\)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
(2)\\

Stand basal area (\emph{G}, in
m\textsuperscript{2~}ha\textsuperscript{-1}) represents the total
cross-sectional area of live trees per unit sample area. \emph{G} was
calculated from individual tree diameter-at-breast-height (\emph{dbh},
in cm):\\

\(G=0.000079\cdot\sum_{i}dbh_{i}^2\cdot \kappa_{i}\),~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~ (3)\\

where \selectlanguage{greek}\emph{κ\textsubscript{i}}\selectlanguage{english} denotes the conversion factor
(ha\textsuperscript{-1}) of the \emph{i}th tree, \emph{viz} the number
of trees per ha represented by that individual. \emph{G} is a key biotic
factor of forest productivity as it represents stand density--- often
used as a surrogate for resource acquisition (through leaf area) and
stand competition (\protect\hyperlink{_ENREF_2_6}{\emph{31}}).
Accounting for basal area as a covariate mitigated the artefact of
different minimum \emph{dbh} across inventories, of different plot
sizes, or of a sampling effect.\\

~~~~~~~~~~~ Primary site productivity (\emph{P}, in
m\textsuperscript{3~}ha\textsuperscript{-1~}yr\textsuperscript{-1}) was
measured as volume productivity in terms of periodic annual increment
(PAI) calculated from the sum of individual tree stem volume (\emph{V},
in m\textsuperscript{3}):\\

\( P=\frac{\sum_{i,2}V_{i,2}\cdot\kappa_i-\sum_{i,1}V_{i,1}\cdot \kappa_i+M}{Y}\),~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~ (4)\\

where \emph{V\textsubscript{i,1}} \textsubscript{} and
\emph{V\textsubscript{i,2}} \textsubscript{} (in m\textsuperscript{3})
represent total stem volume of the tree \emph{i} at the time of the
first inventory and the second inventory, respectively. \emph{M} denotes
total stand mortality (including harvest and thinning) in terms of total
stem volume (in m\textsuperscript{3}ha\textsuperscript{-1}). \emph{Y}
represents the time interval (in years) between two consecutive
inventories. \emph{P} accounted for mortality, ingrowth (i.e.
recruitment between two inventories), and volume growth. Stem volume
values were predominantly calculated using region- and species-specific
allometric equations based on dbh and other tree- and plot-level
attributes (Table 1). For the regions lacking an allometric equation, we
approximated stem volume at the stand level from basal area, total tree
height, and stand form
factors(\emph{\protect\hyperlink{_ENREF_1_42}{42}}). In case of missing
tree height values from ground measurement, we acquired alternative
measures from a global 1-km forest canopy height
database(\emph{\protect\hyperlink{_ENREF_1_43}{43}}). For Tier 2 plots
that lacked remeasurement, \emph{P} was measured in mean annual
increment (MAI) based on total stand volume and stand
age(\emph{\protect\hyperlink{_ENREF_1_41}{41}}), or tree radial growth
measured from increment cores. Since the traditional MAI metric does not
account for mortality, we calculated \emph{P} by adding to MAI the
annual mortality based on regional-specific forest turnover
rates(\emph{\protect\hyperlink{_ENREF_1_44}{44}}). The small and
insignificant correlation coefficient between \emph{P} and the indicator
of plot tier (\emph{I}\textsubscript{1}), together with the negligible
variable importance of \emph{I}\textsubscript{1} (1.8\%, Fig.6) indicate
that PAI and MAI were generally consistent so that MAI could be a good
proxy of PAI in our study. Although MAI and PAI have considerable
uncertainty in any given stand, it is difficult to see how systematic
bias across diversity gradients could occur on a scale sufficient to
influence the results shown here.~ Additionally, although other measures
of productivity (e.g. net ecosystem exchange processed to derive gross
and net primary production; direct measures of aboveground net primary
production including all components; and remotely sensed estimates of
LAI and greenness coupled with models) all have their advantages and
disadvantages, none would be feasible at a similar scale and resolution
as in this study.\\

\textbf{Table 1. Definition, unit, and summary statistics of key
variables.}\\\selectlanguage{english}
\begin{longtable}[]{@{}lllllll@{}}
\toprule
\begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\textbf{Variable}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\textbf{Definition}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\textbf{Unit}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\textbf{Mean}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\textbf{Std.}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\textbf{Source}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\textbf{Nominal Resolution}\\
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\textbf{Response variables}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\textbf{~}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\textbf{~}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\emph{P}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
Primary forest productivity measured in periodic annual increment in
stem volume (PAI)\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
m\textsuperscript{3}\selectlanguage{ngerman}·ha\textsuperscript{-1}·yr\textsuperscript{-1}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
7.57\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
14.52\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
Author generated from volume data\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\textbf{~}\\
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\textbf{Plot Attributes}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\textbf{~}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\textbf{~}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\emph{S}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
Tree species richness, the number of live tree species observed on the
plot\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
unitless\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
5.79\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
8.64\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
ground-measured\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\textbf{~}\\
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\emph{A}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
Plot size, area of the sample plot\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
ha\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
0.04\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
0.12\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
ground-measured\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\textbf{~}\\
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\emph{Y}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
Elapsed time between two consecutive inventories\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
year\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
8.63\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
11.62\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
ground-measured\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\textbf{~}\\
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\emph{G}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
Basal area, total cross-sectional area of live trees measured at 1.3-1.4
m above ground\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
m\textsuperscript{2}\selectlanguage{ngerman}·ha\textsuperscript{-1}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
19.00\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
18.94\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
Author generated from ground-measured data\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\textbf{~}\\
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\emph{E}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
Plot elevation\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
m\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
469.30\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
565.92\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
G/SRTM(\emph{\protect\hyperlink{_ENREF_1_65}{65}})\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\textbf{~}\\
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\emph{I\textsubscript{1}}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
Indicator of plot tier\\

\emph{I\textsubscript{1}}=1 if a plot was Tier-2,\\

\emph{I\textsubscript{1}}=0 if otherwise\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
unitless\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
0.23\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
0.42\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
Author generated from ground-measured data\textbf{}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\textbf{~}\\
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\emph{I\textsubscript{2}}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
Indicator of plot size\\

\emph{I\textsubscript{2}=}1 when 0.01[?]\emph{ps}\textless{}0.05,\\

\emph{I\textsubscript{2}=}2 when 0.05[?]\emph{ps}\textless{}0.15,\\

\emph{I\textsubscript{2}=}3 when 0.15[?]\emph{ps}\textless{}0.50,\\

\emph{I\textsubscript{2}=}4 when 0.50[?]\emph{ps}\textless{}1.00,\\

where \emph{ps} was plot size (ha.)\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
unitless\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
1.43\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
0.80\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
Author generated from ground-measured data\textbf{}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\textbf{~}\\
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\textbf{Climatic Covariates}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\textbf{~}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\textbf{~}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\emph{T\textsubscript{1}}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
Annual mean temperature\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
0.1\selectlanguage{ngerman}°C\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
108.4\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
55.92\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
WorldClim v.1(\emph{\protect\hyperlink{_ENREF_1_66}{66}})\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
1 km\textsuperscript{2}\\
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\emph{T\textsubscript{2}}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
Isothermality\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
Unitless\\

index*100\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
35.43\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
7.05\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
WorldClim v.1\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
1 km\textsuperscript{2}\\
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\emph{T\textsubscript{3}}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
Temperature seasonality\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
Std.(0.001\selectlanguage{ngerman}°C)\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
7786.00\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
2092.39\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
WorldClim v.1\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
1 km\textsuperscript{2}\\
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\emph{C\textsubscript{1}}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
Annual precipitation\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
mm\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
1020.00\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
388.35\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
WorldClim v.1\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
1 km\textsuperscript{2}\\
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\emph{C\textsubscript{2}}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
Precipitation seasonality (coefficient of variation)\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
Unitless\%\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
27.54\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
16.38\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
WorldClim v.1\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
1 km\textsuperscript{2}\\
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\emph{C\textsubscript{3}}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
Precipitation of warmest\\

quarter\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
mm\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
282.00\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
120.88\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
WorldClim v.1\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
1 km\textsuperscript{2}\\
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\emph{PET}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
Global Potential Evapotranspiration\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
mm\selectlanguage{ngerman}·yr\textsuperscript{-1}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
1063.43\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
271.80\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
CGIAR-CSI(\emph{\protect\hyperlink{_ENREF_1_67}{67}})\\

~\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
1 km\textsuperscript{2}\\
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\emph{IAA}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
Indexed Annual Aridity\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
Unitless index*10\textsuperscript{-4}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
9915.09\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
4512.99\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
CGIAR-CSI\\

~\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
1 km\textsuperscript{2}\\
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\textbf{Soil Covariates}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
~\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
~\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
~\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
~\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
~\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\emph{O\textsubscript{1}}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
Bulk density\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
g\selectlanguage{ngerman}·cm\textsuperscript{-3}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
0.70\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
0.57\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
WISE30sec v.1(\emph{\protect\hyperlink{_ENREF_1_68}{68}})\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
1 km\textsuperscript{2}\\
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\emph{O\textsubscript{2}}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
pH measured in water\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
Unitless\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
3.72\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
2.80\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
WISE30sec v.1\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
1 km\textsuperscript{2}\\
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\emph{O\textsubscript{3}}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
Electrical conductivity\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
dS\selectlanguage{ngerman}·m\textsuperscript{-1}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
0.44\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
0.76\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
WISE30sec v.1\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
1 km\textsuperscript{2}\\
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\emph{O\textsubscript{4}}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
C/N ratio\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
Unitless\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
9.64\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
7.78\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
WISE30sec v.1\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
1 km\textsuperscript{2}\\
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\emph{O\textsubscript{5}}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
Total nitrogen\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
g\selectlanguage{ngerman}·kg\textsuperscript{-1}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
2.71\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
4.62\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
WISE30sec v.1\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
1 km\textsuperscript{2}\\
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\textbf{Geographic Coordinates and Classification}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
~\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
~\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
~\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
~\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\emph{x}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
Longitude in WGS84 datum\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
degree\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
~\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
~\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
~\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
~\\
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\emph{y}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
Latitude in WGS84 datum\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
degree\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
~\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
~\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
~\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
~\\
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\emph{Ecoregion}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
Ecoregion defined by World Wildlife
Fund(\emph{\protect\hyperlink{_ENREF_1_69}{69}})\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
~\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
~\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
~\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
~\\
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
~\\
\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

To account for abiotic factors that may influence primary site
productivity, we selected 14 geospatial covariates based on biological
relevance and spatial resolution (Fig.6, Table 1). These covariates,
derived from satellite-based remote sensing and ground-based survey
data, can be grouped into three categories: climatic, soil, and
topographic. We preprocessed all geospatial covariates using ArcMap
10.3(\emph{\protect\hyperlink{_ENREF_1_45}{45}}) and R 2.15.3
(\emph{\protect\hyperlink{_ENREF_1_46}{46}}). All covariates were
extracted to point locations of GFB plots, with a nominal resolution of
1km\textsuperscript{2}.~~\\\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Fig8/Fig8}
\caption{\selectlanguage{ngerman}{Fig.6. Correlation matrix (A) and importance values (B) of potential
variables for the geospatial random forest analysis. There were a total
of 15 candidate variables from three categories, namely plot attributes,
climatic variables, and soil factors (see Table 1 for a detailed
description). Correlation coefficients between these variables were
represented by sizes and colors of circles, and × marks insignificant
coefficients at \emph{\selectlanguage{greek}α}\selectlanguage{english}=0.05 level (A). Variable importance (\%) values
were determined by the geospatial random forest (see Materials and
Methods). Variables with importance values exceeding the 9\% threshold
line (blue) were selected as control variables in the final geospatial
random forest models (B). Unsubstitutability (coefficient), productivity
(dependent variable), and species richness (key explanatory variable)
were not ranked in the variable importance chart, as they were not
potential covariates.%
}}
\end{center}
\end{figure}

\textbf{Geospatial random forest analysis}\\

We developed geospatial random forest--- a data-driven ensemble learning
approach--- to characterize biodiversity--productivity relationship
(BPR), and map BPR in terms of elasticity of
substitution(\emph{\protect\hyperlink{_ENREF_1_26}{26}}) on all sample
sites across the world. This approach was developed to overcome two
major challenges that arose from the size and complexity of GFB data
without assuming any underlying BPR patterns or data distribution.
Firstly, we need to account for broad-scale differences in vegetation
types, but global classification and mapping of homogeneous vegetation
types is lacking(\emph{\protect\hyperlink{_ENREF_1_47}{47}}); and
secondly, correlations and trends that naturally occur through
space(\emph{\protect\hyperlink{_ENREF_1_48}{48}}) can be significant and
influential in forest
ecosystems(\emph{\protect\hyperlink{_ENREF_1_49}{49}}), but due to
computational constraints, most geostatistical models cannot be applied
to account for spatial autocorrelation.\\

Geospatial random forest integrated conventional random
forest(\emph{\protect\hyperlink{_ENREF_1_39}{39}}) and a geostatistical
nonlinear mixed-effects
model(\emph{\protect\hyperlink{_ENREF_1_50}{50}}) to estimate BPR across
the world based on GFB plot data and their spatial dependence. The
underlying model had the following form:\\

\(logP_{ij}\left(u\right)=\theta_i\cdot logS_{ij}\left(u\right)+\alpha_i\cdot X_{ij}\left(u\right)+e_{ij}\left(u\right)\),~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~
(5)\\

where log \emph{P\textsubscript{ij}}(\textbf{u}) and log
\selectlanguage{polish}\emph{Š\textsubscript{ij}}\selectlanguage{english}(\textbf{u}) represent natural logarithm of
productivity and relative species richness (calculated from actual
species richness and the maximal species richness of the training set)
of plot \emph{i} in the \emph{j}th sample at point locations \textbf{u},
respectively. The model was derived from the niche--efficiency model,
and \selectlanguage{greek}\emph{θ} \selectlanguage{english}corresponds to the elasticity of
substitution(\emph{\protect\hyperlink{_ENREF_1_26}{26}}).
\selectlanguage{greek}\textbf{α\textsubscript{i}·X\textsubscript{ij}(u)}\selectlanguage{ngerman}=\selectlanguage{greek}α\selectlanguage{english}\emph{\textsubscript{i0}}
+ \selectlanguage{greek}α\selectlanguage{english}\emph{\textsubscript{i1}}\selectlanguage{ngerman}·\emph{x\textsubscript{ij1}+\ldots{}+}
\selectlanguage{greek}α\selectlanguage{english}\emph{\textsubscript{in}}\selectlanguage{ngerman}·\emph{x\textsubscript{ijn}} represents
\emph{n} covariates and their coefficients (Fig.6, Table 1). To account
for potential spatial autocorrelation, which can bias tests of
significance due to the violation of independence and is especially
problematic in large-scale forest ecosystem studies
(\emph{\protect\hyperlink{_ENREF_1_48}{48},
\protect\hyperlink{_ENREF_1_49}{49}}), we incorporated a spherical
variogram model(\emph{\protect\hyperlink{_ENREF_1_51}{51}}) into the
residual term \emph{e\textsubscript{ij}}(\textbf{u}).\\

The aforementioned geostatistical nonlinear mixed-effects model was
integrated into random
forest(\emph{\protect\hyperlink{_ENREF_1_39}{39}}) by means of model
selection and estimation. In the model selection process, random forest
was employed to assess the contribution of each of the candidate
variables to the dependent variable
log\emph{P\textsubscript{ij}}(\textbf{u}), in terms of the amount of
increase in prediction error as one variable is permuted while all the
others are kept constant. We used the randomForest
package(\emph{\protect\hyperlink{_ENREF_1_52}{52}}) in R to obtain
importance measures for all the covariates to guide our selection of the
final variables in the geostatistical nonlinear mixed-effects model,
\textbf{X\textsubscript{ij}(u)}. We selected stand basal area
(\emph{G}), temperature seasonality (\emph{T}\textsubscript{3}), annual
precipitation (\emph{C}\textsubscript{1}), precipitation of the warmest
quarter (\emph{C}\textsubscript{3}), potential evapotranspiration
(\emph{PET}), indexed annual aridity (\emph{IAA}), and plot elevation
(\emph{E}) as control variables since their importance measures were
greater than the 9 percent threshold (Fig.6). This threshold was preset
so that final variables would account for over 60 percent of the total
variable importance measures.~~\\

The underlying geostatistical assumption was that across the world the
gradient in BPR is inherently spatial--- a common geographical
phenomenon in which neighboring points are more similar to each other
than they are to points that are more distant
(\emph{\protect\hyperlink{_ENREF_1_53}{53}}). In our study, we found
strong evidence for this gradient (Fig.7), indicating that observations
from nearby GFB plots would be more influential than plots that are
farther away. The positive spherical semivariance curves estimated from
a large number of bootstrapping iterations indicated that spatial
dependence increased as plots became closer together.\\\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Fig13/Fig13}
\caption{{Fig.7. Semivariance (gray circles) and estimated spherical variogram
models (blue curves) obtained from geospatial random forest. There was a
general trend that semivariance increased with distance, \emph{i.e.}
spatial dependence of \selectlanguage{greek}θ \selectlanguage{english}weakened as the distance between any two GFB
plots increased. The final spherical models had nugget=0.8, range=50
degrees, and sill=1.3. To avoid identical distances, all plot
coordinates were jittered by adding random noises with a standard normal
distribution.%
}}
\end{center}
\end{figure}

For geospatial random forest analysis of BPR, we first selected control
variables based on the variable importance measures derived from random
forests(\emph{\protect\hyperlink{_ENREF_1_39}{39}}). We then evaluated
the values of elasticity of
substitution(\emph{\protect\hyperlink{_ENREF_1_26}{26}}), which are
expected to be real numbers greater than 0 and less than 1, against the
alternatives, \emph{i.e.} negative BPR (\emph{H}\textsubscript{01}:
\selectlanguage{greek}\emph{θ}\selectlanguage{english}\textless{}0), no effect (\emph{H}\textsubscript{02}:
\selectlanguage{greek}\emph{θ}\selectlanguage{english}=0), linear (\emph{H}\textsubscript{03}: \selectlanguage{greek}\emph{θ}\selectlanguage{english}=1), and convex
positive BPR (\emph{H}\textsubscript{04}: \selectlanguage{greek}\emph{θ}\selectlanguage{english}\textgreater{}1). We
examined all the coefficients by their statistical significance, and
effect sizes, using Akaike information criterion (AIC), Bayesian
information criterion (BIC), and the generalized coefficient of
determination(\emph{\protect\hyperlink{_ENREF_1_54}{54}}).\\

\textbf{\emph{Global analysis}}\\

For the global-scale analysis, we calibrated the nonlinear mixed-effects
model parameters (\selectlanguage{greek}\emph{θ} \selectlanguage{english}and \selectlanguage{greek}\emph{α}\selectlanguage{english}'s) using a subset of sample
points consisting of training sets of 500 plots randomly selected (with
replacement) from the GFB global dataset according to the bootstrap
aggregating (bagging) algorithm. We calibrated a total of 10,000 models
based on the bagging samples, using our own bootstrapping program and
the nonlinear package nlme(\emph{\protect\hyperlink{_ENREF_1_55}{55}})
of R, to get the means and standard errors of final model estimates
(Table 2). This approach overcame computational limits by partitioning
the GFB sample into smaller subsamples to enable the nonlinear
estimation. The size of training sets was selected based on the
convergence and effect size of the geospatial random forest models. In
pilot simulations with increasing sizes of training sets (Fig.8), the
value of elasticity of
substitution(\emph{\protect\hyperlink{_ENREF_1_26}{26}}) fluctuated at
the start until the convergence point at 500 plots. Generalized
\emph{R}\textsuperscript{2} value declined as training set size
increased from 0 to 350 plots, and fluctuated around 0.35 as training
set size increased further. Accordingly, we selected 500 as the size of
the training sets for the final geospatial random forest analysis. Based
on the estimated parameters of the global model (Table 2), we analyzed
the effect of relative species richness, ranged from 0 to 100, on global
forest productivity with a sensitivity analysis by keeping all the other
variables constant at their sample means for each ecoregion. ~~\\\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Fig12/Fig12}
\caption{{Fig.8. Effect of the size of training sets used in the geospatial random
forest on estimated elasticity of substitution (\emph{\selectlanguage{greek}θ}\selectlanguage{english}) and
generalized \emph{R}\textsuperscript{2}. Mean (solid line) and standard
error band (green area) were estimated with 100 randomly selected (with
replacement) training sets for each of the 20 size values (between 50
and 1000 GFB plots, with an increment of 50).%
}}
\end{center}
\end{figure}

\textbf{Table 2. Parameters of the \emph{global} geospatial random
forest model in 10,000 iterations of 500 randomly selected (with
replacement) GFB plots.} Mean and standard error (S.E.) of all the
parameters were estimated using bootstrapping. Effect sizes were
represented by the Akaike information criterion (AIC), Bayesian
information criterion (BIC), and generalized \emph{R}\textsuperscript{2}
(\emph{G-R}\textsuperscript{2}). Const: Constant.\\\selectlanguage{english}
\begin{longtable}[]{@{}llllll@{}}
\toprule
\begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
~\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
\emph{~}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
\emph{~}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
\emph{~}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
~\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
Coefficients\\
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
~\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
\emph{Loglik}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
\emph{AIC}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
\emph{BIC}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
\emph{G-R}\textsuperscript{2}\emph{}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
\emph{const}\\
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
Mean\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
\textbf{-761.41}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
\textbf{1546.71}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
\textbf{1597.08}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
\textbf{0.354}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
\textbf{3.816}\\
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
S.E.\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
\textbf{0.54}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
\textbf{1.10}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
\textbf{1.13}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
\textbf{0.001}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
\textbf{0.011}\\
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
\textbf{Iteration}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
~\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
~\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
~\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
~\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
~\\
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
1\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
-756.89\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
1537.78\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
1588.35\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
0.259\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
4.299\\
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
2\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
-801.46\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
1626.91\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
1677.49\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
0.281\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
3.043\\
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
3\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
-768.71\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
1561.41\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
1611.99\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
0.357\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
5.266\\
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
4\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
-775.19\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
1574.37\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
1624.95\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
0.354\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
4.273\\
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
5\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
-767.66\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
1559.32\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
1609.89\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
0.248\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
2.258\\
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
6\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
-773.76\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
1571.52\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
1622.10\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
0.342\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
3.983\\
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
7\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
-770.26\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
1564.53\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
1615.10\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
0.421\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
4.691\\
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
\ldots{}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
~\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
~\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
~\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
~\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
~\\
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
2911\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
-778.21\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
1580.43\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
1631.00\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
0.393\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
3.476\\
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
2912\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
-755.35\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
1534.71\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
1585.28\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
0.370\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
2.463\\
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
2913\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
-800.52\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
1625.03\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
1675.61\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
0.360\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
4.526\\
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
2914\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
-725.89\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
1475.78\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
1526.36\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
0.327\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
2.639\\
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
2915\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
-753.64\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
1531.28\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
1581.85\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
0.324\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
4.362\\
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
2916\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
-796.75\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
1617.50\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
1668.08\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
0.307\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
3.544\\
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
2917\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
-746.88\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
1517.77\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
1568.34\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
0.348\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
4.427\\
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
\ldots{}\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
~\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
~\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
~\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
~\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
~\\
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
9997\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
-775.08\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
1574.17\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
1624.74\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
0.313\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
1.589\\
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
9998\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
-781.20\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
1586.40\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
1636.98\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
0.438\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
5.453\\
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
9999\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
-734.72\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
1493.43\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
1544.01\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
0.387\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
4.238\\
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
10000\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
-776.14\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
1576.28\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
1626.86\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
0.355\\
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
2.622\\
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

~\\

\textbf{\emph{Mapping BPR across global forest ecosystems}}\\

For the mapping purposes, we first estimated the current extent of
global forests in several steps. We aggregated the `treecover2000' and
`loss' data (\emph{\protect\hyperlink{_ENREF_1_56}{56}}) from 30m pixels
to 30 arc-second pixels (\textasciitilde{}1km) while taking a mean. The
result was \textasciitilde{}1km pixels showing the percent forest cover
for the year 2000 and the percent forest cover lost between 2000 and
2013, respectively. The aggregated forest cover loss was multiplied by
the aggregated forest cover to produce a single raster where each
\textasciitilde{}1km pixel had a percent forest lost between 2000 and
2013. This multiplication was necessary since the loss was only relative
to initial forest cover. Similarly, we estimated percent forest cover
gain by aggregating the forest `gain'
data(\emph{\protect\hyperlink{_ENREF_1_56}{56}}) from 30m to 30
arc-seconds while taking a mean. Then, this gain layer was multiplied by
1 minus the aggregated forest cover noted in the first step to produce a
single raster where each \textasciitilde{}1km pixel had a percent forest
gain from 2000--2013. This multiplication ensured that the gain could
only occur in proportion to areas that were not already forested.
Finally, the percent forest cover for 2013 was computed by taking the
aggregated data from the first step (year 2000) and subtracting the
computed loss and adding the computed gain.\\

\textbf{Country- and ecoregion-scale analyses}\\

To address geospatial differences in vegetation types across the world,
we compared and cross-validated BPR at country- and ecoregion-scales. In
the country-scale analysis, we aggregated 5,000,000 landscape-scale
estimates to the country-scale, taking the mean elasticity of
substitution value for each country or territory. The country-scale
analysis treated each country as an entity and ignored variation within
each country. In the ecoregion-scale analysis, we classified all global
forest areas into 13 ecoregions (Fig. 1), a biome-scale unit delineated
by the World Wildlife Fund (Table S1). Names of ecoregions reflect the
most extensive vegetation type, but areas having greater than 50\% tree
cover occur within all the ecoregions
(\protect\hyperlink{_ENREF_2_3}{\emph{27}}). We then aggregated
5,000,000 (500\selectlanguage{ngerman}×10,000) landscape-scale estimates to study BPR across
ecoregions. We showed the effect of species richness on forest primary
productivity with a sensitivity analysis by keeping all the other
variables constant at their sample means. ~~~~~~~~~~~\\

\textbf{Global-scale analysis}\\

For the global-scale analysis, we first estimated the current extent of
global forests in several steps. We aggregated the `treecover2000' and
`loss' data (\protect\hyperlink{_ENREF_2_2}{\emph{23}}) from 30 meter
pixels to 30 arc-second pixels (\textasciitilde{}1km) while taking a
mean. The result was \textasciitilde{}1km pixels showing the percent
forest cover for the year 2000 and the percent forest cover loss between
2000 and 2013, respectively. The aggregated forest cover loss was
multiplied by the aggregated forest cover to produce a single raster
where each \textasciitilde{}1km pixel had a percent forest cover loss
between 2000 and 2013. This multiplication was necessary since the loss
was only relative to initial forest cover. Similarly, we estimated
percent forest cover gain by aggregating the forest `gain' data
(\protect\hyperlink{_ENREF_2_2}{\emph{23}}) from 30 meter to 30
arc-seconds while taking a mean. Then, this gain layer was multiplied by
1 minus the aggregated forest cover noted in the first step to produce a
single raster where each \textasciitilde{}1km pixel had a percent forest
cover gain from 2000--2013. This multiplication ensured that the gain
could only occur in proportion to areas that were not already forested.
Finally, the percent forest cover for 2013 was computed by taking the
aggregated data from the first step (year 2000) and subtracting the
computed loss and adding the computed gain.\\

\textbf{\emph{Mapping BPR across global forest ecosystems}}\\

For the mapping purposes, we first estimated the current extent of
global forests in several steps. We aggregated the `treecover2000' and
`loss' data (\emph{\protect\hyperlink{_ENREF_1_56}{56}}) from 30m pixels
to 30 arc-second pixels (\textasciitilde{}1km) while taking a mean. The
result was \textasciitilde{}1km pixels showing the percent forest cover
for the year 2000 and the percent forest cover lost between 2000 and
2013, respectively. The aggregated forest cover loss was multiplied by
the aggregated forest cover to produce a single raster where each
\textasciitilde{}1km pixel had a percent forest lost between 2000 and
2013. This multiplication was necessary since the loss was only relative
to initial forest cover. Similarly, we estimated percent forest cover
gain by aggregating the forest `gain'
data(\emph{\protect\hyperlink{_ENREF_1_56}{56}}) from 30m to 30
arc-seconds while taking a mean. Then, this gain layer was multiplied by
1 minus the aggregated forest cover noted in the first step to produce a
single raster where each \textasciitilde{}1km pixel had a percent forest
gain from 2000--2013. This multiplication ensured that the gain could
only occur in proportion to areas that were not already forested.
Finally, the percent forest cover for 2013 was computed by taking the
aggregated data from the first step (year 2000) and subtracting the
computed loss and adding the computed gain.\\

We mapped productivity \emph{P} and elasticity of
substitution(\emph{\protect\hyperlink{_ENREF_1_26}{26}}) across the
estimated current extent of global forests, here defined as areas with
50 percent or more forest cover. Because GFB ground plots represent
approximately 40 percent of the forested areas, we used universal
kriging(\emph{\protect\hyperlink{_ENREF_1_51}{cf. 51}}) to estimate
\emph{P} and \selectlanguage{greek}\emph{θ} \selectlanguage{english}for the areas with no GFB sample coverage. The
universal kriging models consisted of covariates specified in Fig.6(B)
and a spherical variogram model with parameters (i.e. nugget, range, and
sill) specified in Fig.7. We obtained the best linear unbiased
estimators of \emph{P} and \selectlanguage{greek}\emph{θ} \selectlanguage{english}and their standard error across the
current global forest extent with the \emph{gstat} package of
R(\emph{\protect\hyperlink{_ENREF_1_57}{57}}). By combining \selectlanguage{greek}\emph{θ}
\selectlanguage{english}estimated from geospatial random forest and universal kriging, we
produced the spatially continuous maps of the elasticity of substitution
(Fig.3B) and forest productivity (Fig.S1) at a global scale. The effect
sizes of the best linear unbiased estimator of \selectlanguage{greek}\emph{θ} \selectlanguage{english}(in terms of
standard error and generalized \emph{R}\textsuperscript{2}) were shown
in Fig.5. We further estimated percentage and absolute decline in
worldwide forest productivity under two levels-- low (10\% loss), and
high (99\% loss)-- of biodiversity loss (Fig.4). The percentage decline
was calculated based on the general BPR model (Eq.1) and estimated
worldwide spatially explicit values of the elasticity of substitution
(Fig.3B). The absolute decline was the product of the worldwide
estimates of primary forest productivity (Fig.S1) and the percentage
decline (Fig.4A).\\

\textbf{Natural vs. managed forests}\\

Our analysis relies on stands ranging from unmanaged to extensively
managed forests, i.e. managed forests with low operating and investment
costs per unit area, and excludes intensively managed forests with
harvests exceeding 50 percent of the stocking volume. Conditions of
natural forests would not be comparable to forests intensively managed
for timber production that often focus on single or limited number of
highly productive tree species. In intensively managed forests,
saturated resources can weaken the effects of
niche--efficiency(\emph{\protect\hyperlink{_ENREF_1_3}{3}}), and
therefore managed low-diversity forests may have higher productivity
than natural diverse forests of the same climate and site conditions.
For example, the average productivity of managed forests of Germany with
one to five species can be as high as the unmanaged productivity with
100 species in the tropics (\emph{\protect\hyperlink{_ENREF_1_58}{58}}).
Furthermore, if the native German tree species would be replaced by a
single highly productive species, such as \emph{Pseudotsuga menziesii},
productivity is expected to increase to 23--50
m\textsuperscript{3}ha\textsuperscript{-1}y\textsuperscript{-1}
(\emph{\protect\hyperlink{_ENREF_1_59}{59}}). Thus, the positive
concave-down productivity--biodiversity curve may not hold with
intensive management (Fig.S2). This difference between natural and
managed forests may contribute to the negative BPR patterns that account
for 0.13\% of our results (Fig.2).\\

\textbf{Economic Analysis}\\

Estimates of the economic value-added from forests employ a range of
methods. One prominent recent global valuation of ecosystem
services(\emph{\protect\hyperlink{_ENREF_1_60}{60}}) valued global
forest production (in terms of raw materials provided by
forests(\emph{\protect\hyperlink{_ENREF_1_60}{see TableS1 in 60}})) in
2011 at US\$ 649 billion (6.49\selectlanguage{ngerman}×10\textsuperscript{11}, in constant 2007
dollars). Using an alternative method, the UN
FAO(\emph{\protect\hyperlink{_ENREF_1_61}{61}}) estimates gross
value-added in the formal forestry sector at US\$606 billion
(6.06×10\textsuperscript{11}, in constant 2011 dollars). We used these
two reasonably comparable values as bounds on our coarse estimate of the
global economic value of forest productivity, converting to constant
2015 US\$ based on US consumer price
indices(\emph{\protect\hyperlink{_ENREF_1_62}{62}}). As indicated by our
global-scale analyses (Fig.4A), a 10 percent decrease of tree species
richness distributed evenly across the world (from 100\% to 90\%) would
cause a 2.1--3.1 percent decline in productivity which would equate to
US\$13--23 billion per year (constant 2015 US\$). At extremes, a sharp
99 percent drop of species richness would lead to 62--78\% reduction in
forest productivity, equivalent to 396--579 billion US\$ per year
(3.96--5.79×10\textsuperscript{11}, constant 2015 US\$).\\

The aforementioned estimates of the economic value-added from forest BPR
came from two starkly different methods but were reasonably close. We
held forested area and other factors constant to estimate the value of
productivity loss solely due to a decline in tree species richness, and
hence the figures did not include the value of land converted from
forest and losses due to associated fauna and flora decline, and forest
habitat reduction. This estimate only reflects the value of biodiversity
in maintaining global forest productivity, and does not account for
other values of biodiversity, such as genetic and pharmaceutical
resources. Therefore, our estimate only addressed one aspect of the
value of biodiversity, and the total global value of biodiversity would
far exceed this estimate.\\

\subsection*{\texorpdfstring{References and Notes\\
}{References and Notes }}\label{references-and-notes}

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