Positive biodiversity-productivity relationship predominant in global forests

Jingjing  Liang1*, Thomas W. Crowther2, Nicolas Picard3, Susan Wiser4, Mo Zhou1, Giorgio Alberti5, Ernst-Detlef Schulze6, A. David McGuire7, Fabio Bozzato8, Hans Pretzsch9, Sergio de-Miguel10,11, Alain Paquette12, Bruno Hérault13, Michael Scherer-Lorenzen14, Christopher B. Barrett15, Henry B. Glick16, Geerten M. Hengeveld17,17.5, Gert-Jan Nabuurs17,17.6, Sebastian Pfautsch18, Helder Viana19,20, Alexander C. Vibrans21, Christian Ammer22, Peter Schall22, David Verbyla23, Nadja Tchebakova24, Markus Fischer25,26, James V. Watson1, Han Y.H. Chen27, Xiangdong  Lei28, Mart-Jan Schelhaas17, Huicui Lu29, Damiano Gianelle30,31, Elena I. Parfenova24, Christian Salas32, Eungul Lee33, Boknam Lee34, Hyun Seok Kim34,35,36,37, Helge Bruelheide38,39, David A. Coomes40, Daniel Piotto41, Terry Sunderland42,43, Bernhard Schmid44, Sylvie Gourlet-Fleury45, Bonaventure Sonké46, Rebecca Tavani47, Jun Zhu48,49, Susanne Brandl9,49.5, Jordi Vayreda50,51, Fumiaki Kitahara52, Eric B. Searle27, Victor J. Neldner53, Michael R. Ngugi53, Christopher Baraloto54, Lorenzo Frizzera30, Radomir Bałazy55, Jacek Oleksyn56, Tomasz Zawiła-Niedźwiecki57, Olivier Bouriaud58,58.5, Filippo Bussotti59, Leena Finér60, Bogdan Jaroszewicz61, Tommaso Jucker40, Fernando Valladares62, Andrzej M. Jagodzinski56,63, Pablo L. Peri64,65,66, Christelle Gonmadje46,67,William Marthy68, Timothy O'Brien68, Emanuel H. Martin69, Andrew R. Marshall70,70.5, Francesco Rovero71, Robert  Bitariho72, Pascal A. Niklaus73,74, Patricia Alvarez-Loayza75, Nurdin Chamuya76, Renato Valencia77, Frédéric Mortier78, Verginia Wortel79, Nestor L. Engone-Obiang80, Leandro V. Ferreira81, David E. Odeke82, Rodolfo M. Vasquez83, Simon L. Lewis84,85, Peter B. Reich18,86
Affiliations:
1School of Natural Resources, West Virginia University, Morgantown, WV 26505, USA.
2Netherlands Institute of Ecology, 6700 AB Wageningen, the Netherlands.
3Forestry Department, Food and Agriculture Organization of the United Nations, Rome, Italy.
4Landcare Research, Lincoln 7640, New Zealand.
5Department of Agri-Food, Environmental and Animal Sciences, University of Udine via delle Scienze 206, Udine 33100, Italy.
6Max-Planck Institut für Biogeochemie, Hans-Knoell-Strasse 10, 07745 Jena, Germany.
7U.S. Geological Survey, Alaska Cooperative Fish and Wildlife Research Unit, University of Alaska Fairbanks, Fairbanks, AK 99775 USA.
8Architecture & Environment Dept., Italcementi Group, 24100 Bergamo, Italy.
9Chair 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.
10Departament de Producció Vegetal i Ciència Forestal, Universitat de Lleida-Agrotecnio Center (UdL-Agrotecnio), Av. Rovira Roure, 191, E-25198 Lleida, Spain.
11Centre Tecnològic Forestal de Catalunya (CTFC), Ctra. De St. Llorenç de Morunys, km. 2. E-25280 Solsona, Spain.
12Centre d'étude de la forêt (CEF), Université du Québec à Montréal, Montréal, QC H3C 3P8, Canada.
13Cirad, UMR EcoFoG (AgroParisTech, CNRS, INRA, Université des Antilles, Université de la Guyane), Kourou, French Guiana.
14University of Freiburg, Faculty of Biology, Geobotany, D-79104 Freiburg, Germany.
15CH Dyson School of Applied Economics and Management, Cornell University, Ithaca, NY 14853 USA.
16Yale School of Forestry and Environmental Studies, New Haven, CT 06511, USA.
17Team Vegetation, Forest & Landscape Ecology, Alterra – 6700 AA Wageningen UR, Netherlands.  
17.5Forest and Nature Conservation Policy group, Wageningen University, 6700 AA Wageningen UR, Netherlands.  
17.6Forest Ecology and Management group, Wageningen University, 6700 AA Wageningen UR, Netherlands.  
18Hawkesbury Institute for the Environment, Western Sydney University, Richmond NSW 2753, Australia.
19CI&DETS Research Centre / DEAS-ESAV, Polytechnic Institute of Viseu, Portugal.
20Centre for the Research and Technology of Agro-Environmental and Biological Sciences, CITAB, University of Trás-os-Montes and Alto Douro, UTAD, Quinta de Prados, 5000-801 Vila Real, Portugal.
21Departamento de Engenharia Florestal, Universidade Regional de Blumenau, Rua São Paulo, 3250, 89030-000 Blumenau-Santa Catarina, Brazil.
22Department of Silviculture and Forest Ecology of the Temperate Zones, Georg-August University Göttingen, Büsgenweg 1, D-37077 Göttingen, Germany.
23School of Natural Resources and Extension, University of Alaska Fairbanks, Fairbanks, AK 99709, USA.
24V.N. Sukachev Institute of Forests, Siberian Branch, Russian Academy of Sciences, Academgorodok, 50/28, 660036 Krasnoyarsk, Russia.
25Institute of Plant Sciences, Botanical Garden, and Oeschger Centre for Climate Change Research, University of Bern, 3013 Bern, Switzerland.
26Senckenberg Gesellschaft für Naturforschung, Biodiversity and Climate Research Centre (BIK-F), 60325 Frankfurt, Germany.
27Faculty of Natural Resources Management, Lakehead University, Thunder Bay, ON P7B 5E1 Canada.
28Research Institute of Forest Resource Information Techniques, Chinese Academy of Forestry, Beijing 100091, China.
29Forest Ecology and Forest Management Group, Wageningen University, Netherlands.
30Sustainable Agro-Ecosystems and Bioresources Department, Research and Innovation Centre - Fondazione Edmund, Mach, Via E. Mach 1, 38010 - S. Michele all'Adige (TN), Italy.
31Foxlab Joint CNR-FEM Initiative, Via E. Mach 1, 38010 - S.Michele  all'Adige; Adige (TN), Italy.
32Departamento de Ciencias Forestales, Universidad de La Frontera, Temuco, Chile.
33Department of Geology and Geography, West Virginia University, Morgantown, WV 26505, USA.
34Research Institute of Agriculture and Life Sciences, Seoul National University, Seoul, Republic of Korea.
35Department of Forest Sciences, Seoul National University, Seoul 151-921, Republic of Korea.
36Interdisciplinary Program in Agricultural and Forest Meteorology, Seoul National University, Seoul 151-744, Republic of Korea.
37National Center for AgroMeteorology, Seoul National University, Seoul 151-744, Republic of Korea.
38Institute of Biology / Geobotany and Botanical Garden, Martin Luther University Halle-Wittenberg, Am Kirchtor 1, 06108 Halle (Saale), Germany.
39German Centre for Integrative Biodiversity Research (iDiv) Halle-Jena-Leipzig, Deutscher Platz 5e, 04103 Leipzig, Germany.
40Forest Ecology and Conservation, Department of Plant Sciences, University of Cambridge, Cambridge CB2 3EA, UK.
41Universidade Federal do Sul da Bahia, Ferradas, Itabuna 45613-204, Brazil.
42Sustainable Landscapes and Food Systems, Centre for International Forestry Research, Bogor, Indonesia.
43School of Marine and Environmental Studies, James Cook University, Australia.
44Department of Evolutionary Biology and Environmental Studies, University of Zurich, CH-8057 Zurich, Switzerland.
45Département Environnements et Sociétés du CIRAD, 34398 Montpellier Cedex 5, France.
46Plant Systematic and Ecology Laboratory, Department of Biology, Higher Teachers' Training College, University of Yaounde I, P.O. Box 047 Yaounde Cameroon.
47Forestry Department, Food and Agriculture Organization of the United Nations, Rome 00153, Italy.
48Department of Statistics, University of Wisconsin-Madison, Madison, WI 53706 USA.
49Department of Entomology, University of Wisconsin-Madison, Madison, WI 53706 USA.
49.5Bavarian State Institute of Forestry, Hans-Carl-von-Carlowitz-Platz 1, Freising 85354, Germany.
50Center for Ecological Research and Forestry Applications(CREAF), Cerdanyola del Vallès 08193, Spain.
51Univ Autònoma Barcelona, Cerdanyola del Vallés 08193, Spain.
52Shikoku Research Center, Forestry and Forest Products Research Institute, Kochi 780-8077, Japan.
53Ecological Sciences Unit at Queensland Herbarium, Department of Science, Information Technology and Innovation, Queensland government, Toowong, Qld, 4066, Australia.
54International Center for Tropical Botany, Department of Biological Sciences, Florida International University, Miami, FL 33199, USA.
55Forest Research Institute, Sekocin Stary Braci Lesnej 3 Street, 05-090 Raszyn, Poland.
56Institute of Dendrology of the Polish Academy of Sciences, Parkowa 5, PL-62-035 Kornik, Poland.
57Warsaw University of Life Sciences (SGGW), Faculty of Forestry, ul. Nowoursynowska 159, 02-776 Warszawa, Poland.
58Forestry Faculty, University Stefan Cel Mare of Suceava, 13 Strada Universitații,720229 Suceava, Romania.
58.5Institutul Naţional de Cercetare-Dezvoltare în Silvicultură, 128 Bd Eroilor, 077190 Voluntari, Romania.
59Department of Agri-Food Production and Environmental Science, University of Florence, P.le Cascine 28, 51044 Florence, Italy.
60Natural Resources Institute Finland, 80101 Joensuu, Finland.
61Białowieża Geobotanical Station, Faculty of Biology, University of Warsaw, Sportowa 19, 17-230 Białowieża, Poland.
62Museo Nacional de Ciencias Naturales, CSIC Serrano 115 dpdo, E-28006 Madrid, Spain.
63Poznan University of Life Sciences, Department of Game Management and Forest Protection, Wojska Polskiego 71c, PL-60-625 Poznan, Poland.
64Consejo Nacional de Investigaciones Científicas y Tecnicas (CONICET), Rivadavia 1917 (1033) Ciudad de Buenos Aires, Buenos Aires, Argentina.
65INTA EEA Santa Cruz, Mahatma Ghandi 1322 (9400) Río Gallegos, Santa Cruz, Argentina.
66Universidad Nacional de la Patagonia Austral (UNPA), Lisandro de la Torre 1070 (9400) Río Gallegos, Santa Cruz, Argentina.
67National Herbarium, P.O BOX 1601, Yaoundé, Cameroon.
68Wildlife Conservation Society, Bronx NY 10460, USA.
69College of African Wildlife Management, Department of Wildlife Management, P.O. Box 3031, Moshi, Tanzania.
70Environment Department, University of York, Heslington, York, YO10 5NG, UK.
70.5Flamingo Land Ltd., Malton, North Yorkshire, YO10 6UX.
71Tropical Biodiversity Section, MUSE-Museo delle Scienze, Trento, Italy.
72Institute of Tropical Forest Conservation, Kabale, Uganda.
73Department of Evolutionary Biology an Environmental Studies, University of Zurich, Zurich, Switzerland.
75Center for Tropical Conservation, Durham, NC 27705, USA.
76Ministry of Natural resources and Tourism, Forestry and Beekeeping Division, Dar es Salaam, Tanzania.
77Escuela de Ciencias Biológicas, Pontificia Universidad Católica del Ecuador, Aptdo. 1701-2184, Quito, Ecuador.
78CIRAD,UPR Bsef, Montpellier, 34398, France.
79 Forest Management Department, CELOS, Paramaribo, Suriname
80Institut de Recherche Ecologie Tropicale (IRET/CENAREST), B.P. 13354, Libreville, Gabon
81Museu Paraense Emilio Goeldi, Coordenacao de Botanica, Belem, PA, Brasil.
82National Forest Authority, Kampala, Uganda.
83Prog. Bolognesi Mz-E-6, Oxapampa Pasco, Peru.
84Department of Geography, University College London, United Kingdom.
85School of Geography, University of Leeds, United Kingdom.
86Department of Forest Resources, University of Minnesota, St. Paul, MN 55108, USA.
*Correspondence to:  albeca.liang@gmail.com.

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 Skłodowska 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 AöR); 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 Skłodowska-Curie Individual Fellowship (IF-EF) under grant agreement No 655815.
We thank the following agencies and organization for providing the data: the Ministère 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.
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.

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 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.

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(1, 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 (3-10), international society has made substantial efforts to strengthen the conservation and sustainable use of biodiversity(2, 11). Successful international collaboration, however, requires a systematic assessment of the value of biodiversity(11), and quantification of BPR at a global scale is thus urgently needed to facilitate the accurate valuation of biodiversity(12) and accurate forecast of future changes in ecosystem services worldwide(11), and to underpin the integration of biological conservation into international socio-economic development strategies(13).
The evidence of a positive BPR stems primarily from studies of herbaceous plant communities(14). In contrast, the forest BPR has only been explored at regional scales(see 3, 7, 15, and references therein) and remains unclear at the global scale. Forests are the most important global repositories of terrestrial biodiversity(16), but deforestation and climate change are threatening a considerable proportion of tree species worldwide(17, 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. 19, 20), highlighting the potential of forest management in strengthening the conservation and sustainable use of biodiversity worldwide.
Here, we compiled 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).
Fig.1. Global forest biodiversity (GFB) ground-sourced data were collected from in situ re-measurement of 777,126 permanent sample plots consisting of over thirty million trees across 8,737 species. GFB plots extend across 13 ecoregions (vertical axis, delineated by the World Wildlife Fund where extensive forests occur within all the ecoregions (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: (a) the northernmost (73°N, Central Siberia, Russia), (b) southernmost (52°S, Patagonia, Argentina), (c) coldest (-17°C annual mean temperature, Oimyakon, Russia), (d) warmest (28°C annual mean temperature, Palau, USA) plots, and (e) most diverse (405 tree species on the 1-ha plot, Bahia, Brazil). Plots in war-torn regions (e.g. 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.
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 (θ), which represents the degree to which species can substitute for each other in contributing to stand productivity. θ 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 θ corresponds to a greater decline in productivity due to one unit loss in biodiversity. The niche–efficiency (N–E) model(3) and several preceding studies(21-24) provide a framework for interpreting the elasticity of substitution 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 P and S signify primary site productivity (derived from two consecutive inventories) and tree species richness (observed on a 400-m2 area basis on average, see Materials and Methods), respectively,  f(X) a function of a vector of control variables X (selected from stand basal area and 14 climatic, soil, and topographic covariates, see Materials and Methods), and α a constant. This model is capable of representing a variety of potential patterns of BPR. 0<θ<1 represents a positive and concave down pattern (a degressively increasing curve) consistent with the N–E model and preceding studies(21, 22), whereas other θ values can represent alternative BPR patterns, including decreasing or no effect (θ≤0)(e.g. 25), and linear (θ=1) or convex (θ>1)(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).
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 positive and concave-down (i.e. monotonically and degressively increasing) BPR(3, 21, 22), loss in tree species richness may reduce forest productivity(64).  Functional curves in the center represent different BPR under different values of elasticity of substitution (θ). θ values between 0 and 1 correspond to the positive and concave-down BPR (blue curve). The 3D scatter plot (right) shows θ values estimated from observed productivity (P), species richness (S), and other covariates. Out of 5,000,000 estimates of θ (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.
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 positive concave-down relationship (0<θ<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 m3ha-1yr-1 as tree species richness increased from the minimum to the maximum value, which corresponds to a θ value of 0.26 (Fig.3A). 
Fig.3. Estimated global effect of biodiversity on forest productivity was 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 (θ) value of 0.26, with climatic, soil, and other plot covariates being accounted for and kept constant at sample mean. Relative species richness (Š) is in the horizontal axis, and productivity (P, m3ha-1yr-1) in the vertical axis (histograms of the two variables on top and right in the logarithm scale). (B) θ represents the strength of the effect of tree diversity on tree productivity. Spatially explicit values of θ 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.
At the global-scale, we mapped the magnitude of BPR (as expressed by θ) using geospatial random forest and universal kriging. Plotting values of θ 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(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(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).
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 m2ha-1yr-1 decline in periodic annual increment, which accounts for 2–3 percent of current forest productivity.