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Positive biodiversity-productivity relationship predominant in global forests

October 2016
Science 354(6309)

DOI:10.1126/science.aaf8957

Authors:

Jingjing Liang

Purdue University West Lafayette

Thomas W Crowther

ETH Zurich

Nicolas Picard

Susan K. Wiser

Manaaki Whenua - Landcare Research

Show all 84 authorsHide

Global biodiversity and productivity The relationship between biodiversity and ecosystem productivity has been explored in detail in herbaceous vegetation, but patterns in forests are far less well understood. Liang et al. have amassed a global forest data set from >770,000 sample plots in 44 countries. A positive and consistent relationship can be discerned between tree diversity and ecosystem productivity at landscape, country, and ecoregion scales. On average, a 10% loss in biodiversity leads to a 3% loss in productivity. This means that the economic value of maintaining biodiversity for the sake of global forest productivity is more than fivefold greater than global conservation costs. Science , this issue p. 196

Standard error and generalized R 2 of the spatially explicit estimates of elasticity of substitution (q) across the current global forest extent in relation to Š. (A) Standard error increased as a location was farther from those sampled. (B) The generalized R 2 values were derived with a geostatistical nonlinear mixed-effects model for GFB sample locations, and thus (B) only covers a subset of the current global forest extent.

…

GFB ground-sourced data were collected from in situ remeasurement of 777,126 permanent sample plots consisting of more than 30 million trees across 8737 species. GFB plots extend across 13 ecoregions [vertical axis, delineated by the World Wildlife Fund where extensive forests occur within all the ecoregions (72)], and 44 countries and territories. Ecoregions are named for their dominant vegetation types, but all contain some forested areas. GFB plots cover a substantial portion of the global forest extent (white), including some of the most distinct forest conditions: (a) the northernmost (73°N, Central Siberia, Russia),

…

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RESEARCH ARTICLE SUMMARY

◥

FOREST ECOLOGY

Positive biodiversity-productivity

relationship predominant

in global forests

Jingjing Liang,*Thomas W. Crowther, Nicolas Picard, Susan Wiser, Mo Zhou,

Giorgio Alberti, Ernst-Detlef Schulze, A. David McGuire, Fabio Bozzato, Hans Pretzsch,

Sergio de-Miguel, Alain Paquette, Bruno Hérault, Michael Scherer-Lorenzen,

Christopher B. Barrett, Henry B. Glick, Geerten M. Hengeveld, Gert-Jan Nabuurs,

Sebastian Pfautsch, Helder Viana, Alexander C. Vibrans, Christian Ammer, Peter Schall,

David Verbyla, Nadja Tchebakova, Markus Fischer, James V. Watson, Han Y. H. Chen,

Xiangdong Lei, Mart-Jan Schelhaas, Huicui Lu, Damiano Gianelle, Elena I. Parfenova,

Christian Salas, Eungul Lee, Boknam Lee, Hyun Seok Kim, Helge Bruelheide,

David A. Coomes, Daniel Piotto, Terry Sunderland, Bernhard Schmid,

Sylvie Gourlet-Fleury, Bonaventure Sonké, Rebecca Tavani, Jun Zhu, Susanne Brandl,

Jordi Vayreda, Fumiaki Kitahara, Eric B. Searle, Victor J. Neldner, Michael R. Ngugi,

Christopher Baraloto, Lorenzo Frizzera, Radomir Bałazy, Jacek Oleksyn,

Tomasz Zawiła-Niedźwiecki, Olivier Bouriaud, Filippo Bussotti, Leena Finér,

Bogdan Jaroszewicz, Tommaso Jucker, Fernando Valladares, Andrzej M. Jagodzinski,

Pablo L. Peri, Christelle Gonmadje, William Marthy, Timothy O’Brien,

Emanuel H. Martin, Andrew R. Marshall, Francesco Rovero, Robert Bitariho,

Pascal A. Niklaus, Patricia Alvarez-Loayza, Nurdin Chamuya, Renato Valencia,

Frédéric Mortier, Verginia Wortel, Nestor L. Engone-Obiang, Leandro V. Ferreira,

David E. Odeke, Rodolfo M. Vasquez, Simon L. Lewis, Peter B. Reich

INTRODUCTION: The biodiversity-productivity

relationship (BPR; the effect of biodiversity on

ecosystem productivity) is foundational to our

understanding of the global extinction crisis

and its impacts on the functioning of natural

ecosystems. The BPR has been a prominent

research topic within ecology in recent decades,

but it is only recently that we have begun to

develop a global perspective.

RATIONALE: Forests are the most important

global repositories of terrestrial biodiversity,

but deforestation, forest degradation, climate

change, and other factors are threatening

approximately one half of tree species world-

wide. Although there have been substantial

efforts to strengthen the preservation and

sustainable use of forest biodiversity through-

out the globe, the consequences of this di-

versity loss pose a major uncertainty for ongoing

international forest management and conser-

vation efforts. The forest BPR represents a

critical missing link for accurate valuation of

global biodiversity and successful integration

of biological conservation and socioeconomic

development. Until now, there have been limited

tree-based diversity experiments, and the forest

BPR has only been explored within regional-

scale observational studies. Thus, the strength

and spatial variability of this relationship re-

mains unexplored at a global scale.

RESULTS: We explored the effect of tree

species richness on tree volume productivity at

the global scale using repeated forest invento-

ries from 777,126 perma-

nent sample plots in 44

countries containing more

than 30 million trees from

8737 species spanning most

of the global terrestrial bi-

omes. Our findings reveal a

consistent positive concave-down effect of bio-

diversity on forest productivity across the world,

showing that a continued biodiversity loss would

result in an accelerating decline in forest

productivity worldwide.

The BPR shows considerable geospatial var-

iation across the world. The same percentage of

biodiversity loss would lead to a greater relative

(that is, percentage) productivity decline in the

boreal forests of North America, Northeastern

Europe, Central Siberia, East Asia, and scattered

regions of South-central Africa and South-central

Asia. In the Amazon, West and Southeastern

Africa,SouthernChina,Myanmar,Nepal,and

the Malay Archipelago, however, the same per-

centageofbiodiversitylosswouldleadtogreater

absolute productivity decline.

CONCLUSION: Our findings highlight the

negative effect of biodiversity loss on forest

productivity and the potential benefits from

the transition of monocultures to mixed-species

stands in forestry practices. The BPR we dis-

cover across forest ecosystems worldwide

corresponds well with recent theoretical ad-

vances, as well as with experimental and ob-

servational studies on forest and nonforest

ecosystems.Onthebasisofthisrelationship,

the ongoing species loss in forest ecosystems

worldwide could substantially reduce forest pro-

ductivity and thereby forest carbon absorption

rate to compromise the global forest carbon

sink. We further estimate that the economic

value of biodiversity in maintaining commer-

cial forest productivity alone is $166 billion to

$490 billion per year. Although representing

only a small percentage of the total value of

biodiversity, this value is two to six times as

much as it would cost to effectively implement

conservation globally. These results highlight

the necessity to reassess biodiversity valuation

and the potential benefits of integrating and

promoting biological conservation in forest

resource management and forestry practices

worldwide. ▪

RESEARCH

196 14 OCTOBER 2016 •VOL 354 ISSUE 6309 sciencemag.org SCIENCE

The list of author affiliations is available in the full article online.

*Corresponding author. Email: albeca.liang@gmail.com

Cite this article as J. Liang et al., Science 354, aaf8957

(2016). DOI: 10.1126/science.aaf8957

Global effect of tree species diversity on forest productivity. Ground-sourced data from 777,126

global forest biodiversity permanent sample plots (dark blue dots, left), which cover a substantial portion

of the global forest extent (white), reveal a consistent positive and concave-down biodiversity-

productivity relationship across forests worldwide (red line with pink bands representing 95% con-

fidence interval, right).

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RESEARCH ARTICLE

◥

FOREST ECOLOGY

Positive biodiversity-productivity

relationship predominant

in global forests

Jingjing Liang,

*Thomas W. Crowther,

2,3

†Nicolas Picard,

Susan Wiser,

Mo Zhou,

Giorgio Alberti,

Ernst-Detlef Schulze,

A. David McGuire,

Fabio Bozzato,

Hans Pretzsch,

Sergio de-Miguel,

11,12

Alain Paquette,

Bruno Hérault,

Michael Scherer-Lorenzen,

Christopher B. Barrett,

Henry B. Glick,

Geerten M. Hengeveld,

17,18

Gert-Jan Nabuurs,

17,19

Sebastian Pfautsch,

Helder Viana,

21,22

Alexander C. Vibrans,

Christian Ammer,

Peter Schall,

David Verbyla,

Nadja Tchebakova,

Markus Fischer,

27,28

James V. Watson,

Han Y. H. Chen,

Xiangdong Lei,

Mart-Jan Schelhaas,

Huicui Lu,

Damiano Gianelle,

31,32

Elena I. Parfenova,

Christian Salas,

Eungul Lee,

Boknam Lee,

Hyun Seok Kim,

35,36,37,38

Helge Bruelheide,

39,40

David A. Coomes,

Daniel Piotto,

Terry Sunderland,

43,44

Bernhard Schmid,

Sylvie Gourlet-Fleury,

Bonaventure Sonké,

Rebecca Tavani,

Jun Zhu,

49,50

Susanne Brandl,

10,51

Jordi Vayreda,

52,53

Fumiaki Kitahara,

Eric B. Searle,

Victor J. Neldner,

Michael R. Ngugi,

Christopher Baraloto,

56,57

Lorenzo Frizzera,

Radomir Bałazy,

Jacek Oleksyn,

59,60

Tomasz Zawiła-Niedźwiecki,

61,62

Olivier Bouriaud,

63,64

Filippo Bussotti,

Leena Finér,

Bogdan Jaroszewicz,

Tommaso Jucker,

Fernando Valladares,

68,69

Andrzej M. Jagodzinski,

59,70

Pablo L. Peri,

71,72,73

Christelle Gonmadje,

74,75

William Marthy,

Timothy O’Brien,

Emanuel H. Martin,

Andrew R. Marshall,

78,79

Francesco Rovero,

Robert Bitariho,

Pascal A. Niklaus,

Patricia Alvarez-Loayza,

Nurdin Chamuya,

Renato Valencia,

Frédéric Mortier,

Verginia Wortel,

Nestor L. Engone-Obiang,

Leandro V. Ferreira,

David E. Odeke,

Rodolfo M. Vasquez,

Simon L. Lewis,

90,91

Peter B. Reich

20,60

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, spanning 44 countries and most terrestrial biomes, we reveal

a globally consistent positive concave-down BPR, showing that continued biodiversity loss

would result in an accelerating decline in forest productivity worldwide.The value of biodiversity

in maintaining commercial forest productivity alone—US$166 billion to 490 billion per year

according to our estimation—is more than twice what it would cost to implement effective

global conservation. This highlights the need for a worldwide reassessment of biodiversity

values, forest management strategies, and conservation priorities.

The biodiversity-productivity relationship

(BPR) has been a major ecological research

focus over recent decades. The need to

understand this relationship is becoming

increasingly urgent in light of the global

extinction crisis because species loss affects the

functioning and services of natural ecosystems

(1,2). In response to an emerging body of evidence

that suggests that the functioning of natural eco-

systems may be substantially impaired by reductions

in species richness (3–10), global environment-

al authorities, including the Intergovernmental

Platform on Biodiversity and Ecosystem Services

(IPBES) and United Nations Environment Pro-

gramme (UNEP), have made substantial efforts

to strengthen the preservation and sustainable use

of biodiversity (2,11). Successful international

collaboration, however, requires a systematic asses-

sment of the value of biodiversity (11). Quantifi-

cation of the global BPR is thus urgently needed

to facilitate the accurate valuation of biodiversity

(12),theforecastoffuturechangesinecosystem

services worldwide (11), and 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 the regional scale [(3,4,7,15) and

references therein] or within a limited number

of tree-based experiments [(16,17) and references

therein], and it remains unclear whether these

relationships hold across forest types. Forests

are the most important global repositories of

terrestrial biodiversity (18), but deforestation,

climate change, and other factors are threat-

ening a considerable proportion (up to 50%) of

tree species worldwide (19–21). The consequences

of this diversity loss pose a critical uncertainty for

ongoing international forest management and

conservation efforts. Conversely, forest manage-

ment that converts monocultures to mixed-species

stands has often seen a substantial positive effect

on productivity with other benefits (22–24). Al-

though forest plantations are predicted to meet 50

to 75% of the demand for lumber by 2050 (25,26),

nearly all are still planted as monocultures, high-

lighting the potential of forest management in

strengthening the conservation and sustainable

use of biodiversity worldwide.

Here,wecompiledinsituremeasurementdata,

most of which were taken at two consecutive

inventories from the same localities, from 777,126

permanent sample plots [hereafter, global forest

biodiversity (GFB) plots] across 44 countries and

territories and 13 ecoregions to explore the forest

BPR at a global scale (Fig. 1). GFB plots encompass

forests of various origins (from naturally re-

generated to planted) and successional stages

(from stand initiation to old-growth). A total of

more than 30 million trees across 8737 species

were tallied and measured on two or more con-

secutive 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 col-

lected by individuals and organizations (table S1).

On the basis of ground-sourced GFB data, we

quantified BPR at the global scale using a data-

driven ensemble learning approach (Materials

and methods, Geospatial random forest). Our

quantification of BPR involved characterizing

the shape and strength of the dependency func-

tion through the elasticity of substitution (q),

which represents the degree to which species

can substitute for each other in contributing to

forest productivity; qmeasures the marginal

productivity—thechangeinproductivityresulting

from one unit decline of species richness—and

reflects the strength of the effect of tree diversity

on forest productivity, after accounting for cli-

matic, soil, and plot-specific covariates. A higher

qcorresponds to a greater decline in productivity

due to one unit loss in biodiversity. The niche-

efficiency (N-E) model (3) and several preceding

studies (27–30) provide a framework for inter-

preting the elasticity of substitution and approx-

imating BPR with a power function model:

P=a·f(X)·S

(1)

where Pand Ssignify primary site productivity

and tree species richness (observed on a 900-m

area basis on average) (Materials and methods),

respectively; f(X) is a function of a vector of con-

trol variables X(selected from stand basal area

and 14 climatic, soil, and topographic covariates);

and ais a constant. This model is capable of

representing a variety of potential patterns of

RESEARCH

SCIENCE sciencemag.org 14 OCTOBER 2016 •VOL 354 ISSUE 6309 aaf8957-1

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BPR. 0 < q< 1 represents a positive and concave

down pattern (a degressively increasing curve),

which is consistent with the N-E model and pre-

ceding studies (3,27–30), whereas other qvalues

can represent alternative BPR patterns, including

decreasing (q<0),linear(q=1),convex(q>1),or

no effect (q=0)(Fig.2)(14,31). The model (Eq. 1)

was estimated by using the geospatial random

forest technique based on GFB data and covariates

acquired from ground-measured and remote-

sensing data (Materials and methods).

We found that a positive BPR predominated

in forests worldwide. Out of 10,000 randomly se-

lected subsamples (each consisting of 500 GFB

plots), 99.87% had a positive concave-down rela-

tionship with relative species richness (0 < q<1),

whereas only 0.13% show negative trends, and

none was equal to zero or greater than or equal

to 1 (Fig. 2). Overall, the global forest productiv-

ity increased with a declining rate from 2.7 to

11.8 m

−1

year

−1

as relative tree species richness

increased from the minimum to the maximum

value, which corresponds to a qvalue of 0.26

(Fig. 3A).

Attheglobalscale,wemappedthemagnitude

of BPR (as expressed by q) using geospatial

random forest and universal kriging. By plotting

values of qonto a global map, we revealed con-

siderable geospatial variation across the world

(Fig. 3B). The highest q(0.29 to 0.30) occurred

in the boreal forests of North America, North-

eastern Europe, Central Siberia, and East Asia

and the sporadic tropical and subtropical forests

of South-central Africa, South-central Asia, and

the Malay Archipelago. In these areas of the

highest elasticity of substitution (32), the same

percentage of biodiversity loss would lead to a

greater percentage of reduction in forest produc-

tivity (Fig. 4A). In terms of absolute productivity,

thesamepercentageofbiodiversitylosswould

lead to the greatest productivity decline in the

Amazon; West Africa’s Gulf of Guinea; South-

eastern Africa, including Madagascar; Southern

China; Myanmar; Nepal; and the Malay Archi-

pelago (Fig. 4B). Because of a relatively narrow

range of the elasticity of substitution (32) esti-

mated from the global-level analysis (0.2 to 0.3),

the regions of the greatest productivity decline

under the same percentage of biodiversity loss

largely matched the regions of the greatest pro-

ductivity (fig. S1). Globally, a 10% decrease in tree

species richness (from 100 to 90%) would cause a

2 to 3% decline in productivity, and with a de-

crease in tree species richness to one (Materials

and methods, Economic analysis), this decline in

forest productivity would be 26 to 66% even if

other things, such as the total number of trees

and forest stocking, remained the same (fig. S4).

Discussion

Our global analysis provides strong and consistent

evidence that productivity of forests would de-

crease 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

aaf8957-2 14 OCTOBER 2016 •VOL 354 ISSUE 6309 sciencemag.org SCIENCE

School of Natural Resources, West Virginia University, Morgantown, WV 26505, USA.

Netherlands Institute of Ecology, Droevendaalsesteeg 10, 6708 PB Wageningen, Netherlands.

Yale School

of Forestry and Environmental Studies, Yale University, 195 Prospect Street, New Haven, CT 06511, USA.

Forestry Department, Food and Agriculture Organization of the United Nations, Rome,

Italy.

Landcare Research, Lincoln 7640, New Zealand.

Department of Agri-Food, Animal and Environmental Sciences, University of Udine via delle Scienze 206, Udine 33100, Italy.

Max-Planck

Institut für Biogeochemie, Hans-Knoell-Strasse 10, 07745 Jena, Germany.

U.S. Geological Survey, Alaska Cooperative Fish and Wildlife Research Unit, University of Alaska Fairbanks, Fairbanks,

AK 99775, USA.

Architecture and Environment Department, Italcementi Group, 24100 Bergamo, Italy.

Institute of Forest Growth and Yield Science, School of Life Sciences Weihenstephan,

Technical University of Munich (TUM), Hans-Carl-von-Carlowitz-Platz 2, 85354 Freising, Germany.

Departament de Producció Vegetal i Ciència Forestal, Universitat de Lleida-Agrotecnio Center

(UdL-Agrotecnio), Avinguda Rovira Roure, 191, E-25198 Lleida, Spain.

Centre Tecnològic Forestal de Catalunya (CTFC), Carretera De St. Llorenç de Morunys, km. 2, E-25280 Solsona, Spain.

Centre d'étude de la forêt (CEF), Université du Québec à Montréal, Montréal, QC H3C 3P8, Canada.

Centre de Coopération Internationale en la Recherche Agronomique pour le

Développement (CIRAD), UMR Joint Research Unit Ecology of Guianan Forests (EcoFoG) AgroParisTech, CNRS, INRA, Université des Antilles, Université de la Guyane, Kourou, French Guiana.

University of Freiburg, Faculty of Biology, Geobotany, D-79104 Freiburg, Germany.

Charles H. Dyson School of Applied Economics and Management, Cornell University, Ithaca, NY 14853, USA.

Wageningen University and Research (Alterra), Team Vegetation, Forest and Landscape Ecology–6700 AA, Netherlands.

Forest and Nature Conservation Policy Group, Wageningen University

and Research, 6700 AA Wageningen, Netherlands.

Forest Ecology and Forest Management Group, Wageningen University, 6700 AA Wageningen UR, Netherlands.

Hawkesbury Institute for

the Environment, Western Sydney University, Richmond NSW 2753, Australia.

Center for Studies in Education, Technologies and Health (CI&DETS) Research Centre/Departamento de Ecologia

e Agricultura Sustentável (DEAS)–Escola Superior Agrária de Viseu (ESAV), Polytechnic Institute of Viseu, Portugal.

Centre 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.

Departamento de Engenharia Florestal, Universidade

Regional de Blumenau, Rua São Paulo, 3250, 89030-000 Blumenau-Santa Catarina, Brazil.

Department of Silviculture and Forest Ecology of the Temperate Zones, Georg-August University

Göttingen, Büsgenweg 1, D-37077 Göttingen, Germany.

School of Natural Resources and Extension, University of Alaska Fairbanks, Fairbanks, AK 99709, USA.

V. N. Sukachev Institute of

Forests, Siberian Branch, Russian Academy of Sciences, Academgorodok, 50/28, 660036 Krasnoyarsk, Russia.

Institute of Plant Sciences, Botanical Garden, and Oeschger Centre for Climate

Change Research, University of Bern, 3013 Bern, Switzerland.

Senckenberg Gesellschaft für Naturforschung, Biodiversity and Climate Research Centre (BIK-F), 60325 Frankfurt, Germany.

Faculty of Natural Resources Management, Lakehead University, Thunder Bay, ON P7B 5E1 Canada.

Research Institute of Forest Resource Information Techniques, Chinese Academy of

Forestry, Beijing 100091, China.

Sustainable Agro-Ecosystems and Bioresources Department, Research and Innovation Centre - Fondazione Edmund, Mach, Via E. Mach 1, 38010–S. Michele

all’Adige (TN), Italy.

Foxlab Joint CNR–Fondazione Edmund Mach Initiative, Via E. Mach 1, 38010 - S.Michele all’Adige; Adige (TN), Italy.

Departamento de Ciencias Forestales, Universidad de

La Frontera, Temuco, Chile.

Department of Geology and Geography, West Virginia University, Morgantown, WV 26506, USA.

Research Institute of Agriculture and Life Sciences, Seoul National

University, Seoul, Republic of Korea.

Department of Forest Sciences, Seoul National University, Seoul 151-921, Republic of Korea.

Interdisciplinary Program in Agricultural and Forest

Meteorology, Seoul National University, Seoul 151-744, Republic of Korea.

National Center for AgroMeteorology, Seoul National University, Seoul 151-744, Republic of Korea.

Institute of

Biology/Geobotany and Botanical Garden, Martin Luther University Halle-Wittenberg, Am Kirchtor 1, 06108 Halle (Saale), Germany.

German Centre for Integrative Biodiversity Research (iDiv)

Halle-Jena-Leipzig, Deutscher Platz 5e, 04103 Leipzig, Germany.

Forest Ecology and Conservation, Department of Plant Sciences, University of Cambridge, Cambridge CB2 3EA, UK.

Universidade Federal do Sul da Bahia, Ferradas, Itabuna 45613-204, Brazil.

Sustainable Landscapes and Food Systems, Centre for International Forestry Research, Bogor, Indonesia.

School

of Marine and Environmental Studies, James Cook University, Australia.

Institute of Evolutionary Biology and Environmental Studies, University of Zurich, CH-8057 Zurich, Switzerland.

UPR

F&S Montpellier, 34398, France.

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Cameroon.

Forestry Department, Food and Agriculture Organization of the United Nations, Rome 00153, Italy.

Department of Statistics, University of Wisconsin–Madison, Madison, WI 53706,

USA.

Department of Entomology, University of Wisconsin–Madison, Madison, WI 53706, USA.

Bavarian State Institute of Forestry, Hans-Carl-von-Carlowitz-Platz 1, Freising 85354, Germany.

Center for Ecological Research and Forestry Applications (CREAF), Cerdanyola del Vallès 08193, Spain.

Universitat Autònoma Barcelona, Cerdanyola del Vallés 08193, Spain.

Shikoku

Research Center, Forestry and Forest Products Research Institute, Kochi 780-8077, Japan.

Ecological Sciences Unit at Queensland Herbarium, Department of Science, Information Technology

and Innovation, Queensland Government, Toowong, Qld, 4066, Australia.

International Center for Tropical Botany, Department of Biological Sciences, Florida International University, Miami, FL

33199, USA.

INRA, UMR EcoFoG, Kourou, French Guiana.

Forest Research Institute, Sekocin Stary Braci Lesnej 3 Street, 05-090 Raszyn, Poland.

Institute of Dendrology, Polish Academy of

Sciences, Parkowa 5, PL-62-035 Kornik, Poland.

Department of Forest Resources, University of Minnesota, St. Paul, MN 55108, USA.

Warsaw University of Life Sciences (SGGW), Faculty of

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Polish State Forests, ul. Grojecka 127, 02-124 Warszawa, Poland.

Forestry Faculty, University Stefan Cel Mare of Suceava, 13

Strada Universitații,720229 Suceava, Romania.

Institutul Național de Cercetare-Dezvoltare în Silvicultură, 128 Bd Eroilor, 077190 Voluntari, Romania.

Department of Agri-Food Production and

Environmental Science, University of Florence, P. le Cascine 28, 51044 Florence, Italy.

Natural Resources Institute Finland, 80101 Joensuu, Finland.

Białowieża Geobotanical Station, Faculty of

Biology, University of Warsaw, Sportowa 19, 17-230 Białowieża, Poland.

Museo Nacional de Ciencias Naturales, Consejo Superior de Investigaciones Científicas, Serrano 115 dpdo, E-28006

Madrid, Spain.

Universidad Rey Juan Carlos, Mostoles, Madrid, Spain.

Poznan University of Life Sciences, Department of Game Management and Forest Protection, Wojska Polskiego 71c, PL-

60-625 Poznan, Poland.

Consejo Nacional de Investigaciones Científicas y Tecnicas (CONICET), Rivadavia 1917 (1033) Ciudad de Buenos Aires, Buenos Aires, Argentina.

Instituto Nacional de

Tecnología Agropecuaria (INTA) Estación Experimental Agropecuaria (EEA) Santa Cruz, Mahatma Ghandi 1322 (9400) Río Gallegos, Santa Cruz, Argentina.

Universidad Nacional de la Patagonia

Austral (UNPA), Lisandro de la Torre 1070 (9400) Río Gallegos, Santa Cruz, Argentina.

Department of Plant Ecology, Faculty of Sciences, University of Yaounde I, Post Office Box 812,

Yaounde, Cameroon.

National Herbarium, Post Office Box 1601, Yaoundé, Cameroon.

Wildlife Conservation Society, Bronx, NY 10460, USA.

College of African Wildlife Management,

Department of Wildlife Management, Post Office Box 3031, Moshi, Tanzania.

Environment Department, University of York, Heslington, York, YO10 5NG, UK.

Flamingo Land, Malton, North

Yorkshire, YO10 6UX.

Tropical Biodiversity Section, MUSE-Museo delle Scienze, Trento, Italy.

Institute of Tropical Forest Conservation, Kabale, Uganda.

Center for Tropical Conservation,

Durham, NC 27705, USA.

Ministry of Natural Resources and Tourism, Forestry and Beekeeping Division, Dar es Salaam, Tanzania.

Escuela de Ciencias Biológicas, Pontificia Universidad

Católica del Ecuador, Apartado 1701-2184, Quito, Ecuador.

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Institut de

Recherche en Ecologie Tropicale, Institut de Recherche en Ecologie Tropicale (IRET)/Centre National de la Recherche Scientifique et Technologique (CENAREST), B. P. 13354, Libreville, Gabon.

Museu Paraense Emilio Goeldi, Coordenacao de Botanica, Belem, PA, Brasil.

National Forest Authority, Kampala, Uganda.

Prolongación Bolognesi Mz-E-6, Oxapampa Pasco, Peru.

Department of Geography, University College London, UK.

School of Geography, University of Leeds, UK.

*Corresponding author. Email: albeca.liang@gmail.com †Present address: Netherlands Institute of Ecology, Droevendaalsesteeg 10, 6708 PB Wageningen, Netherlands.

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in BPR (3,28–30), as well as with experimental

(27) and observational (14) studies on forest and

nonforest ecosystems. The elasticity of substitu-

tion (32) estimated in this study (ranged between

0.2 and 0.3) largely overlaps the range of values

of the same exponent term (0.1 to 0.5) from

previous theoretical and experimental studies

[(10) and references therein]. Furthermore, our

findings are consistent with the global estimates

of the biodiversity-dependent ecosystem service

debt under distinct assumptions (10) and with

recent reports of the diminishing marginal ben-

efits of adding a species as species richness in-

creases, based on long-term forest experiments

dating back to 1870 [(15,33) and references therein].

Our analysis relied on stands ranging from

unmanaged to extensively managed forests—

managed forests with low operating and invest-

ment costs per unit area. Conditions of natural

forests would not be comparable with intensively

managed forests, because timber production in

the latter systems often focuses on a single or

limitednumberofhighlyproductivetreespecies.

Intensively managed forests, where saturated re-

sources can weaken the effects of niche efficiency

(3), are shown in some studies (34,35)tohave

higher productivity than that of natural diverse

forests of the same climate and site conditions

(fig. S3). In contrast, other studies (6,22–24)com-

pared diverse stands with monocultures at the

same level of management intensity and found

that the positive effects of species diversity on

tree productivity and other ecosystem services

are applicable to intensively managed forests.

As such, there is still an unresolved debate on the

BPR of intensively managed forests. Nevertheless,

becauseintensivelymanagedforestsonlyaccount

for a minor (<7%) portion of global forests (18),

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.

We focused on the effect of biodiversity on

ecosystem productivity. Recent studies on the op-

posite causal direction [productivity-biodiversity

relationship (14,36,37)]suggestthattheremaybe

a potential two-way causality between biodiversity

and productivity. It is admittedly difficult to use

correlative data to detect and attribute causal ef-

fects. Fortunately, substantial progress has been

made to tease the BPR causal relationship from

other potentially confounding environmental

variables (14,38,39), and this study made con-

siderable efforts to account for these otherwise

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Fig. 1. GFB ground-sourced data were collected from in situ remeasure-

ment of 777,126permanent samp le plots consisting of more than 30 million

trees across 8737 species. GFB plots extend across 13 ecoregions [vertical

axis, delineated by the World Wildlife Fund where extensive forests occur within

all the ecoregions (72)], and 44 countries and territories. Ecoregions are named

for their dominant vegetation types, but all contain some forested areas. GFB plots

cover a substantial portion of the global forest extent (white), including some of the

most distinct forest conditions: (a) the northernmost (73°N, Central Siberia, R ussia),

(b) southernmost (52°S, Patagonia, Argentina), (c)coldest(–17°C annual mean

temperature, Oimyakon, Russia), (d) warmest (28°C annual mean temperature,

Palau, United States), and (e) most diverse (405 tree species on the 1-ha plot,

Bahia, Brazil). Plots in war-torn regions [such as (f)] were assigned fuzzed co-

ordinates 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 pro-

ductivity (both on a common logarithmic scale) derived from ground-measured tree-

and plot-level records.The complete list of species is presented in table S2.

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potentially confounding environmental covariates

in assessing likely causal effects of biodiversity

on productivity.

Because taxonomic diversity indirectly incor-

porates functional, phylogenetic, and genomic

diversity, our results that focus on tree species

richnessarelikelyapplicabletotheseotherele-

ments of biodiversity, all of which have been

found to influence plant productivity (1). Our

straightforward analysis makes clear the taxo-

nomic contribution to forest ecosystem produc-

tivity and functioning, and the importance of

preserving species diversity to biological conser-

vation and forest management.

Our findings highlight the necessity to reassess

biodiversity valuation and reevaluate forest man-

agement strategies and conservation priorities in

forests worldwide. In terms of global carbon cycle

andclimatechange,thevalueofbiodiversitymay

be considerable. On the basis of our global-scale

analyses (Fig. 4), the ongoing species loss in forest

ecosystems worldwide (1,21) could substantially

reduce forest productivity and thereby forest car-

bonabsorptionrate,whichwouldinturncom-

promise the global forest carbon sink (40). We

further estimate that the economic value of bio-

diversity in maintaining commercial forest pro-

ductivity is $166 billion to $490 billion per year

(1.66 × 10

to 4.90 × 10

year

−1

in 2015 US$) (Ma-

terials and methods, Economics analysis). By it-

self, this estimate does not account for other values

of forest biodiversity (including potential values

for climate regulation, habitat, water flow regula-

tion, and genetic resources), and represents only a

small percentage of the total value of biodiversity

(41,42). However, this value is already between

two to six times the total estimated cost that would

be necessary if we were to effectively conserve all

terrestrial ecosystems at a global scale [$76.1 billion

per year (43)]. The highbenefit-to-cost ratio under-

lines the importance of conserving biodiversity

for forestry and forest resource management.

Amid the struggle to combat biodiversity loss,

the relationship between biological conservation

and poverty is gaining increasing global atten-

tion (13,44), especially with respect to rural are as

where livelihoods depend most directly on eco-

system products. Given the substantial geographic

overlaps between severe, multifaceted poverty

and key areas of global biodiversity (45), the

loss of species in these areas has the potential

to exacerbate local poverty by diminishing forest

productivity and related ecosystem services (44).

For example, in tropical and subtropical regions,

many areas of high elasticity of substitution (32)

overlapped with biodiversity hotspots (46), in-

cluding 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. As such, the risk of

losing species through deforestation would far

exceed the risk through harvesting (47). De-

forestation and other anthropogenic drivers of

biodiversity loss in these biodiversity hotspots

are likely to have considerable impacts on the

productivity of forest ecosystems, with the po-

tential to exacerbate local poverty. Furthermore,

the greater uncertainty in our results for the

developing countries (Fig. 5) reflects the well-

documented geographic bias in forest sampling,

including repeated measurements, and reiterates

the need for strong commitments toward improving

sampling in the poorest regions of the world.

Our findings reflect the combined strength

of large-scale integration and synthesis of eco-

logical data and modern machine learning methods

to increase our understanding of the global forest

system. Such approaches are essential for gen-

erating global insights into the consequences of

biodiversity loss and the potential benefits of

aaf8957-4 14 OCTOBER 2016 •VOL 354 ISSUE 6309 sciencemag.org SCIENCE

Fig. 2. Theoretical positive and concave-down biodiversity–productivity

relationship supported by empirical evidence drawn from the GFB data. (Left)

The diagram demonstrates that under the theoretical positive and concave-down

(monotonically and degressively increasing) BPR (3,27,28), loss in tree species

richness may reduce forest productivity (73). (Middle) Functional curves rep-

resent different BPR under different values of elasticity of substitution (q). qvalues

between 0 and 1 correspond to the positive and concave-down BPR (blue curve).

(Right) The three-dimensional scatter plot shows qvalues we estimated from ob-

served productivity (P), species richness (S), and other covariates. Out of 5,000,000

estimates of q(mean = 0.26, SD = 0.09), 4,993,500 fell between 0 and 1 (blue) ,wh ereas

only 6500 were negative (red), and none was equal to zero or greater than or equal to

1; the positive and concave-down BPR was supported by 99.9% of our estimates.

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integrating and promoting biological conserva-

tion in forest resource management and forestry

practices—a common goal already shared by in-

tergovernmental organizations such as the Mon-

tréal and Helsinki Process Working Groups. These

findings should facilitate efforts to accurately

forecast future changes in ecosystem services

worldwide, which is a primary goal of IPBES

(11), and provide baseline information necessary

to establish international conservation objectives,

including the United Nations Convention on Bio-

logical Diversity Aichi targets, the United Nations

Framework Convention on Climate Change REDD+

goal, and the United Nations Convention to Combat

Desertification land degradation neutrality goal.

The success of these goals relies on the under-

standing of the intrinsic link between biodiversity

and forest productivity.

Materials and methods

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 and table S1). The measurements were collected

in the field from predesignated sample area units,

i.e., Global Forest Biodiversity permanent sample

plots (hereafter, GFB plots). For the calculation of

primarysiteproductivity,GFBplotscanbecat-

egorized into two tiers. Plots designated as “Tier

1”have been measured at two or more points in

time with a minimum time interval between mea-

surements 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 den-

drochronological 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 in-

vestment costs per unit area. Intensively man-

aged 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 succes-

sional stages (from stand initiation to old-growth).

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Fig. 3. The estimated global effect of biodiversity on forest productivity

was positive and concave-down, and revealed considerable geospatial var-

iation across forest ecosystems worldwide. (A) Global effect of biodiversity on

forest productivity (red line with pink bands representing 95% confidence interval)

corresponds to a global average elasticity of substitution (q) 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,m

−1

year

−1

)

is in the vertical axis(histogramsof the twovariables on top and right in the logarithm

scale). (B)qrepresents the strength of the effect of tree diversity on forest produc-

tivity. Spatially explicit values of qwere estimated by using universal kriging (Materials

and methods) across the current global forest extent (effect sizes of the estimates

are shown in Fig. 5), whereas blank terrestrial areas were nonforested.

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aaf8957-6 14 OCTOBER 2016 •VOL 354 ISSUE 6309 sciencemag.org SCIENCE

Table 1. Definition, unit, and summary statistics of key variables.

Variable Definition Unit Mean Standard

deviation

Source Nominal

resolution

Response variables

.................................... ..................................... ....................................... ..................................... ..................................... ....................................... ..................................... ..................................... .................................

PPrimary forest

productivity measured in

periodic annual increment in stem

volume (PAI)

−1

year

−1

7.57 14.52 Author-generated

from ground-measured

data

Plot attributes

STree species

richness, the number of live tree

species observed on

the plot

unitless 5.79 8.64 ground-measured

APlot size,

area of the

sample plot

ha 0.04 0.12 ground-measured

YElapsed time

between two

consecutive

inventories

year 8.63 11.62 ground-measured

GBasal area,

total cross-sectional

area of live trees

measured at 1.3

to 1.4 m above ground

−1

19.00 18.94 Author-generated

from ground-measured

data

EPlot elevation m 469.30 565.92 G/SRTM (74)

Indicator of plot tier

= 1 if a plot was

Tier-2,

= 0 if otherwise

unitless 0.23 0.42 Author-generated

from ground-measured

data

Indicator of plot size

=1 when 0.01 ≤ps < 0.05,

=2 when 0.05 ≤ps <0.15,

=3 when 0.15 ≤ps <0.50,

=4 when 0.50 ≤ps <1.00,

where ps was plot

size (hectares)

unitless 1.43 0.80 Author-generated

from ground-measured

data

Climatic covariates

Annual mean temperature 0.1°C 108.4 55.92 WorldClim v.1 (75)1km

Isothermality unitless

index*100

35.43 7.05 WorldClim v.1 1 km

Temperature seasonality Std.(0.001°C) 7786.00 2092.39 WorldClim v.1 1 km

Annual precipitation mm 1020.00 388.35 WorldClim v.1 1 km

Precipitation seasonality

(coefficient of variation)

unitless% 27.54 16.38 WorldClim v.1 1 km

Precipitation of warmest

quarter

mm 282.00 120.88 WorldClim v.1 1 km

PET Global Potential Evapotranspiration mm year

−1

1063.43 271.80 CGIAR-CSI (76)1km

IAA Indexed Annual Aridity unitless index*10

−4

9915.09 4512.99 CGIAR-CSI 1 km

Soil covariates

Bulk density g cm

−3

0.70 0.57 WISE30sec v.1 (77)1km

pH measured in water unitless 3.72 2.80 WISE30sec v.1 1 km

Electrical conductivity dS m

−1

0.44 0.76 WISE30sec v.1 1 km

C/N ratio unitless 9.64 7.78 WISE30sec v.1 1 km

Total nitrogen g kg

−1

2.71 4.62 WISE30sec v.1 1 km

Geographic coordinates and classification

xLongitude in WGS84 datum degree

yLatitude in WGS84 datum degree

Ecoregion Ecoregion defined by World Wildlife Fund (78)

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For each GFB plot, we derived three key at-

tributes from measurements of individual trees—

tree species richness (S), stand basal area (G), and

primary site productivity (P). Because for each of

all the GFB plot samples, Sand Pwere derived

from the measurements of the same trees, the

sampling issues commonly associated with bio-

diversity estimation (48) had little influence on

the S–Prelationship (i.e., BPR) in this study.

Species richness, S, represents the number of

different tree species alive at the time of inventory

within the perimeter of a GFB plot with an aver-

age size of approximately 900 m

. Ninety-five

percent of all plots fall between 100 and 1,100 m

in size. To minimize the species-area effect (49),

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 apart (see §Geospatial random

forest).Becausenearbyplotsaremostlikelyfrom

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 re-

flected patterns under the same plot area basis.

To investigate the potential effects of plot size on

our results, we plotted the estimated elasticity of

substitution (q) against plot size, and found that

the scatter plot was normally distributed with no

discernible pattern (fig. S2). In addition, the fact

that the plot size indicator I

had the second

lowest (0.8%) importance score (50) among all

the covariates (Fig. 6) further supports that the

influence of plot size variation in this study

was negligible.

Across all the GFB plots, there were 8,737 species

in 1,862 genera and 231 families, and Svalues

ranged from 1 to 405 per plot. We verified all

the species names against 60 taxonomic data-

bases, including NCBI, GRIN Taxonomy for Plants,

Tropicos–Missouri Botanical Garden, and the

International Plant Names Index, using the

‘taxize’package in R (51). Out of 8737 species

recorded in the GFB database, 7425 had verified

taxonomic information with a matching score

(51) of 0.988 or higher, whereas 1312 species names

partially matched existing taxonomic databases

with a matching score between 0.50 and 0.75,

indicating that these species may have not been

documented in the 60 taxonomic databases. To

facilitate inter-biome comparison, we further

developed relative species richness (Š), a con-

tinuous percentage score converted from species

richness (S) and the maximal species richness of

asetofsampleplots(S*) using

⌣¼S

S*ð2Þ

Stand basal area (G,inm

−1

) represents the

total cross-sectional area of live trees per unit

sample area. Gwas calculated from individual

tree diameter-at-breast-height (dbh, in cm):

G¼0:000079⋅X

dbh2

i⋅kið3Þ

where k

denotes the conversion factor (ha

−1

)of

the ith tree, viz. the number of trees per ha

represented by that individual. Gis a key biotic

factor of forest productivity as it represents

stand density—often used as a surrogate for re-

source acquisition (through leaf area) and stand

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Fig. 4. Estimated percentage and absolute decline in forest productivity under 10 and 99% decline in current tree species richness (values in par-

entheses correspond to 99%), holding all the other terms constant. (A) Percent decline in productivity was calculated according to 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% reduction in tree species richness would lead to a 0.001 to 0.597 m

−1

year

−1

decline in periodic annual increment, which accounts for 2 to 3% of current forest productivity. The raster data are displayed in 50-km resolution witha3SDstretch.

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competition (52). Accounting for basal area as a

covariate mitigated the artifact of different min-

imum dbh across inventories, and the artifact of

different plot sizes.

Primary site productivity (P,inm

−1

)

was measured as tree volume productivity in

terms of periodic annual increment (PAI) cal-

culated from the sum of individual tree stem

volume (V,inm

)

P¼

i;2

Vi;2⋅ki−X

i;1

Vi;1⋅kiþM

Yð4Þ

where V

i,1

and V

i,2

(in m

) represent total stem

volume of the ith tree at the time of the first

inventory and the second inventory, respectively.

Mdenotes total removal of trees (including mor-

tality, harvest, and thinning) in stem volume

(in m

−1

). Yrepresents the time interval (in

years) between two consecutive inventories. P

accounted for mortality, ingrowth (i.e., recruit-

ment between two inventories), and volume

growth. Stem volume values were predominantly

calculated using region- and species-specific al-

lometric 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 (53). In

case of missing tree height values from the

ground measurement, we acquired alternative

measures from a global 1-km forest canopy height

database (54). For Tier 2 plots that lacked re-

measurement, Pwas measured in mean annual

increment (MAI) based on total stand volume

and stand age (52), or tree radial growth mea-

sured from increment cores. Since the traditional

MAI metric does not account for mortality, we

calculated Pby adding to MAI the annual mor-

tality based on regional-specific forest turnover

rates (55). The small and insignificant correla-

tion coefficient between Pand the indicator of

plot tier (I

), together with the negligible variable

importance of I

(1.8%, Fig. 6), indicate that PAI

and MAI were generally consistent, such that MAI

could be a good proxy of PAI in our study. Al-

though MAI and PAI have considerable uncer-

tainty 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.

P, a lthough only representing a fraction of total

forest net primary production, has been an im-

portant and widely used measure of forest pro-

ductivity, because it reflects the dominant

aboveground biomass component and the long-

lived biomass pool in most forest ecosystems

(56). Additionally, although other measures of

productivity (e.g., net ecosystem exchange pro-

cessed to derive gross and net primary produc-

tion; 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 dis-

advantages, none would be feasible at a similar

scale and resolution as in this study.

To account for abiotic factors that may in-

fluence primary site productivity, we compiled

14 geospatial covariates based on biological rel-

evance and spatial resolution (Fig. 6). These co-

variates, derived from satellite-based remote sensing

and ground-based survey data, can be grouped in to

three categories: climatic, soil, and topographic

(Table 1). We preprocessed all geospatial covar-

iates using ArcMap 10.3 (57)andR2.15.3(58). All

covariates were extracted to point locations of

GFB plots, with a nominal resolution of 1 km

Geospatial random forest

We developed geospatial random forest—adata-

driven ensemble learning approach—to characterize

aaf8957-8 14 OCTOBER 2016 •VOL 354 ISSUE 6309 sciencemag.org SCIENCE

Fig. 5. Standard error and generalized R

of the spatially explicit estimates of elasticity of substitution (q) across the current global forest extent

in relation to Š.(A) Standard error increased as a location was farther from those sampled. (B) The generalized R

values were derived with a geostatistical

nonlinear mixed-effects model for GFB sample locations, and thus (B) only covers a subset of the current global forest extent.

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the biodiversity–productivity relationship (BPR),

and to map BPR in terms of elasticity of sub-

stitution (31) 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.

First, we need to account for broad-scale dif-

ferences in vegetation types, but global classi-

fication and mapping of homogeneous vegetation

types is lacking (59); and secondly, correlations

and trends that naturally occur through space

(60) can be significant and influential in forest

ecosystems (61). Geostatistical models (62)have

been developed to address the spatial auto-

correlation, but the size of the GFB data set far

exceeds the computational constraints of most

geostatistical software.

Geospatial random forest integrated conven-

tional random forest (50) and a geostatistical

nonlinear mixed-effects model (63) to estimate

BPR across the world based on GFB plot data

and their spatial dependence. The underlying

model had the following form

log PijðuÞ¼qi⋅log S

⌣

ijðuÞþai⋅Xij ðuÞ

þeij ðuÞ;u∈D⊂ℜ2

;ð5Þ

where logP

(u)andlogŠ

(u) represent natural

logarithm of productivity and relative species

richness (calculated from actual species rich-

ness and the maximal species richness of the

training set) of plot iin the jth training set at

point locations u, respectively. The model was

derived from the niche–efficiency model, and q

corresponds to the elasticity of substitution

(31). a

·X

(u)=a

·x

ij1

+…+a

·x

ijn

repre-

sents ncovariates and their coefficients (Fig. 6

and Table 1).

To account for potential spatial autocorrelation,

which can bias tests of significance due to the

violation of independence assumption and is

especially problematic in large-scale forest eco-

system studies (60,61), we incorporated a

spherical variogram model (62)intotheresidual

term e

(u). The underlying geostatistical assump-

tion was that across the world BPR is a second-

order stationary process—a common geographical

phenomenon in which neighboring points are

more similar to each other than they are to points

that are more distant (64). In our study, we found

strong evidence for this gradient (Fig. 7), indi-

cating that observations from nearby GFB plots

would be more influential than plots that are

fartheraway.Thepositivesphericalsemivariance

curves estimated from a large number of boot-

strapping iterations indicated that spatial de-

pendence increased as plots became closer together.

The aforementioned geostatistical nonlinear

mixed-effects model was integrated into random

forest analysis (50) 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 logP

(u), in terms of the amount of in-

crease in prediction error as one variable is per-

muted while all the others are kept constant. We

used the randomForest package (65)inRtoob-

tain importance measures for all the covariates

to guide our selection of the final variables in the

geostatistical nonlinear mixed-effects model, X

(u).

We selected stand basal area (G), temperature

seasonality (T

), annual precipitation (C

), pre-

cipitation of the warmest quarter (C

), potential

evapotranspiration (PET), indexed annual aridity

(IAA), and plot elevation (E) as control variables

since their importance measures were greater than

the 9 percent threshold (Fig. 6) preset to ensure

that the final variables accounted for over 60 per-

cent of the total variable importance measures.

For geospatial random forest analysis of BPR,

we first selected control variables based on the

variable importance measures derived from ran-

dom forests (50). We then evaluated the values of

elasticity of substitution (32), which are expected

to be real numbers greater than 0 and less than 1,

against the alternatives, i.e., negative BPR (H

q< 0), no effect (H

:q= 0), linear (H

:q= 1),

and convex positive BPR (H

:q>1).We

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Fig. 6. Correlation matrix and importance values of potential variables for the geospatial random

forest analysis. (A)There were a total of 15 candidate variables from three categories, namely plot at-

tributes, climatic variables, and soil factors (a detailed description is provided in Table 1). Correlation

coefficients between these variables were represented by sizes and colors of circles, and “×”marks co-

efficients not significant at a=0.05level.(B) Variable importance (%) values were determined by the

geospatial random forest (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. Elasticity of

substitution (coefficient), productivity (dependent variable), and species richness (key explanatory variable)

were not ranked in the variable importance chart because they were not potential covariates.

Fig. 7. Semivariance and esti-

mated spherical variogram

models (blue curves) obtained

from geospatial random forest

in relation to Š.Gray circles,

semivariance; blue curves, esti-

mated spherical variogram

models. There was a general trend

that semivariance increased with

distance; spatial dependence of q

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 id entical distances, all

plot coordinates were jittered by

adding normally distributed

random noises.

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examined all the coefficients by their statistical

significance and effect sizes, using Akaike in-

formation criterion (AIC), Bayesian information

criterion (BIC), and the generalized coefficient of

determination (66).

Global analysis

For the global-scale analysis, we calibrated the

nonlinear mixed-effects model parameters (qand

a’s) using 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 (63) of R, to calculate

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

(32) fluctuated at the start until the convergence

pointat500plots.GeneralizedR

values declined

as the size of training sets increased from 0 to

350 plots, and stabilized at around 0.35 as train-

ing 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 on global forest productivity with a sen-

sitivity analysis by keeping all the other variables

constant at their sample means for each ecoregion.

Mapping BPR across global

forest ecosystems

For mapping purposes, we first estimated the

current extent of global forests in several steps.

We aggregated the “treecover2000”and “loss”

data (67) from 30 m pixels to 30 arc-second pixels

(~1 km) by calculating the respective means. The

result was ~1 km pixels showing the percentage

forest cover for the year 2000 and the percentage

of this forest cover lost between 2000 and 2013,

respectively. The aggregated forest cover loss was

multiplied by the aggregated forest cover to pro-

duce a single raster value for each ~1 km pixel

representing a percentage forest lost between

2000 and 2013. This multiplication was neces-

sary since the initial loss values were relative to

initial forest cover. Similarly, we estimated the

percentage forest cover gain by aggregating the

forest “gain”data (67) from 30 m to 30 arc-

seconds while taking a mean. Then, this gain

layer was multiplied by 1 minus the aggregated

forest cover from the first step to produce a

single value for each ~1 km pixel that signifies

percentage forest gain from 2000–2013. This

multiplication ensured that the gain could only

occur in areas that were not already forested.

Finally, the percentage 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 Pand elasticity of

substitution (32) 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 (62) to estimate Pand qfor the areas

with no GFB sample coverage. The universal

kriging models consisted of covariates speci-

fied in Fig. 6B 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 Pand qand their stan-

dard error in relation to Šacross the current

global forest extent with the gstat package of R

(68). By combining qestimated 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 q(in terms of

standard error and generalized R

) are shown

in Fig. 5. We further estimated percentage and

absolute decline in worldwide forest produc-

tivity under two scenarios of loss in tree species

richness—low (10% loss) and high (99% loss).

These levels represent the productivity decline

(in both percentage and absolute terms) if local

species richness across the global forest extent

would decrease to 90 and 1 percent of the cur-

rent values, respectively. 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).

aaf8957-10 14 OCTOBER 2016 •VOL 354 ISSU E 6309 sciencemag.org SCIENCE

Table 2. Parameters of the global geospatial random forest model in 10,000 iterations of 500 randomly selected (with replacement) GFB plots.

Mean and SE of all the parameters were estimated by using bootstrapping. Effect sizes were represented by the Akaike information criterion (AIC), Bayesi an

information criterion (BIC), and generalized R

(G-R

). Const, constant.

Coefficients

Loglik AIC BIC G-R

const qG T3 C1 C3 PET IAA E

Mean –761.41 1546.71 1597.08 0.354 3.816 0.2625243 0.014607 –0.000106 0.001604 0.001739 –0.002566 –0.000134 –0.000809

SE 0.54 1.10 1.13 0.001 0.011 0.0009512 0.000039 0.000001 0.000008 0.000008 0.000009 0.000001 0.000002

Iteration

1–756.89 1537.78 1588.35 0.259 4.299 0.067965 0.014971 –0.000100 0.002335 0.001528 –0.003019 –0.000185 –0.000639

2–801.46 1626.91 1677.49 0.281 3.043 0.167478 0.018232 –0.000061 0.000982 0.002491 –0.001916 –0.000103 –0.000904

3–768.71 1561.41 1611.99 0.357 5.266 0.299411 0.008571 –0.000145 0.002786 0.002798 –0.003775 –0.000258 –0.000728

4–775.19 1574.37 1624.95 0.354 4.273 0.236135 0.016808 –0.000126 0.001837 0.003755 –0.003075 –0.000182 –0.000768

5–767.66 1559.32 1609.89 0.248 2.258 0.166024 0.018491 –0.000051 0.000822 0.002707 –0.001575 –0.000078 –0.000553

6–773.76 1571.52 1622.10 0.342 3.983 0.266962 0.018675 –0.000113 0.001372 0.001855 –0.002824 –0.000101 –0.000953

7–770.26 1564.53 1615.10 0.421 4.691 0.353071 0.009602 –0.000127 0.002390 –0.001151 –0.003337 –0.000172 –0.000441

2911 –778.21 1580.43 1631.00 0.393 3.476 0.187229 0.020798 –0.000069 0.001826 0.001828 –0.002695 –0.000135 –0.000943

2912 –755.35 1534.71 1585.28 0.370 2.463 0.333485 0.013165 –0.000005 0.001749 0.000303 –0.002447 –0.000119 –0.000223

2913 –800.52 1625.03 1675.61 0.360 4.526 0.302214 0.021163 –0.000105 0.001860 0.001382 –0.003207 –0.000166 –0.000974

2914 –725.89 1475.78 1526.36 0.327 2.639 0.324987 0.013195 –0.000057 0.001322 0.000778 –0.001902 –0.000080 –0.000582

2915 –753.64 1531.28 1581.85 0.324 4.362 0.202992 0.014003 –0.000146 0.001746 0.002229 –0.002844 –0.000143 –0.000750

2916 –796.75 1617.50 1668.08 0.307 3.544 0.244332 0.010373 –0.000118 0.002086 0.002510 –0.002667 –0.000152 –0.000650

2917 –746.88 1517.77 1568.34 0.348 4.427 0.290416 0.008630 –0.000107 0.002203 –0.000314 –0.002770 –0.000155 –0.000945

9997 –775.08 1574.17 1624.74 0.313 1.589 0.193865 0.012525 –0.000056 –0.000589 0.000550 –0.000066 –0.000155 –0.000839

9998 –781.20 1586.40 1636.98 0.438 5.453 0.412750 0.014459 –0.000169 0.002346 0.002175 –0.003973 –0.000117 –0.000705

9999 –734.72 1493.43 1544.01 0.387 4.238 0.211103 0.013415 –0.000118 0.001896 0.002450 –0.002927 –0.000076 –0.000648

10000 –776.14 1576.28 1626.86 0.355 2.622 0.468073 0.015632 –0.000150 –0.000093 0.001151 –0.000756 –0.000019 –0.000842

RESEARCH |RESEARCH ARTICLE

on October 14, 2016http://science.sciencemag.org/Downloaded from

The absolute decline was the product of the world-

wide estimates of primary forest productivity

(fig. S1) and the standardized percentage decline

at the two levels of biodiversity loss (Fig. 4A).

Economic analysis

Estimates of the economic value-added from

forestsemployarangeofmethods.Onepromi-

nent recent global valuation of ecosystem services

(69) valued global forest production [in terms of

‘raw materials’(including timber, fiber, biomass

fuels, and fuelwood and charcoal] provided by

forests (table S1) (69)in2011atUS$649billion

(6.49 × 10

, in constant 2007 dollars). Using an

alternative method, the UN FAO (25,26) esti-

mates gross value-added in the formal forestry

sector, a measure of the contribution of forestry,

wood industry, and pulp and paper industry to

the world’s economy, at US$606 billion (6.06 ×

, in constant 2011 dollars). Because these two

reasonably comparable values are directly im-

pacted by and proportional to forest productivity,

we used them as bounds on our coarse estimate

of the global economic value of commercial forest

productivity, converted to constant 2015 US$

based on the US consumer price indices (70,71).

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 to 3.1 percent decline

in productivity, which would equate to US$13–

23 billion per year (constant 2015 US$). For the

assessment of the value of biodiversity in main-

taining forest productivity, a drop in species

richness from the current level to one species

would lead to 26–66% reduction in commercial

forest productivity in thebiomesthatcontribute

substantially to global commercial forestry (fig.

S4), equivalent to 166–490 billion US$ per year

(1.66 × 10

to 4.90 × 10

,constant2015US$,cal-

culated by multiplying the foregoing economic

value-added from FAO and the other study by 26

and 66%, respectively.) Therefore, we estimated

that the economic value of biodiversity in main-

taining commercial forest productivity worldwide

would be 166 billion to 490 billion US$ per year.

We held the total number of trees, global forest

area and stocking, and other factors constant to

estimate the value of productivity loss solely due

to a decline in tree species richness. As such, these

estimates did not include the value of land con-

verted from forest and losses due to associated

fauna and flora decline or forest habitat reduction.

This estimate only reflects the value of biodiver-

sity in maintaining commercial forest productiv-

ity that contributes directly to forestry, wood

industry, and pulp and paper industry, and does

not account for other values of biodiversity, in-

cluding potential values for climate regulation,

habitat, water flow regulation, genetic resources,

etc. The total global value of biodiversity could ex-

ceed this estimate by orders of magnitudes (41,42).

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(2002).

ACKNOW LEDGM ENTS

We are grateful to all the people and agencies that helped in

collection, compilation, and coordination of the field data, including

but not limited to T. Malone, J. Crowe, M. Sutton, J. Lovett,

P. Munishi, M. Rautiainen, staff members from the 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 part by West Virginia University under the United

States Department of Agriculture (USDA) McIntire-Stennis Funds

WVA00104 and WVA00105; U.S. National Science Foundation

(NSF) Long-Term Ecological Research Program at Cedar Creek

(DEB-1234162); the University of Minnesota Department of Forest

Resources and Institute on the Environment; 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

L’Agence Nationale de la Recherche (ANR) (Centre d’Étude de la

Biodiversité Amazonienne: ANR-10-LABX-0025); the General

Directory of State Forest National Holding DB; General Directorate

of State Forests, Warsaw, Poland (Research Projects 1/07

and OR/2717/3/11); the 12th Five-Year Science and Technology

Support Project (grant 2012BAD22B02) of China; the U.S.

Geological Survey and the Bonanza Creek Long Term Ecological

Research Program funded by NSF 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 (grant

NRF-2015R1C1A1A02037721), Korea Forest Service (grants

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 Deutsche

Forschungsgemeinschaft (DFG) Priority Program 1374 Biodiversity

Exploratories; Chilean research grants Fondo Nacional de

Desarrollo Científico y Tecnológico (FONDECYT) 1151495 and

11110270; Natural Sciences and Engineering Research Council of

Canada (grant RGPIN-2014-04181); Brazilian Research grants

CNPq 312075/2013 and FAPESC 2013/TR441 supporting Santa

Catarina State Forest Inventory (IFFSC); the General Directorate of

State Forests, Warsaw, Poland; the Bavarian State Ministry for

Nutrition, Agriculture, and Forestry project W07; the Bavarian

State Forest Enterprise (Bayerische Staatsforsten AöR); German

Science Foundation for project PR 292/12-1; the 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; the EU H2020 PEGASUS

project (no 633814), EU H2020 Simwood project (no 613762);

and the European Union’s Horizon 2020 research and innovation

program within the framework of the MultiFUNGtionality Marie

Skłodowska-Curie Individual Fellowship (IF-EF) under grant

agreement 655815. The expeditions in Cameroon to collect the

data were partly funded by a grant from the Royal Society and the

Natural Environment Research Council (UK) to Simon L. Lewis.

Pontifica Universidad Católica del Ecuador offered working facilities

and reduced station fees to implement the census protocol in

Yasuni National Park. We thank the following agencies and

organization for providing the data: USDA Forest Service; School of

Natural Resources and Agricultural Sciences, University of Alaska

Fairbanks; 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

National Vegetation Survey Databank (New Zealand); Italian and

Friuli Venezia Giulia Forest Services (Italy); Bavarian State Forest

Enterprise (Bayerische Staatsforsten AöR) and the Thünen

Institute of Forest Ecosystems (Germany); Queensland Herbarium

(Australia); Forestry Commission of New South Wales (Australia);

Instituto de Conservação da Natureza e das Florestas (Portugal).

M'Baïki data were made possible and provided by the ARF Project

(Appui la Recherche Forestière) and its partners: AFD (Agence

Française de Développement), CIRAD (Centre de Coopération

Internationale en Recherche Agronomique pour le Développement),

ICRA (Institut Centrafricain de Recherche Agronomique),

MEDDEFCP (Ministère de l'Environnement, du Développement

Durable des Eaux, Forêts, Chasse et Pêche), SCAC/MAE (Service

de Coopération et d’Actions Culturelles, Ministère des Affaires

Etrangères), SCAD (Société Centrafricaine de Déroulage), and

the University of Bangui. 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, the Valuing the Arc Project (Leverhulme Trust), and

other donors. The Exploratory plots of FunDivEUROPE received

funding from the European Union Seventh Framework Programme

(FP7/2007-2013) under grant agreement 265171. The Chinese

Comparative Study Plots (CSPs) were established in the

framework of BEF-China, funded by the German Research

Foundation (DFG FOR891); The Gabon data set was provided by

the Institut de Recherche en Ecologie Tropicale (IRET)/Centre

National de la Recherche Scientifique et Technologique

(CENAREST); Dutch inventory data collection was done with the

help of Probos, Silve, Bureau van Nierop and Wim Daamen,

financed by the Dutch Ministry of Economic Affairs. 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. We are grateful to the Polish State Forest

Holding for the data collected in the project “Establishment of a

forest information system covering the area of the Sudetes and

the West Beskids with respect to the forest condition monitoring

and assessment”financed by the General Directory of State Forest

National Holding. We thank two reviewers who provided

constructive and helpful comments to help us further improve

this paper. The data used in this manuscript are summarized in

the supplementary materials (tables S1 and S2). All data needed

to replicate these results are available at https://figshare.com

and www.gfbinitiative.org. New Zealand data (doi:10.7931/V13W29)

are available from S.W. under a materials agreement

with the National Vegetation Survey Databank managed by

Landcare Research, New Zealand. Access to Poland data needs

additional permission from Polish State Forest National Holding,

as provided to T.Z.-N.

SUPPLEMENTARY MATERIALS

www.sciencemag.org/content/354/6309/aaf8957/suppl/DC1

Figs. S1 to S4

Tables S1 to S2

References (79–134)

6 May 2016; accepted 22 August 2016

10.1126/science.aaf8957

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Global Forest Biodiversity Initiative (GFBI)- Dataset Global#1

Data

October 2016

Jingjing Liang · GFBI

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TableS2 List of GFB Tree Species

Data

October 2016

Jingjing Liang · Thomas W Crowther · Nicolas Picard · Susan K. Wiser · Peter B Reich

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Table S1

Data

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Jingjing Liang · Thomas W Crowther · Nicolas Picard · Susan K. Wiser · Peter B Reich

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Supplementary Materials aaf8957Liang

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October 2016

Jingjing Liang · Thomas W Crowther · Nicolas Picard · Susan K. Wiser · Peter B Reich

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Jingjing Liang · Thomas W Crowther · Nicolas Picard · Susan K. Wiser · Peter B Reich

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