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This is the final version of the article. Available from Wiley via the DOI in this record. ; Quantifying the relationship between tree diameter and height is a key component of efforts to estimate biomass and carbon stocks in tropical forests. Although substantial site-to-site variation in height-diameter allometries has been documented, the time consuming nature of measuring all tree heights in an inventory plot means that most studies do not include height, or else use generic pan-tropical or regional allometric equations to estimate height. Using a pan-tropical dataset of 73 plots where at least 150 trees had in-field ground-based height measurements, we examined how the number of trees sampled affects the performance of locally derived height-diameter allometries, and evaluated the performance of different methods for sampling trees for height measurement. Using cross-validation, we found that allometries constructed with just 20 locally measured values could often predict tree height with lower error than regional or climate-based allometries (mean reduction in prediction error = 0.46 m). The predictive performance of locally derived allometries improved with sample size, but with diminishing returns in performance gains when more than 40 trees were sampled. Estimates of stand-level biomass produced using local allometries to estimate tree height show no over- or under-estimation bias when compared with biomass estimates using field measured heights. We evaluated five strategies to sample trees for height measurement, and found that sampling strategies that included measuring the heights of the ten largest diameter trees in a plot outperformed (in terms of resulting in local height-diameter models with low height prediction error) entirely random or diameter size-class stratified approaches. Our results indicate that even limited sampling of heights can be used to refine height-diameter allometries. We recommend aiming for a conservative threshold of sampling 50 trees per location for height measurement, and including the ten trees with the largest diameter in this sample. ; This paper is a product of the RAINFOR, AfriTRON and T-FORCES networks, for which we are indebted to the hundreds of institutions, field assistants and local communities across many countries that have supported and hosted fieldwork. The three networks have been supported by the Natural Environment Research Council (NERC) Urgency Grants and NERC Consortium Grants "AMAZONICA" (NE/F005806/1), "TROBIT" (NE/D005590/1) and "BIO-RED" (NE/N012542/1), a NERC New Investigators Grant, a European Research Council grant ("Tropical Forests in the Changing Earth System"), the Gordon and Betty Moore Foundation, the David and Lucile Packard Foundation, the European Union's Seventh Framework Programme (283080, "GEOCARBON"; 282664, "AMAZALERT"), the Royal Society and Gabon's National Parks Agency (ANPN). R.J.W.B. is funded by a NERC research fellowship (grant ref: NE/I021160/1). S.L.L. was supported by a Royal Society University Research Fellowship, ERC Advanced Grant and a Phillip Leverhulme Prize. O.L.P. is supported by an ERC Advanced Grant and a Royal Society Wolfson Research Merit Award. L.F.B. was supported by a NERC studentship, RGS-IBG Henrietta Hutton Grant and Royal Society Dudley Stamp Award. R.H. and M.C. were supported through the long-term research development project no. RVO 67985939 and a KBFSC research fellowship (2011, to R.H.). M. Svátek was funded by the Ministry of Education, Youth and Sports of the Czech Republic (grant number INGO II LG15051). We thank Georgia Pickavance for assistance with database curation, and Natacha Nssi Bengone, Sylvester Chenikan, Eric Chezeaux, Armandu Daniels, Jean-Louis Doucet, Kath Jeffery, Edi Mirmanto, Abel Monteagudo-Mendoza, Faustin Mpanya Lukasu, Reuben Nilus, Guido Pardo, Lourens Poorter, Sylvester Tan, Marisol Toledo, Armando Torres-Lezama, John Tshibamba Mukendi, Richard Tshombe, Geertje van der Heijden, Lee White, Hannsjoerg Woell and John Woods, Gabon's National Parks Agency (ANPN), the Forest Development Authority of Liberia and Wildlife Conservation Society-Democratic Republic of Congo for assistance with access to datasets. We thank an anonymous reviewer for constructive comments on this manuscript.

Tropical forests are global centres of biodiversity and carbon storage. Many tropical countries aspire to protect forest to fulfil biodiversity and climate mitigation policy targets, but the conservation strategies needed to achieve these two functions depend critically on the tropical forest tree diversity-carbon storage relationship. Assessing this relationship is challenging due to the scarcity of inventories where carbon stocks in aboveground biomass and species identifications have been simultaneously and robustly quantified. Here, we compile a unique pan-tropical dataset of 360 plots located in structurally intact old-growth closed-canopy forest, surveyed using standardised methods, allowing a multi-scale evaluation of diversity-carbon relationships in tropical forests. Diversity-carbon relationships among all plots at 1 ha scale across the tropics are absent, and within continents are either weak (Asia) or absent (Amazonia, Africa). A weak positive relationship is detectable within 1 ha plots, indicating that diversity effects in tropical forests may be scale dependent. The absence of clear diversity-carbon relationships at scales relevant to conservation planning means that carbon-centred conservation strategies will inevitably miss many high diversity ecosystems. As tropical forests can have any combination of tree diversity and carbon stocks both require explicit consideration when optimising policies to manage tropical carbon and biodiversity. ; This paper is a product of the RAINFOR, AfriTRON and T-FORCES networks, for which we are hugely indebted to hundreds of institutions, field assistants and local communities across many countries that have hosted fieldwork. The three networks have been supported by a European Research Council (ERC) grant ("T-FORCES" - Tropical Forests in the Changing Earth System), the Gordon and Betty Moore Foundation, the David and Lucile Packard Foundation, the European Union's Seventh Framework Programme (283080, 'GEOCARBON'; 282664, 'AMAZALERT'), and Natural Environment Research Council (NERC) Urgency Grants and NERC Consortium Grants 'AMAZONICA' (NE/F005806/1) and 'TROBIT' (NE/D005590/1), 'BIO-RED' (NE/N012542/1) and a NERC New Investigators Grant, the Royal Society, the Centre for International Forestry (CIFOR) and Gabon's National Parks Agency (ANPN). Additional data were included from the Tropical Ecology Assessment and Monitoring (TEAM) Network, a collaboration between Conservation International, the Missouri Botanical Garden, the Smithsonian Institution and the Wildlife Conservation Society, and partly funded by these institutions, the Gordon and Betty Moore Foundation, and other donors. J.T. was supported by a NERC PhD Studentship with CASE sponsorship from UNEP-WCMC. R.J.W.B. is funded by a NERC research fellowship (grant ref: NE/I021160/1). S.L.L. was supported by a Royal Society University Research Fellowship, ERC Advanced Grant (T-FORCES) and a Phillip Leverhulme Prize. O.L.P. is supported by an ERC Advanced Grant (T-FORCES) and a Royal Society Wolfson Research Merit Award. L.F.B. was supported by a NERC studentship and RGS-IBG Henrietta Hutton Grant. We thank the National Council for Science and Technology Development of Brazil (CNPq) for support to Project Cerrado/Amazonia Transition (PELD/403725/2012-7), Project Phytogeography of Amazonia/Cerrado Transition (CNPq/PPBio/457602/2012-0) and Productivity Grant to B.S.M and B.H.M-J. Funding for plots in the Udzungwa Mountains (Tanzania) was obtained from the Leverhulme Trust under the Valuing the Arc project. We thank the ANPN (Gabon), WCS-Congo and WCS-DR Congo, Marien Ngouabi University and the University of Kisangani for logistical support in Africa, and the Tropenbos Kalimantan project (ITCI plots) and WWF (KUB plots) for providing data from Asia. This study is contribution number 706 to the Technical Series (TS) of the BDFFP – (INPA-STRI). For assistance with access to datasets we thank Adriana Prieto, Agustín Rudas, Alejandro Araujo-Murakami, Alexander G. Parada Gutierrez, Anand Roopsind, Atila Alves de Oliveira, Claudinei Oliveira dos Santos, C. E. Timothy Paine, David Neill, Eliana Jimenez-Rojas, Freddy Ramirez Arevalo, Hannsjoerg Woell, Iêda Leão do Amaral, Irina Mendoza Polo, Isau Huamantupa-Chuquimaco, Julien Engel, Kathryn Jeffery, Luzmila Arroyo, Michael D. Swaine, Nallaret Davila Cardozo, Natalino Silva, Nigel C. A. Pitman, Niro Higuchi, Raquel Thomas, Renske van Ek, Richard Condit, Rodolfo Vasquez Martinez, Timothy J. Killeen, Walter A. Palacios, Wendeson Castro. We thank Georgina Mace and Jon Lloyd for comments on the manuscript. We thank our deceased colleagues, Samuel Almeida, Kwaku Duah, Alwyn Gentry, and Sandra Patiño, for their invaluable contributions to this work and our wider understanding of tropical forest ecology.