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The Relationship between Maturation Size and
Maximum Tree Size from Tropical to Boreal Climates

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Valentin Journé,<fnref n="1" />,<fnref n="2" /> Michał Bogdziewicz,<fnref n="2" /> Benoit Courbaud,<fnref n="1" /> Georges Kunstler,<fnref n="1" /> Tong Qiu,<fnref n="3" />

Marie-Claire Aravena Acuña,<fnref n="4" /> Davide Ascoli,<fnref n="5" /> Yves Bergeron,⁶ Daniel Berveiller,⁷ Thomas Boivin,⁸

Raul Bonal,⁹ Thomas Caignard,¹⁰ Maxime Cailleret,¹¹ Rafael Calama,¹² J. Julio Camarero,¹³ Chia-

Hao Chang-Yang,¹⁴ Jerome Chavez,¹⁵ Francesco Chianucci,¹⁶ Thomas Curt,¹⁷ Andrea Cutini,¹⁸

Adrian Das,¹⁹ Evangelia Daskalakou,²⁰ Hendrik Davi,⁸ Nicolas Delpierre,⁷ Sylvain Delzon,¹⁰ Michael

Dietze,²¹ Sergio Donoso Calderon,²² Laurent Dormont,²³ Josep Maria Espelta,²⁴ William Farfan-

Rios,²⁵ Michael Fenner,²⁶ Jerry Franklin,²⁷ Catherine Gehring,²⁸ Gregory Gilbert,²⁹ Georg Gratzer,³⁰

Cathryn H. Greenberg,³¹ Arthur Guignabert,³² Qinfeng Guo,³³ Andrew Hacket-Pain,³⁴ Arndt Hampe,³⁵

Qingmin Han,³⁶ Mick E. Hanley,³⁷ Janneke Hille Ris Lambers,³⁸ Jan Holík,³⁹ Kazuhiko Hoshizaki,⁴⁰

Ines Ibanez,⁴¹ Jill F. Johnstone,⁴² Johannes M. H. Knops,⁴³ Richard K. Kobe,⁴⁴ Hiroko Kurokawa,⁴⁵

Jonathan Lageard,⁴⁶ Jalene LaMontagne,⁴⁷ Mateusz Ledwon,⁴⁸ François Lefèvre,⁸ Theodor Leininger,⁴⁹

Jean-Marc Limousin,⁵⁰ James Lutz,⁵¹ Diana Macias,⁵² Anders Mårell,⁵³ Eliot McIntire,⁵⁴ Emily V.

Moran,⁵⁵ Renzo Motta,<fnref n="5" /> Jonathan Myers,⁵⁶ Thomas A. Nagel,⁵⁷ Shoji Naoe,⁵⁸ Mahoko Noguchi,⁵⁸

Julian Norghauer,⁵⁹ Michio Oguro,⁴⁵ Jean-Marc Ourcival,⁵⁰ Robert Parmenter,⁶⁰ Ian Pearse,⁶¹ Ig-

nacio M. Pérez-Ramos,⁶² Łukasz Piechnik,⁶³ Tomasz Podgórski,⁶⁴ John Poulsen,⁶⁵ Miranda D.

Redmond,⁶⁶ Chantal D. Reid,⁶⁷ Pavel Samonil,³⁹ C. Lane Scher,⁶⁷ William H Schlesinger,⁶⁷ Barbara

Seget,⁶³ Shubhi Sharma,⁶⁸ Mitsue Shibata,⁴⁵ Miles Silman,⁶⁹ Michael Steele,⁷⁰ Nathan Stephenson,¹⁹

Jacob Straub,⁷¹ Samantha Sutton,⁶⁷ Jennifer J. Swenson,⁷² Margaret Swift,⁶⁷ Peter A. Thomas,⁷³

Maria Uriarte,⁷⁴ Giorgio Vacchiano,⁷⁵ Amy Whipple,⁷⁶ Thomas Whitham,⁷⁶ S. Joseph Wright,⁷⁷ Kai

Zhu,⁷⁸ Jess Zimmerman,⁷⁹ Magdalena Żywiec,⁶³ James S. Clark,<fnref n="1" />,⁶⁷

<footnote n="1">¹Universite Grenoble Alpes, Institut National de Recherche pour Agriculture, Alimentation et Environnement (INRAE), Laboratoire EcoSystemes et Societes En Montagne (LESSEM), 38402 St. Martin-d'Heres, France.</footnote>

<footnote n="2">²Forest Biology Center, institute of environmental biology, Adam Mickiewicz University in Poznan, Poland.</footnote>

<footnote n="3">³Department of Ecosystem Science and Management, Pennsylvania State University, University Park, PA 16802 USA.</footnote>

<footnote n="4">⁴Centro Austral de Investigaciones Científicas (CADIC), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), B. Houssay 200 (9410) Ushuaia, Tierra del Fuego, Argentina.</footnote>

<footnote n="5">⁵Department of Agriculture, Forest and Food Sciences, University of Torino, 10095 Grugliasco, TO, Italy.</footnote>
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⁶Forest Research Institute, University of Quebec in Abitibi-Temiscamingue, Rouyn-Noranda, QC J9X 5E4, Canada.

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⁷Université Paris-Saclay, CNRS, AgroParisTech, Ecologie Systématique et Evolution, 91190, Gif-sur-Yvette, France.

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⁸Institut National de Recherche pour Agriculture, Alimentation et Environnement (INRAE), Ecologie des Forets Mediterranennes, 84000 Avignon, France.

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⁹Department of Biodiversity, Ecology and Evolution, Complutense University of Madrid, 28040 Madrid, Spain.

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¹⁰Université Bordeaux, Institut National de Recherche pour Agriculture, Alimentation et Environnement (IN-RAE), Biodiversity, Genes, and Communities (BIOGECO), 33615 Pessac, France.

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¹¹INRAE, Aix-Marseille University, UMR RECOVER, Aix-en-Provence, France.

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¹²ICIFOR (Forest Research Institute). INIA-CSIC. 28040 Madrid. Spain.

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¹³Instituto Pirenaico de Ecologla, Consejo Superior de Investigaciones Cientificas (IPE-CSIC), 50059 Zaragoza, Spain.

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¹⁴Department of Biological Sciences, National Sun Yat-sen University, Kaohsiung 80424, Taiwan.

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¹⁵Unité Evolution et Diversité Biologique (EDB), CNRS, IRD, UPS, 118 route de Narbonne, 30162 Toulouse, France.

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¹⁶CREA - Research Ventre for Forestry and Wood, Viale S. Margherita 80, 52100 Arezzo, Italy.

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¹⁷Aix Marseille universite, Institut National de Recherche pour Agriculture, Alimentation et Environnement (INRAE), 13182 Aix-en-Provence, France.

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¹⁸Research Centre for Forestry and Wood, Arezzo, Italy.

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¹⁹USGS Western Ecological Research Center, Three Rivers, CA, 93271 USA.

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²⁰Institute of Mediterranean and Forest Ecosystems, Hellenic Agricultural Organization, 11528 Athens, Greece.

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²¹Earth and Environment, Boston University, Boston, MA, 02215 USA.

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²²Universidad de Chile, Facultad de Ciencias Forestales y de la Conservacion de la Naturaleza (FCFCN), La Pintana, 8820808 Santiago, Chile.

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²³Centre d'Ecologie Fonctionnelle et Evolutive (CEFE), Centre National de la Recherche Scientifique (CNRS), 34293 Montpellier, France.

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²⁴Centre de Recerca Ecologica i Aplicacions Forestals (CREAF), Bellaterra, Catalunya 08193, Spain.

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²⁵Biology Department, Center for Energy, Environment, and Sustainability, Wake Forest University, Winston Salem, NC, United States.

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²⁶Biology Department, University of Southampton, United Kingdom.

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²⁷Forest Resources, University of Washington, Seattle, WA 98195 USA.

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²⁸Department of Biological Sciences and Center for Adaptive Western Landscapes.

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²⁹Department of Environmental Studies, University of California, Santa Cruz, CA 95064 USA.

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³⁰Institute of Forest Ecology; Department of Forest- and Soil Sciences, University of Natural Resources and Life Sciences, Vienna.

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³¹Bent Creek Experimental Forest, USDA Forest Service, Asheville, NC 28801 USA.

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³²INRAE, Bordeaux Sciences Agro, UMR 1391 ISPA, Villenave d'Ornon, France.

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³³Eastern Forest Environmental Threat Assessment Center, USDA Forest Service, Southern Research Station, Research Triangle Park, NC 27709 USA.

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³⁴Department of Geography and Planning, School of Environmental Sciences, University of Liverpool, Liver-
75 pool, United Kingdom.

76 ³⁵BIOGECO, INRA, University of Bordeaux, Cestas, France.

77 ³⁶Department of Plant Ecology Forestry and Forest Products Research Institute (FFPRI), Tsukuba, Ibaraki, 305-8687 Japan.

79 ³⁷School of Biological and Marine Sciences, University of Plymouth, Plymouth, United Kingdom.

80 ³⁸Plant Ecology, Institute of Integrative Biology, D-USYS, ETH Zürich, Zürich, Switzerland.

81 ³⁹Department of Forest Ecology, Silva Tarouca Research Institute, 60200 Brno, Czech Republic.

82 ⁴⁰Department of Biological Environment, Akita Prefectural University, Akita 010-0195, Japan.

83 ⁴¹School for Environment and Sustainability, University of Michigan, Ann Arbor, MI 48109.

84 ⁴²Institute of Arctic Biology, University of Alaska, Fairbanks, AK 99700, USA.

85 ⁴³Health and Environmental Sciences Department, Xian Jiaotong-Liverpool University, Suzhou, China, 215123.

86 ⁴⁴Department of Plant Biology, Program in Ecology, Evolutionary Biology, and Behavior, Michigan State University, East Lansing, MI 48824.

88 ⁴⁵Department of Forest vegetation, Forestry and Forest Products Research Institute, Tsukuba, Ibaraki, 305-8687, Japan.

90 ⁴⁶Department of Natural Sciences, Manchester Metropolitan University, Manchester M1 5GD, UK.

91 ⁴⁷Department of Biological Sciences, DePaul University, Chicago, IL 60614 USA.

92 ⁴⁸Institute of Systematics and Evolution of Animals, Polish Academy of Sciences, Slawkowska 17, 31-016 Krakow, Poland.

94 ⁴⁹USDA, Forest Service, Southern Research Station, PO Box 227, Stoneville, MS 38776.

95 ⁵⁰CEFE, Univ Montpellier, CNRS, EPHE, IRD, 1919 route de Mende, 34293 Montpellier Cedex 5, France.

96 ⁵¹Department of Wildland Resources, and the Ecology Center, Utah State University, Logan, UT 84322 USA.

97 ⁵²Department of Biology, University of New Mexico, Albuquerque, NM 87131 USA.

98 ⁵³INRAE, UR EFNO, FR-45290 Nogent-sur-Vernisson, France.

99 ⁵⁴Pacific Forestry Centre, Victoria, British Columbia, V8Z 1M5 Canada.

100 ⁵⁵School of Natural Sciences, UC Merced, Merced, CA 95343 USA.

101 ⁵⁶Department of Biology, Washington University in St. Louis, St. Louis, MO.

102 ⁵⁷Department of forestry and renewable forest resources, Biotechnical Faculty, University of Ljubljana, Ljubljana, Slovenia.

104 ⁵⁸Tohoku Research Center, Forestry and Forest Products Research Institute, Morioka, Iwate, 020-0123, Japan.

106 ⁵⁹Institute of Plant Sciences, University of Bern, Altenbergrain 21, Bern 3013, Switzerland.

107 ⁶⁰Valles Caldera National Preserve, National Park Service, Jemez Springs, NM 87025 USA.

108 ⁶¹Fort Collins Science Center, 2150 Centre Avenue, Bldg C, Fort Collins, CO 80526 USA.

109 ⁶²Inst. de Recursos Naturales y Agrobiologia de Sevilla, Consejo Superior de Investigaciones Científicas (IRNAS-CSIC), Sevilla, Andalucia, Spain.

111 ⁶³W. Szafer Institute of Botany, Polish Academy of Sciences, Lubicz 46, 31-512 Krakow, Poland.

112 ⁶⁴Department of GameManagement and Wildlife Biology, Faculty of Forestry and Wood Sciences, Czech University of Life Sciences Prague; Kamýcká 129, 165 00 Prague, Czech Republic.

114 ⁶⁵The Nature Conservancy, Boulder, CO 80302.

115 ⁶⁶Department of Environmental Science Policy and Management, University of California Berkeley, Berkeley,
116 California, USA.

117 ⁶⁷Nicholas School of the Environment, Duke University, Durham, NC 27708 USA.

118 ⁶⁸Ecology and Evolutionary Biology Department, Yale University, 165 Prospect Street, New Haven, USA.

119 ⁶⁹Department of Biology, Wake Forest University, 1834 Wake Forest Rd, Winston-Salem, NC 27106 USA.

120 ⁷⁰Department of Biology, Wilkes University, 84 West South Street, Wilkes-Barre, PA 18766 USA.

121 ⁷¹Department of Environmental Science and Ecology, State University of New York-Brockport, Brockport, NY 14420 USA.

123 ⁷²Data Science, College of William and Mary, Williamsburg, VA, USA.

124 ⁷³School of Life Sciences, Keele University, Staffordshire ST5 5BG, UK.

125 ⁷⁴Department of Ecology, Evolution and Environmental Biology, Columbia University, 1113 Schermerhorn Ext., 1200 Amsterdam Ave., New York, NY 10027.

127 ⁷⁵Department of Agricultural and Environmental Sciences - Production, Territory, Agroenergy (DISAA), University of Milan, 20133 Milano, Italy.

129 ⁷⁶Department of Biological Sciences, Northern Arizona University, Flagstaff, AZ 86011 USA.

130 ⁷⁷Smithsonian Tropical Research Institute, Apartado 0843n03092, Balboa, Republic of Panama.

131 ⁷⁸School for Environment and Sustainability, University of Michigan, Ann Arbor, Michigan, USA.

132 ⁷⁹Department of Environmental Sciences, University of Puerto Rico, Rio Piedras, PR 00936 USA.

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The fundamental trade-off between current and future reproduction has long been considered to result in a tendency for species that can grow large to begin reproduction at a larger size. Due to the prolonged time required to reach maturity, estimates of tree maturation size remain very rare and we lack a global view on the generality and the shape of this trade-off. Using seed production from five continents, we estimate tree maturation sizes for 486 tree species spanning tropical to boreal climates. Results show that a species' maturation size increases with maximum size, but in a non-proportional way: the largest species begin reproduction at smaller sizes than would be expected if maturation were simply proportional to maximum size. Furthermore, the decrease in relative maturation size is steepest in cold climates. These findings on maturation size drivers are key to accurately represent forests' responses to disturbance and climate change.

keywords: tree fecundity | size | seed production | tree maturation | life-history | allometry

Running title:
Relation between Maturation and Maximum Tree Size

Type of article: Synthesis

\#Total word count abstract: ~149 \#Total word count main text: ~ 5300 \# 78 references \# 1
Table and 6 Figures (color) \# 1 supplementary material

Data and code availability statement

Data and code supporting our results are archived on the Open Science Framework (OSF)
Repository: https://doi.org/10.17605/OSF.I0/U23VY. All analyses used R Core Team
(2023) (v4.3.0) and published R packages.

Author contributions

V.J., G.K. and J.S.C performed analyses, led the paper, and designed the study. V.J., M.B., B.C., G.K., T.Q, and J.S.C co-wrote the paper. J.S.C compiled the MASTIF network, and wrote the MASTIF model and software. All authors contributed data and revised the paper.

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167 **correspondence:**

168 Journé Valentin*: journey.valentin@gmail.com & James S. Clark†: jimclark@duke.edu

169 *Forest Biology Center, institute of environmental biology, Adam Mickiewicz University in Poznan, Poland.

170 † Nicholas School of the Environment, Duke University, Durham, NC 27708 USA.
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# Introduction

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The size or age at maturity is critical for tree population fitness and forest regeneration because recruitment opportunities can occur when trees are any size or age (Dietze & Clark, 2008; McDowell et al., 2020; Qiu et al., 2021). In trees, reproduction follows an extended maturation phase (Thomas, 1996; Clark et al., 2004). Juvenile allocation to leaves and the roots and architecture that supports them build the large light- and water-harvesting capacity characteristic of the tree life form. Allocation can then shift to include reproduction. This delayed maturation of trees is linked to the fundamental trade-off between current and future reproduction (Stearns, 1989).

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On one hand, delayed reproduction sacrifices early seed production to reap future benefits. In environments marked by intense competition and a reliable future, delayed reproduction benefits from large size and the resources that accumulate if juveniles allocate to growth and survival (Falster & Westoby, 2003; Wenk & Falster, 2015). On the other hand, the advantages of large size can come with costs, including water transport high into the crown and biomechanical risk of bole fracture or windthrow (Niklas, 1994; Koch et al., 2004; Dietze & Clark, 2008; Lines et al., 2012). Current reproduction avoids the risks of an uncertain future, and it contributes most to fitness in non-competitive or frequently disturbed environments (Charlesworth, 2000).

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Among tree species, the potential trade-off between current and future reproduction might require a balance of benefits and risks and result in a positive association across species in maturation and maximum size or age (Loehle, 1988; Thomas, 1996; Davies & Ashton, 1999; Westoby et al., 2002; Falster & Westoby, 2003; Wenk & Falster, 2015; Visser et al., 2016). Our understanding of the variation of maturation size among tree species is, however, extremely limited and there are no large-scale studies on this topic. We thus have a poor understanding of how maturation size varies with species maximum size and the relative importance of other factors such as species climate niche and functional traits.

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In the absence of maturation estimates, earth system models (ESMs) incorporate assumptions that are expected to bias lifetime reproduction. Many ESMs omit impacts of life history on disturbance response entirely (see McDowell et al. 2020 for a review). In models that do accommodate life history, maturation size — *d*<sub>mat</sub> (for diameter) — is independent of maximum size — *d*<sub>max</sub> (Kohler & Huth, 2004; Wallentin et al., 2008; Yang et al., 2022) (Fig. 1, black dotted line). An alternative hypothesis is that maturation size is proportional to maximum size. It is consistent with a study at Barro Colorado Island in Panama, where Visser et al. (2016) reported that *d*<sub>mat</sub> = *d*<sub>max</sub>/2 (red dashed line in Fig. 1). This is related to the classical prediction of a proportionate increase in maturation age with increased maximum age from simple optimization models in animals (Charnov & Berrigan, 1990, 1991; Jensen, 1996; Thorson et al., 2017) and trees (Clark, 1991). Indeed, if the predictions for age also apply to size, then this **proportionate risk model** means that the maturation delay incurred for increased maximum size is the same for species large and small, represented by the red line in Fig. 1.

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In fact, it would be remarkable if this relationship was the same for species of all sizes because the constraints on the large size and the relative contribution to fitness of early seed production could vary widely depending on the species' maximum size. If mortality risks and allocation demands change with age and size (Charnov & Berrigan, 1990), then the strictly proportional relationship between maturation size (*d*<sub>mat</sub>) and maximum size (*d*<sub>max</sub>) can be generalized to a power relationship,
$$d_{mat} = \alpha \times d_{max}^{\beta_d} \qquad (1)$$

The proportionate model means that $\beta_d = 1$ in Eq. (1) (Fig. 1a). An accelerating risk model refers to the case where the maturation delay required for large species to increase maximum size is greater than for small species. If $\beta_d > 1$ (purple in Fig. 1), the relative size at maturation ($d_{rel} = d_{mat}/d_{max}$) continues to increase for species in the largest size classes (Fig. 1b). Consider, for example, an expected fitness gain from extending end-of-life reproduction that comes with increased size and age. The early life investments in structural support or defenses needed for an incremental increase in maximum size might be especially high for the largest species.

Alternatively, a diminishing risk model refers to the case where the need to further delay maturation size declines for species already at large size. If $0 < \beta_d < 1$, then species that reach large size do not incur the same proportionate delay risk as small species. As $\beta_d$ approaches zero, the largest species mature at nearly the same size as the small species. Then, the relative size at maturation $d_{rel}$ declines with maximum size (Fig. 1b).

Improved understanding of maturation size confronts challenges posed by slow dynamics and limited observation. Where there is a dense canopy, the reproductive status of individual trees is often not detected, and crop failures (little or no seed production in trees that have reached maturity) are common. Likewise, seed traps often fail to recover seeds from nearby reproductive trees, especially the low seed production of newly mature individuals (LaDeau & Clark, 2001). Detection error can be minimized where observations come from above the canopy or open settings like savannas, seed orchards, or common gardens (LaDeau & Clark, 2001; Caignard et al., 2021). Still, a time series of observations is needed because an individual reproducing this year will have matured at some time in the past. Estimates of maturation status from time series data allow for detection error similar to the way it is used in capture-recapture models. Maturation can be treated as a hidden Markov process (see detailed Supplements to Clark et al. 2004, 2019). As in capture-recapture models, the probability that an individual is mature in a given year depends not only on failure to detect in the current year but also on the history and future of observations on the same individual. The more times that reproduction is not detected in the past (or future), the lower the probability that a tree is mature now. In tree-fecundity studies, the complexity is compounded by the "masting" phenomenon, where quasi-synchronous, quasi-periodic crops require observations over several years, making a large number of observations in a single year insufficient. Most studies where maturation size has been estimated focus on open-grown trees and/or have limited taxonomic breadth, habitat variation, or both (Wenk et al., 2018; Thomas, 1996; Davies & Ashton, 1999; Kohyama et al., 2003; Wright et al., 2005; Visser et al., 2016; Minor & Kobe, 2019).

Inferring the relationship between maturation and maximum size has also to control for the environment (Wenk & Falster, 2015) and species characteristics (Visser et al., 2016). While the effects of climate on maturation size are unknown, tree fecundity responds to seasonal temperature and moisture, soils, and light availability, which depends on the local competitive environment (Clark et al., 2014; Caignard et al., 2017; Minor & Kobe, 2019; Le Roncé et al., 2021; Qiu et al., 2022; Journé et al., 2022). Also, fast growth and accelerated competition that comes from long growing seasons in the wet tropics do not necessarily imply small or large maturation sizes.
<figure><img src="image_1.png" /><figcaption>Figure 1: Hypothesized association between maturation size ($d_{mat}$) and maximum size ($d_{max}$) (a) and the relative size at maturation ($d_{rel} = d_{mat}/d_{max}$) (b) (Eq. (1)). To highlight the effects of size (parameter $\beta_d$), values of parameter $\alpha$ are selected to yield an equivalent diameter at $d_{max} = 60$ cm. Two "baseline" hypotheses (dashed lines) are independence between $d_{mat}$ and $d_{max}$ (black dotted) and proportionate delay (red dotted), the latter is expected if increased size incurs the same maturation delay at all size classes. Two alternative hypotheses are increasing (purple - accelerating risk model) or decreasing (blue - diminishing risk model) maturation delays in the largest size classes.</figcaption></figure>
The relationship between maturation and maximum size could be associated with other plant functional traits, that would reflect diverse plant strategies. Fast growth in open environments is often associated with low wood density and high specific leaf area (SLA) (Moles et al., 2004, 2006; Thomas et al., 2015; Visser et al., 2016; Wenk et al., 2018). However, it is unclear whether the same traits that are involved in fast growth are also associated with maturation at a small size. Furthermore, if large-seeded species need to accumulate resource reserves, then there could be a positive association between seed size and maturation size (Moles et al., 2004). Relatedly, high reproductive expenditures, measured as seed size × seed number (Qiu et al., 2022), might be associated with delayed maturation size. Due to their co-dependence, it is necessary to model all of these traits jointly, while accounting for the effects of habitat and phylogenetic groups (Clark, 2016; Seyednasrollah & Clark, 2020; Bogdziewicz et al., 2023; Qiu et al., 2023).

In this study, we provide the first comprehensive estimates of tree maturation size, obtained for 486 tree species on five continents, incorporating effects of the environment over a large range of tree diameters and habitats. We use the Masting Inference and Forecasting (MASTIF) network and modeling framework to accommodate the dependence between observations between trees and within trees over time (Clark et al., 2021; Sharma et al., 2022; Qiu et al., 2022; Journé et al., 2022). Based on MASTIF estimates we derive maturation size as tree diameter at the onset of female reproductive function allowing us to compare maturation sizes across species that vary in reproductive biology (e.g., Pinaceae commonly produce male cones earlier than female cones; many species have no such separation) and where pollen production can be hard to quantify. We first evaluate how maturation varies with species' maximum size and test the three alternative models of Fig. 1 with our estimates of maturation size and estimates of species' maximum size. Then, we evaluate how the relationship between maturation size and maximum size is influenced by climate and its association with other plant functional traits.

## Materials and Methods

Our analysis includes three elements (Fig. 2). We first parameterize a model for individual maturation status and fecundity based on diameter, shade conditions, and environmental variables (Fig. 2a). The year in which an individual achieves maturity is almost never observed. Instead, seeds counted in traps or in crowns vary from year to year. Successive observations represent a time series for every tree. This first step estimates maturation status and conditional fecundity (seeds per tree per year given that it is mature) for all trees in the network. From this fitted model, we generate predictive distributions of maturation status across diameter with other variables held at intermediate values to estimate $d_{mat}$ from the model. Again, this prediction from the model is necessitated by the fact that true maturation status is an estimate, not a state that is directly observed. Second, we estimated the model of Fig. 1 to obtain estimates of $\alpha$ and $\beta_d$ (Fig. 2b), while controlling for other variables that could affect their relationship. Finally, we evaluate the species-level trait relationship that includes maturation size (Fig. 2c). The following section describes these elements of the analysis.
<figure><img src="image_2.png" /><figcaption>Figure 2: Three elements of the analysis include a) an individual-scale analysis (blue) to estimate maturation status each year and to parameterize relationships that control maturation. This fitted model is the basis for species-level prediction of maturation size (red). b) Species-level expected maturation size based on the proportionate risk model, controlling for species' differences in their climate domains. c) Analysis of species-level trait relationships with maturation size.</figcaption></figure>

MASTIF data and model

The MASTIF model and data summarized here are detailed in Clark *et al.* (2019) and its extended Supplement (see also Qiu *et al.* 2021, 2022; Journé *et al.* 2022). Data are of two types, crop counts on trees and seed traps in mapped inventory plots (MASTIF) (Clark *et al.*, 2019) (Fig. S1). The initial sample size is approximately 12 million tree-years from five continents on 898 species and 112 families. The majority of observations (99%) are derived from longitudinal studies, involving repeated observations of all trees on a plot or individual trees. The remaining crop count observations (1%) are collected opportunistically through the iNaturalist project MASTIF (Clark *et al.*, 2019). The number of species observed per plot ranges from 1 to 221 species. The number of species observations is larger for seed trap monitoring (476 species in total, 22,929 tree-year observations on average) than for crop count monitoring (130 species in total, 1,058 tree-year observations on average). Most plots are localized in North America and central Europe (97%), whereas most species observations are coming from South America (54%). On average, 75% of individual tree year observation are coming from the tropics. Additional information is provided in Table S1 and Supplementary Files 1 and 2. For both data types, observations include species, diameter, shade class (ranging from "full sun", class 1, to "full shade", class 5), number of fruiting structures, and an estimate of the fraction of the total crop represented by the count. For crop counts, the data model is beta-binomial, with binomial uncertainty for the counts given crop fraction, and beta uncertainty for crop fraction. The seed traps data additionally include mapped locations of trees and seed traps, which is used to jointly estimate fecundity, dispersal, and, for seeds identified only to
genus, species identity. For seed traps, the data model is Poisson for counts given dispersal and species, a bivariate Student's t (i.e. 2Dt) redistribution kernel for dispersal (Clark et al., 1999), and a multinomial species probability (many seeds are identified only to genus level).

The MASTIF model is a dynamic model for year-to-year and tree-to-tree seed production. The model allows for conditional independence in crop counts and seed traps data through latent states. It estimates maturation state and conditional fecundity (seed production given the individual is mature), which depend on tree size, shading, local climate, and soil conditions. Random effects on individuals and years allow for wide variation between trees and over time. The posterior distribution includes the parameters and latent states presented in Clark et al. (2019), and summarized in Qiu et al. (2022) and Journé et al. (2022). Model fitting was accomplished with Gibbs sampling, a Markov chain Monte Carlo technique based on sampling from conditional distributions. Model structure and methodology are implemented with the R package Mast Inference and Forecasting (mastif, v1.0.1) (Clark et al., 2019).

## Derivation of tree maturation size from fitted MASTIF model

Tree maturation size ($d_{mat}$) is derived from an individual-scale model fitted to each species with MASTIF. We define tree maturation size ($d_{mat}$) as the diameter when a tree is mature and has the capacity to produce enough seed to construct one fruiting structure, $f_{min}$. For species that produce one-seeded fruits (e.g., Quercus, Juglandaceae), $f_{min} = 1$. For species that produce cones (e.g., Pinaceae, Cupressaceae), pods (e.g., Fabaceae, Bignoniaceae), or other capsules that house multiple seeds (e.g., Fagus capsules), $f_{min}$ is the number of seeds contained in that structure. The data and definitions we use to determine $d_{mat}$ differ from those employed in previous studies (e.g. Visser et al. 2016), as we use both crop count and seed trap observation and not only maturation status. The estimation of individual fecundities, obtained through MASTIF model, is also included, taking into account tree characteristics and environment (Clark et al., 2021; Qiu et al., 2021; Journé et al., 2022). MASTIF models the effects of environmental predictors on conditional fecundity (given mature status), because immature trees do not respond to predictors (it is always zero). [Modeling environmental effects on (unconditional) fecundity would make no more sense than including immature individuals in studies of masting intervals or synchronicity.] Conditional fecundity $\psi$ is represented by a log-normal distribution, which allows for the effects of the environment. The log-normal is undefined for zero seeds. Zeros are accommodated by the fact that trees can be in the immature state ($\rho = 0$), or conditional fecundity can be below the threshold $f_{min}$, as in a failed seed crop (Clark et al., 2004, 2019),

$$f = \begin{cases} \psi & \rho = 1 \\ 0 & (\rho = 0) + (\rho = 1)(\psi < f_{min}) \end{cases} \qquad (2)$$

An individual is immature until the first time fecundity rises above the threshold for producing fruit, i.e., ($\rho_{i,t} = 1$)($\psi_{i,t} > f_{min}$). Specifically for tree i in year t,
$$
\begin{align}
f_{i,t} &= \psi_{i,t} \times \rho_{i,t} \\
\rho_{i,t} | \rho_{i,t-1}, \rho_{i,t+1} &\sim \text{Bernoulli}(\rho_{i,t-1} + (1 - \rho_{i,t-1})\rho_{i,t+1}\Phi(\beta_0^\rho + \beta_1^\rho d_{i,t})) \\
\log \psi_{i,t} &\sim N(\mathbf{x}'_{i,t}\beta^x + \dots, \sigma^2) \tag{3}
\end{align}
$$

where $\Phi(\cdot)$ is the standard normal cumulative distribution function for the probit probability of transitioning to the mature state, depending on tree diameter $d_{i,t}$. Importantly, $\Phi(\beta_0^\rho + \beta_1^\rho d_{i,t})$ is the probability of making the transition for an individual that is now in the immature state. For this reason, the coefficients $\beta_0^\rho, \beta_1^\rho$ for maturation in the second line of Eq. (3) engage only for the transition tree-years, $[\rho_{i,t}|\rho_{i,t-1} = 0, \rho_{i,t+1} = 1]$. Predictors in the design vector for conditional fecundity $\mathbf{x}'_{i,t}$ include the mean climate variables (defined at the species level) tested here and competition by neighbors, and $\beta^x$ is the estimated parameter vector. The ellipses (...) in Eq. (3) includes individual effects (subscript i) and year effects (subscript t) (Clark et al., 2019). The variance not assigned to predictors is $s^2 = \sigma^2 + \text{Var}(\text{individuals}) + \text{Var}(\text{years})$.

Setting all other fitted variables at their mean values and intermediate shade (shade class 3 on the scale from 1 to 5), we obtained (unconditional) fecundity $f$ from the fitted model. We first factored the joint distribution of conditional fecundity and maturation,

$$ [\psi > f_{\text{min}}, \rho = 1] = [\psi > f_{\text{min}} | \rho = 1] [\rho = 1] \quad (4) $$

Using Bayes' theorem, the cumulative distribution function for maturation diameter is

$$
\begin{align}
[d_{\text{matr}} > d | \psi > f_{\text{min}}, \rho = 1] &\propto [\psi > f_{\text{min}}, \rho = 1 | d] [d] \nonumber \\
&= [\psi > f_{\text{min}} | \rho = 1, d] [\rho = 1] [d] \nonumber \\
&= \Phi(z_1) \Phi(z_2) [d] \tag{5}
\end{align}
$$

where $z_1 = \frac{\log f_{\text{min}}}{s} - \mathbf{x}'\beta^\psi$ (log normal fecundity), $z_2 = \beta_0^\rho + \beta_1^\rho d$ (probit maturation), and again, $s^2$ is the marginal variance for conditional fecundity. We have taken the diameter distribution $[d]$ to be uniform. The distribution of maturation size is obtained using inverse distribution sampling from Eq. (5), and we estimated $d_{\text{mat}}$ as the mean of this distribution. We selected species for which maturation and fecundity schedules could be estimated with confidence. The selection was based on estimates of maturation status from the MASTIF model, and we retained species with at least 10 immature and 10 mature individuals. This included 486 species observed over a range of values for diameters.

## Trait and climate data

Like maximum tree height or age, maximum tree diameter is a useful concept, despite the fact that it cannot be known. To incorporate the concept of size differences, we use extreme sizes available from literature and our inventory data, recognizing that the concept of a maximum becomes most meaningful with large sample sizes, which are not available for all species. For the final analysis here, we kept the highest estimates
of $d_{max}$. Sources in Table S3 include tropical species from large plots in central Panama (189 species) and French Guyana (33 species), which together represent 45.7% of values. Estimates extracted from the internet (e.g. encyclopedia, online flora) include 173 species (35.6%) (Table S3). For species not estimated in other sources, we used forest inventory data, evaluated by two approaches, both based on order statistics. We avoided using the absolute largest reported value in forest/MASTIF inventories due to the high noise levels associated with extremes. Order statistics were preferred over quantiles, the latter being determined by whether there are huge numbers of small trees in the data set; quantiles are based on the entire stand structure, whereas here the goal is to estimate the largest sizes, regardless of whether there are few or many small trees. For species present in national forest inventories we estimated $d_{max}$ following Qiu et al. (2021) by using the tenth largest order statistic (38 species, 7.8%). For the remaining species present in MASTIF inventories, and with at least more than 90 unique individuals, we used the fifth largest order statistics (representing in total 8.4%). For species having only maximal plant height (Liu et al., 2019), but no $d_{max}$, we converted them to $d_{max}$ using allometric equations of Feldpausch et al. (2011) (12 species, <2.5%). Observations of $d_{max}$ coming from the internet are usually higher than data from National Forest Inventories, allometric predictions, and MASTIF inventories (Fig. S2). Seed size estimates came from measurements in our lab (Clark et al., 2021), the primary literature, and the TRY Plant Trait Database (Kattge et al., 2011). Wood density and SLA are from the compilation of Carmona et al. (2021). We used genus- or family-level means for seed size, SLA, and wood density values that were missing at the species level (15%, 28%, and 26%, respectively). We defined a species' seed productivity as (mass per seed) × (mean seeds per tree basal area) (Qiu et al., 2022).

For species' climate, we extracted average temperature (in °C) and moisture deficit (evapotranspiration minus precipitation, in mm) for each species based on all occurrences in the Global Biodiversity Information Facility (GBIF) through the R package rgbif (Chamberlain & Boettiger, 2017). The GBIF request is available from reference GBIF.org (2022). For species that are absent from GBIF, we extracted temperature and deficit from the MASTIF sites where those species were reported (162 species, 33%). Climate variables were obtained from CHELSA (Karger et al., 2017).

## Maturation and maximum size

To test the alternative hypotheses that the maturation diameter decreases ($\beta_d < 1$) or increases ($\beta_d > 1$) with maximum species size (Fig. 2b), we estimated parameters in Eq. (1) with the model

$$ \log_{10}(d_{\text{mat}_s}) = \log_{10}(\alpha) + \beta_d \times \log_{10}(d_{\text{max}_s}) + \dots + \epsilon_s \\ \epsilon \sim N(0, \sigma^2) \qquad (6) $$

for species s, where the ellipsis includes climatic variables (moisture deficit and temperature) and their interactions with $d_{max}$. We tested alternative models including independence between maturation and maximum size (fitted $\alpha$ with $\beta_d$ fixed at zero), proportionate increase (fitted $\alpha$ with $\beta_d = 1$), and changing relationship with size (both $\alpha$ and $\beta_d$ estimated). Models were fitted with regression by using species average
estimates of $d_{mat}$ as a response, and we included the inverse of the standard error of $d_{mat}$ as weights. Model selection and fit were evaluated with AIC and root-mean-square error (RMSE). Regression dilution could cause underestimation of the strength between here $d_{mat}$ and $d_{max}$ when a predictor (i.e. $d_{max}$) contains errors (Frost & Thompson, 2000; Detto et al., 2019). We thus ran additional analyses to test the robustness of our results to the regression dilution effect (see Supplementary material A.2). First, we corrected the parameter $\hat{\beta}_d$ from measurement error by using the R package *mecor* (Nab, 2021) (v1.0). Secondly, we tested if the relationship between $d_{mat}$ and $d_{max}$ varies depending on the origin of $d_{max}$.

## Joint trait analysis

We evaluated the association between maturation size and other species' traits from the ability of $d_{mat}$ to predict other trait values while allowing for climate and phylogeny effects (Fig. 2c). The marginal correlations that are commonly used for this purpose do not account for the many ways that traits can be related to one another. For instance, maturation size might be associated with maximum size because both tend to be high in warm climates, or in the phylogenetic groups that tend to occur in warm climates. To accommodate co-dependence between trait values we used Generalized Joint Attribute Modeling (GJAM) with traits as responses (Clark 2016). To account for phylogeny in the joint traits model, we diverged from traditional assumptions concerning residual covariance. Instead, we adopted a direct inference of the effects of phylogenetic groups. Traditional approaches of phylogenetic correction build on highly specific assumptions for the residual variance (random walk, or more complex models representing stabilizing selection such as the Ornstein-Uhlenbeck model). Our departure from these assumptions stems from the recognition that natural selection does not operate uniformly, neither within a given species pair nor across a broad spectrum of species. Our GJAM analysis explored phylogenetic contributions, with species groups treated as random effects and covariance that is unconstrained by assumptions on divergence rates (Qiu et al., 2023). Explanatory variables included temperature, moisture deficit, and their interaction. Traits included wood density (g m⁻³), specific leaf area (SLA) (mm² mg⁻¹), species seed productivity (kg m⁻² basal area), seed size (g), maximum diameter ($d_{max}$) (cm), and maturation diameter ($d_{mat}$) (cm). All traits were log-transformed. We included a random phylogenetic group effect in the joint trait analysis (Qiu et al., 2022; Bogdziewicz et al., 2023; Qiu et al., 2023). For species in speciose genera (more than 10 species), genus was used as the phylogenetic group. For species in less speciose genera but belonging to families with more than five species, family was used as the phylogenetic group. For the remaining species (<25% of the total), an 'other' category was used. To estimate the direct effect of traits (i.e. SLA, wood density, species seed productivity, seed size) and climatic variables on $d_{mat}$, we report conditional parameters from GJAM. Conditional parameters are estimated by extracting the parameters of the conditional distribution of traits conditioned on $d_{mat}$. Conditional parameters estimate the direct associations between traits while accounting for climate and phylogeny. Conditional parameters were obtained with the *gjam* R package (v2.6.2) (Supplementary Material, Section A.1).
## Relation of $d_{mat}$ along the phylogeny

We visualized how $d_{rel}$ varies across species phylogeny by making a phylogenetic tree plot. We used the phylogeny from Zanne *et al.* (2014), and retrieved phylogenetic information for 400 out of the 486 studied species. Of the species missing from the phylogeny (i.e. 86 species), the relative proportion of missing phylogenetic information is about 13.2% for temperate species and about 19.4% for tropical species. We then tested for a phylogenetic signal in $d_{rel}$ and $d_{mat}$ using Pagel's $\lambda$ (Pagel, 1999) (which test for a Brownian motion evolutionary signal), with values close to 0 indicating low phylogenetic signal and values close to 1 suggesting a phylogenetic correlation. We plotted the phylogenetic tree with ggtree R package (v3.8) (Yu *et al.*, 2017). We estimated the Pagel's $\lambda$ by using the phylosig function from phytools (v1.5) (Revell, 2012).

<table><caption>Table 1: Coefficient estimates and fit to Eq. (6). The selected model with the lowest AIC (bold font at top) includes temperature ($\beta_T$) and the interaction between $d_{max}$ and temperature ($\beta_{dT}$). The proportional cost model has $\beta_d$ fixed at 1. The independence model has $\beta_d$ fixed at 0. Additional models that include moisture deficit and temperature have higher AIC values (Table S4).</caption><thead><tr><th>α</th><th>β<sub>d</sub></th><th>β<sub>T</sub></th><th>β<sub>dT</sub></th><th>σ</th><th>AIC</th><th>RMSE</th></tr></thead><tbody><tr><td>3.71 [1.94, 7.07]</td><td>0.30 [0.15, 0.46]</td><td>-0.023 [-0.035, -0.011]</td><td>0.012 [0.0058, 0.019]</td><td>0.089</td><td><strong>-62</strong></td><td>10.2</td></tr><tr><td>1.08 [0.93, 1.25]</td><td>0.59 [0.55, 0.63]</td><td>-</td><td>-</td><td>0.090</td><td>-52</td><td>10.0</td></tr><tr><td>0.24 [0.23, 0.26]</td><td>1</td><td>-</td><td>-</td><td>0.12</td><td>248</td><td>18.8</td></tr><tr><td>9.25 [8.69, 9.85]</td><td>0</td><td>-</td><td>-</td><td>0.15</td><td>447</td><td>15.4</td></tr></tbody></table>

## Results

Maturation size is associated with maximum size, but not proportionately so (Fig. 3a). Large inter-specific variation in $d_{mat}$ estimates had 95% quantiles that ranged from 4.0 to 51 cm, with relative maturation size ($d_{rel} = d_{mat}/d_{max}$) quantiles of (0.07, 0.65). Contrary to the baseline independence model ($\beta_d = 0$), trees did not start to reproduce at a constant size (dashed black line in Fig. 3a). If we force proportionality (fix $\beta_d$ at 1), the estimate of $\hat{\alpha} = 0.24(0.23, 0.26)$ (line 3 of Table 1) is consistent with Loehle's (1988) range for hardwoods (1/5 to 1/4), but far outside his range for conifers (1/15 to 1/10). The 95% CI that is well below 0.5. This differs from the Visser *et al.* (2016)'s estimate of 1/2 for Barro Colorado Island (N = 60 species), Panama, and with Minor & Kobe (2019) La Selva, Costa Rica (N = 16 species). It is crucial to acknowledge that the aforementioned authors employed a distinct definition of $d_{mat}$ and estimated larger $d_{mat}$ (Fig. S3). Moreover, this proportional cost model ($\beta_d = 1$) fits poorly, with twice the RMSE and a higher AIC than the best-fitting model (Table 1).

Fitting both $\alpha$ and $\beta_d$ (line 2 of Table 1) shows strong support for the diminishing risk model ($0 < \hat{\beta}_d < 1$). Allowing for environmental predictors further decreases the estimate to $\hat{\beta}_d = 0.30$ (0.15, 0.46). The exponent $0 < \beta_d < 1$ means that relative size at maturation ($d_{rel}$) decreases in large species (blue in Fig. 3a).

The best-fitting model (lowest AIC and RMSE) includes a negative effect of temperature (maturation at small size for species most common in cold climates) and a positive interaction between temperature T and $d_{max}$ (Table 1). This positive interaction means that the relationship between maturation and maximum size
<figure><img src="image_3.png" /></figure>

Figure 3: Tree maturation size (a, b), and relative size at maturation (c, d) for 486 species. Each dot represents one species. Alternative models are dashed lines, black for independence between maturation size and maximum size ($\beta_d = 0$), and red for the proportional cost model ($\beta_d = 1$). The best fitting model (blue with 95%CI) supports the diminishing risk model ($\beta_d < 1$, Table 1). Panels b and d are predictions from the fitted model with an interaction between continuous $d_{max}$ and temperature (line 1 of Table 1). This model gives a continuous surface plot of maturation size as a function of maximum size and temperature (see Fig. S4). However, for clarity, we represent only the prediction at cold (8°C, purple) and warm temperatures (25°C, green) spanning observed diameter ranges.
tends to steepen for species in warm climates (Fig. 3b, d), approaching the proportionate risk model (Table 1); the rise in $d_{mat}$ with $d_{max}$ increases with temperature. However, the main plus interaction effect remains below 1 even in warm climates showing that the diminishing risk model is supported across this temperature range. The $\beta_d$ remained below 1 even when we restricted the analysis to a single source of $d_{max}$ (Table A1 and Figure A1, see Supplementary Section 2). After correcting for risks of regression dilution, the average value of $\beta_d$ remained below 1, with corrected $\beta_d = 0.73$, however, the confidence interval is between 0.03 to 1.43 (Table A2, see Supplementary Section 2).

<figure><img src="image_4.png" /><figcaption>Figure 4: Conditional parameter estimates for the direct effect of traits on tree size at maturation diameter ($d_{mat}$) while accounting for trait covariance, climate, and phylogeny. Conditional parameters are evaluated on a standardized scale (predictors are centered and standardized) making trait effects on $d_{mat}$ respective to their variation in the data set. Shown are posterior means and 95% credible intervals. Blue and red represent positive and negative associations where 95% of the posterior does not include zero. SLA = specific leaf area</figcaption></figure>

The joint trait model incorporating random phylogenetic group and climate exhibits a root mean square prediction error 1.17 units smaller compared to the model that includes only climate. Conditional parameter estimates from the joint trait analysis show that $d_{max}$ has a stronger effect on $d_{mat}$ than other traits. There is a weak positive association with seed size, and a negative association with species fecundity (see Methods, Trait and climate data section) (Fig. 4). There are no meaningful associations with wood density or SLA. The joint trait analysis also confirms the absence of a direct climate effect on $d_{mat}$ after accounting for $d_{max}$ in the conditional trait analysis (see Table S5 for joint trait model and Table S6 for conditional parameters). Previous linear models showed that temperature was significant only in the interaction with $d_{max}$ (Table S4). Joint trait analysis indicates that the temperature effect on maturation size in Fig. 2c could be due to the abundance of small species (small $d_{max}$) in warm climates (Figure S5). The trait relationships do not depend on the source of climatic data: i) GBIF species occurrence in Fig. 4 or ii) more narrowly, where they occur in the MASTIF data network (Fig. S6).

Both maturation ($d_{mat}$) and relative size ($d_{rel}$) show evidence of phylogenetic conservation ($\lambda_{mat} = 0.83$, $p < 0.0001$; $\lambda_{rel} = 0.51$, $p < 0.0001$, $n = 400$, Fig. S7a), yet with substantial variation within some groups.
The two-sample t-test for unequal variances shows differences between gymnosperms and angiosperms. 469
Gymnosperms have high mean values for both *d*<sub>mat</sub> and *d*<sub>max</sub> and low mean values for *d*<sub>rel</sub> (all *p* < 0.0001). 470
Within gymnosperms, Pinales and Cupressaceae mature at large size, but large *d*<sub>max</sub> gives them lower *d*<sub>rel</sub> 471
than most angiosperms (Fig. S8, S9). Most Pinaceae (*Picea, Pinus*) and Cupressaceae (*Thuja, Sequoia*), 472
Fagaceae (*Quercus and Fagus*), and Juglandaceae have low *d*<sub>rel</sub> (Fig. S10). Plant groups with both tree 473
and shrub habits, such as Rosales, Magnoliales, Rubiaceae, and Fabaceae, have mixed *d*<sub>rel</sub>. However, we 474
did not find a significant effect of tree versus shrub habit on *d*<sub>rel</sub>, possibly due to high variation in the data 475
(Fig. S10). Shrubs may tend to have high *d*<sub>rel</sub>, but higher *d*<sub>rel</sub> is also observed in trees genera like *Magnolia* 476
and *Poulsenia*. 477

Discussion

Our analysis suggests a diminishing risk model for the relationship between maturation and maximum size (i.e. *d*<sub>mat</sub> and *d*<sub>max</sub>). The novelty here comes from the low coupling we find. Indeed, the coefficient *β*<sub>d</sub> = 0.30 in Table 1 that we found is closer to zero (no relationship) than one. In contrast, the estimated exponent values fitted to vertebrates are greater than 1/2 (Prothero, 1993; Herculano-Houzel, 2019), twice the value of *β*<sub>d</sub> we find for trees. Nevertheless, the comparison across groups is complex due to the uncertainty on maximum size (*d*<sub>max</sub>), which could influence the value of the exponent *β*<sub>d</sub>, but this issue remained unexplored in other taxa. The biological difference of *β*<sub>d</sub> may arise because trees differ from other species groups in the gains that come from allocation to growth, as the gain is due to the relative difference in height with other competitive individuals. In most tree species, individuals in the understory produce no seed at all, while dominant stature can yield multi-order-of-magnitude gains in fecundity over crowded neighbors (Clark *et al.*, 2004). In contrast, in vertebrates, improved parental condition and size can translate to incremental increases in clutch size or survival of well-provisioned offspring. Gestation times and physical limits on clutch size (e.g., one offspring) may allow only muted near-term benefits of reproductive delay.

In trees, large size comes with uncertainty that could weaken the potential benefit of delaying maturation. 492
Wind exposure and risk of hydraulic failure both increase with size (Bennett et al., 2015; Jackson et al., 493
2021; Gardiner, 2021; Barrere et al., 2023). The vanishing probability that a seed survives to large size, 494
combined with the fact that fecundity can plateau and even decline late in life (Qiu et al., 2021) means that 495
the competitive advantages of extremely large size can rarely make up for lost benefits of early reproduction. 496
At a stand scale, the risk of stand-replacing disturbances can increase with stand age and development (e.g., 497
accumulated fuels increase fire risk), such that species that fail to reach minimum reproductive size before 498
the next disturbance can be excluded from communities (Clark, 1991; McDowell et al., 2020). The fact that 499
maturation size increases with maximum size means that the two are not independent. But the cost is not 500
proportionate (Fig. 3). 501

The fact that some correlation exists does not conflict with a disproportionate importance of near-term 502
gains that can follow delayed maturation. Instead, it suggests that the benefits of large size probably do not 503
come at the end of life. The capacity to reach a large size pays benefits throughout life, contributing with many 504
other variables to current size and fecundity, not just as a tree approaches the maximum. 505
Both climate and species traits contribute to the relationships between maturation and maximum size. The negative main effect of temperature and its positive interaction steepens the relationship with maximum size in warm climates (Fig. 3), where growth and mortality rates are generally higher than in temperate forests (Stephenson & Van Mantgem, 2005; Locosselli et al., 2020). Abundant resources may offer a disproportionate advantage to early maturation (van Noordwijk & de Jong, 1986; Kozłowski, 1992; Wenk & Falster, 2015). Long growing seasons in warm climates might have similar effects. However, intense competition on nutrient-rich sites might also favor delayed reproduction as trees compete for canopy access. Theoretical studies (Falster et al., 2017; Detto et al., 2022) have shown that a trade-off between maximum size and maturation size can promote niche diversification and maintain species coexistence, and can be typically observed in tropical where there is a wide range of maximum sizes forests (Falster et al., 2017).

We did not find that high specific leaf area (SLA) is associated with maturation at small size (Visser et al., 2016) or early age (Wenk et al., 2018). The relationship reported in Wenk et al. (2018) includes leaf area from one year and one site, and the correlation estimated in that study does not appear to control for phylogeny. Similarly, lack of association with wood density in our study does not agree with suggestions that shade-tolerant species with high wood density mature at small size (Thomas et al., 2015). The inclusion of a wider range of plant species may reveal a different pattern of traits. For example, a comparison over a large number of perennial plant species such as herbs, graminoids, shrubs, and trees shows that traits that promote longevity are associated with greater variability in seed production (Journé et al., 2023). The fact that species that produce large seeds also allocate more to reproductive effort (Qiu et al., 2022) could contribute in a small way to delayed maturation. The differences between our result and previous work may be due to the larger species coverage, and to the control of the effect of climate and phylogeny in our joint analysis.

Results highlight the importance of large data sets and how they are modelled. This first compilation of tree maturation size for hundreds of species on five continents shows strong support for a diminishing risk model — trees that can get big can still mature at relatively small sizes. The result is a decline in the relative size of maturation for large trees (Fig. 3d). The benefits of extensive data here parallel the shift from early theory that argued for a constant relative maturation size ($d_{rel}$) in fish (Charnov & Berrigan, 1990), followed by studies showing an exponent that is less than one (Froese & Binohlan, 2000; Tsikliras & Stergiou, 2014; Thorson et al., 2017). It is, however, important to acknowledge that our coverage of tree species diversity is still patchy, with most data coming from Europe and North America and limited spatial coverage in Africa, South America, Asia, and Oceania as data are concentrated in a few large plots in these areas (Daru & Rodriguez, 2023).

New insight from this analysis comes first from extending observations beyond a small number of tropical sites, few species, or limited sample size (Thomas, 1996; Wright et al., 2005; Thomas, 2011; Visser et al., 2016; Minor & Kobe, 2019). The expanded coverage of species and sites permitted the incorporation of climatic drivers into the analysis of $d_{mat}$ in relation to $d_{max}$, which influenced the estimation of $\alpha$ and $\beta_d$. Secondly, this study also benefited from accommodating detection and temporal dependence to infer maturation. The estimation of $d_{mat}$ was possible by combining diverse datasets, either based from direct crop measurement and seed trap monitoring and by the use of MASTIF model which could estimate jointly a probability of maturation and individual fecundities. For instance, estimates of $d_{mat}$ from Visser et al. (2016) are, on average, approximately 1.8 times larger than our estimates for the species in common in the two studies
(Fig. S3). This discrepancy could be attributed to a different definition of size at maturation and methods of analysis, as our method also includes the number of seeds produced.

Due to the high juvenile mortality, the maturation sizes quantified here are expected to impact predictions from demographic vegetation models, including earth system models (ESMs) that include effects of maturation size. In one ESM study that considered the effects of maturation height, variation in a single value applied to all species did not have a large impact on simulated stand productivity (Raczka et al., 2018). However, when differences in species maturation size are accounted for in models, the effect can be larger. Few individuals survive to large size and, thus, their ability to reproduce early can be important. The fact that species capable of large size tend to retain this capacity to reproduce while still small highlights the importance of understanding maturation size. Accurate estimation of maturation size ($d_{mat}$) is likewise important for assessing response to disturbance regimes, especially as the time to maturity begins to exceed the interval between disturbances. For instance, several species that compared pairs of species found that species with smaller size at maturation can have better post-disturbance dynamics than species with larger maturation size (Alfaro-Sánchez et al., 2022; Andrus et al., 2020). Our results provided the data to test such hypotheses at a much larger scale. This effect can even scale up at the ecosystem scale. In boreal habitats, exposure to more frequent disturbances that exceed the tree maturation time can completely change a tree community to a grass-dominated community without a return to a forest stand within centuries (Buma et al., 2013).

Current ESMs suffer from limited information on allocation to reproduction (Wenk & Falster, 2015), including empirical data (Hanbury-Brown et al., 2022b). Similarly, management actions intended to assure regeneration from seed also need to consider if the minimum harvest diameter is smaller than maturation size (Ouédraogo et al., 2018). Maturation size may play an important role in the ability of species to respond to disturbance and climate change (McDowell et al., 2020) when tree maturation can be reached faster under elevated CO₂ exposure (LaDeau & Clark, 2001). Considering the difference in maturation size between species may be crucial, although it can be more challenging to comprehend due to the impact of CO₂ on maturation size. Understanding how fecundity strategies differ between species and phylogenetic groups, such as lower relative size at maturation ($d_{rel}$) for gymnosperms than angiosperms, may open a new avenue to better understand species diversification and responses to disturbances (Bond, 1989; Verdu, 2002; Qiu et al., 2022). Developing a model that represents the size at which a species begins to produce seeds could improve the representation of the regeneration of each functional type (Hanbury-Brown et al., 2022a) and colonization rates (Snell, 2014) and improve our understanding of species coexistence. Our study contributes to the maturation sizes needed for each of these objectives.
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Acknowledgements
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We thank the National Ecological Observatory Network (NEON) for access to sites and vegetation struc-
ture data. The project has been funded by grants to JSC from the National Science Foundation, most
recently DEB-1754443, and by the Belmont Forum (1854976), NASA (AIST16-0052, AIST18-0063), and
the Programme d'Investissement d'Avenir under project FORBIC (18-MPGA-0004) (Make Our Planet Great
Again). Jerry Franklin's data remain accessible through NSF LTER DEB-1440409. Puerto Rico data were
funded by NSF grants, most recently, DEB 0963447 and LTREB 11222325. Data from the Andes Biodiversity
and Ecosystem Research Group were funded by the Gordon and Betty Moore Foundation and NSF LTREB
1754647. VJ was supported by project FORBIC (18-MPGA-0004) and project No. 2021/43/P/NZ8/01209 co-
funded by the Polish National Science Centre and the EU H2020 research and innovation programme under
the MSCA GA No. 945339. For the purpose of Open Access, the author has applied a CC-BY public copyright
licence to any Author Accepted Manuscript (AAM) version arising from this submission. MB was supported
by grant no. 2019/35/D/NZ8/00050 from the Polish National Science Centre, and Polish National Agency for
Academic Exchange Bekker programme PPN/BEK/2020/1/00009/U/00001. Research by the USDA Forest
Service and the USGS was funded by these agencies. Any use of trade, firm, or product names is for de-
scriptive purposes only and does not imply endorsement by the U.S. Government.
780

781

Competing interests

783 The authors declare no competing interests

784

785 Supplementary Materials

Section A1 - A2
786

787 Table S1 – S6

788 Fig S1 - S9

789
790 Supplementary material

791 A.1 Conditional parameters

One way to evaluate relationships between traits is to ask how well a trait like $d_{mat}$ predicts other traits, while controlling for effects of climate and phylogeny. We start with the joint distribution of $M$ traits for each species $s = 1, \dots, S$ fitted with GJAM (Methods). All traits were log-transformed. The joint distribution is

where $MVN$ is the multivariate normal distribution, $g[s]$ is a random vector for the phylogenetic group to which $s$ belongs, and $\Omega$ is the $M \times M$ covariance between traits taken over phylogenetic groups (Clark et al., 2016). With this fitted model, we consider the effects of $d_{mat}$ on all other traits, organized in the vector $T = [u, d]$, where $d$ is the length-$S$ vector of maturation sizes, and $u$ is a $S \times M - 1$ matrix holding all traits in $T$ other than $d_{mat}$.

We partition the coefficients in $B$ and trait covariance $\Sigma$ as

For $M$ traits and $Q$ climate predictors in $x_s$, $B_u$ is the $Q \times M - 1$ matrix of climate effects on traits other than $d_{mat}$, $B_d$ is the $Q \times 1$ vector of climate effects on $d_{mat}$, with similar partition of $\Sigma$. We then write the conditional distribution of responses in $u$ as

A is the vector of effects of $d_{mat}$ on each response in $u$, C holds the effects of $x$, and P is the conditional residual covariance. Other applications can be found in Qiu et al. (2021); Bogdziewicz et al. (2023). We report in Fig. 4 the estimates from A.

$$ [T_s|P,X] = MVN_M(T_s|B'x_s + g[s], \Sigma) \\ g \sim MVN(0, \Omega) \qquad (A1) $$

$$ B = \begin{bmatrix} B_u \\ B_d \end{bmatrix}, \Sigma = \begin{bmatrix} \Sigma_{u,u} & \Sigma_{u,d} \\ \Sigma_{d,u} & \Sigma_{d,d} \end{bmatrix} \qquad (A2) $$

$$ \begin{align*} u_s|d_{mat,s} &\sim MVN(Ad_{mat,s} + Cx_s + g[s], P) \\ A &= \Sigma_{u,d}\Sigma_{d,d}^{-1} \\ C &= B'_u - AB'_d \\ P &= \Sigma_{u,u} - A\Sigma_{d,d} \end{align*} \qquad (A3) $$
## A.2 Impact of error on estimates of maximum size ($d_{max}$)

### A.2.1 Robustness of the model relating maturation size to maximum size to data sources

In this additional analysis, we aimed to test the relationship between maturation size ($d_{mat}$) and maximum size ($d_{max}$) using different data sources for $d_{max}$. The estimates $d_{max}$ used in the main analysis are based on online open sources and are on average higher than other sources of $d_{max}$ (Figure S2) which could underestimate the parameter $\beta_d$. The analysis was restricted to the most abundant data source of $d_{max}$. We conducted separate regression analyses using $d_{max}$ estimates from unpublished data (J. Wright, N = 233 species), National Forest Inventories (N = 158 species), and MASTIF inventories (N = 346 species) based on the model from Equation (6). In the three different models (i.e. one model per data source of $d_{max}$), we used the inverse of the standard error of $d_{mat}$ as weights in the models. We then extracted coefficient estimates for all three models. Results are reported in Table A1 and visualized in Figure A1.

<table><caption>Table A1: Coefficient estimates from the model Eq. (6) according to the origin of $d_{max}$. Data sources of $d_{max}$ are National Forest Inventories (NFI), MASTIF inventories, and unpublished field tropical measurements.</caption><thead><tr><th>Origin of d<sub>max</sub></th><th>α</th><th>β<sub>d</sub></th><th>σ</th></tr></thead><tbody><tr><td>NFI</td><td>1.40 [0.89, 2.20]</td><td>0.56 [0.45, 0.68]</td><td>0.089</td></tr><tr><td>MASTIF</td><td>1.30 [1.10, 1.60]</td><td>0.64 [0.58, 0.70]</td><td>0.078</td></tr><tr><td>Unpublished</td><td>0.88 [0.73, 1.10]</td><td>0.65 [0.60, 0.70]</td><td>0.090</td></tr></tbody></table>

<figure><img src="image_5.png" /><figcaption>Figure A1: Tree maturation size and relative size at maturation relationship to maximum size according to the origin of maximum size observations. The orange line represents predictions from the regression between $d_{mat}$ and $d_{max}$ based on unpublished data (obtained from J. Wright field observation, N = 233 species). In blue, the prediction from the regression between $d_{mat}$ and $d_{max}$ comes only from National Forest Inventories estimates (N = 158 species). In yellow, the prediction from the regression between $d_{mat}$ and $d_{max}$ comes only from MASTIF inventories (N = 346 species).</figcaption></figure>
### A.2.2 Correction of maximum size error measurement

Measurement error in a covariate is common and often ignored which could have implications in the estimation of the relationship between a response and a covariate (Nab et al., 2021). Indeed, the true value of a covariate, here of $d_{max}$, is not available, and using a log-log model exposed to regression dilution could flatten the slope ($\beta_d$) (Detto et al., 2019). To correct for measurement error we benefit here from the R package mecor (Nab, 2021) by using additional observation of our variable $d_{max}$. We specified here the error-prone measurement of $d_{max}$, coming from the highest estimates of $d_{max}$. We then used here four different additional observations of $d_{max}$, where this covariate can be obtained from Online Open-access resources, National Forest Inventories, Unpublished data, and MASTIF inventories. We ran the analysis on a simple model from Equation (6), that would include only $d_{max}$, or both $d_{max}$ and temperature as covariates. The function does not allow to take into account weights in the analysis. To make a fair comparison, we reported here both coefficients, uncorrected and corrected (Table A2).

<table><caption>Table A2: Coefficient estimates uncorrected and corrected from measurement errors fitted to Eq. (6). Values are reported with a mean estimate and 95% CI.</caption><thead><tr><th>Model</th><th>Coefficient Parameter</th><th>Uncorrected value</th><th>Corrected value</th></tr></thead><tbody><tr><td rowspan="3">d<sub>max</sub>; T</td><td>α</td><td>1.404 [1.092, 1.804]</td><td>0.826 [0.022, 31.637]</td></tr><tr><td>β<sub>d</sub></td><td>0.58 [0.53, 0.62]</td><td>0.732 [-0.049, 1.51]</td></tr><tr><td>β<sub>T</sub></td><td>-0.0005 [-0.0029, 0.0019]</td><td>-0.0003 [-0.012, 0.011]</td></tr><tr><td rowspan="2">d<sub>max</sub></td><td>α</td><td>1.357 [1.132, 1.627]</td><td>0.810 [0.048, 13.555]</td></tr><tr><td>β<sub>d</sub></td><td>0.582 [0.539, 0.625]</td><td>0.733 [0.031, 1.434]</td></tr></tbody></table>
Supplementary Tables and Figures

<table><caption>Table S1: Numbers of species, plots, tree-year observations coming from crop count and seeds traps, and individual species tree year observations according to region. Additional details about MASTIF network are provided in Supplementary Files 1 and 2, and in Table S2.</caption><thead><tr><th>Region</th><th>Nb. of plots</th><th>Nb. of species</th><th>Crop year</th><th>count x</th><th>Seed-trap x year</th><th>Nb. Ind/Year</th></tr></thead><tbody><tr><td>Africa</td><td>2</td><td>19</td><td>416</td><td></td><td>9,705</td><td>12</td></tr><tr><td>Asia</td><td>4</td><td>59</td><td>0</td><td></td><td>1,589,946</td><td>1,475</td></tr><tr><td>Eastern North America</td><td>155</td><td>92</td><td>20,983</td><td></td><td>1,389,998</td><td>142</td></tr><tr><td>Western North America</td><td>280</td><td>29</td><td>83,042</td><td></td><td>715,132</td><td>576</td></tr><tr><td>Europe</td><td>156</td><td>21</td><td>30,763</td><td></td><td>158,991</td><td>28</td></tr><tr><td>South America</td><td>7</td><td>267</td><td>2,280</td><td></td><td>7,050,620</td><td>863</td></tr></tbody></table>
<table><caption>Table S2: MASTIF plots listed by WWF eco-regions, with principal investigator list and references. The column ST/CC indicates seed traps (ST) and crop counts (CC) sites.</caption><thead><tr><th>Eco-region</th><th>Plot</th><th>PI(s)</th><th>lon</th><th>lat</th><th>ST/CC</th><th>Citation</th></tr></thead><tbody><tr><td>A/W Turkey sclerophyllous/mixed</td><td>PNPG</td><td>E. Daskalakou</td><td>24</td><td>38</td><td>CC</td><td>Daskalakou et al. (2019)</td></tr><tr><td>Alps conifer/mixed forests</td><td>ROTH</td><td>G. Gratzer</td><td>15</td><td>48</td><td>ST</td><td></td></tr><tr><td></td><td>BELLE</td><td>G. Kunstler; B. Courbaud</td><td>6</td><td>45</td><td>ST CC</td><td></td></tr><tr><td></td><td>RNNPT</td><td>L. Dormon</td><td>7</td><td>45</td><td>CC</td><td>Dormont et al. (2006)</td></tr><tr><td></td><td>PNPP</td><td>D. Ascoli; R. Motta; R. Berretta; G. Vacchiano</td><td>12</td><td>46</td><td>ST</td><td>Hackett-Pain et al. (2019)</td></tr><tr><td>Appalachian-Blue Ridge forests</td><td>BCEF</td><td>C. Greenberg</td><td>-83</td><td>35</td><td>CC</td><td>Rose et al. (2012)</td></tr><tr><td></td><td>CWT</td><td>J. S. Clark</td><td>-83</td><td>35</td><td>ST CC</td><td>Clark et al. (2004)</td></tr><tr><td></td><td>EPENN</td><td>M. Steele</td><td>-76</td><td>41</td><td>CC</td><td></td></tr><tr><td></td><td>GRAN</td><td>C. Greenberg</td><td>-82</td><td>36</td><td>CC</td><td>Rose et al. (2012)</td></tr><tr><td></td><td>GRSM</td><td>J. S. Clark</td><td>-83</td><td>36</td><td>ST</td><td></td></tr><tr><td></td><td>MARS</td><td>J. S. Clark; S. Pearson</td><td>-83</td><td>36</td><td>ST CC</td><td>Clark et al. (2014)</td></tr><tr><td></td><td>MLBS</td><td>J. S. Clark</td><td>-81</td><td>37</td><td>ST CC</td><td></td></tr><tr><td></td><td>PISG</td><td>C. Greenberg</td><td>-83</td><td>35</td><td>CC</td><td>Rose et al. (2012)</td></tr><tr><td></td><td>SCBI</td><td>B. McShea</td><td>-78</td><td>39</td><td>ST</td><td>Bourg et al. (2013)</td></tr><tr><td>Appalachian mixed mesophytic forests</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Arizona Mountains forests</td><td>MOPA</td><td>M. Redmond</td><td>-106</td><td>33</td><td>CC</td><td>Redmond et al. (2012)</td></tr><tr><td></td><td>REMO</td><td>A. Whipple; C. Gering; T. Whitham</td><td>-112</td><td>36</td><td>CC</td><td>Whipple et al. (2019)</td></tr><tr><td></td><td>SICI</td><td>A. Wion; M. Redmond</td><td>-108</td><td>33</td><td>CC</td><td></td></tr><tr><td></td><td>WHIT</td><td>A. Wion; M. Redmond</td><td>-109</td><td>33</td><td>CC</td><td></td></tr><tr><td></td><td>WINO</td><td>A. Whipple; C. Gering; T. Whitham</td><td>-111</td><td>35</td><td>CC</td><td>Whipple et al. (2019)</td></tr></tbody></table>
<table><caption>Table S2 – continued from previous page</caption><thead><tr><th>Eco-region</th><th>Plot</th><th>PI(s)</th><th>lon</th><th>lat</th><th>ST/CC</th><th>Citation</th></tr></thead><tbody><tr><td>Atlantic coastal pine barrens</td><td>BARBEAU</td><td>N. Delpierre; D. Berveiller</td><td>3</td><td>48</td><td>ST</td><td></td></tr><tr><td>Atlantic mixed forests</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Balkan mixed forests</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Baltic mixed forests</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>British Columbia mainland coastal forests</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td>GLCR1</td><td>J. Franklin</td><td>-122</td><td>49</td><td>CC</td><td></td></tr><tr><td></td><td>GLCR2</td><td>J. Franklin</td><td>-122</td><td>49</td><td>CC</td><td></td></tr><tr><td></td><td>HEME</td><td>J. Franklin</td><td>-122</td><td>49</td><td>CC</td><td></td></tr><tr><td></td><td>STPA</td><td>J. Franklin</td><td>-121</td><td>47</td><td>CC</td><td></td></tr><tr><td>California Central Valley grasslands</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>California interior chaparral/woodlands</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>California montane chaparral/woodlands</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td>HNHR</td><td>J. Knops; W. Koenig</td><td>-122</td><td>36</td><td>CC</td><td>Knops &amp; Koenig (2012)</td></tr><tr><td>Carpathian montane forests</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td>BGNP</td><td>M. Zywiec; L. Piechnik; B. Seget; M. Ledwon</td><td>20</td><td>50</td><td>CC</td><td></td></tr><tr><td>Cascade Mountains leeward forests</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td>TUCR</td><td>J. Franklin</td><td>-121</td><td>48</td><td>CC</td><td></td></tr><tr><td>Celtic broadleaf forests</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td>BENWE</td><td>A. Hacket-Pain</td><td>-2</td><td>55</td><td>CC</td><td>Bogdziewicz et al. (2020)</td></tr><tr><td></td><td>CONGL</td><td>A. Hacket-Pain</td><td>-2</td><td>53</td><td>CC</td><td>Bogdziewicz et al. (2020)</td></tr><tr><td></td><td>GILLF</td><td>A. Hacket-Pain</td><td>-2</td><td>54</td><td>CC</td><td>Bogdziewicz et al. (2020)</td></tr><tr><td></td><td>HIMLE</td><td>A. Hacket-Pain</td><td>-2</td><td>53</td><td>CC</td><td>Bogdziewicz et al. (2020)</td></tr><tr><td></td><td>KEELE</td><td>A. Hacket-Pain</td><td>-2</td><td>53</td><td>CC</td><td>Bogdziewicz et al. (2020)</td></tr><tr><td></td><td>KILLE</td><td>A. Hacket-Pain</td><td>-3</td><td>51</td><td>CC</td><td>Bogdziewicz et al. (2020)</td></tr><tr><td></td><td>RIPON</td><td>A. Hacket-Pain</td><td>-1</td><td>54</td><td>CC</td><td>Bogdziewicz et al. (2020)</td></tr><tr><td></td><td>SPENN</td><td>A. Hacket-Pain</td><td>-2</td><td>55</td><td>CC</td><td>Bogdziewicz et al. (2020)</td></tr></tbody></table>
<table><caption>Table S2 – continued from previous page</caption><thead><tr><th>Eco-region</th><th>Plot</th><th>PI(s)</th><th>lon</th><th>lat</th><th>ST/CC</th><th>Citation</th></tr></thead><tbody><tr><td></td><td>WOODB</td><td>A. Hacket-Pain</td><td>-3</td><td>51</td><td>CC</td><td>Bogdziewicz et al. (2020)</td></tr><tr><td rowspan="3">Central Canadian Shield forests</td><td>COCH</td><td>Y. Bergeron; Y. Messaoud</td><td>-81</td><td>49</td><td>CC</td><td>Messaoud et al. (2007)</td></tr><tr><td>LDUPT</td><td>Y. Bergeron; Y. Messaoud</td><td>-79</td><td>48</td><td>CC</td><td>Messaoud et al. (2007)</td></tr><tr><td>MASK</td><td>Y. Bergeron; Y. Messaoud</td><td>-79</td><td>50</td><td>CC</td><td>Messaoud et al. (2007)</td></tr><tr><td rowspan="2">Central European mixed forests</td><td>UKFS</td><td>J. S. Clark</td><td>-95</td><td>39</td><td>ST CC</td><td></td></tr><tr><td>WUSL</td><td>J. Myers</td><td>-91</td><td>39</td><td>ST</td><td></td></tr><tr><td>Central Pacific coastal forests</td><td>MAPK</td><td>J. Franklin</td><td>-124</td><td>45</td><td>CC</td><td></td></tr><tr><td>Central Ranges xeric scrub</td><td>LS</td><td>B. Wright</td><td>132</td><td>-24</td><td>CC</td><td>Wright &amp; Zuur (2014)</td></tr><tr><td rowspan="10">Central tall grasslands</td><td>BERK</td><td>J. Franklin</td><td>-122</td><td>43</td><td>CC</td><td></td></tr><tr><td>BLLK</td><td>J. Franklin</td><td>-122</td><td>46</td><td>CC</td><td></td></tr><tr><td>DECU</td><td>J. Franklin</td><td>-122</td><td>45</td><td>CC</td><td></td></tr><tr><td>IRMT</td><td>J. Franklin</td><td>-122</td><td>44</td><td>CC</td><td></td></tr><tr><td>MOLK</td><td>J. Franklin</td><td>-122</td><td>46</td><td>CC</td><td></td></tr><tr><td>MORA</td><td>J. HilleRisLambers</td><td>-122</td><td>47</td><td>ST</td><td></td></tr><tr><td>PEPR</td><td>J. Franklin</td><td>-122</td><td>46</td><td>CC</td><td></td></tr><tr><td>SAMT</td><td>J. Franklin</td><td>-122</td><td>44</td><td>CC</td><td>Redmond et al. (2012)</td></tr><tr><td>SAPA</td><td>J. Franklin</td><td>-122</td><td>45</td><td>CC</td><td></td></tr><tr><td>SIRK</td><td>J. Franklin</td><td>-122</td><td>46</td><td>CC</td><td></td></tr><tr><td>SLBE</td><td>J. Franklin</td><td>-122</td><td>46</td><td>CC</td><td></td></tr></tbody></table>
<table><caption>Table S2 – continued from previous page</caption><thead><tr><th>Eco-region</th><th>Plot</th><th>PI(s)</th><th>lon</th><th>lat</th><th>ST/CC</th><th>Citation</th></tr></thead><tbody><tr><td rowspan="7">Chihuahuan desert</td><td>STMT</td><td>J. Franklin</td><td>-122</td><td>46</td><td>CC</td><td></td></tr><tr><td>TIRD</td><td>J. Franklin</td><td>-122</td><td>46</td><td>CC</td><td></td></tr><tr><td>WIMT1</td><td>J. Franklin</td><td>-122</td><td>44</td><td>CC</td><td></td></tr><tr><td>WIMT2</td><td>J. Franklin</td><td>-122</td><td>44</td><td>CC</td><td></td></tr><tr><td>WISP</td><td>J. Franklin</td><td>-122</td><td>43</td><td>CC</td><td></td></tr><tr><td>WREF</td><td>J. S. Clark; J. HilleRisLambers</td><td>-122</td><td>46</td><td>ST CC</td><td></td></tr><tr><td>FOBA</td><td>M. Redmond</td><td>-108</td><td>33</td><td>CC</td><td>Redmond et al. (2012)</td></tr><tr><td rowspan="10">Colorado Plateau shrublands</td><td>ALBU</td><td>A. Wion; M. Redmond</td><td>-106</td><td>35</td><td>CC</td><td>Wion et al. (2020)</td></tr><tr><td>CEBO</td><td>A. Wion; M. Redmond</td><td>-106</td><td>36</td><td>CC</td><td>Rodman et al. (2020)</td></tr><tr><td>DOLO</td><td>A. Wion; M. Redmond</td><td>-109</td><td>38</td><td>CC</td><td>Rodman et al. (2020)</td></tr><tr><td>GLPA</td><td>A. Wion; M. Redmond</td><td>-109</td><td>39</td><td>CC</td><td>Rodman et al. (2020)</td></tr><tr><td>HOND</td><td>A. Wion; M. Redmond; K. Rodman</td><td>-106</td><td>37</td><td>CC</td><td></td></tr><tr><td>HOTC</td><td>A. Wion; M. Redmond; K. Rodman</td><td>-108</td><td>39</td><td>CC</td><td>Rodman et al. (2020)</td></tr><tr><td>LASA</td><td>A. Wion; M. Redmond</td><td>-109</td><td>39</td><td>CC</td><td>Rodman et al. (2020)</td></tr><tr><td>MAGD</td><td>A. Wion; M. Redmond</td><td>-107</td><td>34</td><td>CC</td><td>Rodman et al. (2020)</td></tr><tr><td>MONT</td><td>A. Wion; M. Redmond</td><td>-108</td><td>38</td><td>CC</td><td>Rodman et al. (2020)</td></tr><tr><td>NATU</td><td>A. Wion; M. Redmond</td><td>-109</td><td>38</td><td>CC</td><td>Rodman et al. (2020)</td></tr><tr><td>SEV</td><td>R. Zlotin; D. Macias</td><td>-107</td><td>34</td><td>CC</td><td>Parmenter et al. (2018)</td></tr><tr><td>SUCR</td><td>A. Whipple; C. Gering; T. Whitham</td><td>-111</td><td>36</td><td>CC</td><td>Whipple et al. (2019)</td></tr><tr><td rowspan="5">Colorado Rockies forests</td><td>BOCA</td><td>I. Pearse</td><td>-105</td><td>40</td><td>CC</td><td></td></tr><tr><td>CANJ</td><td>A. Wion; M. Redmond</td><td>-106</td><td>36</td><td>CC</td><td>Rodman et al. (2020)</td></tr><tr><td>HAYM</td><td>A. Wion; M. Redmond</td><td>-105</td><td>39</td><td>CC</td><td></td></tr><tr><td>LAK</td><td>K. Rodman</td><td>-106</td><td>36</td><td>CC</td><td>Rodman et al. (2020)</td></tr><tr><td>LV</td><td>M. Redmond</td><td>-105</td><td>36</td><td>CC</td><td>Redmond et al. (2012)</td></tr></tbody></table>
<table><caption>Table S2 – continued from previous page</caption><thead><tr><th>Eco-region</th><th>Plot</th><th>PI(s)</th><th>lon</th><th>lat</th><th>ST/CC</th><th>Citation</th></tr></thead><tbody><tr><td rowspan="15">Cross-Sanaga-Bioko coastal forests</td><td>MG</td><td>K. Rodman</td><td>-106</td><td>36</td><td>CC</td><td>Rodman et al. (2020)</td></tr><tr><td>MON</td><td>K. Rodman</td><td>-106</td><td>36</td><td>CC</td><td>Rodman et al. (2020)</td></tr><tr><td>MR</td><td>K. Rodman</td><td>-106</td><td>36</td><td>CC</td><td>Rodman et al. (2020)</td></tr><tr><td>MVG</td><td>K. Rodman</td><td>-106</td><td>36</td><td>CC</td><td>Rodman et al. (2020)</td></tr><tr><td>NIWO</td><td>J. S. Clark</td><td>-106</td><td>40</td><td>ST CC</td><td></td></tr><tr><td>PC</td><td>K. Rodman</td><td>-106</td><td>36</td><td>CC</td><td>Rodman et al. (2020)</td></tr><tr><td>PECO</td><td>M. Redmond</td><td>-106</td><td>36</td><td>CC</td><td>Redmond et al. (2012)</td></tr><tr><td>POND</td><td>A. Wion; M. Redmond</td><td>-107</td><td>36</td><td>CC</td><td>Wion et al. (2020)</td></tr><tr><td>RATN</td><td>M. Redmond</td><td>-104</td><td>37</td><td>CC</td><td>Redmond et al. (2012)</td></tr><tr><td>SAFE</td><td>A. Wion; M. Redmond</td><td>-106</td><td>36</td><td>CC</td><td>Rodman et al. (2020)</td></tr><tr><td>WACA</td><td>A. Wion; M. Redmond</td><td>-105</td><td>39</td><td>CC</td><td></td></tr><tr><td>WEMO</td><td>A. Wion; M. Redmond</td><td>-105</td><td>38</td><td>CC</td><td></td></tr><tr><td>Dinaric Mountains mixed forests</td><td>KNP</td><td>J. Norghauer</td><td>9</td><td>5</td><td>CC</td><td>Norghauer &amp; Newbery (2015)</td></tr><tr><td>E Cascades forests</td><td>LMONT</td><td>Y. Bergeron; Y. Messaoud</td><td>-79</td><td>48</td><td>CC</td><td>Messaoud et al. (2007)</td></tr><tr><td>E forest-boreal transition</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>E Great Lakes lowland forests</td><td>BEECH</td><td>A. Hacket-Pain</td><td>0</td><td>52</td><td>CC</td><td>Bogdziewicz et al. (2020)</td></tr><tr><td>English Lowlands beech forests</td><td>BUCKH</td><td>A. Hacket-Pain</td><td>-2</td><td>52</td><td>CC</td><td>Bogdziewicz et al. (2020)</td></tr><tr><td></td><td>FISHH</td><td>A. Hacket-Pain</td><td>-2</td><td>52</td><td>CC</td><td>Bogdziewicz et al. (2020)</td></tr><tr><td></td><td>NETTL</td><td>A. Hacket-Pain</td><td>-1</td><td>52</td><td>CC</td><td>Bogdziewicz et al. (2020)</td></tr><tr><td></td><td>PAINS</td><td>A. Hacket-Pain</td><td>-2</td><td>52</td><td>CC</td><td>Bogdziewicz et al. (2020)</td></tr><tr><td></td><td>PATCH</td><td>A. Hacket-Pain</td><td>-0</td><td>51</td><td>CC</td><td>Bogdziewicz et al. (2020)</td></tr><tr><td></td><td>STP</td><td>M. Fenner M. Hanley</td><td>-1</td><td>51</td><td>CC</td><td>Hanley et al. (2018)</td></tr></tbody></table>
<table><caption>Table S2 – continued from previous page</caption><thead><tr><th>Eco-region</th><th>Plot</th><th>PI(s)</th><th>lon</th><th>lat</th><th>ST/CC</th><th>Citation</th></tr></thead><tbody><tr><td>Great Basin shrub steppe</td><td>DSP</td><td>M. Redmond</td><td>-119</td><td>39</td><td>CC</td><td></td></tr><tr><td rowspan="4">Iberian sclerophyllous/semi-deciduous</td><td>CARB</td><td>C. Perez-Izquierdo</td><td>-6</td><td>40</td><td>CC</td><td></td></tr><tr><td>HUEC</td><td>R. Bonal</td><td>-4</td><td>40</td><td>CC</td><td></td></tr><tr><td>SIOE</td><td>R. Calama</td><td>-4</td><td>40</td><td>CC</td><td></td></tr><tr><td>VALT</td><td>J. Espelta</td><td>-4</td><td>41</td><td>CC</td><td></td></tr><tr><td>Illyrian deciduous forests</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Interior Alaska-Yukon lowland taiga</td><td>EAPL</td><td>J. Johnstone</td><td>-137</td><td>66</td><td>CC</td><td>Viglas et al. (2013)</td></tr><tr><td></td><td>BONA</td><td>J. Johnstone</td><td>-148</td><td>65</td><td>ST</td><td></td></tr><tr><td></td><td>FAIR</td><td>J. Johnstone</td><td>-148</td><td>65</td><td>CC</td><td>Viglas et al. (2013)</td></tr><tr><td></td><td>LAGE</td><td>J. Johnstone</td><td>-145</td><td>64</td><td>CC</td><td>Viglas et al. (2013)</td></tr><tr><td></td><td>LELA</td><td>J. Johnstone</td><td>-138</td><td>64</td><td>CC</td><td>Viglas et al. (2013)</td></tr><tr><td></td><td>SMR</td><td>J. Johnstone</td><td>-141</td><td>64</td><td>CC</td><td>Viglas et al. (2013)</td></tr><tr><td>Interior Yukon-Alaska alpine tundra</td><td>CHIC</td><td>J. Johnstone</td><td>-143</td><td>63</td><td>CC</td><td>Viglas et al. (2013)</td></tr><tr><td>Isthmian-Atlantic moist forests</td><td>BCI</td><td>S.J. Wright</td><td>-80</td><td>9</td><td>ST</td><td></td></tr><tr><td>Italian sclerophyllous/semi-deciduous</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Klamath-Siskiyou forests</td><td>ASRN</td><td>J. Franklin</td><td>-123</td><td>42</td><td>CC</td><td></td></tr><tr><td></td><td>MEOV</td><td>J. Franklin</td><td>-123</td><td>42</td><td>CC</td><td></td></tr><tr><td>Mid Atlantic coastal forests</td><td>BLSF</td><td>D. Brockway</td><td>-79</td><td>35</td><td>CC</td><td>Chen et al. (2018)</td></tr><tr><td></td><td>CALL</td><td>J. S. Clark</td><td>-79</td><td>35</td><td>ST CC</td><td></td></tr><tr><td></td><td>CROA</td><td>S. Cohen</td><td>-77</td><td>35</td><td>CC</td><td></td></tr></tbody></table>
<table><caption>Table S2 – continued from previous page</caption><thead><tr><th>Eco-region</th><th>Plot</th><th>PI(s)</th><th>lon</th><th>lat</th><th>ST/CC</th><th>Citation</th></tr></thead><tbody><tr><td rowspan="2"></td><td>GRSW</td><td>J. S. Clark</td><td>-78</td><td>34</td><td>ST</td><td></td></tr><tr><td>SASF</td><td>D. Brockway</td><td>-81</td><td>34</td><td>CC</td><td>Chen et al. (2018)</td></tr><tr><td rowspan="5">Mississippi lowland forests</td><td>CHICK</td><td>J. Straub; T. Leininger</td><td>-90</td><td>36</td><td>CC</td><td>Straub et al. (2016)</td></tr><tr><td>DELTA</td><td>J. Straub; T. Leininger</td><td>-91</td><td>33</td><td>CC</td><td>Straub et al. (2016)</td></tr><tr><td>MINGO</td><td>J. Straub; T. Leininger</td><td>-90</td><td>37</td><td>CC</td><td>Straub et al. (2016)</td></tr><tr><td>TENAS</td><td>J. Straub; T. Leininger</td><td>-91</td><td>32</td><td>CC</td><td>Straub et al. (2016)</td></tr><tr><td>WHITE</td><td>J. Straub; T. Leininger</td><td>-91</td><td>34</td><td>CC</td><td>Straub et al. (2016)</td></tr><tr><td>Montana Valley/Foothill grasslands</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>N California coastal forests</td><td>UCSC</td><td>G. Gilbert; Kai Zhu</td><td>-122</td><td>37</td><td>ST</td><td></td></tr><tr><td>N Central Rockies forests</td><td>WBP</td><td>E. McIntire</td><td>-114</td><td>48</td><td>CC</td><td></td></tr><tr><td>N short grasslands</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>NE coastal forests</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>NE Spain/S France Mediterranean</td><td>ISS</td><td>H. Davi</td><td>6</td><td>44</td><td>CC</td><td>Davi et al. (2016)</td></tr><tr><td></td><td>PCMEJEAN</td><td>T. Curt</td><td>3</td><td>44</td><td>CC</td><td>Debain et al. (2003)</td></tr><tr><td></td><td>PUECHEXP1</td><td>J. Limousin; J. Ourcival</td><td>4</td><td>44</td><td>ST</td><td></td></tr><tr><td></td><td>RBI</td><td>T. Boivin</td><td>5</td><td>44</td><td>CC</td><td>Doublet et al. (2019)</td></tr><tr><td></td><td>RBLL</td><td>H. Davi</td><td>6</td><td>44</td><td>CC</td><td>Davi et al. (2016)</td></tr><tr><td></td><td>VALLI</td><td>F. Lefevre; F. Courbet</td><td>5</td><td>44</td><td>CC</td><td></td></tr><tr><td></td><td>VEN</td><td>H. Davi</td><td>5</td><td>44</td><td>CC</td><td>Davi et al. (2016)</td></tr><tr><td></td><td>VENT</td><td>H. Davi</td><td>5</td><td>44</td><td>CC</td><td>Davi et al. (2016)</td></tr><tr><td></td><td>VES</td><td>H. Davi</td><td>7</td><td>44</td><td>CC</td><td>Davi et al. (2016)</td></tr><tr><td>New England-Acadian forests</td><td>ASWP</td><td>C. Moore; J. S. Clark</td><td>-69</td><td>45</td><td>ST CC</td><td></td></tr></tbody></table>
<table><caption>Table S2 – continued from previous page</caption><thead><tr><th>Eco-region</th><th>Plot</th><th>PI(s)</th><th>lon</th><th>lat</th><th>ST/CC</th><th>Citation</th></tr></thead><tbody><tr><td rowspan="4"></td><td>BART</td><td>I. Fer; M. Dietze</td><td>-71</td><td>44</td><td>ST</td><td></td></tr><tr><td>COMPT</td><td>W. Schlesinger</td><td>-67</td><td>45</td><td>CC</td><td></td></tr><tr><td>HARV</td><td>J. S. Clark</td><td>-72</td><td>42</td><td>ST CC</td><td></td></tr><tr><td>HBEF</td><td>T. Fahey; N. Cleavitt</td><td>-72</td><td>44</td><td>ST</td><td>Cleavitt & Fahey (2017)</td></tr><tr><td rowspan="2">Nihonkai montane deciduous forests</td><td>KANU</td><td>K. Hoshizaki</td><td>141</td><td>39</td><td>ST</td><td></td></tr><tr><td>JNP</td><td>Q. Han; D. Kabeya; K. Noguchi</td><td>139</td><td>37</td><td>ST</td><td>Han et al. (2014)</td></tr><tr><td>NW Congolian lowland forests</td><td>CONGO</td><td>J. Poulson; C. Nunez</td><td>16</td><td>2</td><td>ST</td><td></td></tr><tr><td>Pannonian mixed forests</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Peruvian Yungas</td><td>ABERG</td><td>M. Silman; W. Farfan</td><td>-72</td><td>-13</td><td>ST</td><td></td></tr><tr><td>Piney Woods forests</td><td>KINF</td><td>D. Brockway</td><td>-92</td><td>31</td><td>CC</td><td>Chen et al. (2018)</td></tr><tr><td>Pontic steppe</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Puerto Rican dry forests</td><td>GUA</td><td>M. Uriarte</td><td>-67</td><td>18</td><td>ST</td><td>Uriarte et al. (2012)</td></tr><tr><td>Puerto Rican moist forests</td><td>LUQ</td><td>M. Uriarte</td><td>-66</td><td>18</td><td>ST</td><td>Uriarte et al. (2012)</td></tr><tr><td>Puget lowland forests</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Pyrenees conifer/mixed forests</td><td>PNVO</td><td>J. Camarero</td><td>-1</td><td>43</td><td>ST</td><td>de Andrés et al. (2014)</td></tr><tr><td></td><td>PNP</td><td>S. Delzon; T. Caignard</td><td>-0</td><td>43</td><td>CC</td><td>Caignard et al. (2017)</td></tr><tr><td>Rodope montane mixed forests</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>S Central Rockies forests</td><td>YELL</td><td>J. S. Clark</td><td>-110</td><td>45</td><td>ST CC</td><td></td></tr><tr><td>S Great Lakes forests</td><td></td><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>
<table><caption>Table S2 – continued from previous page</caption><thead><tr><th>Eco-region</th><th>Plot</th><th>PI(s)</th><th>lon</th><th>lat</th><th>ST/CC</th><th>Citation</th></tr></thead><tbody><tr><td></td><td>ANNA</td><td>I. Ibanez</td><td>-84</td><td>42</td><td>ST</td><td>Redmond et al. (2012)</td></tr><tr><td rowspan="7">SE conifer forests</td><td>APNF</td><td>D. Brockway</td><td>-85</td><td>30</td><td>CC</td><td>Chen et al. (2018)</td></tr><tr><td>BRSF</td><td>D. Brockway</td><td>-87</td><td>31</td><td>CC</td><td>Chen et al. (2018)</td></tr><tr><td>DSNY</td><td>J. S. Clark</td><td>-81</td><td>28</td><td>ST CC</td><td></td></tr><tr><td>EAFB</td><td>D. Brockway</td><td>-87</td><td>30</td><td>CC</td><td>Chen et al. (2018)</td></tr><tr><td>EEF</td><td>D. Brockway</td><td>-87</td><td>31</td><td>CC</td><td>Chen et al. (2018)</td></tr><tr><td>JERC</td><td>D. Brockway</td><td>-84</td><td>31</td><td>CC</td><td>Chen et al. (2018)</td></tr><tr><td>OSBS</td><td>J. S. Clark</td><td>-82</td><td>30</td><td>ST CC</td><td></td></tr><tr><td rowspan="2">SE mixed forests</td><td>STCB</td><td>D. Brockway</td><td>-85</td><td>31</td><td>CC</td><td>Chen et al. (2018)</td></tr><tr><td>TTRS</td><td>D. Brockway</td><td>-86</td><td>31</td><td>CC</td><td>Chen et al. (2018)</td></tr><tr><td rowspan="4">Sierra Nevada forests</td><td>DUKE</td><td>J. S. Clark</td><td>-79</td><td>36</td><td>ST CC</td><td>Berdanier &amp; Clark (2016)</td></tr><tr><td>FBMB</td><td>D. Brockway</td><td>-85</td><td>32</td><td>CC</td><td>Chen et al. (2018)</td></tr><tr><td>SERC</td><td>J. S. Clark</td><td>-77</td><td>39</td><td>ST CC</td><td>van Mantgem et al. (2006)</td></tr><tr><td>TALL</td><td>J. S. Clark</td><td>-87</td><td>33</td><td>ST CC</td><td></td></tr><tr><td rowspan="3">SW Iberian Mediterranean S/M</td><td>SEQU</td><td>A. Das; N. Stephenson</td><td>-119</td><td>37</td><td>ST</td><td>van Mantgem et al. (2006)</td></tr><tr><td>SOAP</td><td>J. S. Clark</td><td>-119</td><td>37</td><td>ST CC</td><td></td></tr><tr><td>YOSE</td><td>A. Das; N. Stephenson</td><td>-120</td><td>38</td><td>ST</td><td>van Mantgem et al. (2006)</td></tr><tr><td rowspan="3">Taiwan subtropical evergreen forests</td><td>ALCO</td><td>I. Perez-Ramos</td><td>-6</td><td>36</td><td>CC</td><td>Pérez-Ramos et al. (2014)</td></tr><tr><td>PNLA</td><td>A. Hampe</td><td>-6</td><td>37</td><td>CC</td><td>Hampe &amp; Bairlein (2000)</td></tr><tr><td>SJDV</td><td>F. Rodriguez-Sanchez</td><td>-6</td><td>37</td><td>CC</td><td></td></tr><tr><td>Upper Midwest forest-savanna transition</td><td>FFDF</td><td>C. Chang-Yang; I-Fang Sun</td><td>122</td><td>25</td><td>ST</td><td></td></tr></tbody></table>
<table><caption>Table S2 – continued from previous page</caption><thead><tr><th>Eco-region</th><th>Plot</th><th>PI(s)</th><th>lon</th><th>lat</th><th>ST/CC</th><th>Citation</th></tr></thead><tbody><tr><td colspan="7"><strong>Valdivian temperate forests</strong></td></tr><tr><td></td><td>LNP</td><td>J. Sanguinetti; T. Kitzberger</td><td>-71</td><td>-39</td><td>CC</td><td>Sanguinetti & Kitzberger (2008)</td></tr><tr><td></td><td>ARAU</td><td>M. Aravena; S. Donoso Calderon</td><td>-71</td><td>-38</td><td>CC</td><td></td></tr><tr><td colspan="7"><strong>W European broadleaf forests</strong></td></tr><tr><td colspan="7"><strong>W Great Lakes forests</strong></td></tr><tr><td></td><td>CADI</td><td>R. Kobe</td><td>-86</td><td>44</td><td>ST CC</td><td></td></tr><tr><td></td><td>MANI</td><td>R. Kobe</td><td>-86</td><td>44</td><td>ST CC</td><td></td></tr><tr><td></td><td>MICH</td><td>J. LaMontagne</td><td>-88</td><td>47</td><td>CC</td><td></td></tr><tr><td></td><td>PAFA</td><td>J. LaMontagne</td><td>-90</td><td>46</td><td>CC</td><td></td></tr><tr><td></td><td>TREE</td><td>J. S. Clark</td><td>-90</td><td>45</td><td>ST CC</td><td></td></tr><tr><td></td><td>UMBS</td><td>I. Ibanez</td><td>-85</td><td>46</td><td>ST</td><td></td></tr><tr><td></td><td>UNDE</td><td>J. S. Clark</td><td>-90</td><td>46</td><td>ST CC</td><td></td></tr><tr><td></td><td>WILW</td><td>J. LaMontagne</td><td>-90</td><td>46</td><td>CC</td><td></td></tr><tr><td></td><td>WORU</td><td>J. LaMontagne</td><td>-90</td><td>46</td><td>CC</td><td></td></tr><tr><td colspan="7"><strong>W Gulf coastal grasslands</strong></td></tr><tr><td colspan="7"><strong>W short grasslands</strong></td></tr><tr><td></td><td>CMNM</td><td>M. Redmond</td><td>-104</td><td>37</td><td>CC</td><td>Redmond et al. (2012)</td></tr><tr><td></td><td>KENT</td><td>M. Redmond</td><td>-103</td><td>37</td><td>CC</td><td>Redmond et al. (2012)</td></tr><tr><td colspan="7"><strong>Willamette Valley forests</strong></td></tr><tr><td></td><td>CAMT</td><td>J. Franklin</td><td>-123</td><td>45</td><td>CC</td><td></td></tr><tr><td colspan="7"><strong>Wyoming Basin shrub steppe</strong></td></tr><tr><td></td><td>NORT</td><td>A. Wion; M. Redmond</td><td>-109</td><td>41</td><td>CC</td><td></td></tr></tbody></table>
<table><caption>Table S3: Origin of maximum diameter ($d_{max}$), with the number of species for each data source retained for the analysis used in this study.</caption><thead><tr><td>Data source of d<sub>max</sub></td><td>Nb of species</td><td>Comments</td></tr></thead><tbody><tr><td>National Forest Inventories</td><td>38</td><td>Used near maximum diameter forest inventory and analysis in the United States (Gray et al., 2012); forest inventory in Europe (Kunstler et al., 2021); tree census data in Japan (Ishihara et al., 2011).</td></tr><tr><td>Unpublished field tropical measurements</td><td>222</td><td>Maximum diameter value observed from French Guyana (33 species) and from Panama (189 species).</td></tr><tr><td>Allometric equation</td><td>12</td><td>Maximum trait height (Liu et al., 2019; Carmona et al., 2021) and allometric equation from pan-tropical for Africa region, South America equation for South America region and Asia equation for Asia region.</td></tr><tr><td>MASTIF inventories</td><td>41</td><td>Used tree size observations and near maximum diameter for species with > 90 individual unique diameter.</td></tr><tr><td>Online open sources</td><td>173</td><td>Wikipedia, https://www.wikipedia.org/; American conifers society, https://conifersociety.org/; Monumental trees https://www.monumentaltrees.com/en/; iPlantz, https://www.iplantz.com/, Useful tropical plants, https://tropical.theferns.info/)</td></tr></tbody></table>
<table><caption>Table S4: Summary of all fitted linear models between maturation size ($d_{mat}$) and maximum size ($d_{max}$) in log$_{10}$-log$_{10}$ testing alternative effects of climatic variables. The mean value of estimates with a confidence interval of 95%, and their p-values (p) are reported. All models have the initial structure log$_{10}$(d$_{mat_s}$) = α + β$_{d}$ × log$_{10}$(d$_{max_s}$) represented here by the ellipse (...). Other parameters included are temperature (T) and deficit (D).</caption><thead><tr><th>Parameters</th><th>Estimate</th><th>2.5%</th><th>97.5%</th><th>p</th><th>AIC</th></tr></thead><tbody><tr><td colspan="6">... + β<sub>T</sub> × T + β<sub>dT</sub> × T × log<sub>10</sub>(d<sub>maxs</sub>)</td></tr><tr><td>α</td><td>3.7100</td><td>1.94000</td><td>7.0700</td><td>&lt; 0.001</td><td>-62.84</td></tr><tr><td>β<sub>d</sub></td><td>0.3050</td><td>0.15100</td><td>0.4590</td><td>&lt; 0.001</td><td></td></tr><tr><td>β<sub>T</sub></td><td>-0.0233</td><td>-0.03520</td><td>-0.0114</td><td>&lt; 0.001</td><td></td></tr><tr><td>β<sub>dT</sub></td><td>0.0126</td><td>0.00586</td><td>0.0193</td><td>&lt; 0.001</td><td></td></tr><tr><td colspan="6">... + β<sub>D</sub> × D + β<sub>dD</sub> × D × log<sub>10</sub>(d<sub>max</sub>) + β<sub>T</sub> × T + β<sub>dT</sub> × T × log<sub>10</sub>(d<sub>maxs</sub>)</td></tr><tr><td>α</td><td>4.15e+00</td><td>1.99e+00</td><td>8.65e+00</td><td>&lt; 0.001</td><td>-59.29</td></tr><tr><td>β<sub>d</sub></td><td>2.81e-01</td><td>1.09e-01</td><td>4.53e-01</td><td>&lt; 0.001</td><td></td></tr><tr><td>β<sub>T</sub></td><td>-2.43e-02</td><td>-3.66e-02</td><td>-1.20e-02</td><td>&lt; 0.001</td><td></td></tr><tr><td>β<sub>D</sub></td><td>2.73e-05</td><td>-7.98e-05</td><td>1.34e-04</td><td>0.617000</td><td></td></tr><tr><td>β<sub>dT</sub></td><td>1.31e-02</td><td>6.18e-03</td><td>2.00e-02</td><td>&lt; 0.001</td><td></td></tr><tr><td>β<sub>dD</sub></td><td>-1.29e-05</td><td>-7.62e-05</td><td>5.03e-05</td><td>0.688000</td><td></td></tr><tr><td colspan="6">...</td></tr><tr><td>α</td><td>1.080</td><td>0.929</td><td>1.250</td><td>0.325</td><td>-52</td></tr><tr><td>β<sub>d</sub></td><td>0.592</td><td>0.552</td><td>0.631</td><td>&lt; 0.001</td><td></td></tr><tr><td colspan="6">... + β<sub>D</sub> × D + β<sub>dD</sub> × D × log<sub>10</sub>(d<sub>max</sub>)</td></tr><tr><td>α</td><td>1.06e+00</td><td>8.17e-01</td><td>1.38e+00</td><td>0.657</td><td>-48.12</td></tr><tr><td>β<sub>d</sub></td><td>5.93e-01</td><td>5.27e-01</td><td>6.59e-01</td><td>&lt; 0.001</td><td></td></tr><tr><td>β<sub>D</sub></td><td>-6.10e-06</td><td>-1.13e-04</td><td>1.01e-04</td><td>0.910</td><td></td></tr><tr><td>β<sub>dD</sub></td><td>1.40e-06</td><td>-6.18e-05</td><td>6.47e-05</td><td>0.964</td><td></td></tr><tr><td colspan="6">... + β<sub>D</sub> × D + β<sub>T</sub> × T</td></tr><tr><td>α</td><td>1.19e+00</td><td>9.32e-01</td><td>1.51e+00</td><td>0.165</td><td>-49.48</td></tr><tr><td>β<sub>d</sub></td><td>5.83e-01</td><td>5.42e-01</td><td>6.25e-01</td><td>&lt; 0.001</td><td></td></tr><tr><td>β<sub>D</sub></td><td>-3.90e-06</td><td>-2.53e-05</td><td>1.75e-05</td><td>0.721</td><td></td></tr><tr><td>β<sub>T</sub></td><td>-1.59e-03</td><td>-4.29e-03</td><td>1.10e-03</td><td>0.246</td><td></td></tr><tr><td colspan="6">... + β<sub>D</sub> × D</td></tr><tr><td>α</td><td>1.07e+00</td><td>9.09e-01</td><td>1.25e+00</td><td>0.433</td><td>-50.12</td></tr><tr><td>β<sub>d</sub></td><td>5.92e-01</td><td>5.53e-01</td><td>6.31e-01</td><td>&lt; 0.001</td><td></td></tr><tr><td>β<sub>D</sub></td><td>-3.70e-06</td><td>-2.52e-05</td><td>1.77e-05</td><td>0.732</td><td></td></tr><tr><td colspan="6">... + β<sub>T</sub> × T</td></tr><tr><td>α</td><td>1.20000</td><td>0.94800</td><td>1.52000</td><td>0.129</td><td>-51.35</td></tr><tr><td>β<sub>d</sub></td><td>0.58300</td><td>0.54100</td><td>0.62500</td><td>&lt; 0.001</td><td></td></tr><tr><td>β<sub>T</sub></td><td>-0.00159</td><td>-0.00429</td><td>0.00111</td><td>0.248</td><td></td></tr><tr><td colspan="6">α + 1 × β<sub>d</sub></td></tr><tr><td>α</td><td>0.244</td><td>0.232</td><td>0.257</td><td>0</td><td>248.1</td></tr><tr><td>β<sub>d</sub></td><td>1</td><td>-44</td><td>-</td><td>-</td><td></td></tr><tr><td colspan="6">α</td></tr><tr><td>α</td><td>9.25</td><td>8.69</td><td>9.85</td><td>0</td><td>447.83</td></tr><tr><td>β<sub>d</sub></td><td>0</td><td>-</td><td>-</td><td>-</td><td></td></tr></tbody></table>
<table><caption>Table S5: Summary of the best joint trait model. The best model has been selected based on the lowest DIC value (Table S7). Traits have been included as responses ($d_{max}$, $d_{mat}$, SLA, Wood density, seed size, and species seed productivity), with temperature (T), deficit (D), and their interaction (T : D) as predictors, with genus as a random effect. For each response, estimate, standard error (SE), and credible interval (95%) with significance are reported (CI does not overlap 0).</caption><thead><tr><th>Climate variable</th><th>Estimate</th><th>SE</th><th>2.5%</th><th>97.5%</th><th>significance</th></tr></thead><tbody><tr><td><strong>d<sub>max</sub></strong></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>T</td><td>-0.230</td><td>0.068</td><td>-0.360</td><td>-0.097</td><td>*</td></tr><tr><td>D</td><td>0.150</td><td>0.050</td><td>0.054</td><td>0.250</td><td>*</td></tr><tr><td>T:D</td><td>-0.096</td><td>0.065</td><td>-0.220</td><td>0.031</td><td></td></tr><tr><td><strong>d<sub>mat</sub></strong></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>T</td><td>-0.190</td><td>0.065</td><td>-0.320</td><td>-0.064</td><td>*</td></tr><tr><td>D</td><td>0.077</td><td>0.049</td><td>-0.018</td><td>0.170</td><td></td></tr><tr><td>T:D</td><td>0.010</td><td>0.064</td><td>-0.110</td><td>0.140</td><td></td></tr><tr><td><strong>SLA</strong></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>T</td><td>-0.006</td><td>0.073</td><td>-0.150</td><td>0.140</td><td></td></tr><tr><td>D</td><td>0.190</td><td>0.051</td><td>0.083</td><td>0.280</td><td>*</td></tr><tr><td>T:D</td><td>-0.047</td><td>0.065</td><td>-0.180</td><td>0.079</td><td></td></tr><tr><td><strong>Wood density</strong></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>T</td><td>0.160</td><td>0.067</td><td>0.030</td><td>0.300</td><td>*</td></tr><tr><td>D</td><td>0.064</td><td>0.050</td><td>-0.033</td><td>0.160</td><td></td></tr><tr><td>T:D</td><td>0.019</td><td>0.064</td><td>-0.110</td><td>0.150</td><td></td></tr><tr><td><strong>Seed size</strong></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>T</td><td>0.046</td><td>0.071</td><td>-0.093</td><td>0.180</td><td></td></tr><tr><td>D</td><td>-0.180</td><td>0.050</td><td>-0.270</td><td>-0.078</td><td>*</td></tr><tr><td>T:D</td><td>-0.075</td><td>0.064</td><td>-0.200</td><td>0.054</td><td></td></tr><tr><td><strong>Seed productivity</strong></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>T</td><td>-0.130</td><td>0.061</td><td>-0.250</td><td>-0.012</td><td>*</td></tr><tr><td>D</td><td>-0.061</td><td>0.048</td><td>-0.150</td><td>0.032</td><td></td></tr><tr><td>T:D</td><td>-0.037</td><td>0.064</td><td>-0.160</td><td>0.085</td><td></td></tr></tbody></table>
<table><caption>Table S6: Summary of conditional parameters for the effect on *d<sub>mat</sub>* from the GJAM joint trait model. Conditioning was done on SLA, wood density, species seed productivity, seed size, and *d<sub>max</sub>*. Standardized coefficient values are coming from matrix **A**, for direct trait effect, and **C**, for direct climate effect.</caption><thead><tr><th>Conditional variable</th><th>Estimate</th><th>SE</th><th>2.5%</th><th>97.5%</th><th>significance</th></tr></thead><tbody><tr><td><strong>Traits</strong></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td><em>d</em><sub>max</sub></td><td>0.5460</td><td>0.0266</td><td>0.4940</td><td>0.5960</td><td>*</td></tr><tr><td>SLA</td><td>-0.0569</td><td>0.0576</td><td>-0.1720</td><td>0.0552</td><td></td></tr><tr><td>Wood density</td><td>-0.1300</td><td>0.0856</td><td>-0.3020</td><td>0.0384</td><td></td></tr><tr><td>Seed size</td><td>0.0403</td><td>0.0120</td><td>0.0169</td><td>0.0639</td><td>*</td></tr><tr><td>Seed productivity</td><td>-0.0385</td><td>0.0100</td><td>-0.0574</td><td>-0.0180</td><td>*</td></tr><tr><td><strong>Climate</strong></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Intercept</td><td>8.36e-01</td><td>2.69e-01</td><td>3.22e-01</td><td>1.36e+00</td><td>*</td></tr><tr><td>T</td><td>4.11e-03</td><td>4.66e-03</td><td>-4.93e-03</td><td>1.33e-02</td><td></td></tr><tr><td>D</td><td>-1.59e-04</td><td>9.53e-05</td><td>-3.49e-04</td><td>3.28e-05</td><td></td></tr><tr><td>T:D</td><td>8.30e-06</td><td>4.60e-06</td><td>-8.00e-07</td><td>1.73e-05</td><td></td></tr></tbody></table>
<table><caption>Table S7: Joint traits model selection (based on the lowest DIC values). GJAM models ran with different combinations of climate covariates (*T*, temperature, and *D*, deficit).</caption><thead><tr><td>Climatic predictors in GJAM</td><td>DIC</td></tr></thead><tbody><tr><td>T × D</td><td>20,575</td></tr><tr><td>T + D</td><td>20,603</td></tr><tr><td>T</td><td>20,661</td></tr><tr><td>D</td><td>20,898</td></tr></tbody></table>
<figure><img src="image_6.png" /></figure>

Figure S1: MASTIF data network, including seed traps data and crop count data limited here to species-genus used. The dot size represents the number of initial tree-year observations at the log10 scale. Crop count data (green dots, CC) includes 137,484 tree years observations and seed traps (orange dots, ST) 10,914,392 observations in total.
<figure><img src="image_7.png" /></figure>

Figure S2: a) Comparison of *d*<sub>max</sub> obtained from online open sources to *d*<sub>max</sub> obtained from National Forest Inventories (NFI), MASTIF inventories, and from the unpublished dataset (n=191 species). b) Comparison of *d*<sub>max</sub> obtained from National Forest Inventories (NFI) to *d*<sub>max</sub> obtained from MASTIF inventories (N = 118 species). For both panels, the black line is the 1:1 relationship.
<figure><img src="image_8.png" /><figcaption>Figure S3: a) Comparison of maturation size ($d_{mat}$) from the main analysis (probability to produce the first fruiting structure) to maturation size (probability to reproduce at 50%) based on the reference in Visser *et al.* (2016), restricted to Barro Colorado Island, Panama. Each dot represents a single species, with the black dotted line indicating a 1:1 relationship (N = 56 species). b) Relationship between $d_{mat}$ and $d_{max}$ restricted to species used by Visser *et al.* (2016). The model fitted between $d_{mat}$ and $d_{max}$ is shown in blue for the model based on our estimates of $d_{mat}$ and in red for estimates of $d_{mat}$ from Visser *et al.* (2016). The regressions are reported with a confidence interval of 0.95. The average parameters $\alpha$ and $\beta_d$ are reported for both models.</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>Figure S4: a) Maturation size response to *d*<sub>max</sub> and temperature and b) Uncertainty of maturation size. Convex hulls are defined by observations (red), including the 486 tree species. In b) the surface scale color decreases as the inverse of the predictive standard error-blue edges reflect increased uncertainty at data extremes.</figcaption></figure>
<figure><img src="image_10.png" /><figcaption>Figure S5: Relationship between *d*<sub>max</sub> with latitude (in absolute degree) across species. The color gradient represents the average temperature (in °C). The average latitude for each species was determined by using MASTIF inventories. Each dot represents one species.</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>Figure S6: Conditional parameter estimates for the direct effect of traits on maturation size ($d_{mat}$), while accounting for trait covariance, climate and phylogeny. The climate used here has been extracted from the MASTIF inventories. Conditional parameters are evaluated on a standardized scale, making trait effects on $d_{mat}$ respective to their variation in the data set. Points represent the posterior mean with their 95% credible intervals. Blue and red represent positive and negative associations where 95% of the posterior does not include zero. SLA, specific leaf area.</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>Figure S7: (a) Relative size at maturation (*d*<sub>rel</sub>) includes a phylogenetic signal (400 species in our data have phylogenies in Zanne *et al.* 2014, Pagel's *λ* = 0.51, *p* < 0.0001). (b) Boxplot of relative size at maturation (*d*<sub>rel</sub>) for gymnosperms and angiosperms (number of species is 48 for gymnosperm and 438 for angiosperm).</figcaption></figure>
a

<figure><img src="image_13.png" /></figure>

b

<figure><img src="image_14.png" /></figure>

**Figure S8:** Boxplot of a) *d*<sub>mat</sub> and b) *d*<sub>max</sub> for gymnosperms (n = 48) and angiosperms (n = 438). *** indicates *p* < 0.0001 based on the sample t-test for unequal variances.
<figure><img src="image_15.png" /><figcaption>Figure S9: Boxplot of *d*<sub>rel</sub> for families with more than one species. Green is for gymnosperms and purple for angiosperms.</figcaption></figure>
<figure><img src="image_16.png" /><figcaption>Figure S10: Boxplot with violin of variation of *d*<sub>rel</sub> across growth forms (n = 419 species). The violin here is a mirrored density plot and showed the distribution of the data. Growth form follows a compilation from Díaz *et al.* (2022), with samples: trees, n = 361 species; shrubs, n = 17 species; shrub/tree n = 41 species. Groups were compared with a t-test for unequal variance and detected no differences according to plant growth forms (non-significant adjusted p-values with *p* > 0.05).</figcaption></figure>
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