<p>Supplementary Material</p><p>A trait-based approach to advance coral reef science</p><p>Joshua S. Madin1, Mia Hoogenboom2, Sean R. Connolly2, Emily Darling3, Daniel Falster1, </p><p>Danwei Huang4, Sally Keith5, Toni Mizerek1, John M. Pandolfi6, Hollie Putnam7, and </p><p>Andrew H. Baird2</p><p>1. Department of Biological Sciences, Macquarie University NSW 2109, Australia</p><p>2. Australian Research Council Centre of Excellence for Coral Reef Studies and College of </p><p>Marine and Environmental Sciences, James Cook University, Townsville 4811, Australia</p><p>3. Marine Program, Wildlife Conservation Society, Bronx, New York 10460, USA.</p><p>4. Department of Biological Sciences & Tropical Marine Science Institute, National </p><p>University of Singapore, Singapore 117543, Singapore </p><p>5. Center for Macroecology, Evolution & Climate, Natural History Museum of Denmark, </p><p>University of Copenhagen, DK-2100, Copenhagen, Denmark</p><p>6. Australian Research Council Centre of Excellence for Coral Reef Studies, School of </p><p>Biological Sciences, The University of Queensland, St Lucia, Queensland, 4072, </p><p>Australia</p><p>7. University of Hawaii, Hawaii Institute of Marine Biology 46-007 Lilipuna Rd. Kaneohe, </p><p>HI 96744 USA Supplementary Method S1</p><p>Growth rate and growth form (typical) data were downloaded from the Coral Trait </p><p>Database (https://coraltraits.org) with “include taxonomic detail” checked to also obtain molecular family classification for species. Growth rates were converted to mm per year linear (or radial) extension based on the unit categories (e.g., “mm per 6 months” were doubled; “mm per day” were multiplied by 365; and so on). Three species did not have a growth form categorisation (Acropora eurystoma, Orbicella faveolata and Orbicella franksi).</p><p>The Acropora species was categorised as digitate and the two Orbicella species as massive. </p><p>First, we measured the phylogenetic signal of growth rate for the 105 species on 1000 </p><p>Bayesian posterior trees obtained from [S1]. These trees combined data from a molecular phylogeny of 474 species, 13 morphological trees and a taxonomic tree. We used Pagel's lambda [S2] to quantify phylogenetic signal. This metric is a scaling parameter that determines if shared branches on the phylogeny can give rise to the observed patterns of similarity in linear extension rate. A lambda value of 0 signifies no correlation between species while a value of 1 indicates correlation equivalent to the Brownian expectation. We determined if the value obtained for each tree is significantly different from the two standard values using a likelihood ratio test. Growth rates were found to be phylogenetically conserved</p><p>(lambda = 0.687 ± SD 0.035; p < 0.001 for lambda = 0, p > 0.999 for lambda = 1).</p><p>Next, using log-transformed growth rate, a linear model was run in R with molecular family and growth form as predictor variables using the lm function [S3] (Table S1). An interaction term was not included, because geometric constraints were assumed to act similarly across family groupings. In total, there were 1374 growth rate measurements for </p><p>105 species spanning 16 of the 23 molecular families. There were no growth form measurements for species in Coscinaraeidae, Euphylliidae, Incertae sedis, Lobophylliidae, </p><p>Pachyseridae and Rhizangiidae. The predict function was then used to return and plot model estimates and standard errors for all existing combinations of family and growth form. </p><p>Combinations for which no data exist were marked in red. These estimates are based purely on the family and growth form of a species.</p><p>Table S1. Results of multiple regression showing estimates, estimate standard errors, t-values and probability of differing from the intercept. ***: <0.001, **: <0.01, *: <0.05, and .: <0.1</p><p>Std. Estimate Error t-value Pr(>|t|) (Intercept) 1.69606 0.07935 21.376 0.000 *** growthformbranching_open 0.02556 0.08114 0.315 0.753 growthformcolumnar -0.18328 0.09648 -1.9 0.058 . growthformcorymbose -0.38777 0.12804 -3.029 0.003 ** growthformdigitate -0.18008 0.11726 -1.536 0.125 growthformencrusting -0.77013 0.17046 -4.518 0.000 *** growthformencrusting_long_uprights -0.02718 0.09999 -0.272 0.786 growthformhispidose 0.4103 0.2383 1.722 0.085 . growthformlaminar -0.64349 0.09067 -7.097 0.000 *** growthformmassive -0.52736 0.07997 -6.594 0.000 *** growthformsubmassive -0.93648 0.14917 -6.278 0.000 *** growthformtables_or_plates -0.32702 0.1244 -2.629 0.009 ** family_moleculesAgariciidae -0.48809 0.07251 -6.732 0.000 *** family_moleculesAstrocoeniidae -0.69158 0.2342 -2.953 0.003 ** family_moleculesDendrophylliidae 0.16305 0.23453 0.695 0.487 family_moleculesDiploastraeidae -0.79297 0.08998 -8.812 0.000 *** family_moleculesFungiidae -0.48293 0.07153 -6.752 0.000 *** family_moleculesMeandrinidae -0.64913 0.15022 -4.321 0.000 *** family_moleculesMerulinidae -0.3793 0.06721 -5.643 0.000 *** family_moleculesMontastraeidae -0.33599 0.0856 -3.925 0.000 *** family_moleculesMussidae -0.41013 0.07913 -5.183 0.000 *** family_moleculesOculinidae -0.58349 0.34782 -1.678 0.094 . family_moleculesPlesiastreidae -0.63199 0.13031 -4.85 0.000 *** family_moleculesPocilloporidae -0.26469 0.08236 -3.214 0.001 ** family_moleculesPoritidae -0.3916 0.06619 -5.916 0.000 *** family_moleculesPsammocoridae 0.40344 0.19023 2.121 0.034 * family_moleculesSiderastreidae -0.41337 0.07937 -5.208 0.000 ***</p><p>Supplementary Method S2</p><p>Growth rate, skeletal density and growth form (typical) data were downloaded from the Coral Trait Database (https://coraltraits.org). 29 species had data for all three traits. </p><p>Growth rates were converted to mm per year linear (or radial) extension based on the unit categories. Given the lack of surface area to volume ratio (SA:V) data, we estimated ratios for growth forms based on simple geometric objects made up from 1000 cubes of 1 cm3 [S4]. </p><p>Surface areas given in Table S2 all have the same pattern of number of parts x (four sides + one top + one bottom), where parts are repeated units of morphology and sum to 1000 cubes. </p><p>For colonies attached to the substrate, the bottom was not included. For example, the massive growth form has 1 part with four 10x10 cm sides and one 10x10 cm top (and the bottom surface is cemented to the substrate and not included). The surface area (500 cm2) was then divided by volume (1000 cm3) to give SA:V. The columnar growth had four parts, each with four 10x5 cm sides and a 5x5 cm top. </p><p>Table S2. Approximations of surface area to volume ratio using 1000 cubes of 1 cm3.</p><p>Growth form Example Surface area SA:V Massive 1x(4x10x10+1x10x10) 0.5</p><p>Columnar 4x(10x5x4+5x5x1) 0.9</p><p>Encrusting 1x(32x1x4+32x32x1) 1</p><p>Tables or plates 1x(23x2x4+23x23x1 1.242 +23x23x1)</p><p>Encrusting (long 1x(22x1x4+22x22x1) 1.576 uprights) + 13x(10x2x4+2x2x1) Branching (closed) 6.25x(40x2x4+2x2x1) 2.025</p><p>Branching (open) 6.25x(40x2x4+2x2x1) 2.025</p><p>Laminar 1x(32x1x4+32x32x1 2.176 +32x32x1) </p><p>Digitate 50x(5x2x4+2x2x1) 2.2</p><p>Corymbose 50x(20x1x4+1x1x1) 4.05</p><p>Colony mass per area (CMA) was calculated according to Eq. 1 in Box 2 (i.e., skeletal density divided by estimated SA:V). Two linear models were subsequently run [S3]. The first with colony growth rate as a function of CMA (Table S3) and the second as a function of volume per surface area (i.e., the reciprocal of SA:V). The CMA model explained more variation (73%) and was 2.1 AICc points stronger (11.7 vs. 13.8).</p><p>Table S3. Results of multiple regression showing estimates, estimate standard errors, t-values and probability of differing from the intercept. ***: <0.001, **: <0.01, *: <0.05, and .: <0.1</p><p>Estimate Std. Error t-value Pr(>|t|) (Intercept) 1.25143 0.05215 23.999 0.000 *** log10(density/ sa_v) -1.01491 0.12104 -8.385 0.000 *** Supplementary References</p><p>S1. Huang, D. and Roy, K. (2015) The future of evolutionary diversity in reef corals. Phil. </p><p>Trans. R. Soc. B 370, 20140010 </p><p>S2. Pagel, M. (1994) Detecting Correlated Evolution on Phylogenies: A General Method for </p><p> the Comparative Analysis of Discrete Characters. Proc. Roy. Soc. B 255, 37–45</p><p>S3. R Core Team (2015) R: A language and environment for statistical computing. R </p><p>Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/.</p><p>S4. Jackson, J. B. C. (1979) Morphological strategies of sessile animals. In: Biology and </p><p> systematics of colonial organisms (eds. Larwood, G. P. and Rosen, B. R.) 499–555. </p><p>Academic Press</p>