## 2 Materials and Methods
### Overview of Approach
\begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Model/Analysis Type** & **Model Y(s)** & **Model X’s** & **Validation Type** & **Data Location** \\ \hline \multicolumn{5}{c}{**CORAL PHYSIOLOGICAL DATASET EXPLORATION**} \\ PCA & 12 PRV a & NA & NA & Figure 4a \\ MDS & 12 PRV a & NA & NA & Figure 4b \\ Factor analysis & 16 PRV & NA & NA & Not shown \\ \hline \multicolumn{5}{c}{**ENVIRONMENTAL EFFECTS ON CORAL PHYSIOLOGY**} \\ NP-MANOVA & 4 PRV factors & ENV 1 & NA & Table 2 \\ NPALS & 4 PRV factors & ENV 1, ENV 2, ENV 3 & Kfold7, val col, val w/test & Table S1 \\ NIPALS & 4 PRV factors & ENC 1, ECO 2, ECO-RS & Kfold7, val col, val w/test & Table S1 \\ NIPALS & 4 PRV factors & (ENV + ECO) 1, (ENV + ECO) 2 & Kfold7, val col, val w/test & Table S1 \\ NIPALS & 4 PRV factors & (ENV + ECO) 1, (ENV + ECO) 2 & Kfold7, val col, val w/test & Table S1 \\ NIPALS & 16 PRV & ENV 1, ENV 2, ENV 3 & Kfold7, val col, val w/test & Table S1 \\ NIPALS & 16 PRV & ENV-RS & Kfold7, val col, val w/test & Table S1 \\ NIPALS & 16 PRV & (ENV 1, ECO 2, ECO-RS & Kfold7, val col, val w/test & Table S1 \\ NIPALS & 16 PRV & (ENV + ECO) 1, (ENV + ECO) 2 & Kfold7, val col, val w/test & Table S1 \\ Predictor screen & CHI & ENV 1 & NA & Figure 4c \\ Model screen & CHI & ENV 1 & Kfold7, val col, val w/test & Table 3 and Table S2 \\ NN GUI-HL(1) & CHI & ENV 1, ENV 2, ENV 3, & Kfold7, val col, val w/test, 20\% & Table 3 and Table S2 \\ NN GUI-HL(2) & CHI & ENV-RS & HB & Table 3 and Table S2 \\ NIPALS & CHI & ENV 1, ENV 2, ENV 3, & Kfold7, val col, val w/test & Table 3 and Table S2 \\  & & ENV-RS & Kfold7, val col, val w/test & Table 3 and Table S2 \\ \hline \multicolumn{5}{c}{**ECOLOGICAL EFFECTS ON CORAL PHYSIOLOGY**} \\ Predictor screen & CHI & ECO 1 & NA & Table 3 and Table S2 \\ Model screen & CHI & ECO 1 & Kfold7, val col, val w/test & Table 3 and Table S2 \\ NN GUI-HL(1) & CHI & ECO 1, ECO(15) 1 & Kfold7, val col, val w/test, 20\% & Table 3 and Table S2 \\  & & ENV 1, ENV 2, ENV 3, & Kfold7, val col, val w/test & Table 3 and Table S2 \\  & & ENV-RS & Kfold7, val col, val w/test & Table 3 and Table S2 \\ \hline \multicolumn{5}{c}{**ENVIRONMENTAL + ECOOLOGICAL EFFECTS ON CORAL PHYSIOLOGY**} \\ Predictor screen & CHI & ENV 1 + ECO 1 & Kfold7, val col, val w/test & Table 3 and Table S2 \\ Model screen & CHI & ENV 1 + ECO 1 & Kfold7, val col, val w/test & Table 3 and Table S2 \\ NN GUI-HL(1) & CHI & ENV 1 + ECO 1 & Kfold7, val col, val w/test & Table 3 and Table S2 \\ NN GUI-HL(2) & CHI & ENV 1 + ECO 1 & Kfold7, val col, val w/test & Table 3 and Table S2 \\ NIPALS & CHI & ENV 1 + ECO 1 & Kfold7, val col, val w/test & Table 3 and Table S2 \\ \hline \end{tabular}  
* SinH-ArcsinH (SHASH)-transformed data.  
\end{table} 
Table 1: Environmental (ENV) effects on coral physiology. For the multivariate analyses, either all coral physiological response variables (PRV) were considered (“16 PRV” or “12 PRV,” depending on the analysis) or the factor loading scores derived from a factor analysis of these PRV were analyzed (“4 PRV factors,” which explained 84% of the variation). In addition to all 50 benthic categories found in the vicinity of the sampled corals (“ECO”), the 15-factor loading scores from a factor analysis of the benthic data were also considered (“ECO(15)”). Those NIPALS (non-iterative partial least squares [PLS]) models whose PRESS was minimized with zero factors (i.e., no statistically meaningful conclusion) are instead found in Tables S1 and S2 (Supplementary File S1) for the multivariate and univariate (coral health index [CHI]) data, respectively. Superscripts following values in the “Model X’s” column denote the factorial degree (1 st, 2 nd, or 3 rd). HB = holdback. HL = hidden layer. MDS = multi-dimensional scaling. NA = not applicable. NN = neural network. NP-MANOVA = non-parametric multivariate ANOVA. PCA = principal components analysis. RS = response surface. Val col = validation column. Val w/test = both validation and test data columns used for validation.