## 3 Results and Discussion
### Coral Physiological Data  
From a PCA of 12 coral physiological response variables (Figure 4a), a two-dimensional ordination explained nearly 70% of the variation, and MDS (Figure 4b) revealed a strong outlier. Only island and site significantly affected the multivariate coral phenotype (Table 2), and the PLS models of multivariate coral physiology were generally not robust (Table S1). Even those with several thousand predictors (representing various interactions among the environmental and benthic parameters) could explain <60% of the variation in the coral phenotype. For this reason, we have generally focused the remainder of the article on attempting to instead predict a singular coral health metric: the CHI. Over 80,000 predictive models of the CHI were built, with the goal of ultimately using a series of cheaper, easier-to-measure environmental and/or ecological survey parameters to instead assess coral resilience. Reef site explained the highest percentage of spatio-temporal variation in the CHI (37%) of the initial 14 environmental parameters assessed (Figure 4c), with depth as the second most influential parameter. Of the large number of models featuring various combinations of the environmental and ecological parameters (Table 3 and Table S2), in virtually all cases the superior model type for robustly predicting a coral's CHI was the machine-learning-based neural network. The most parsimonious neural network whose validation (or test) R2 was above the a priori cutoff of 0.8 featured only the 14 environmental parameters in a 1 st-order factorial (Table 3 and Figure S1a; R2 = 0.83). The machine-learning-based desirability analysis associated with this model was programmed to output the environmental conditions that would yield the highest theoretical CHI (Figure S1b), and it projected that a relatively deep (28 m), protected, fringing fore reef would be characterized by corals with the highest CHI based  
Figure 3: Spatial variation in seawater quality (**a,b**) and general benthic parameters (**c,d**). Values in (**c,d**) represent percentages (%) of total bentnos. on data held back from the model (i.e., validation column data). One other neural network with a single hidden layer (Table 3) was characterized by a higher R\({}^{2}\) (0.86), yet it required more boosting (a type of ensemble modeling approach) and so was far more complex with only a modest increase in fit. \begin{table}
\begin{tabular}{l l l l} \hline
**Environmental Parameter** & \(\mathbf{n}\) & \(\mathbf{F}\) & \(\mathbf{p}\) \\ \hline Island & 10 & 2.20 & **<0.01** \({}^{\text{a}}\) \\ Site & 33 & 1.56 & **<0.01** \\ Latitude & 33 & 0.98 & 0.42 \\ Longitude & 33 & 3.24 & 0.02 \\ Survey date & 19 & 1.69 & 0.16 \\ Survey time & 3 & 0.78 & 0.54 \\ Survey depth & 4 & 1.31 & 0.21 \\ Reef exposure & 3 & 1.19 & 0.31 \\ Reef type & 3 & 1.94 & 0.06 \\ Lagoon & 2 & 2.36 & 0.06 \\ Reef emergence & 2 & 0.46 & 0.76 \\ Reef location & 3 & 1.85 & 0.07 \\ Temperature & 13 & 0.63 & 0.64 \\ Salinity & 10 & 0.99 & 0.42 \\ \hline \end{tabular} \({}^{\text{a}}\) Scales with the magnitude of longitudinal distance.  
\end{table} 
Table 2: Non-parametric multivariate ANOVA of the effects of the 14 environmental parameters on coral phenotype (as four-factor loading scores derived from a factor analysis of 16 coral physiological response variables). Statistically significant differences (\(\alpha\) = 0.01) have been highlighted in bold. Figure 4: Multivariate analysis of the coral physiological data and a predictor screen of the coral health index (CHI). Both principal components analysis (PCA; on correlations; **[a]**) and multi-dimensional scaling (MDS; on standardized data; **[b]**) were undertaken with the 12-physiological response variable coral dataset (\(n\) = 110 samples).