Subsequently, Linear Mixed Effects (LME) models (Wood 2006) were used to test multi-level relationships (i.e. at each site and for all sites) between Ba/Cacoral vs. in-situ seawater variables. For the full site-level LME model, fixed effects components included the predictors “Sal” “Temp,” suspended solids (SS) (i.e. either “TSS”, “OSS” or “ISS”), and sedimentation rate (SD) (i.e. either “TSD”, “OSD” or “ISD”), and random effect in “id” (individual colony). Despite some differences in the temporal variation of the total, organic and inorganic components of SS as well as SD, the component terms were significantly collinear (Fig. S3). As such, only one term of each predictor variable was used to avoid unstable parameter estimates from the LME models (Pinheiro and Bates 2000). We heuristically tested all permutations for the LME models (a total of 930 models) to search for the best 5 models based on AICC for each site, and at the global level (i.e. all sites). All models had each individual coral as a random effect along with a continuous temporal autoregressive correlation structure i.e. allowing values ± 1 month to correlate with each other (to account for possible temporal lag or mismatch of data due to the monthly spot measurements). The top models fits were tested using the leave-one-out-cross-validation method (LOOCV) (REF). In brief, n-1 data points to train a potential model and letting it predict the value of the left-out data point. The square error for each LOOCV run was obtained and repeated n times, and cross-validated residual mean standard error normalized to the range of observed values (NRMSE) for each model calculated. All statistical analyses were performed using the statistical program R (version 3.0.3) (R Core Team 2014), using packages “stats”, “nlme” (Pinheiro et al. 2017), caret (REF) and glmulti (REF).