Data analyses
Sensitivity was estimated in two ways, using both an unweighted and a weighted percentage of bleached corals. The unweighted method calculated the percentage of coral colonies that were pale to fully bleached as the percentage of all corals sampled. The weighted or bleaching intensity metric placed colonies into seven categories of bleaching ranging from normal to 100% bleached white and uses these categories to weight the responses of bleaching (McClanahan et al. 2007). Bleaching susceptibility is a related metric used to estimate the sensitivity of the community to bleaching, where the relative abundance of each taxa was multiplied by the mean bleaching intensity for that taxa based on either historical or recent observations and summed. Here, we used the 2016 bleaching intensity observations for each taxon. Bleaching susceptibility provides a single number for each site, where higher values indicate a coral assemblage with a higher susceptibility to bleaching and lower values indicate a coral assemblage that is less susceptible to bleaching. The two estimates were highly correlated (r = 0.92, p < 0.0001).
The timing of the exposure (satellite temperature observations) and ecological sensitivity as percentage of bleached corals were evaluated for their predictive strength based on AIC values of relationships with predictor variables possible relationships before combining into a resistance metric. First, we extracted daily 5-km SST time series for 90 days prior to field survey at each site and calculated the date of maximum observed DHMs. We found that all of the final 226 selected sites were sampled within 21 days after peak SSTs. Thereafter, we evaluated the two metrics of sensitivity (the unweighted percent bleaching and weighted bleaching intensity metrics) for their distributions, outliers, and associations with seven predictor variables. We found that 10 sites in Ningaloo reefs were outliers as per the multivariate Mahanalobis distance method. Exploration of these outliers suggest local oceanographic effects at Ningaloo were overriding the broader-scale satellite measurement values (Woo et al. 2006; Xu et al. 2016). Some error is expected in these analyses due to the scale mismatch of the satellite and field surveys, where field surveys are contained with satellite measurements dimensions but cover a smaller area. Nevertheless, we decided to retain these sites in all analysis as they represented some of this natural and scaler variability and possible influence on the models that we explored.
To evaluate resistance, we first normalized the exposure of the two metrics and the metric of ecological sensitivity selection for all sites between 0 and +1, added +1 to all values and then divided exposure by sensitivity. These transformations eliminated zeroes and negative numbers and produced resistance values between 0.5 and 1.75 (Supplementary Fig. 1). Prior to calculating resistance, we evaluated statistical attributes of the single variables, interacting variable, and the ratio versus subtraction method to calculate resistance. Comparison of AIC values for bleaching versus the bleaching index against predictor variables indicated lower values for the percentage (AIC = 125.7+ 97.1(+ SD) n=28 comparisons) versus bleaching index (AIC = 141.1+ 78.1, n=28). Similarly, comparing the subtraction and the ratio method for estimating resistance found the ratios produced considerably lower AIC values (AIC = 62.8+ 56.6, n=28) than subtraction (AIC = 204.1+ 46.1, n=28).
Distributions of these chosen exposure, sensitivity, and the two metrics of resistance showed continuous distributions with weak centralization that should increase the probabilities of detecting patterns (Supplementary Fig. 1). Visualization of the scatterplot matrix of the 7 variables indicated that mean SST and kurtosis were strongly correlated (r=0.83) while all other variables correlations were <0.56. Therefore, we specified the model to not simultaneously include kurtosis and mean SST. Variance inflation scores – another indicator of multicollinearity – are presented for each top model and are all <3 (Table 1), indicating collinearity is not a serious concern. Sites were pooled into a general location for the analysis until the fit of a Generalized Linear Mixed Model (GLMM) with location as a random effect revealed nonuniformity and under-dispersion of the residuals. Consequently, location was removed from the final Generalized Linear Model (GLM) approach, and no spatial auto-correlation was found. Thereafter, we used a multi-model inference framework and fit the GLMs with the resistance ratio calculated from each of the two exposure models (CTA vs CE) against the 7 predictor variables with a Gaussian log-link error structure. All possible sub-models were computed using the dredge function from the MuMIn package in R. We present all the results of the top set models where delta AICc values < 2 and where mean SST was excluded. This multi-model approach of evaluating all possible models reduces the changes of subjectively selecting significant but the not best models (Burnham and Anderson 1998).
We tested for difference in resistance, thermal environments, coral communities, and bleaching by major taxon for sites with all comparable variables within (n=27) and outside the Coral Triangle (n=199). Most data failed to pass tests of normality (using Kolmogorov-Smirnov-Lilliefors, KSL, tests) and therefore non-parametric Wilcoxon tests were undertaken for comparisons of all variables. Temperature data were pooled to visualize their distributions in the two regions. Coral communities were evaluated by multivariate Community Correspondence Analysis using the vegan package in R. The first and second values for each site were extracted and tested for differences between the two regions.
Both exposure and sensitivity metrics show good spread across the geographic coverage of this study (Supplementary Fig. 1). We then estimated resistance as exposure divided by sensitivity, and tested the hypotheses that resistance differed locally and geographically as influenced by biogeographical location, recent environmental forces over the past two decades, and attributes of the coral taxa and communities. We specifically evaluated whether the marine biodiversity center, known as the Coral Triangle (Spalding et al. 2007), had the same resistance and future prognosis as lower diversity peripheral reefs outside the Coral Triangle.
Previous studies have suggested that background SST mean and distribution (i.e. skewness and kurtosis) and its timing can influence bleaching and mortality by influencing coral acclimation and adaptation mechanisms (Ateweberhan and McClanahan 2010; Grottoli et al. 2014; Ainsworth et al. 2016; Langlais et al. 2017; Safaie et al. 2018). Temperature mean, skewness, and kurtosis describe the average and extreme temperature conditions, and can covary to inflate covariance in multivariate models. For example, kurtosis increases strongly and exponentially with increasing SSTs while skewness declines but is highly variable at high SSTs depending on the local geography. To avoid selectivity of model selection based on significance alone, we used a multi-model framework where all possible models were evaluated and compared (Burnham and Anderson 1998). Multicollinearity was evaluated and temperature metrics with high correlations were included separately when exploring the strength of 128 model combinations. To account for non-random sampling, we included the geographic variables of longitude and latitude in addition to SST variables of mean, kurtosis, and skewness, and coral community variables comprising hard coral cover and genera richness. Sampling of longitude and latitude was not random and therefore evaluated as fixed covariates in models.