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.