S3 Fig. Spatial trends in the DHW dose response of the coral assemblage, with removal of three northern observations from 1998 which were suggested to potentially influence spatial effects.

Positive spatial random field (SRF) values represent locations where observed bleaching severity was worse than would have been expected based on DHW alone, and negative SRF values show locations where bleaching was less severe than DHW-based predictions. Figure shows (a) spatial trends, (b) the DHW dose response for severe bleaching following the beta distribution, and (c) a comparison of spatially correlated error between hotspots and thermal refugia, with significance computed from a Wilcoxon Sum Rank test.

https://doi.org/10.1371/journal.pclm.0001046.s001

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S4 Fig. Spatial trends in the DHW-bleaching relationship, and the sensitivity of these results to sampling effort and mesh resolution.

Positive spatial random field (SRF) values represent locations where observed bleaching severity was worse than would have been expected based on DHW alone, and negative SRF values show locations where bleaching was less severe than DHW-based predictions. Results are based on 100 independent runs of INLA models set up as follows: (i) Imbalances in sampling effort across bleaching surveys were accounted for by removing years with less than 30 records. This left 1998, 2010, and 2017 with 29, 80 and 63 records, respectively. Then for each replicate INLA model, 29 random records for 2010 and 29 random records for 2017 were chosen to keep and the rest were discarded to achieve a fully balanced design of N = 29 per year over 3 years. (ii) Each replicate INLA model was given a unique low-resolution Delaunay triangulation mesh with a maximum triangle edge length of 8 km achieving 465–502 nodes across replicate meshes, compared with the high-resolution mesh used in the main manuscript with max edge length of 8km achieving 5,710 nodes overall. Results presented here show: (a) the mean spatial random field across all replicate INLA runs (gridded at 5km CoralTemp resolution before averaging to account for mismatch in meshes between replicate runs); (b) the difference in spatial random field values between hotspot and thermal refugia reef cells in terms of the median (bold horizontal line), interquartile range (box) and minimum-to-maximum (vertical feather) computed first for each INLA model and then averaged across all replicate runs for the figure; and (c) Histogram of statistically significant differences in SRF values between hotspots and refugia (as in b) in terms of a P value for each replicate run based on Wilcoxon sum rank tests with an alpha level of 0.05 with Bonferroni correction (red dashed line) and log₁₀-scale x-axis.

https://doi.org/10.1371/journal.pclm.0001046.s002

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S5 Fig. Spatial trends in the DHW-bleaching relationship, and the sensitivity of these results to sampling effort and mesh resolution, as in S3 Fig.

S3 Fig figure description also applies to this figure, except bleaching severity scores were used as a response variable (0, 1, 2, 3) with a Gaussian error distribution rather than the beta distribution used for the main manuscript and S3 Fig.

https://doi.org/10.1371/journal.pclm.0001046.s003

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S6 Fig. Ordinal analysis of mass bleaching data, showing probability of the four different mass bleaching severity categories: no bleaching (a-b, 0%), mild bleaching (c-d, 1–10%), moderate bleaching (e-f, 11–50%), severe bleaching (g-h, > 50%).

Because it is not possible to explicitly account for spatial correlation with an ordinal analysis, the results shown are for a cumulative link model in the form: bleaching_severity ~ DHW + Latitude. Here we use latitude as a proxy of the change in thermal regimes, showing hotspots (red) and thermal refugia (blue) with representative latitudes of 7 and 8°N, respectively. This result reflects that in the main study that mass bleaching is predicted to be lesser for a given DHW in hotspots rather than thermal refugia.

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S7 Fig. Simulated marine heatwave experiment.

(A) Temperature profiles for the ten replicate heat stress tanks (Tanks 1–8, 11, and 12) and procedural control tanks (Tanks 9 and 10), sharing the colour legend with panel B. The local climatological baseline (MMM_adj) and the corresponding stress accumulation threshold (MMM_adj + 1°C) are shown for each of the 6 coral collection sites. Specific values for each site are shown in S1 Table. (B) The average accumulated heat stress profile (DHW–degree heating weeks) is shown as the average across all sites in each experimental tank (colour legend). The shaded region shows the total range of absolute DHW across all sites and tanks.

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S8 Fig. Relationship between the compliment of mean BMI (i.e., a measure of heat tolerance) and DHW₅₀, the heat stress dosage at which a colonies response is predicted to pass a BMI of 0.5.

https://doi.org/10.1371/journal.pclm.0001046.s006

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S9 Fig. Ordinal analysis of experimental bleaching and mortality data for Acropora digitifera, showing probability of the five different health status categories: healthy (a), partial bleaching (b), bleached (c), partial mortality (d), dead (e).

These predictions are from the cumulative link model in form: health_status ~ DHW + Region, with a random intercept for colony ID (to account for multiple fragments per colony), and site (multiple sites per region). There is a significant effect of DHW (z = 97.01, P < 0.001) on the declining health status of coral fragments, and significantly more DHW resistance at thermal refugia than hotspots (z = 2.54, P < 0.05), which equates to an additional 0.8°C-weeks for a probability of 0.5 (dashed horizontal line).

https://doi.org/10.1371/journal.pclm.0001046.s007

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S11 Fig. Model residuals from the DHW dose response shown in Fig 2A, for all bleaching survey records in the three most-extensive bleaching survey years conducted in (a) 1998, (b) 2010, and (c) 2016.

Residuals are calculated as the vertical distance between the observed bleaching severity (0–1, transformed from severity scores) and the predicted DHW dose response curve in Fig 2A. Colours for each year are shown with a blue-white-red scale, centred on the mean residual for that year. Satellite 5km grid cells identified as hotspots and thermal refugia are shown in dark grey and black, respectively. Comparison of mean residuals of hotspots versus thermal refugia for each year are given in white text on each map.

https://doi.org/10.1371/journal.pclm.0001046.s008

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S12 Fig. The heat stress (degree heating week DHW) dose response curve for severe mass bleaching for all of Palau (black), only hotspots (red) and only thermal refugia (blue).

Predictions are based on the logistic model presented in Fig 2, with an intercept value of -2.08, a slope value of 0.36, and an intercept offset for hotspots and thermal refugia of -0.24 and 0.36, respectively. The DHW required to elicit a 50% chance of severe mass bleaching at hotspots (DHW₅₀ = 6.4°C-weeks) is 1.7 DHWs greater than that of thermal refugia (DHW₅₀ = 4.7°C-weeks).

https://doi.org/10.1371/journal.pclm.0001046.s009

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S13 Fig. Risk of severe Acropora bleaching (i.e., > 50% of corals bleached) during the 2010 marine heatwave to be compared to the assemblage-level result in the main manuscript.

(a) Bleaching survey records from 2010 are overlayed on thermal regime classifications, with (b) the same points also shown on the high-resolution Delaunay triangulation mesh (comprising 4,325 nodes), used to calculate spatial correlated uncertainty in predictions of severe Acropora bleaching. (c) The Gaussian Markov spatial random field reports the spatial correlated uncertainty (residual bleaching susceptibility) as u values (see linear combination equation). Compared to what would have been predicted based on DHW alone (i.e., without a spatial random effect), areas of higher bleaching susceptibility are shown in red (underpredictions), and areas of higher bleaching resistance are shown in blue (overpredictions). (d) Thermal refugia have marginally higher Acropora mass bleaching susceptibility for a given heat stress dosage (u values) than hotspots (Wilcoxon sum rank test). (e) The difference in Acropora bleaching susceptibility to the 2010 marine heatwave at thermal refugia (blue) versus hotspots (red) translates to only a small yet significant 4% increase in the chances of severe Acropora mass bleaching (P(SB)).

https://doi.org/10.1371/journal.pclm.0001046.s010

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S14 Fig. Probability of total Acropora bleaching (i.e., percentage of corals bleached, reaching up to 100% of colonies) during the 2010 marine heatwave to be compared to S13 Fig.

(a) Bleaching survey records from 2010 are overlayed on thermal regime classifications, with (b) the same points also shown on the high-resolution Delaunay triangulation mesh (comprising 4,325 nodes), used to calculate spatial correlated uncertainty in predictions of severe Acropora bleaching. (c) The Gaussian Markov spatial random field reports the spatial correlated uncertainty (residual bleaching susceptibility) as u values (see linear combination equation). Compared to what would have been predicted based on DHW alone (i.e., without a spatial random effect), areas of higher bleaching susceptibility are shown in red (underpredictions), and areas of higher bleaching resistance are shown in blue (overpredictions). (d) Thermal refugia have marginally higher probability of Acropora mass bleaching for a given heat stress dosage (u values) than hotspots (Wilcoxon sum rank test). (e) The difference in Acropora bleaching susceptibility to the 2010 marine heatwave at thermal refugia (blue) versus hotspots (red) translates to only a small yet significant 4% increase in the probability of total Acropora mass bleaching (P(TB)).

https://doi.org/10.1371/journal.pclm.0001046.s011

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S15 Fig. Probability of total corymbose Acropora bleaching (i.e., percentage of colonies bleached, reaching up to 100% of colonies) during the 2010 marine heatwave.

(a) Bleaching survey records from 2010 are overlayed on thermal regime classifications, with (b) the same points also shown on the high-resolution Delaunay triangulation mesh (comprising 2,595 nodes), used to calculate spatial correlated uncertainty in predictions of severe corymbose Acropora bleaching. (c) The Gaussian Markov spatial random field reports the spatial correlated uncertainty (residual bleaching susceptibility) as u values (see linear combination equation). Compared to what would have been predicted based on DHW alone (i.e., without a spatial random effect), areas of higher bleaching susceptibility are shown in red (underpredictions), and areas of higher bleaching resistance are shown in blue (overpredictions). (d) Thermal refugia have higher probability of corymbose Acropora mass bleaching for a given heat stress dosage (u values) than hotspots (Wilcoxon sum rank test). (e) The difference in corymbose Acropora bleaching susceptibility to the 2010 marine heatwave at thermal refugia (blue) versus hotspots (red) translates to a 10% increase in the probability of total corymbose Acropora mass bleaching (P(TB)).

https://doi.org/10.1371/journal.pclm.0001046.s012

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