High-resolution modeling of thermal thresholds and multiple environmental influences on coral bleaching for regional and local reef managements

Corals are one of the communities most threatened by global and local stressors. Excessive summer sea temperatures can cause coral bleaching, resulting in decreases in living coral coverage. Coral bleaching may begin with rising sea temperatures, although the widely used threshold of 1 °C over the local climatological maximum sea temperature has been reconsidered. In this study, we refine thermal indices predicting coral bleaching at high resolution (1 km) by statistically optimizing the thermal threshold and multiple environmental influences on bleaching, such as ultraviolet (UV) radiation, water turbidity, and cooling effects on corals. We use a dataset of coral bleaching events observed during 2004–2016 in Japan derived from the Web-based monitoring system, the Sango (Coral) Map Project, aiming at regional to local conservation of Japanese corals. We show how the ability to predict coral bleaching is improved by the choice of thermal index, statistical optimization of thermal thresholds, usage of multiple environmental influences, and modeling methods (generalized linear model and random forest). After optimization, the differences among the thermal indices in the ability to predict coral bleaching were slight. Among environmental influences, cooling effects, UV radiation, and water turbidity, in addition to a thermal index, well explain the occurrence of coral bleaching. Prediction based on the best explanatory model reveals that recent Japanese coral reefs are experiencing bleaching in many areas, although we show a practical way to reduce bleaching frequency significantly by screening UV radiation. Thus, our high-resolution models may provide a quantitative basis for the management of local reefs under current global and local stressors. The results of this study may be useful to other researchers for selecting a predictive method according to their needs or skills.

is quite effective in Japan, because internet service is available to the vast majority of people 98 in Japan, who are able to use common Japanese much better than English, and most Japanese 99 coral reefs develop around populated islands where diving services are available. The 100 outcome of this project has been commented on in the IYOR international "Year in Review" 101 report (Staub & Chhay, 2009). 102 thermal stress on coral bleaching, we also constructed prediction models of bleaching using 244 two modeling methods: generalized linear model (GLM) with a binomial error distribution 245 and a logit link function, and random forest (RF) (Breiman, 2001). Although both models give 246 prediction in the form of probability, the underling algorithms are quite different between the 247 models. GLM is an extension of regression models, whereas RF is a machine learning method 248 using randomly repeating classifications (Table 2). Therefore, the fitted model of GLM can be 249 written as a formula that is easy to be used subsequently. In contrast, RF can only be saved 250 electronically, despite its high predictive performance. We confirmed that the data met the 251 assumption of binomial GLM that the residual deviance per degree of freedom was less than 252 1.5 (Zuur et al., 2009). RF was performed using the randomForest function of the 253 randomForest R package. RF was used under the standard settings to avoid overfitting to 254 training data, except that we followed the recommendation of Hijmans et al. (2017), using 255 "regression model" even though the response variable was classification. Additionally, the 256 relative importance of variables was calculated using the "importance" function of the 257 MuMIn package (Bartoń, 2015) for GLM and the "importance" function of the randomForest 258 package for RF (Liaw & Wiener, 2002). 259 The predicted probability was transformed into bleaching and nonbleaching by the 260 threshold that maximizes the sum of TPR and TNR (Liu et al., 2005). As the threshold, 0.5 261 (i.e., the midpoint) is frequently used, although its transformed prediction of occurrences and 262 absences will be biased, particularly if numbers are unequal between observed occurrences 263 and absences in the source data (Liu et al., 2005). This problem is known in studies of species 264 distribution modeling, although only a few studies of coral bleaching have addressed it (van 265 The models were evaluated by 10 repeated cross-validations, using TSS as the 268 evaluation index. In each repeat, we separated 30% of the data as testing data and used the 269 remaining 70% of the data for constructing GLM and RF (Table 1). We optimized the filtering 270 thresholds for DHM and DHWs by cross-validation, while the filtering threshold is fixed at 271 1.0 °C in the standard indices (Table 1). We searched the optimum filtering threshold between 272 0 and 1.5 °C for indices using constant threshold (a), whereas we examined the coefficient of 273 s m (b) between 0.1 and 2.5 (Table 1) at 0.01 precision (i.e., 151 and 241 submodels, 274 respectively). For models with multiple explanatory variables, we considered DCW, historical 275 SST variability, UV-B, water turbidity, water depth, and current speed, in addition to a 276 thermal index. The optimum set of explanatory variables was also specified through 277 cross-validation, i.e., selecting the set of variables that best explains the testing data among all 278 15 possible combinations, excluding the two most influential variables (DCW and UV-B), 279 which are always included in models with multiple explanatory variables (Table 1). Therefore, 280 we totally evaluated 22,650 or 36,150 models (10 cross-validations × 15 variable 281 combinations × 151 or 241 submodels) for each GLM and RF model. 282 Finally, we predicted coral bleaching in the warmest month of the main coral habitat 283 in the study area using the optimized best prediction model. We also assessed the reduced 284 UV-B effect on coral bleaching as a possible adaptive measure, applying the 40% reduction in 285 UV-B radiation from the original values by the 40% increase in screening effect (water 286 turbidity). These levels of reduction and increase in variables were consistent with in situ 287 examination in Onna Village in the Ryukyu Islands (Okinawa Prefecture, 2017). Prediction 288 was performed using each model built in each of the 10 cross-validations and subsequently 289 averaged among the 10 models. The source of the data for the Japanese map was the Global 290

Effect of each environmental variable 295
GLMs using a single environmental variable indicated various relationships with 296 coral bleaching (Fig. 2). The predicted probability of bleaching increased with the thermal 297 indices, including SSTs, DHM, DHWs, and UV-B, and decreased with DCW, water turbidity, 298 and water depth. The responses to historical SST variability and current speed were not 299 significant, with 95% confidence intervals (CIs) ranging from negative to positive responses. 300 Both of the predicted responses to monthly and weekly SSTs were positive, although their 301 95% CIs were too wide, suggesting they were not reliable indices of coral bleaching. At the 302 same time, the predicted bleaching alert thresholds to discriminate coral bleaching were found 303 to be lower than the standard thresholds, except for DHM (Table 3A). 304 We compared the importance of different environmental variables (Fig. 3). The 305 ranking of variables was almost the same for GLM and RF: the best was DHW, followed by 306 DCW. UV-B, water turbidity, and historical SST variability were also found to be good 307 explanatory variables for coral bleaching. Historical SST variability and current speed were 308 not the worst variables, despite their inconsistent relationships with coral bleaching, as shown 309 above. 310

Optimization and assessment of the filtering threshold 311
Optimization of the filtering threshold improved the predictive performance of 312 DHM and DHWs, although the improvement was particularly small for models consisting of 313 multiple environmental variables, whereas the improvement was significant for models 314 consisting of thermal index only (Fig. 4). 315 Further, we compared the predictive performance among all the models including 316 the standard or the optimized thermal index, and the optimized set of multiple explanatory in predictive performance between models with multiple explanatory variables with optimized 343 evaluation thresholds and those with optimized evaluation and filtering thresholds was 344 smaller than that between GLM and RF: RF models were always better than GLM among 345 models with multiple explanatory variables. Although the TPRs of GLMs were better than 346 those of RFs in most cases, the TNRs of GLMs were worse than those of RFs in all models 347 with multiple explanatory variables; i.e., the risk of false positives was higher. Among the 348 models with multiple explanatory variables, the RF model consisting of DHW with MMM + 349 0.97 °C filtering threshold, DCW, UV-B, water turbidity, historical SST variability, and 350 current speed (Table 3D)  bleaching prediction for the Ryukyu Islands using DHW at 1-km resolution improved the 440 may not be very much, although the predictive performance is also improved by optimizing 443 thermal thresholds of DHW. Further, prediction of coral bleaches was much improved by 444 incorporating other environmental variables, such as cooling effect, UV radiation, and 445 turbidity, in addition to thermal indices. 446 The high performance of our bleaching model at 1-km resolution has practical 447 implications for regional and local management of coral reefs. The prediction revealed high 448 frequencies of coral bleaching in many parts of the Ryukyu Islands. Note that spatial variation 449 was found in the predicted bleaching frequency, and the prediction was based on the lowest 450 rank of severity of bleaching, resulting in overemphasis of the bleaching risk.  and 95% confidential interval, respectively. Dotted line represents the threshold 678 discriminating bleaching and nonbleaching, which was optimized by the true positive rate-679 true negative rate (TPR-TNR) sum maximization approach (see Table 2).     Step 3 Evaluation and model assessment Optimizing evaluation threshold Optimizing the threshold to discriminate occurrence and absence from the predicted probability of statistical models of bleaching.
Although statistical models to predict occurrence or absence usually give results as probabilities, using a 0.5 (i.e., midpoint) threshold can yield biased results under unequal prevalences. To avoid this problem, the TPR-TNR sum maximization approach was used to optimize the threshold (see Table 2 Randomly selected 30% of data were separated as testing data, and the remaining data were used as training data. Prediction models Hijmans et al.
were built using the training data and evaluated using the testing data.
The test was repeated 10 times for each filtering threshold and combination of explanatory variables Step