Introduction

In the tropics, marine heatwaves—periods of anomalously high temperature have been associated with historical and present-day mass coral bleaching events1,2,3. These events are projected to worsen with further ocean warming and cause major degradation of tropical coral reefs due to widespread bleaching and mortality events4,5,6.

Coral endosymbionts, dinoflagellates of the family Symbiodiniaceae7, are important contributors to holobiont metabolism, as they provide the corals with oxygen and up to 95% of their daily energy requirements through photosynthetic carbon translocation8,9. The term coral bleaching describes the process by which the symbiosis between corals and their algal endosymbionts breaks down, resulting in corals appearing pale or bleached10,11. The loss of photosynthetic symbionts represents a metabolic disruption, involving the shutdown of photosynthetic production supporting organic carbon and oxygen supply to the coral host12,13,14. Although corals can recover from bleaching, it often leads to coral mortality1,2.

Metabolic traits of marine ectotherms are characteristically temperature dependent. Thermal performance curves measure how metabolic rates change across temperatures within their thermal range15,16,17,18. Metabolic rates generally increase along a rising thermal gradient at a rate characterized by the activation energy (E, measured in eV) until they reach a thermal optimum (Topt). Beyond the Topt, metabolic rates fall, and the abruptness of this decline is measured by the deactivation energy (ED)19,20,21,22. While most characterizations of thermal performance curves depict a unimodal shape, individual assessments of coral performance curves show an especially asymmetric shape, where deactivation energies for photosynthesis are consistently larger than those for respiration23,24,25,26. Although these individual assessments indicate the potential for a mismatch between rates of photosynthetic oxygen production and holobiont oxygen consumption under peak temperatures, we lack a synthesis of the available data to test whether this is a consistent trend among coral holobionts.

Here, we aimed to test the hypothesis that, in hermatypic corals, respiratory demand for oxygen increases faster than photosynthetic production after the optimum temperature for net production is reached. To achieve this, we used published metabolic rates to construct thermal performance curves and analysed the E, Topt, and ED of coral holobiont metabolism across a range of temperatures. In this analysis, accounting for all factors influencing coral metabolism proves challenging. This is especially true when considering the potential of corals to acclimate to higher temperatures over time, as well as the thermal history of individual corals and Symbiodiniaceae assemblages. Obtaining this information from experimental assessments for accurate extrapolation remains difficult. However, the analysis presented here serves as a crucial initial step to test the hypothesis regarding the presence of a metabolic mismatch at high temperatures, which subsequently affects the oxygen budget of the holobiont. Furthermore, it sheds light on the under-represented role of oxygen in comprehending the breakdown of coral symbioses.

Results

From the published literature we compiled a dataset comprising 291 individual mean metabolic rates across 35 species of zooxanthellate corals from tropical and temperate locations across 33 different geographical locations. The dataset was dominated by corals from tropical regions (216 rates), with fewer entries originating from subtropical (60 rates) and scarce reports from temperate (15 rates) regions. Overall, metabolic rates were measured at temperatures that ranged from 6˚C to 36˚C. Using the data obtained we were able to construct thermal performance curves of respiration, net and gross productivity and P: R ratio, and from these we could calculate the optimum temperature (Topt), activation energy (E) and deactivation energy (ED) for each metabolic rate.

More than half of the metabolic rates in the dataset were measured during summer (53%), with 15% assessed in winter, 14% in autumn and 8% in spring. The lowest rates of metabolism for both respiration and net productivity were recorded in summer, likely reflecting the higher temperatures observed in this season. However, the date that incubations were conducted was not specified for the remaining 10% of articles used and thus, the season in which the experiments were conducted could not be resolved. Temperature ramping regimes of the experiments ranged from + 0.02 °C per hour to 2.5 °C per hour. The duration of experiments ranged from a few hours to a few weeks, with an average of 10 days.

Daily respiration rates reached a maximum of 19.33 µmol O2 cm−2 d−1 at 31.0 ˚C, which was more than twice the rate of net productivity (Pnet) at that temperature (7.88µmol O2 cm−2 d−1), (Table S1, Fig. 1). Overall, the fitted thermal performance curve indicated that the maximum rate of net productivity occurred at 28.0 ˚C (11.09 µmol O2 cm−2 d−1) (Table S1, Fig. 1b). The Topt for respiration was l.3 ˚C higher (30.5 ± 1.8 ˚C) than net productivity (29.2 ± 1.4˚C), implying that respiration rates continue to increase with warming beyond the temperature at which net productivity reaches its maximum (Table 1; Fig. 1e), however no significant difference was detected (95% CI: −1.96-6.38, Figure S4a). The Topt for gross productivity was also lower than that for respiration rates at 29.9 ± 1.0 ˚C (Table 1), with the highest rate of 27.21 µmol O2 cm−2 d−1 occurring at 31.0 ˚C (Table S1, Fig. 1c). The Topt for gross productivity was not significantly different than those of R (95% CI: −2.93-5.88, Figure S4b) and Pnet (95% CI: −5.21-2.97, Figure S4d).

Table 1 Parameter estimates for activation energy (E), deactivation energy (ED) and the optimum temperature (Topt) for coral metabolic rates based on thermal performance curves of the total dataset. Collated from 291 individual mean values from the literature, aggregated into 1.0 °C intervals (n = 24). Values in parentheses represent one standard error of the parameter estimates. The units for E and ED are eV (electron Volts) and for the Topt units are ˚C.
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The estimated P: R ratio curve began to decline when temperature exceeded 24.8˚C (± 1.2), although not as rapidly as the rates for R, Pnet and Pgross (Table 1), with holobiont metabolism becoming net heterotrophic (i.e. P: R ratio < 1) at, on average, 36.0 ˚C (Fig. 1d). The Topt for P: R ratio was significantly lower than that of R (95% CI: 2.33–10.12, Figure S4c), Pnet (95% CI: 0.08–6.36, Figure S4e) and Pgross (95% CI: 0.92–7.62, Figure S4f). The activation energy, E, was relatively consistent across all metabolic rates (0.46–0.47 eV, Table 1), with the exception of P: R Ratio (0.24 ± 0.08 eV, Table 1). E for all metabolic rates examined were within the reported ranges described for biological reactions of ~ 0.2–1.2 eV15,17 and consistent with other recent assessments for hermatypic corals26,27. No statistically meaningful differences were detected between E for all metabolic rates (Figure S2b).

Fig. 1
figure 1

Thermal performance curves of coral metabolism for the total dataset: a) Respiration (R), b) Net Productivity (Pnet), c) Gross Productivity (Pgross), d) the photosynthesis to respiration ratio (P: R Ratio) and e) R, Pnet and Pgross plotted together to compare visually the differences in thermal optima (Topt), activation energy (E) and deactivation energy (ED). All rates are in the units µmol O2 cm−2 d−1, except for the P: R ratio which is unitless. Data points represent the mean rate per temperature across the entire dataset, across all species and locations, and shaded ribbons represent the bootstrapped 95% confidence intervals of the fitted thermal performance curves. Dashed lines represent the thermal optima (Topt) where the peak rates of metabolism are observed, and horizontal lines represent in b) where net productivity is no longer occurring and d) the point at which productivity and respiration are equal. Note, the differences in scale for the y-axes.

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As expected, the thermal performance curves for Pnet and Pgross were left skewed (Fig. 1b, c and e) and both exhibited high deactivation energies, illustrating a rapid decline in productivity when the Topt is exceeded (Table 1). Pnet had the highest ED (8.44 ± 5.28 eV, Table 1), indicating that Pnet exhibited the steepest decline upon exceeding Topt among all the metabolic rates examined. On the other hand, the ED was much lower for R and the P: R Ratio (2.98 and 2.40 eV respectively, Table 1), which describes a more gradual decline in respiration rates and overall metabolic balance (Fig. 1a and d). ED values for Pnet and Pgross were lower than those reported by Anton et al., 2020 for Red Sea corals26, unfortunately no values for respiration were available for comparison. Similar to E, no statistically significant differences were detected in the ED between metabolic rates, however this is likely due to the large margin of error associated with this estimate because of the low number of data points after the Topt (Figure S2c).

Latitudinal changes in coral thermal performance curves

Metabolic rates were further separated by latitude, and we constructed thermal performance curves for tropical and temperate corals, to evaluate if the differences in Topt observed between rates of R and Pnet in the overall analysis would be repeated.

Table 2 Activation energy (E), deactivation energy (ED) and optimum temperature (Topt) estimated from thermal performance curves for metabolic rates of tropical, and temperate corals. The units for E and ED are in eV and for Topt is °C. Values in brackets represent one standard error of each mean estimate. The n represents the mean rates (1 per temperature) used to construct the thermal performance curve. We were unable to gain estimates for the E and Topt of the P: R ratio of tropical corals given the incomplete nature of the curve (Fig. 2d).
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The Topt for rates of R, Pnet and Pgross were remarkably close for tropical corals at ~ 30.0 ˚C, with all values within a range of 0.1˚C (Table 2; Fig. 2a, b and c). However, there was a larger separation between the Topt of temperate metabolic rates, with the Topt for R being highest at 27.3 ˚C followed by Pgross at 26.6 ˚C, and Pnet at 24.5 ˚C (Fig. 2a, b and c). Net productivity for tropical corals reached near to zero (0.42 µmol O2 cm−2 d−1, Table S2) at 34.0 ˚C and became net heterotrophic by 36˚C (Fig. 2b, Table S2). Although temperate net productivity did not reach zero at high temperatures, the maximum temperature of temperate incubations was 32˚C, which is 4˚C lower than that of tropical corals.

Fig. 2
figure 2

Thermal performance curves comparing metabolic rates of tropical (orange) and temperate (blue) corals: (a) Respiration (R) (b) Net Productivity (Pnet), (c) Gross Productivity (Pgross) (d) and the photosynthesis to respiration ratio (P: R ratio). Metabolic rates are expressed in µmol O2 cm−2 d−1, except for the P: R ratio which is unitless. Data points represent the mean rate per temperature. Vertical dashed lines indicate the thermal optima (Topt) and horizontal lines represent where rates reach zero, except in d) where the horizontal line marks the point at photosynthesis is equivalent to respiration. Shaded ribbons represent bootstrapped 95% confidence intervals around the fitted curves. Note the differing scales on the y-axis.

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The E for all metabolic rates were similar between tropical and temperate corals, but the ED for Pnet in tropical corals (12.00 ± 9.92) was much steeper than that for temperate corals (3.00 ± 0.64). This steep decline further indicates that net productivity in tropical corals is likely to become heterotrophic as the temperature rises within a few ˚C above the Topt.

The Topt for P: R Ratio in temperate corals was 21.1 ± 3.1 ˚C and the E and ED were 0.31 ± 0.38 and 1.02 ± 0.67 respectively (Fig. 2d). Tropical coral holobionts showed a steep ED (4.97 ± 1.46, Fig. 2d) and became heterotrophic beyond 34.0 ˚C. However, temperate corals did not reach heterotrophy in the range of temperatures tested by studies examined (Fig. 2d). Due to the non-unimodal shape of the curve of the tropical P: R ratio, we were unable to resolve estimates for the E and Topt (Table 2; Fig. 2d).

Taxonomic differences in thermal performance curves

Metabolic rates were extracted from 35 different corals (identified to species level), though the dataset was dominated by corals from the Acropora and Porites genera, including 86 and 75 individual mean rates recorded for each genus, respectively. This reflects the reported prevalence of corals from the family Acroporidae in coral heat-stress studies, comprising approximately 63% of all reported experiments, with a further 27% of experiments conducted on corals of the family Poritidae28. Metabolic rates for these genera were also examined across the highest range of temperatures (Table 3).

Table 3 Activation energy (E), deactivation energy (ED) and optimum temperature (Topt) from thermal performance curves for metabolic rates of corals by genus. The units for E and ED is eV and for Topt is °C. Values in brackets represent the standard error of each estimate. n refers to the number of mean rates extracted per temperature to construct the thermal performance curves for individual genera.
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Thermal performance curves were constructed for corals of the genera Acropora, Porites, Astrangia and Orbicella to assess differences in Topt, E and ED between genera and to compare between the different metabolic rates. The Topt for R was generally consistent across genera (between 30–31.0 ˚C), with the exception of the temperate Astrangia, which showed the lowest Topt at 27.13 ± 0.95 °C(Fig. 3a; Table 3). The Topt for Pnet was lower than for R across all genera except Orbicella, however, this estimate had a larger margin of error than for other genera (Fig. 3b; Table 3). Orbicella also displayed the highest ED for Pnet and Pgross (20.00 ± 44.92 and 17.21 ± 10.14 respectively, Fig. 3b and c). Indeed, these extremely steep declines and high margins of error indicate that the parameter estimates carry great uncertainty for Orbicella due to the small number of data points between the Topt and the rate reaching zero.

Astrangia spp. consistently exhibited the lowest Topt across all genera, since experiments conducted on corals from this genus were exclusively collected from temperate regions. Parameter estimates for P: R ratios could not be determined for individual genera due to insufficient temperature ranges to capture the thermal performance curve for this response.

Fig. 3
figure 3

Thermal performance curves of metabolic rates by coral genera including Acropora (pink), Astrangia (blue), Orbicella (purple) and Porites (yellow) (a) Respiration (R), (b) Net Productivity (Pnet) and (c) Gross Productivity (Pgross). All rates are expressed as µmol O2 cm−2 d−1 and dashed vertical lines represent the thermal optimum (Topt) for each individual thermal performance curve.

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Experimental Topt versus environmental Tmax

To evaluate how the Topt of coral metabolic rates aligns with environmental thermal regimes, we compiled published Topt values derived from individual experimental assessments that also reported the in situ maximum temperature (Tmax) measured at the sites where corals were collected during the experimental period. A pairwise analysis was then performed to compare the Topt of R and Pnet rates from each experiment with the corresponding environmental Tmax reported in each study (n = 8, data available in Supplementary Table 4 for data sources and details). The median Topt reported from experimental assessments for R averaged 3.1 °C higher than the median in situ Tmax (retrieved for each of the corresponding locations), but there was no trend for Topt to be lower or higher than the in situ Tmax (Wilcoxon signed-rank test, p = 0.195, Fig. 4). For Pnet, however, the median Topt was significantly lower than the median Tmax (p = 0.008) and was on average 5.1˚C lower than the Tmax in each location (Fig. 4). Together these findings indicate that respiration rates approach optimum performance when the in situ Tmax is reached. However, photosynthetic rates have declined when Tmax is reached, thus as the environmental Tmax increases with worsening marine heatwaves the imbalance between oxygen and organic carbon production and consumption is expected to escalate further.

Fig. 4
figure 4

Boxplots comparing the thermal optima (Topt) from experimental assessments in the literature (n = 8) for a) Net Productivity (Pnet) and b) Respiration (R) with the maximum environmental temperature (Tmax) recorded in situ where corals were collected for the same experiments. Tmax is presented in the same colour across both panels, as represents the same variable; however some site-specific differences exist between panels due to the inclusion of two studies which only measured either net productivity or respiration, but not both. Data used to generate these plots and the associated pairwise analysis can be accessed in Supplementary Table 4, as well as references of the studies where these values were retrieved from. Asterisks represent significant differences (p < 0.01) and circles denote outliers.

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Discussion

Although thermal performance curves are widely used to predict organismal responses to warming21,29, metabolic theory has seldom been applied to assess coral performance. This is likely due to the difficulty of fitting models to coral thermal performance when only a narrow range of temperatures are examined, which is common for most individual experimental assessments30. However, the major strength of synthesis-based approaches is their ability to resolve thermal responses of organisms to climate change across taxa15,17,27,31,32,33. By combining available data from the literature, we could describe composite thermal performance curves for scleractinian corals and resolve differences between tropical and temperate corals and among selected coral genera.

Specifically, we were able to not only quantify the activation energy of the rise of the performance curves but also quantify the deactivation energy of the fall in metabolism after the optimum temperature is reached. Activation energy is also an effective way to describe the temperature dependence of metabolism16 and compare the results of thermal performance curves across multiple studies, and has been used as an effect size in prior studies15,17,27. The resulting thermal performance curves from our analysis are however consistent with published coral thermal performance curves which show the expected gradual increase with temperature followed by a sharp decline after the thermal optimum is reached23,24,25,26.

From our combined dataset the activation energy required for coral respiration and photosynthesis (the rise portion of the thermal performance curve) was similar (0.47 and 0.46 eV respectively, from Table 1) but there was a much bigger difference in deactivation energy (2.98 and 8.44 eV, from Table 1). The higher deactivation energy for photosynthesis indicates that the rate of decrease here is a much more thermally sensitive process than for respiration, and indeed the optimum temperature for photosynthesis was lower than respiration.

Our results show that the differential thermal responses of respiration and photosynthesis lead to a mismatch in coral holobiont respiration and photosynthesis with warming, leading to metabolic challenges after the Topt, at approximately 30.0 °C, is exceeded, when rates of oxygen consumption outpace photosynthetic oxygen production. While the statistical analysis did not reveal significant differences between Topt values across metabolic rates or taxa, a consistent trend is observed across all levels of comparison (except Orbicella), showing that respiration outpaces photosynthesis under warming conditions. This pattern suggests metabolic challenges, as rates of oxygen consumption surpass those of oxygen production when the thermal optimum is exceeded. We also may have detected significantly meaningful differences between Topt values with the addition of more data points after the peak metabolic rate is reached, allowing for a more definitive conclusion but unfortunately are constrained by the data available.

Nevertheless, our findings are also supported by recent thermal performance curves of Symbiodiniaceae metabolism, where the optimum temperature for photosynthesis in cultured symbionts ranged between 20.0 and 30.0 °C for photosynthesis between species, whilst it ranged between 30.0 and 40.0 °C for respiration34. The results obtained, therefore, support the hypothesis that warming temperatures on coral reefs during marine heatwaves cause the metabolic disruption of coral holobionts35,36, leading to oxygen and organic carbon limitation and, eventually metabolic collapse. Specifically, our results show that the metabolic balance, reflected in the P: R ratio, of coral holobionts declines beyond 24.8 °C and shifts to net heterotrophy (P < R) beyond 34.0 °C.

The disruption of metabolism with thermal stress not only reduces the supply of organic carbon from the photosynthetic symbionts12,14,37, thereby impacting the carbon budget of the holobiont, but also leads to an oxygen deficit when the holobiont becomes net heterotrophic (i.e. T > 34.0 °C for tropical corals). In theory, an oxygen deficit at elevated temperatures that shifts coral holobionts into a net heterotrophic state could lead to internal oxygen limitation, increasing reliance on passive diffusion across the diffusive boundary layer to meet heightened metabolic demand38,39,40. Over prolonged periods, diffusion may be insufficient to meet respiratory demands, potentially contributing to the breakdown of the symbiosis and the onset of bleaching41.

Indeed, oxygen stress can occur through reduced oxygen solubility and increased stratification in the water column with increasing temperature31,42,43, but is further propelled by increased rates of community respiration due to increased oxygen demands under warming15,44,45,46. Hence, corals under thermal stress are already exposed to environments depleted in oxygen particularly at night, when photosynthetic oxygen production is not occurring47, which can further aggravate the consequences of the heterotrophic metabolism of corals under these conditions. A number of studies have recently highlighted the under-represented threat that deoxygenation plays in the persistence of coral reef ecosystems48,49,50 and experimental evidence of coral bleaching under hypoxic conditions48,51,52,53 as well as reported observations of bleaching and mortality in the field in response to localized deoxygenation events is increasing54,55,56.

Although the majority of rates in our dataset were obtained experimentally which is why a 12:12 dark/light cycle was assumed in the daily rate calculations, the estimates for respiration and P: R ratio are likely somewhat conservative owing to the fact that most studies only report dark respiration. This is expected given the methodical challenges associated with the difficulty of measuring light enhanced respiration. Nonetheless, because light enhanced respiration rates exceed dark respiration rates in coral holobionts40,57,58, the transition to net heterotrophy likely occurs at lower temperatures than reported here, though this remains to be formally investigated. Whilst very few studies measure light enhanced respiration, no studies investigate the effects of changes in temperature on light enhanced respiration and hence this remains a crucial research gap that is yet to be explored.

There is some capacity of the coral holobiont to modify its metabolism, for example in response to seasonal changes in temperature63,64 or the supplementation of photosynthates with heterotrophic feeding65. However, one key question that remains is how temperature extremes may limit this capacity. Some corals naturally rely on a more heterotrophic feeding strategy and hence rising temperatures will likely lead to a community shift where the faster-growing, more autotrophic corals such as Acropora may lose out66. Although our genus-level analysis does not strongly support the hypothesis that Acropora may be more vulnerable, given the relatively small difference (0.5 °C) between the optimum temperature for respiration and net productivity, Acropora exhibited one of the highest deactivation energy values in our analysis. This suggests a rapid decline in net productivity beyond the thermal optimum. As a highly autotrophic genus, Acropora may be less capable of compensating for the loss of photosynthetically derived energy at elevated temperatures compared to more mixotrophic genera, potentially rendering it more susceptible to thermal stress66. Although our analysis does not take into account seasonality or the metabolic compensation that subsequently occurs, the vast majority of rates in our dataset were collected from tropical regions where traditional seasonality is less explicit.

Importantly, the aim of this study is not to claim that bleaching occurs for all corals when the Topt exceeds 30.0 °C as there is significant variation amongst bleaching thresholds of individual species of corals and even within species depending on thermal history, depth, microhabitat on the reef, genotype etc59,60,61,62. Corals in the Red Sea for example, have much higher bleaching thresholds than those of the Great Barrier Reef67, and the majority of papers within our synthesis did not report bleaching during their experiments. However, by pooling the data we have constructed robust thermal performance curves of coral metabolism and quantified the thermal sensitivity of the rate of decrease after the optimum temperature is reached for both respiration and photosynthesis. Despite several limitations of our approach – for instance, the inability to account for all factors that influence thermal resistance59,60,61,62 – this analysis offers valuable insight into how the oxygen budget of the coral holobiont may be affected by future warming.

Conclusion

The analysis of coral metabolic thermal performance curves show that the optimum temperature for oxygen production is lower than that of oxygen consumption, and that production declines more steeply beyond this point, impacting the oxygen budget of the holobiont. The thermal performance curve of the P: R ratio indicates that once temperatures exceed 34.0 °C the holobiont shifts to net heterotrophy, likely resulting in a metabolic imbalance that may render the coral-Symbiodiniaceae association no longer mutually beneficial (P < R).

Our results add to the growing body of evidence pointing to a role of oxygen deficiency in coral bleaching48,51,54,68, however, experimental evidence to support our hypothesis is needed. Due to the complex nature of symbioses, it is extremely difficult to investigate the mechanisms of the breakdown of the coral holobiont experimentally, but this information will be crucial in adding to our understanding how this breakdown occurs and the role that oxygen plays in this complex relationship.

Methods

Literature search and study eligibility criteria

The published literature on thermal performance of coral metabolic rates was searched using the Web of Science® database. The search was conducted in February of 2021 and produced 532 published articles using the following search term: TI=(“CORAL”) AND TS=(“RESPIRATION” OR “OXYGEN CONSUMPTION”) (Figure S1). Each article was assessed for suitability and we retained those that assessed responses of scleractinian corals in symbiosis with photosynthetic dinoflagellates of the Symbiodiniaceae family (i.e., zooxanthellate corals), reported empirical measures of respiration, net photosynthesis, and/or gross photosynthesis rates at one or more reported temperatures, measured metabolic rates in µmol O2 cm−2 h−1 or units that permitted the conversion of metabolic rates into µmol O2 cm−2 h−1 and allowed for the data to be pooled among studies, and reported mean values of metabolic rates, a measure of variance (e.g. standard deviation (SD), standard error (SE), or confidence interval (CI)), and the number of biological replicates used (n) for the metabolic responses measured at each temperature level tested.

Dataset characteristics

The published literature included data from manipulative laboratory experiments and empirical measurements of metabolic rates conducted in situ. Where studies included additional experimental treatments (e.g., increased irradiance, mimicking ocean acidification), metabolic rates measured only in the control (or ambient) treatment were extracted to ensure thermal responses were not confounded by factors other than temperature. 113 studies were removed for not reporting metabolic rates and another 102 studies were excluded because metabolic rates were not reported in units that permitted the conversion of rates into µmol O2 cm−2 h−1. We further excluded 25 studies to restrict the dataset to mature corals since most coral larvae acquire Symbiodiniaceae over time and most measures of metabolic rates on larvae are standardized per larva (i.e., not surface area). We also excluded 42 studies that measured metabolic rates at the community-scale and removed eight studies that did not report temperature when metabolic rates were measured. We further excluded studies examining corals grown in long-term culture (months to years) and/or did not report the geographical location of coral collection. Another 6 studies were inaccessible, which precluded their inclusion. Rates were also extracted from a further study26 which did not appear in the Web of Science® search due to the focus on algae in the keywords, but was included in the database since the co-authors of this study were aware of its relevance. The resulting dataset comprised 36 studies from which 291 records of coral metabolic rates were extracted.

Thermal performance curves

To aggregate thermal response curves of hermatypic corals, we extracted mean rates of dark respiration, net and gross photosynthesis, measures of variance (e.g., SD, SE, CI), and sample sizes (n) for each temperature level tested. Where this data was not reported in the main article or supplementary material, we used Webplot Digitizer © (version 4.0) to extract this information from figures. Levels of photosynthetic active radiation (PAR) measured during the experimental incubations were recorded, as well as at the location of coral collection. Corals were also classified as tropical (0-23.5° latitude), subtropical (23.5–40 °C) or temperate (> 40° latitude) based on the geographical location of their collection. We also identified the season in which each experiment was conducted, however many studies did not disclose the dates of the experiments, so we were unable to resolve the season. Given this limitation and the resulting unbalanced dataset, we decided not to include any further interpretation of seasonal effects in our analysis.

Where respiration (R) and net photosynthesis (Pnet), but not gross photosynthesis (Pgross), were reported, Pgross was calculated using the following equation:

$$P_{{{\text{gross}}}} = R + P_{{{\text{net}}}}$$
(1)

The P: R ratio, when not reported, was calculated as follows:

$$P:R{\text{ }}ratio = P_{{gross}} /\left|R \right|$$
(2)

After the dataset was assembled, metabolic rates were averaged into 1.0 °C temperature bins and rates were converted from rates h−1 to rates day−1, by multiplying rates of respiration by 24 h and rates of photosynthesis by 12 h, assuming 12 h of daylight. Whilst we acknowledge that this approach simplifies natural variability in light availability over diel cycles, it facilitates comparison with daily respiration, which continues throughout both the light and dark phases. Daily rates of Pgross were calculated from daily R and Pnet rates, and P: R Ratios were calculated per day.

The temperature-dependence of metabolic performance was described using a modified version of the Sharpe-Schoolfield equation for high-temperature inactivation22,69:

$$B\left( T \right) = B_{0} \:.\:\frac{{e^{{\frac{{ - E}}{k}\:\:.\:\:\left( {\frac{1}{{T_{{{\text{ref}}}} }} - \frac{1}{T}} \right)\:}} }}{{1 + \left( {\frac{E}{{E_{D} - E}}} \right)*e^{{\frac{{E_{D} }}{k}\:.\:\:\left( {\frac{1}{{T_{{opt}} }} - \frac{1}{T}} \right)}} }}$$
(3)

where, E is the activation energy that describes the rise phase of the slope of the thermal performance curve, ED is the deactivation energy, characterizing the decline of the curve after the peak is reached, and T represents the temperature in Kelvin. Tref is the chosen reference temperature. In this study, we selected 25.0 °C as the reference temperature for total dataset analyses and those for tropical corals, representing a midway-point in the thermal performance curve at which metabolic rates are not constrained by the breakdown of key enzymes22,69. For temperate corals and the overall P: R ratio, the reference temperature chosen was 20.0 ˚C, as for some rates the Topt had already been exceeded at 25.0 °C (e.g. Pnet and P: R ratio, Fig. 2b and d) and the reference temperature should not exceed the peak rate22. B(T) is the metabolic rate at a given temperature and B0 is the value of the metabolic rate at the reference temperature. Topt is the optimum temperature (at which the maximum rate occurs) and finally k is the Boltzmann’s constant in electron volts (8.62 × 10−5 eV).

All analysis was performed in R using the nls.multstart and rTPC packages70, however we were unable to construct thermal performance curves for subtropical corals due to large uncertainty around the parameter estimates. Residual resampling was used as the bootstrapping method for the 95% confidence intervals around the thermal performance curves, according to Padfield et al., 202071. To compare the parameters of Topt, E and ED between metabolic rates and between latitudes and coral genera, differences between parameters were evaluated graphically (Figure S2 and S3), following the methods employed by other studies comparing thermal performance between groups where the use of formal tests is not possible due to low power25,26,71,72,73. Parameter estimates were considered to be significantly different from each other if confidence intervals were non-overlapping, however we acknowledge that this a conservative method and overlapping confidence intervals do not necessarily reflect non-significance74,75,76. Where some differences were detected visually, pairwise comparisons were conducted by estimating the 95% confidence interval of the difference between two parameters. If the confidence interval of the difference between the two parameters does not pass 0 then the difference is considered to be statistically meaningful.

Analysis of published Topt values and environmental Tmax

To assess whether environmental temperatures are already exceeding the thermal optima of coral metabolic processes, we compiled published values of Topt for respiration and net productivity (net photosynthesis), along with the corresponding maximum environmental temperatures (Tmax) recorded at the sites where the experimental corals were collected. We then performed a pair-wise comparison of Topt and Tmax for each dataset. A Wilcoxon signed-ranks test was used to evaluate whether significant differences existed between the experimental optima (Topt) and local maximum temperatures (Tmax) for each metabolic rate. Prior to analysis, Shapiro-Wilk tests were conducted to confirm the normality of the differences of the paired values. The final dataset included eight paired estimates for each metabolic rate. All values and references are listed in Supplementary Table 4.

Data availability

All data analysed is available within the supplementary information and the full dataset of extracted metabolic rates is publicly available through the Dryad repository (https://doi.org/10.5061/dryad.qz612jmv8).