Reef-building coral populations are at serious risk of collapse due to the combined effects of ocean warming and acidification. However, many corals show potential to adapt to changing ocean conditions. Here, we examine the broad sense heritability (H²) of coral calcification rates across an ecologically and phylogenetically diverse sampling of eight of the primary reef-building corals across the Indo-Pacific. We show that all eight species exhibit relatively high heritability of calcification rates under combined warming and acidification (0.23-0.56). Further, tolerance to each factor is positively correlated, and the two factors do not interact in most species, contrary to the idea of tradeoffs between temperature and pH sensitivity. All eight species can co-evolve tolerance to elevated temperature and reduced pH. Using these values together with historical data, we estimate potential increases in thermal tolerance of 1.0-1.7 °C over the next 50 years, depending on species. None of these species are likely capable of keeping up with a high global change scenario, and climate change mitigation is essential if reefs are to persist. Such estimates are critical for our understanding of how corals may respond to global change, accurately parameterizing modeled responses, and predicting rapid evolution.

Coral collection: Corals were collected using a hammer and chisel at 2±1 m depth from a total of six locations around O‘ahu, Hawai‘i (Fig. 1). Each species was collected from 3-5 of the sites, depending on their local abundances and sizes, for a total of 22 colonies of *Montipora flabellata* and 30 colonies (genets) of the remaining seven species. The eight species examined in this study were *Montipora capitata*, *Montipora flabellata*, *Montipora patula*, *Porites compressa*, *Porites evermanni*, *Porites lobata*, *Pocillopora acuta*, and *Pocillopora meandrina*.

After collection, corals were returned to the Hawai‘i Institute of Marine Biology (HIMB) on Moku o Lo‘e (Coconut Island), fragmented into 4-12 replicate nubbins (3-5 cm coral fragments, referred to as ‘ramets’) using a diamond-coated band saw, individually attached to a labeled ceramic tile using cyanoacrylate gel, and allowed to recover for 2.5 months in a common garden under present-day average temperature for O‘ahu and ambient pH conditions, with both temperature and pH following the seasonal cycle (Fig. S1).

Approach: There was a need to include both within genet variation and among genet variation in our estimates. Given logistical constraints about how many coral ramets could possibly be accommodated, we attempted to balance these conflicting needs by including 1) three replicate ramets from four genets for each coral species within each treatment, and 2) one ramet per genet per treatment for the remaining genets (N = 22 total genets for *Montipora flabellata*; N= 30 for the other seven species, four of which were replicated within treatments per species). All coral ramets were randomly divided among mesocosms with no more than 1 ramet per genet in each mesocosm, resulting in 3-4 ramets per species within each mesocosm tank (Fig. 1).

This experiment was part of a larger mesocosm project, other components of which have been described elsewhere [1–7]. The experimental system received constant flow-through of unfiltered sea water from the adjacent reef, and was initially set up with reef sand, rubble, algae, invertebrates, and fish to provide a reef-like habitat (see Supplementary Information for additional details regarding the mesocosm design). Temperature and pH of the incoming seawater were adjusted according to treatment in a series of header tanks, using aquarium heaters and CO2 gas injection, prior to flowing into the 70 L mesocosms at a rate of about 1.2 L min-1, for a residence time of about 1 hr. Additional water circulation (4900 L hr-1) was generated by seawater pumps within each mesocosm to provide water flow speeds (10-15 cm s-1) similar to those *in situ*. Both temperature and pH were allowed to vary according to natural daily and seasonal cycles while maintaining appropriate offsets according to treatment: control treatment (present-day temperature and pH), ocean warming treatment (+2 °C and present-day pH), ocean acidification treatment (present-day temperature and -0.2 pH units), or combined future ocean treatment (+2 °C and -0.2 pH units) with 10 replicate mesocosms per treatment in a 40 mesocosm system (see Supplementary Information; Fig. S1). The corals were then randomly assigned to mesocosm with either 1 or 3 replicate nubbins (ramets) per colony (genet) in each treatment, and no more than 1 ramet per genet in each mesocosm.

After 2.5 months of acclimation in a common garden, temperature and pH were slowly adjusted starting on 1 February 2016 until target values were reached on 20 February 2016. The corals were then allowed 5.5 months to acclimate to treatment conditions before calcification rates were evaluated, thereby excluding short-term history as a factor in their responses. Corals experienced heat stress during the final 9 weeks of the study, during which the calcification assay was conducted (Fig. S1). Calcification rates were assessed via the buoyant weighing technique [8], with initial weights taken 3-15 August 2016 (shortly after the onset of thermal stress in the heated treatments), final weights taken 26 September – 8 October 2016 (shortly after the seasonal peak in temperatures), and calcification rates were normalized to initial weight. In total, the study was conducted over nearly 1 year with about 8 months of exposure under experimental treatment conditions, and the calcification assay was conducted over the last 8 weeks of the experiment.

Coral genotyping

Multilocus genotyping of coral hosts was performed following published methods [9,10]. Briefly, total genomic DNA was isolated using the E.Z.N.A. Tissue DNA Kit (Omega Bio-tek, Inc., Norcross, GA, USA) following the manufacturer protocol. Amplicons were generated via PCR using microsatellite primers [11], but with short unique barcodes [12] added to each primer to identify each position in a 96 well plate. Amplicons were pooled equimolarly, and a dual-index system of adaptors was used to identify individuals on each plate and libraries were sequenced on an Illumina MiSeq platform (v3 2x300 PE) at the Hawaiʻi Institute of Marine Biology. We used a custom bioinformatic genotyping workflow pipeline [9] to call alleles, which were then converted to GenoDive v. 2.0b27 [13] file format for analyses. Individual genotypes were created using two different methods. First, we used sequence length (equivalent to peak calling in a microsatellite fragment analysis *sensu *[14]), such that all sequences of the same length, regardless of underlying sequence variation, would be scored as the same allele (sequence length). Second, we identified alleles by their sequence (ID) so that only two exactly identical alleles had the same ID, whereas alleles with the same length but differing in nucleotide composition would have different allelic IDs. Similar to previous findings [9], both approaches gave the same result. Using the 'assign clones' feature of GenoDive [15], we tested whether coral colonies sampled in the field had a unique multilocus genotype. To be conservative, we allowed for up to 2 scoring errors among individuals and checked potential clones against the location of collection. 

Historical temperature tolerances

Over the last 50 years, the mean seawater temperature around O‘ahu has warmed at a rate of 1.9 °C century-1 and acidified at a rate of 0.13 pH units century-1 [16,17] (but note that pH data first become available in 1992) (Fig. S2). The rate of acidification will accelerate in the future as a consequence of reduced seawater buffer capacity [18]. In 1970, survivorship of corals exposed to temperatures near their upper thermal limits (31.0 °C) were assessed for two of the species included in this study (*Montipora capitata* and *Pocillopora acuta)* [19]. In 2017 this study was repeated (31.4 °C) [16] (data shown in the original publications). We examined changes in their temperature tolerances by fitting logistic regressions to survivorship using the R package “MASS” in the following way (given differences in data overlap among datasets). For *Montipora capitata* we assessed the LD20 (Degree Heating Weeks, DHW, which result in 20% mortality at these upper thermal limits) and for *Pocillopora acuta* we assessed the LD50 (DHW which result in 50% mortality at these upper thermal limits) in each of 1970 and 2017, again using “MASS” to define these values. These fits resulted in the following estimates: LD20 for *Montipora capitata *of 1.30±0.39 and 20.17±2.46 DHW in 1970 and 2017, respectively; LD50 for *Pocillopora acuta* of 1.47±0.56 and 18.68±1.24 DHW in 1970 and 2017, respectively. We then estimated the change in these DHW tolerances for each species as proxies for their responses to selection (R) over the period 1970-2017, as described below.

Statistics: To examine treatment effects on calcification rates, for each species individually, an ANOVA was fit with temperature, pH, and collection site as fixed factors, and coral colony (genet), header tank, and mesocosm as nested factors. Due to the smaller sample size for *Montipora flabellata*, there were an insufficient number of degrees of freedom to fit the full model. Instead, we first fit a model with all factors included except coral genet. Mesocosm effects were not significant, so this factor was dropped and a second model was then fit which included genet. Model fits were assessed via diagnostic plots of the residuals and in all cases the data adequately satisfied ANOVA assumptions. A Tukey HSD was used as a *post hoc* to examine significant treatment effects.

Broad sense heritability (H2) was estimated using a Bayesian modelling approach, similar to that used in previous work [20,21]. The models were fit with the R package “MCMCglmm” [22] with temperature and pH as fixed effects and coral genet, collection site, header tank, and mesocosm as random effects. Models were run for 100,000 iterations, storing the Markov chain every 50 iterations, and with the first 15,000 iterations used as a burn-in period. Heritability was estimated as the proportion of the phenotypic variance which was explained by genotype [20,21].          

To test for possible tradeoffs between temperature and pH tolerance, and the hypothesis that these tolerances are related to a general stress-tolerance strategy, the association between temperature and pH response was examined for each species using Pearson’s correlation. Temperature tolerance was calculated as the change in mean calcification rate between the control and the ocean warming treatment, whereas pH tolerance was the difference between the control and the ocean acidification treatment. Further, we considered if there were interactive effects between temperature and pH on calcification rates identified by the ANOVAs, as another indicator of tradeoffs in these tolerances.

For *Montipora capitata* and *Pocillopora acuta* we estimated their responses to selection (R) based on changes in their LD20 and LD50 values, respectively, from 1970 to 2017. The error associated with these estimates was determined from Monte Carlo simulations using the R package “propagate”, and derived from 100,000 simulations. Along with our heritability estimates, as described above, as well as the classical (univariate) breeder’s equation, R = H2S, we estimate the selection coefficients for these species under the selective pressure that they have experienced over the last 50 years, where H2 is the broad sense heritability (including additive, dominance and epistatic variance) which represents the proportion of the selection differential (S) that can be realized as the response (R) to selection [20,23–25], and with the error associated with S propagated in the same way. Again, we assume that broad sense heritability (H2) provides an upper bound for narrow sense heritability (h2), though the two values are likely similar if these traits are influenced by many genetic loci. Selection differentials for the remaining 6 species are unknown, so to be conservative we assumed that they experience selection similar to that for *Montipora capitata* (the lower of the two selection coefficients) and estimated their responses to selection (R) based on these assumed values and their measured heritabilities, with uncertainties propagated as above.

Analyses were performed in R v.4.0.3. [26].

Effects of unbalanced sampling design: We considered how an unbalanced sampling design might affect our estimates. In particular, our study was slightly unbalanced because most of the coral genets contributed one ramet per treatment whereas four genets per species contributed three ramets per treatment. In addition, a small percentage of the ramets died during the acclimation phase (18 nubbins, or 1.5% of the total, and affecting 12 of the 232 genets) resulting in representation of 87-100% of the genets across all four treatments, depending on species.

For the ANOVAs, this slight unbalance has very little effect. ANOVA is highly robust to modest discrepancies in sample size and missing observations, such as occur in this study. With the heritability estimates, modeling work [24,25] suggests that our sampling design results in a <3% additional uncertainty in H2 for *Pocillopora acuta* and* Pocillopora meandrina*, and far less among the other species. This small uncertainty yields only a trivial effect on our estimates of selection coefficients (S) or responses to selection (R).

Supplementary Methods:

This study was conducted at the University of Hawai‘i at Mānoa, Hawai‘i Institute of Marine Biology (HIMB) on Moku o Lo‘e (Coconut Island), immediately adjacent to the island of O‘ahu in the Hawaiian Archipelago. After collection, coral colonies were fragmented into either 4 or 12 replicate nubbins, attached to ceramic tiles with cyanoacrylate gel, and allowed to recover under present-day average temperature and ambient sea water chemistry in a 40 tank mesocosm system for at least 2.5 months.

The mesocosms received constant flow-through of unfiltered seawater drawn from the adjacent coral reef (2-3 m depth, depending on tide). Relative to the offshore source water, seawater temperature and chemistry are naturally modified by reef-associated physical and biogeochemical processes as the water flows through Kāne‘ohe bay. To restore water temperature and chemistry of the incoming seawater close to that of the original source water, all incoming seawater was directed into a mixing tank where temperature was adjusted using a commercial heat pump on a temperature controller and chemistry was adjusted with small additions of 1.0 N NaOH via a peristaltic pump to achieve average present-day offshore temperature and chemistry conditions in Hawaiʻi (temperature 23.5-27.5 °C, pH 7.97-8.07, annually). These small adjustments resulted in modifications to the temperature, pH, and total alkalinity in the seawater input which, when combined with the same physical and biogeochemical processes in the mesocosms, allowed us to achieve conditions very similar to those observed on the reef [27–29]. This incoming water was then split off into a series of header tanks where it was heated or acidified according to treatment, with 2 replicate header tanks per treatment. Temperature was adjusted using commercial aquarium heaters on temperature controllers and seawater was dosed with CO₂ gas using high precision needle valves connected to venturi valves on aquarium pumps to deliver a precisely controlled quantity of CO₂ gas that was completely dissolved into the seawater in the header tanks before flowing into the mesocosms. The heated treatments were set to remain 2 °C above the control (i.e., present-day average) temperature, whereas the acidified treatments were maintained at 0.2 pH units below the control treatment, thereby replicating conditions expected at the end of the century. All mesocosms experienced natural daily and seasonal fluctuations in light, seawater temperature, and carbonate chemistry with appropriate offsets according to treatment (Fig. 3). 

Two approaches were used to characterize the water temperature and chemistry in the mesocosms. First, water samples were taken from each mesocosm at 1200 hr local time once per week for total alkalinity and spectrophotometric pH, whereas salinity and temperature were measured with a YSI multimeter. All these procedures followed standard protocols [30]. The precision of these measurements were: pH ±0.002 units, salinity ±0.01 psu, temperature ±0.01 °C, total alkalinity ±7 µmol kg-1. The accuracies of these measurements are estimated as: pH ±0.005 units, salinity ±0.3 psu, temperature ±0.1 °C, total alkalinity ±7 µmol kg-1. The accuracy and precision of total alkalinity titrations were assessed using Certified Reference Materials (CRMs) obtained from Andrew Dickson (Scripps Institution of Oceanography). Second, the temperature and chemistry measurements as described above, were assessed every 4 hr over the diel cycle once per quarter. For the remaining two months per quarter, bottle samples were taken for pH and total alkalinity only at 1200 and 0000 hr and a pH meter was used to assess pH at the other diel sampling points (1600, 2000, 0400, and 0800 hr). The pH meter was empirically calibrated to the 1200 and 0000 hr pH bottle samples at the time of collection, yielding an uncertainty of ±0.02 units for these sample points. The monthly diel samples were used to assess the hourly temperature and chemistry variation in the mesocosms as well as the daily mean values on those sampling dates. The weekly water samples, along with the empirically derived relationships between the offset of the mesocosm sea water to the incoming sea water measured at 1200 hr and the daily mean values (characterized during the diel sampling), were used to estimate the daily mean parameters for these remaining dates. These estimates yielded the following uncertainties in the calculated daily means: salinity ±0.12 psu, pH ±0.03 units, temperature ±0.17 °C, and total alkalinity ±16 µmol kg-1. The remaining carbonate chemistry parameters were calculated with CO2SYS [31]. This sampling protocol yielded data resolution similar to or greater than that used in previous studies [8,32,33], but over a longer timeframe and at a much higher level of replication. 

To reach initial target treatment temperature and pH values at the beginning of the experiment, adjustments were made in 0.5 °C and 0.03-0.05 pH unit increments every 10 days (starting on 1 February 2016 from baseline values that were intermediate between the temperature and pH treatment levels) until target values were reached (20 February 2016). The slow ramp to target temperature and pH during the winter minimized the chances of shocking the communities and was slower than many natural warming events. The design included 40 mesocosms (0.5×0.5×0.3 m, 70 L). The mesocosms were randomly assigned to treatment. Seawater inflow rate was adjusted to 1.2 L min-1 for a residence time of 1 hr in all mesocosms. Additional water circulation was generated within each mesocosm by submerged seawater pumps with one Maxi-Jet Pro propeller pump (4900 L hr-1) in each 70 L mesocosm. Flow speeds in the vicinity of the benthic communities (10-15 cm s-1) were estimated from visual inspection of particle tracks and verified with an independent product review of the pumps [34].

Changes in seawater temperature and chemistry near O‘ahu were estimated using three datasets. First, temperature was derived from a dataset collected off Koko Head on the south-east shore of O‘ahu from 1970-1992. Second, temperature was provided by a global climate product (IGOSS) for the area around O‘ahu (1992-2020) and adjusted by -0.19 °C to correspond to the Koko Head record immediately offshore of O‘ahu, as described previously[35]. The pH record was derived from values for the upper 30 m of the water column as measured at Station ALOHA, north of O‘ahu [36].

The 40 mesocosms were initially stocked with a 2 cm layer of carbonate reef sand and gravel as well as pieces of reef rubble (3 replicate 10-20 cm pieces randomly divided among mesocosms) collected from the adjacent reef, thereby including natural infaunal and surface-attached communities. In addition, a juvenile (3-8 cm) Convict surgeonfish (*Acanthurus triostegus*) and Threadfin butterflyfish (*Chaetodon auriga*), 5 herbivorous reef snails (*Trochus* sp.), and the eight regionally most common reef-building coral species were added to the mesocosms. Over the course of the experiment, additional *Trochus* snails recruited into the mesocosms, ranging from about 10-40 snails per mesocosm at the end. Corals were attached to ceramic plugs with cyanoacrylate gel, to allow them to be moved or manipulated during the experiment. The corals and rubble were placed on a plastic grate 6 cm above the bottom soft sediments, to simulate their attachment to hard substrate in nature. The surgeonfish is a generalist grazer on benthic algae whereas the butterflyfish is a generalist grazer on non-coral invertebrates. Together, the fish provided the essential ecological functions of herbivory and predation in the mesocosms, and at fish biomass values similar to those reported for Hawaiian reefs[37]. Fish were supplementally fed 3 g wet weight of frozen mysis or brine shrimp daily (which they consumed within about 5 min), thereby provisioning the fish and wider reef communities with allochthonous (i.e., non-local, imported) zooplankton at a rate similar to that measured in nature [38].

The eight coral species included in the mesocosms (*Montipora capitata, Montipora flabellata, Montipora patula, Pocillopora acuta, Pocillopora meandrina, Porites compressa, Porites evermanni,* and *Porites lobata*) are the dominant species across the Hawaiian archipelago and collectively comprise >95% of the coral cover on Hawaiian reefs [39,40]. Historically, four of these species were once thought to be Hawaiian endemics (Montipora flabellata, Montipora patula, Porites compressa, and Porites evermanni), though more recent analyses have shown that all eight species (or their genetically indistinguishable kin) are in fact widespread across the Indo-Pacific [41–43]. These eight species represent both major lineages of reef-building corals (Complexa and Robusta) [44], and all  four of the major life history strategies exhibited by corals[45] including competitive (Montipora capitata, Pocillopora meandrina, and Porites compressa), generalist (Montipora flabellata and Montipora patula, inferred from the ecologically similar Montipora monasteriata), stress-tolerant (Porites lobata and Porites evermanni, with the strategy for Porites evermanni inferred from the ecologically similar Porites lutea), and weedy strategies (Pocillopora acuta, inferred from its ecologically similar sister species *Pocillopora damicornis*). These species also differ in trophic strategies [46] and microbial composition [47]. In prior thermal stress events these species have shown differing resistance to bleaching ranging from low (Montipora flabellata, Pocillopora acuta, and Pocillopora meandrina), to moderate (Montipora capitata, Montipora patula, Porites compressa, and Porites lobata), to high (Porites evermanni) [35]. They also include the major reef-building coral families worldwide (Acroporidae, Pocilloporidae, and Poritidae) yielding broad ecological and spatial relevance to this study. Corals were collected at 2±1 m depth from a total of six locations around O‘ahu [28] between 17 August 2015 and 13 November 2015, and conspecifics were separated by at least 5 m to minimize the chances of accidentally sampling clones or biasing the sampling towards particular microenvironments [28]. All coral parent colonies sampled for this study were genotyped to ensure that they were distinct genets and results were not biased by inclusion of clonally derived colonies. After collection, the corals were allowed 12 weeks to recover and acclimate to the mesocosm system under the same temperature and pH conditions, thereby standardizing their short-term histories prior to beginning the experiment on 1 February 2016.

Sunlight was attenuated with 30% shade cloth to provide irradiance similar to that at mean collection depth (2 m) with a maximum instantaneous irradiance of about 1730 µmol m-2 s-1 in the mesocosms and 2470 µmol m-2 s-1 in the air. A handheld quantum meter was used to take periodic spot checks to ensure that the desired level of shading was achieved. Light spectrum was not adjusted due to the trivial differences between 0.3 m (mesocosm depth) and 2 m (mean collection depth). The nominal coral bleaching threshold (27.98 °C) was estimated as the mean monthly maximum temperature for the Main Hawaiian Islands (26.98 °C) [48] +1 °C.

References

1.         Bahr KD, Tran T, Jury CP, Toonen RJ. 2020 Abundance, size, and survival of recruits of the reef coral Pocillopora acuta under ocean warming and acidification. *PLOS ONE* **15**, e0228168. (doi:10.1371/journal.pone.0228168)

2.         McLachlan RH, Price JT, Muñoz-Garcia A, Weisleder NL, Levas SJ, Jury CP, Toonen RJ, Grottoli AG. 2022 Physiological acclimatization in Hawaiian corals following a 22-month shift in baseline seawater temperature and pH. *Sci. Rep.* **12**, 3712. (doi:10.1038/s41598-022-06896-z)

3.         Henley EM, Bouwmeester J, Jury CP, Toonen RJ, Quinn M, Lager CVA, Hagedorn M. 2022 Growth and survival among Hawaiian corals outplanted from tanks to an ocean nursery are driven by individual genotype and species differences rather than preconditioning to thermal stress. *PeerJ* **10**, e13112. (doi:10.7717/peerj.13112)

4.         Timmers MA, Vicente J, Webb M, Jury CP, Toonen RJ. In press. Sponging up diversity: Evaluating metabarcoding performance for a taxonomically challenging phylum within a complex cryptobenthic community. *Environ. DNA* **n/a**. (doi:10.1002/edn3.163)

5.         Vicente J, Timmers MA, Webb MK, Bahr KD, Jury CP, Toonen RJ. 2022 Ecological succession of the sponge cryptofauna in Hawaiian reefs add new insights to detritus production by pioneering species. *Sci. Rep.* **12**, 15093. (doi:10.1038/s41598-022-18856-8)

6.         Vicente J, Webb MK, Paulay G, Rakchai W, Timmers MA, Jury CP, Bahr K, Toonen RJ. 2022 Unveiling hidden sponge biodiversity within the Hawaiian reef cryptofauna. *Coral Reefs* **41**, 727–742. (doi:10.1007/s00338-021-02109-7)

7.         Timmers MA, Jury CP, Vicente J, Bahr KD, Webb MK, Toonen RJ. 2021 Biodiversity of coral reef cryptobiota shuffles but does not decline under the combined stressors of ocean warming and acidification. *Proc. Natl. Acad. Sci.* **118**, e2103275118. (doi:10.1073/pnas.2103275118)

8.         Jokiel PL, Rodgers KS, Kuffner IB, Andersson AJ, Cox EF, Mackenzie FT. 2008 Ocean acidification and calcifying reef organisms: a mesocosm investigation. *Coral Reefs* **27**, 473–483. (doi:10.1007/s00338-008-0380-9)

9.         Cros A, Toonen RJ, Davies SW, Karl SA. 2016 Population genetic structure between Yap and Palau for the coral Acropora hyacinthus. *PeerJ* **4**, e2330. (doi:10.7717/peerj.2330)

10.       Cros A, Toonen RJ, Donahue MJ, Karl SA. 2017 Connecting Palau’s marine protected areas: a population genetic approach to conservation. *Coral Reefs* **36**, 735–748. (doi:10.1007/s00338-017-1565-x)

11.       Concepcion GT, Polato NR, Baums IB, Toonen RJ. 2010 Development of microsatellite markers from four Hawaiian corals: Acropora cytherea, Fungia scutaria, Montipora capitata and Porites lobata. *Conserv. Genet. Resour.* **2**, 11–15. (doi:10.1007/s12686-009-9118-4)

12.       Faircloth BC, Glenn TC. 2012 Not All Sequence Tags Are Created Equal: Designing and Validating Sequence Identification Tags Robust to Indels. *PLOS ONE* **7**, e42543. (doi:10.1371/journal.pone.0042543)

13.       Meirmans P. In press. GenoDive version 2.b14.

14.       Selkoe KA, Toonen RJ. 2006 Microsatellites for ecologists: a practical guide to using and evaluating microsatellite markers. *Ecol. Lett.* **9**, 615–629. (doi:10.1111/j.1461-0248.2006.00889.x)

15.       Meirmans PG, Tienderen PHV. 2004 genotype and genodive: two programs for the analysis of genetic diversity of asexual organisms. *Mol. Ecol. Notes* **4**, 792–794. (doi:10.1111/j.1471-8286.2004.00770.x)

16.       Coles SL, Bahr KD, Rodgers KS, May SL, McGowan AE, Tsang A, Bumgarner J, Han JH. 2018 Evidence of acclimatization or adaptation in Hawaiian corals to higher ocean temperatures. *PeerJ* **6**, e5347. (doi:10.7717/peerj.5347)

17.       Dore JE, Lukas R, Sadler DW, Church MJ, Karl DM. 2009 Physical and biogeochemical modulation of ocean acidification in the central North Pacific. *Proc. Natl. Acad. Sci.* **106**, 12235–12240. (doi:10.1073/pnas.0906044106)

18.       Jury CP, Thomas FIM, Atkinson MJ, Toonen RJ. 2013 Buffer Capacity, Ecosystem Feedbacks, and Seawater Chemistry under Global Change. *Water* **5**, 1303–1325. (doi:10.3390/w5031303)

19.       Jokiel PL, Coles SL. 1977 Effects of temperature on the mortality and growth of Hawaiian reef corals. *Mar. Biol.* **43**, 201–208. (doi:10.1007/BF00402312)

20.       Wright RM, Mera H, Kenkel CD, Nayfa M, Bay LK, Matz MV. 2019 Positive genetic associations among fitness traits support evolvability of a reef-building coral under multiple stressors. *Glob. Change Biol.* **25**, 3294–3304. (doi:10.1111/gcb.14764)

21.       Muller EM, Dungan AM, Million WC, Eaton KR, Petrik C, Bartels E, Hall ER, Kenkel CD. 2021 Heritable variation and lack of tradeoffs suggest adaptive capacity in Acropora cervicornis despite negative synergism under climate change scenarios. *Proc. R. Soc. B Biol. Sci.* **288**, 20210923. (doi:10.1098/rspb.2021.0923)

22.       Hadfield JD. 2010 MCMC Methods for Multi-Response Generalized Linear Mixed Models: The MCMCglmm R Package. *J. Stat. Softw.* **33**, 1–22. (doi:10.18637/jss.v033.i02)

23.       Falconer DS, Mackay TFC. 1996 *Introduction to quantitative genetics*. Fourth edition. Benjamin-Cummings.

24.       Schmidt P, Hartung J, Rath J, Piepho H-P. 2019 Estimating Broad-Sense Heritability with Unbalanced Data from Agricultural Cultivar Trials. *Crop Sci.* **59**, 525–536. (doi:10.2135/cropsci2018.06.0376)

25.       Piepho H-P, Möhring J. 2007 Computing Heritability and Selection Response From Unbalanced Plant Breeding Trials. *Genetics* **177**, 1881–1888. (doi:10.1534/genetics.107.074229)

26.       R Core Team. 2020 R: A language and environment for statistical computing.

27.       Shamberger KEF, Feely RA, Sabine CL, Atkinson MJ, DeCarlo EH, Mackenzie FT, Drupp PS, Butterfield DA. 2011 Calcification and organic production on a Hawaiian coral reef. *Mar. Chem.* **127**, 64–75. (doi:10.1016/j.marchem.2011.08.003)

28.       Jury CP, Delano MN, Toonen RJ. 2019 High heritability of coral calcification rates and evolutionary potential under ocean acidification. *Sci. Rep.* **9**, 20419. (doi:10.1038/s41598-019-56313-1)

29.       Guadayol Ò, Silbiger NJ, Donahue MJ, Thomas FIM. 2014 Patterns in Temporal Variability of Temperature, Oxygen and pH along an Environmental Gradient in a Coral Reef. *PLOS ONE* **9**, e85213. (doi:10.1371/journal.pone.0085213)

30.       Dickson AG, Sabine CL, Christian JR. 2007 Guide to Best Practices for Ocean CO2 Measurements.

31.       In press. OCADS - Program Developed for CO2 System Calculations. See [https://www.ncei.noaa.gov/access/ocean-carbon-data-system/oceans/CO2SYS/co2rprt.html](https://www.ncei.noaa.gov/access/ocean-carbon-data-system/oceans/CO2SYS/co2rprt.html) (accessed on 22 March 2021).

32.       Comeau S, Cornwall CE, Pupier CA, DeCarlo TM, Alessi C, Trehern R, McCulloch MT. 2019 Flow-driven micro-scale pH variability affects the physiology of corals and coralline algae under ocean acidification. *Sci. Rep.* **9**, 12829. (doi:10.1038/s41598-019-49044-w)

33.       Dove SG, Brown KT, Van Den Heuvel A, Chai A, Hoegh-Guldberg O. 2020 Ocean warming and acidification uncouple calcification from calcifier biomass which accelerates coral reef decline. *Commun. Earth Environ.* **1**, 1–9. (doi:10.1038/s43247-020-00054-x)

34.       Riddle D. In press. Product Review: Maxi-Jet Pro Series Pumps. *Reefs.com*. See [https://reefs.com/magazine/product-review-maxi-jet-pro-series-pumps/](https://reefs.com/magazine/product-review-maxi-jet-pro-series-pumps/) (accessed on 22 March 2021).

35.       Jokiel PL, Brown EK. 2004 Global warming, regional trends and inshore environmental conditions influence coral bleaching in Hawaii. *Glob. Change Biol.* **10**, 1627–1641. (doi:[https://doi.org/10.1111/j.1365-2486.2004.00836.x](https://doi.org/10.1111/j.1365-2486.2004.00836.x))

36.       Karl DM, Church MJ. 2019 Station ALOHA: A Gathering Place for Discovery, Education, and Scientific Collaboration. *Limnol. Oceanogr. Bull.* **28**, 10–12. (doi:10.1002/lob.10285)

37.       Gorospe KD, Donahue MJ, Heenan A, Gove JM, Williams ID, Brainard RE. 2018 Local Biomass Baselines and the Recovery Potential for Hawaiian Coral Reef Fish Communities. *Front. Mar. Sci.* **5**. (doi:10.3389/fmars.2018.00162)

38.       Hamner WM, Jones MS, Carleton JH, Hauri IR, Williams DMcB. 1988 Zooplankton, Planktivorous Fish, and Water Currents on a Windward Reef Face: Great Barrier Reef, Australia. *Bull. Mar. Sci.* **42**, 459–479.

39.       Rodgers KS, Jokiel PL, Brown EK, Hau S, Sparks R. 2015 Over a Decade of Change in Spatial and Temporal Dynamics of Hawaiian Coral Reef Communities1. *Pac. Sci.* **69**, 1–13. (doi:10.2984/69.1.1)

40.       Franklin EC, Jokiel PL, Donahue MJ. 2013 Predictive modeling of coral distribution and abundance in the Hawaiian Islands. *Mar. Ecol. Prog. Ser.* **481**, 121–132. (doi:10.3354/meps10252)

41.       Forsman ZH, Barshis DJ, Hunter CL, Toonen RJ. 2009 Shape-shifting corals: Molecular markers show morphology is evolutionarily plastic in Porites. *BMC Evol. Biol.* **9**, 45. (doi:10.1186/1471-2148-9-45)

42.       Boulay JN, Hellberg ME, Cortés J, Baums IB. 2014 Unrecognized coral species diversity masks differences in functional ecology. *Proc. R. Soc. B Biol. Sci.* **281**, 20131580. (doi:10.1098/rspb.2013.1580)

43.       Veron JEN, Stafford-Smith MG, Turak E, DeVantier LM. 2016 *Corals of the World,*.

44.       Stolarski J, Kitahara MV, Miller DJ, Cairns SD, Mazur M, Meibom A. 2011 The ancient evolutionary origins of Scleractinia revealed by azooxanthellate corals. *BMC Evol. Biol.* **11**, 316. (doi:10.1186/1471-2148-11-316)

45.       Darling ES, Alvarez‐Filip L, Oliver TA, McClanahan TR, Côté IM. 2012 Evaluating life-history strategies of reef corals from species traits. *Ecol. Lett.* **15**, 1378–1386. (doi:[https://doi.org/10.1111/j.1461-0248.2012.01861.x](https://doi.org/10.1111/j.1461-0248.2012.01861.x))

46.       Price JT, McLachlan RH, Jury CP, Toonen RJ, Grottoli AG. 2021 Isotopic approaches to estimating the contribution of heterotrophic sources to Hawaiian corals. *Limnol. Oceanogr.* **66**, 2393–2407. (doi:10.1002/lno.11760)

47.       Price JT, McLachlan RH, Jury CP, Toonen RJ, Wilkins MJ, Grottoli AG. 2021 Effect of species, provenance, and coral physiology on the composition of Hawaiian coral-associated microbial communities. *Coral Reefs* **40**, 1537–1548. (doi:10.1007/s00338-021-02164-0)

48.       NOAA Coral Reef Watch. 2018 NOAA Coral Reef Watch Version 3.1 Daily Global 5-km Satellite Coral Bleaching Degree Heating Week Product.