Coral collection: Coral plugs were collected in December 2012 from massive Porites colonies at a naturally low-Ω_ar reef site (7.324 N, 134.493 E; mean Ω_ar = 2.3; n = 78) and a naturally high-Ω_ar reef site (7.268 N, 134.522 E; mean Ω_ar = 3.7; n = 75). At each reef site, small skeletal cores (diameter = 3.5 cm) were removed from massive colonies (one core per colony) at 2-3m depth using underwater pneumatic drills, and cores were cut with a lapidary table saw to approximately 1 cm below the tissue layer. The plugs were affixed to nylon square base screws with marine epoxy, secured to egg crate racks, and returned to their original reefs to allow the corals to recover from the coring procedure. All corals survived two months of recovery on the reef and on all corals living tissue had fully overgrown the sides of the plugs so that no underlying skeleton was exposed. Corals were recovered in February 2013.

CO₂ manipulation experiment: Corals from two reefs were cultured at three CO₂levels for eight weeks in March to May 2013 (n = 10 corals per treatment, n = 60 corals total). The corals were individually incubated in independently manipulated plastic cups (volume = 750 ml) to increase statistical power. Cups were placed within a large, temperature-controlled water bath. The corals were maintained at mean (± SD) temperatures of 29.4C ± 0.1C. Light was provided by LED aquarium lights (Coralife) at average levels of 334 ± 48 umol photons m^-2s^-1 (measured by an underwater quantum sensor, LI-COR) on a 12h:12h light:dark schedule. Corals were fed live Artemia brine shrimp larvae every other evening by pipetting 1 ml of concentrated brine shrimp in filtered seawater into each cup. Coral cups were cleaned weekly to prevent algae overgrowth.

Mean pH (total scale)/Ω_arlevels for the three treatment conditions were 7.98/3.0, 7.83/2.3, and 7.60/1.5. In each coral cup, carbon system chemistry was regulated using a combination of flow-through pre-equilibrated water and bubbling of mixed air/CO₂gas. Incoming seawater (filtered to 0.35 um) from the reef was aerated and split into three header tanks. In the low-CO₂header tank, water was bubbled with air. In the mid-CO₂ and high-CO₂header tanks, CO₂levels were regulated by a pH controller (Drs. Foster and Smith) connected to a solenoid valve that introduced CO₂ gas into the header tank through a column diffuser. Water was siphoned from the three header tanks into each coral cup at a rate of approximately 375 ml per hour. Each coral cup was also bubbled with either compressed air (low CO₂ treatment) or mixed compressed air and CO₂ gas (mid and high CO₂ treatment) controlled by pairs of mass flow controllers (Aalborg Instruments) at approximately 200 ml per minute. Low alkalinity levels in the source water to the Palau International Coral Reef Center (drawn from within the lower-alkalinity Rock Islands) prevented Ω_ar in the low-CO₂condition (Ω_ar = 3.0) from reaching values that were as high as those measured on the barrier reef site (Ω_ar = 3.7).

To characterize the carbonate chemistry in each cup, total alkalinity (TA), pH, temperature, and salinity were measured weekly. Spectrophotometric pH measurements were made with 2 mM m-Cresol purple indicator dye using a spectrometer with a 100 mm flow cell (Ocean Optics, mean precision = 0.005) following procedures in Clayton and Byrne (1993) and Dickson et al. (2007) and using the equation of Liu et al. (2011). Samples for TA were collected in 20 ml glass vials and poisoned with saturated mercuric chloride. Automated gran titrations for TA were run on duplicate 1 ml samples using a Metrohm Titrando 808 and 730 Sample Changer (mean precision = 4 umol/kg), and TA values were standardized to certified reference materials obtained from Andrew Dickson [Scripps Institution of Oceanography (Dickson, 2001)]. Salinity was measured in each cup using an YSI salinity probe, and temperatures were measured using an Omega thermocouple (accuracy = 0.1 degree C). Full CO₂ system parameters were calculated from temperature, salinity, TA, and pH using CO2SYS (Lewis and Wallace, 1998) with the constants of Mehrbach et al. (1973) as refit by Dickson and Millero (1987).

Coral calcification analysis: Calcification rates were measured using both buoyant weight (Davies, 1989) and alkalinity anomaly (Chisholm and Gattuso, 1991) techniques. Buoyant weights for each coral were collected at the beginning of the experiment, after three weeks in experimental CO₂ conditions, and then weekly during weeks four to eight. Corals were weighed using a balance with a weigh-below hook (Sartorius GC803S), which allows for beneath-balance weighing of coral plugs that remain entirely submerged in experimental cups maintained at treatment Ω_ar levels. Wet weight data were converted to dry weights using an aragonite density of 2.93 grams per cubic centimeterand the density of seawater determined using a standard of known weight and density. Repeated buoyant weight measurements on the same coral yielded mean precision estimates of ± 0.03 g.

Day/night alkalinity depletion experiments were conducted at the end of the eight-week experiment. Water flow to each coral cup was stopped during this time but gas bubbling was continued in order to maintain pH levels. Samples for TA were collected for each coral cup at the beginning and end of two four-hour periods (one four-hour period during the day and one at night). Alkalinity depletion incubations were simultaneously run in control cups containing only filtered seawater (n=3 per experiment). Because the net change in TA values in control cups was within analytical precision (mean = 3 umol per kilogram), coral calcification was assumed to be the only process impacting the alkalinity in the cups, where two moles of alkalinity were consumed for every one mole of calcium carbonate produced. TA pre and post incubation was determined following the titration procedure described in section 2.2 with samples run in triplicate.

Calcification rates for both buoyant weight and alkalinity anomaly measurements were normalized to coral tissue surface areas. Surface areas were measured following the general procedure for aluminum foil wrapping, in which the weight of aluminum foil needed to cover the entire surface of the coral skeleton is converted to area using a calibration curve (Marsh 1970). However, skeletons were wrapped with electrical tape instead of aluminum foil because the use of electric tape provided tighter control and minimization of tape overlap, which can significantly overestimate surface area. The area of each coral skeleton occupied by living tissue was wrapped in electrical tape that was subsequently carefully trimmed to eliminate any overlay. The weight of tape used to cover the coral tissue for each skeleton were converted to surface areas using a weight-to-area calibration, where ten pieces of electrical tape of known area were weighed to build a weight-per-unit area curve. Replicated electrical tape surface area estimates on ten coral skeletons produced a mean precision of 0.43 square cm, or ~1% of calculated surface areas.