Full details of the experimental design and analytical methods are in:
Schoepf V, Levas SJ, Rodrigues LJ, McBride M, Aschaffenburg MD, Matsui Y, Warner ME, Hughes AD, Grottoli AG. 2014. Kinetic and metabolic isotope effects in coral skeletal carbon isotopes: A re-evaluation using experimental coral bleaching as a case study. Geochimica et Cosmochimica Acta, 146: 164-178. doi:10.1016/j.gca.2014.09.033

A brief description of the methods follows:

Pacific coral bleaching experiments
A detailed description of the first bleaching experiment in Hawaii can be found in Rodrigues and Grottoli (2006). Briefly, coral fragments from branching Porites compressa and branching Montipora capitata were collected from Point Reef, Kaneohe Bay, Hawaii in late August 2003 from 2 m depth. After allowing them to acclimate for two weeks, half of all fragments were placed in shaded outdoor tanks with ambient seawater (26.8 degrees C +/- 0.04 SE) (non-bleached controls), while the other half were placed in tanks with elevated temperature seawater (30.1 degrees C +/- 0.05 SE) (bleached corals). Temperature was gradually elevated over the course of three days. Corals were not fed during the experiment, and inflow pipes were fitted with a 50 um-filter. To minimize positional effects, corals were rotated within and among tanks of the same treatment daily. After one month, 25% of all treatment and control fragments were collected and frozen for isotopic analyses (= 0 month recovery), whereas the remaining corals were placed back on the reef to recover in situ. To assess short and long term recovery, a third of all remaining treatment and control corals were collected after 1.5, 4, and 8 months, respectively. A second, similar bleaching experiment was performed in summer 2006 to assess bleaching impacts on mounding Porites lobata.

Caribbean coral bleaching experiment
Coral fragments of mounding Orbicella faveolata (formerly Montastraea faveolata), encrusting to mounding Porites astreoides, and branching Porites divaricata were collected in July 2009 from shallow reefs (3–8 m) near Puerto Morelos Reefs National Park, Mexico. After allowing them to acclimate for 5 days, half of the coral fragments were placed in tanks with ambient seawater temperature (30.66 +/- 0.24 degrees C) (nonbleached controls), while the other half were placed in tanks with elevated temperature seawater (31.48 +/- 0.20 degrees C) (bleached corals). Seawater temperature in the treatment tanks was gradually elevated over the course of seven days. Corals were not fed, but had access to unfiltered seawater. Fragments were rotated daily within and among tanks of the same treatment to minimize any positional effects. After a total of 15 days, temperature in all tanks was returned to ambient levels, and all coral fragments were placed on the back reef to recover in situ for one full year. In July 2010, the bleaching treatment was repeated using the same experimental protocol. To assess short- and long-term recovery from repeat bleaching, one fragment from each colony and treatment was recollected from the reef after 1.5 and 11 months of recovery and then frozen for isotopic analyses.

Photosynthesis to respiration ratios
Net photosynthesis (P) and day respiration (R) rates were measured by quantifying changes in dissolved oxygen by incubating non-bleached and bleached corals in UV-transparent acrylic chambers under light and dark conditions. Refer to Schoepf et al. 2014 Geochimica et Cosmochimica Acta (doi:10.1016/j.gca.2014.09.033) for equations used in calculations (equation 1).

Isotopic analyses
Seawater dissolved inorganic carbon (DIC) isotopes: A total of nine filtered seawater samples from Kaneohe Bay, Hawaii, were collected throughout 2006/07 for d13CDIC analyses. They were preserved with anhydrous HgCl. In the laboratory, each sample was acidified on a vacuum extraction line under high-purity helium flow, with the resulting CO2 gas cryogenically isolated under vacuum, and the DIC concentration was determined. The CO2 from each DIC sample was sealed in Pyrex ampoules and introduced into a Finnigan Delta IV Stable Isotope Ratio Mass Spectrometer (SIRMS) via an automated 10-port inlet. All d13C values were reported as per mil values relative to Vienna-Pee Dee Belemnite limestone standard (v-PDB). d13CDIC analyses were not performed for seawater from Puerto Morelos, Mexico.

Tissue and skeletal isotopes: A detailed description of the isotopic analyses for the Pacific corals can be found in Rodrigues and Grottoli (2006) and Levas et al. (2013), and for the Caribbean corals in Schoepf (2013).

Data correction: Coral skeletal carbon isotopes (d13Csorig) were corrected (d13Cscorr) using skeletal oxygen isotopes (d18Os) to remove kinetic effects according to the equation developed by Heikoop et al. (2000). Refer to equation 2 of Schoepf et al. 2014 Geochimica et Cosmochimica Acta (doi:10.1016/j.gca.2014.09.033).

Carbon isotopic equilibrium: Carbon isotopic equilibrium (d13Ceq) for aragonite was calculated following the precedence of McConnaughey et al. (1997) and Heikoop et al. (2000) using the equation of Romanek et al. (1992). Refer to equation 3 of Schoepf et al. 2014 Geochimica et Cosmochimica Acta (doi:10.1016/j.gca.2014.09.033).

Oxygen isotopic equilibrium: Two different methods, Grossman and Ku (1986) and Maier (2004), exist in the literature to calculate oxygen isotopic equilibrium in carbonates (d18Oeq), where only Grossman and Ku (1986) incorporate temperature-dependent fractionation. Both methods were used in this study. Refer to equations 4 and 5 of Schoepf et al. 2014 Geochimica et Cosmochimica Acta (doi:10.1016/j.gca.2014.09.033).

Isotope-based P/R ratios: P/R ratios were calculated from skeletal and tissue isotopes according following the equations of Maier (2004) and Kaandorp et al. (2005). Refer to equations 6 and 7 of Schoepf et al. 2014 Geochimica et Cosmochimica Acta (doi:10.1016/j.gca.2014.09.033).