**OVERVIEW**
This is a compilation of isotopic data from different modern taxa.
We denote a range of environmental parameters (Temperature, Depth, DIC d13C, Water d18O, pH) in the *environmental variability plots*.
In the *equilibrium offset taxa and taxon-specific plots*, inferred pH from d11B measured in biominerals is compared to measured seawater pH, using expected thermodynamic equilibrium for the borate ion at in situ temperature, salinity, and depth. In a different plot, measured d11B is compared directly to measured seawater pH.
When environmental parameters are available for a given measurement, we also normalize d13C and d18O to the expected values for inorganic calcite or aragonite in equilibrium with the relevant environment.
Best fit lines for d13C_biomin - d13C_equil vs. d18Obiomin - d18O_equil are calculated as described below.
Data are also plotted separately for heterotrophs without symbionts and for photosynthesizers and heterotrophs with photosynthesizing symbionts. In all plots, the data from the other group are displayed in light gray for reference. Mineralogy and laboratory vs. wild are also denoted.
**ENVIRONMENTAL PARAMETER NOTES**
For Brand2013 & Brand2015 used the W d18O & DIC d13C data from closest depth & location.
For Keith1965 used water measurements from Brand2015 for Jamaica.
For Lee2001 used water measurements from Saenger2013 for Bahamas.
For McConnaughy1989 used SST from Shen1992 for Galapagos sst
**EQUILIBRIUM CALCULATIONS**
The M - Eq parameters are calculated as the difference from an assumed equilibrium composition of calcite or aragonite, based on the local conditions of T, P, water d18O, and DIC. The equations used are provided in the references, code and below:
References Used to Calculate Equilibrium Estimates for Calcite & Aragonite:
*d13C - Calcite and Aragonite:*
Romanek, C.S., Grossman, E.L. and Morse, J.W., 1992. Carbon isotopic fractionation in synthetic aragonite and calcite: effects of temperature and precipitation rate. Geochimica et cosmochimica acta, 56(1), pp.419-430.
https://doi.org/10.1016/0016-7037(92)90142-6
*d18O - Calcite:*
Both references listed below were compared. Kim and O'Neil, 1997 is used in all of the plots.
Kim, S.T. and O'Neil, J.R., 1997. Equilibrium and nonequilibrium oxygen isotope effects in synthetic carbonates. Geochimica et cosmochimica acta, 61(16), pp.3461-3475.
https://doi.org/10.1016/S0016-7037(97)00169-5
Anderson, N.T., Kelson, J.R., Kele, S., Daëron, M., Bonifacie, M., Horita, J., Mackey, T.J., John, C.M., Kluge, T., Petschnig, P. and Jost, A.B., 2021. A unified clumped isotope thermometer calibration (0.5–1,100 C) using carbonate‐based standardization. Geophysical Research Letters, 48(7), p.e2020GL092069.
https://doi.org/10.1029/2020GL092069
*d18O - Aragonite:*
Kim et al., 2007 with adjustment from Lachniet, 2015
Kim, S.T., O’Neil, J.R., Hillaire-Marcel, C. and Mucci, A., 2007. Oxygen isotope fractionation between synthetic aragonite and water: Influence of temperature and Mg2+ concentration. Geochimica et Cosmochimica Acta, 71(19), pp.4704-4715.
https://doi.org/10.1016/j.gca.2007.04.019
Lachniet, M.S., 2015. Are aragonite stalagmites reliable paleoclimate proxies? Tests for oxygen isotope time-series replication and equilibrium. Bulletin, 127(11-12), pp.1521-1533.
https://doi.org/10.1130/B31161.1
*d11B Calcite & Aragonite:*
Rae, J.W., 2018. Boron isotopes in Foraminifera: Systematics, biomineralisation, and CO 2 reconstruction. Boron Isotopes, pp.107-143.
https://doi.org/10.1007/978-3-319-64666-4_5
**BEST FIT LINES**
In order to avoid differences in scaling between axes and to capture the errors in measurements in both axes, best-fit lines in panels C and D were determined by the lines whose slope and intercept minimize the sum of the product of the residuals in the x- and y-coordinate; that is the line that minimizes the sum of the areas of triangles formed by projecting each point to the line along the x- and y-axes. Independent fits were done for each species and each mineralogy within a species. 95% confidence intervals in fit parameters and on the plots were estimated through 1000 bootstrap datasets generated by resampling of the half-residuals in both x and y with respect to the initial best-fit.
