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Animal collection and holding for this project was conducted under Marine Research Permit RE-19–28 issued by the Ministry of Natural Resources, Environment, and Tourism of the Republic of Palau (10.03.2019), Marine Research/Collection Permit and Agreement 62 issued by the Koror State Government (08.10.2019), Queensland Government GBRMPA Marine Parks Permit G14/36689.1, Queensland Government DNPRSR Marine Parks Permits QS2014/MAN247 and QS2014/MAN247a, Queensland Government General Fisheries Permit 168991, Queensland Government DAFF Animal Ethics approval CA2013/11/733, approval by The Bahamas Department of Marine Resources, approval by the Animal Care Officer of both the University of Bremen and the Leibniz Centre for Tropical Marine Research (ZMT), and in accordance with UK and Germany animal care guidelines.Sample collectionWe collected fish carbonate samples at four study locations across three tropical and subtropical regions: Eleuthera (24°50’N, 76°20’W), The Bahamas, between 2009 and 201127,37; Heron Reef (23°27’S, 151°55’E) and Moreton Bay (27°29’S, 153°24’E) in Queensland, Australia, in 2014 and 201528; and Koror (7°20’N, 134°28’E), Palau, during November and December 2019. These are located within four distinct marine biogeographic provinces and three realms (Tropical Atlantic, Central Indo-Pacific, and Temperate Australasia)43. At each location fish were collected using barrier nets, dip nets, clove oil or hook and line, and immediately transferred to aquaria facilities at the Cape Eleuthera Institute, Heron Island and Moreton Bay Research Stations, and the Palau International Coral Reef Center. Fish were held in a range of tanks (60, 400, or 1400 L in the Bahamas, 10, 60, 100, 120, or 400 L in Heron Island and Moreton Bay, and 8, 80, 280, or 400 L in Palau) of suitable dimensions for different fish sizes ( 5). Each sample was titrated with 0.01–0.5 N HCl (with continuous aeration with CO2-free air) until the end point (grey-lavender; pH~4.80) was reached and stable for at least 10 min. If the sample was over-titrated (pink), 0.01–0.1 N NaOH was added to titrate back to the end point and the amount of base used was subtracted from the amount of acid. Acid and base were added using an electronic multi-dispenser pipette (Eppendorf Repeater ®E3X, Eppendorf, Hamburg, Germany) with a precision of  ± 1 ({{{{{rm{mu }}}}}})L. Additionally, the pH of several samples was monitored using a pH microelectrode (Mettler Toledo InLab Micro) to ascertain the correctness of the colorimetric end point. The amount of carbonate in the sample was then calculated using Eq. (1). The method was validated using certified reference material (Alkalinity Standard Solution, 25,000 mg/L as CaCO3, HACH) and the accuracy in the determination of solid samples was verified using certified CaCO3 powder (Suprapur, ≥ 99.95% purity, Merck) samples (60–500 ({{{{{rm{mu }}}}}})g) and resulted in 96.53 ± 1.94% accuracy (mean ± SE; n = 8).To compare values obtained with the two titration methods we further analysed 12 samples collected at Lizard Island, Australia, in February 2016. Samples were collected at 24 h intervals from one individual of Lethrinus atkinsoni (f. Lethrinidae, body mass: 245 g), a group of five Lutjanus fulvus (f. Lutjanidae, mean body mass: 21 g), and an individual of Cephalopholis cyanostigma (f. Serranidae, body mass: 295 g), following the procedures described above. During sample collection water temperature ranged from 29.1 °C during the night to 32.6 °C during the day, with an average of ~31 °C, mean salinity was 35.4, and pHNBS ranged from 8.13 to 8.21. To compare the amount of carbonate measured by the two methods we added carbonate samples to 20 ml ultrapure water and disaggregated crystals via sonication. We then used a Metrohm Titrando autotitrator and Metrohm Aquatrode pH electrode to measure initial pH of the suspension of carbonates, then titrated each sample of carbonate in two stages. Firstly, they were titrated down to pH 4.80 using 0.1 M HCl, adding 20 µl increments of acid until this was sufficient to keep pH below 4.80 for 10 min whilst bubbling with CO2-free air. This first stage was comparable to the single end point titration used for samples collected in Palau. Secondly, whilst continuing to bubble with CO2-free air, further acid was added to the sample until it reached pH 3.89 and was stable for 1 min. Then 0.1 M NaOH was added to the samples to return them to the initial pH. For all samples the first end point titration (to pH 4.80) yielded slightly higher values for carbonate content than the second double titration. The ratio between the two methods (single end point/double titration) was 1.08 ± 0.01 (mean ± SE; range: 1.04–1.14; Supplementary Table 2). As we found a small but consistent difference between the two methods, all following analyses were initially performed on the actual data obtained with the double titration for samples from Australia and The Bahamas, and the single end point titration for samples from Palau. Then, to assess the robustness of the results, we repeated the analyses after applying a correction factor of 1.08 to the excretion rates of Palauan fishes (that used the single end point titration method). All results were consistent and robust to the measured difference between the titration methods (Supplementary Figs. 8, 9).Finally, measurements of multiple samples from each individual collected over periods of 18–169 h (median: 64 h) were combined to produce an average individual excretion rate in ({{{{{rm{mu }}}}}})mol h−1. For fish held in groups, carbonate excretion rates per individual (of average biomass) were obtained by averaging the total excretion rate of the group across the sampling period and dividing it by the number of individuals in the tank. Excretion rates obtained from fish groups thus evened the intraspecific variability within tanks, and are therefore more robust than those directly obtained from fish held individually. This aspect was considered in our models by fitting weighted regressions (see the “Statistical modelling” section). In total, we measured the carbonate excretion rates of 382 individual fishes arranged in 192 groups (i.e., independent observations), representing 85 species from 35 families across three tropical regions (180 individuals from 29 species in Australia, 90 individuals from 10 species in the Bahamas, and 112 individuals from 46 species in Palau; Supplementary Table 1).We assume that during the sampling of carbonates fishes were close to their resting metabolic rate and that their carbonate excretion rates are representative of fish at rest. Although the ratio of tank volume to fish volume in our study (median ~660; inter-quartile range ~180–1700) typically greatly exceeds the guideline ideal range for measuring resting metabolic rate (20–50)85, fishes were fasted prior to and throughout sampling, and in most instances their movement was somewhat constrained by tank volume. Fasting reduces metabolic rate in all animals, including fish, as they do not undergo energy-intensive digestive processes and use energy reserves to support vital processes, triggering metabolic changes in many tissues and reducing activity levels86,87. Additionally, other than the carbonate syphoning ( More

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