We thank the many local institutions that supported and facilitated field data collection. Data collection in the tropical western Atlantic was supported through a Leverhulme Trust International Research Network grant (F/00426/G) to C.T.P. and data collection carried out specifically in Mexico was supported through a Royal Society - Newton Advanced Research Fellowship (NA-150360) to L.A.-F. and C.T.P., in Florida and Puerto Rico as part of the National Coral Reef Monitoring Program through NOAA’s Coral Reef Conservation Program and Ocean Acidification Program to D.P.M. and in the eastern Caribbean through a National Geographic Research Grant to R.S.S. Data collection in the Indian Ocean was supported in Kenya and Mozambique through a NERC-ESPA-DFiD: Ecosystem Services for Poverty Alleviation Programme Grant (NE/K01045X/1) to C.T.P., in the Maldives through a NERC Grant (NE/K003143/1) and a Leverhulme Trust Research Fellowship (RF-2015-152) to C.T.P., in the Chagos Archipelago through a DEFRA Darwin Initiative grant (19-027), in the Seychelles through an Australian Research Council grant (DE130101705) and Royal Society grant (RS-UF140691) to N.A.J.G. and in Ningaloo through the BHP-CSIRO Ningaloo Outlook Marine Research Partnership. P.J.M. acknowledges the Australian Research Council and World Bank/GEF CCRES project for funding. Rebecca Fisher (Australian Institute of Marine Science, Western Australia) provided statistical advice.

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Nature thanks I. D. Haigh and I. Kuffner for their contribution to the peer review of this work.