1. Norström, A. V. et al. Guiding coral reef futures in the Anthropocene. Front. Ecol. Environ. 14, 490–498 (2016).

2. Williams, G. J. et al. Coral reef ecology in the Anthropocene. Funct. Ecol. 33, 1014–1022 (2019).

3. Frieler, K. et al. Limiting global warming to 2 °C is unlikely to save most coral reefs. Nat. Clim. Change 3, 165–170 (2013).

4. Hughes, T. P. et al. Global warming transforms coral reef assemblages. Nature 556, 492–496 (2018).

5. Perry, C. T. et al. Loss of coral reef growth capacity to track future increases in sea level. Nature 558, 396–400 (2018).

6. Guest, J. R. et al. A framework for identifying and characterising coral reef “oases” against a backdrop of degradation. J. Appl. Ecol. 55, 2865–2875 (2018).

7. Denis, V., Ribas-Deulofeu, L., Sturaro, N., Kuo, C.-Y. & Chen, C. A. A functional approach to the structural complexity of coral assemblages based on colony morphological features. Sci. Rep. 7, 9849 (2017).

8. González-Barrios, F. J. & Álvarez-Filip, L. A framework for measuring coral species-specific contribution to reef functioning in the Caribbean. Ecol. Indic. 95, 877–886 (2018).

9. Darling, E. S., Alvarez-Filip, L., Oliver, T. A., McClanahan, T. R. & Côté, I. M. Evaluating life-history strategies of reef corals from species traits. Ecol. Lett. 15, 1378–1386 (2012).

10. Perry, C. T. & Alvarez-Filip, L. Changing geo-ecological functions of coral reefs in the Anthropocene. Funct. Ecol. 33, 976–988 (2019).

11. Wilson, S. K., Robinson, J. P. W., Chong-Seng, K., Robinson, J. & Graham, N. A. J. Boom and bust of keystone structure on coral reefs. Coral Reefs https://doi.org/10.1007/s00338-019-01818-4 (2019).

12. Darling, E. S. et al. Relationships between structural complexity, coral traits, and reef fish assemblages. Coral Reefs 36, 561–575 (2017).

13. Robinson, J. P. W. et al. Productive instability of coral reef fisheries after climate-driven regime shifts. Nat. Ecol. Evol. 3, 183–190 (2019).

14. Alvarez-Filip, L., Carricart-Ganivet, J. P., Horta-Puga, G. & Iglesias-Prieto, R. Shifts in coral-assemblage composition do not ensure persistence of reef functionality. Sci. Rep. 3, 3486 (2013).

15. Darling, E. S., McClanahan, T. R. & Côté, I. M. Life histories predict coral community disassembly under multiple stressors. Glob. Change Biol. 19, 1930–1940 (2013).

16. Graham, N. A. J., Chong-Seng, K. M., Huchery, C., Januchowski-Hartley, F. A. & Nash, K. L. Coral reef community composition in the context of disturbance history on the Great Barrier Reef, Australia. PLoS ONE 9, e101204 (2014).

17. Sommer, B., Harrison, P. L., Beger, M. & Pandolfi, J. M. Trait-mediated environmental filtering drives assembly at biogeographic transition zones. Ecology 95, 1000–1009 (2014).

18. Kayal, M. et al. Predicting coral community recovery using multi-species population dynamics models. Ecol. Lett. 21, 1790–1799 (2018).

19. Cinner, J. E. et al. Bright spots among the world’s coral reefs. Nature 535, 416–419 (2016).

20. Kittinger, J. N., Finkbeiner, E. M., Glazier, E. W. & Crowder, L. B. Human dimensions of coral reef social–ecological systems. Ecol. Soc. 17, 17 (2012).

21. Gilmour, J. P., Smith, L. D., Heyward, A. J., Baird, A. H. & Pratchett, M. S. Recovery of an isolated coral reef system following severe disturbance. Science 340, 69–71 (2013).

22. Graham, N. A. J., Jennings, S., MacNeil, M. A., Mouillot, D. & Wilson, S. K. Predicting climate-driven regime shifts versus rebound potential in coral reefs. Nature 518, 94–97 (2015).

23. Green, D. H., Edmunds, P. J. & Carpenter, R. C. Increasing relative abundance of Porites astreoides on Caribbean reefs mediated by an overall decline in coral cover. Mar. Ecol. Prog. Ser. 359, 1–10 (2008).

24. Montaggioni, L. F. History of Indo-Pacific coral reef systems since the last glaciation: development patterns and controlling factors. Earth Sci. Rev. 71, 1–75 (2005).

25. Hughes, T. P. et al. Spatial and temporal patterns of mass bleaching of corals in the Anthropocene. Science 359, 80–83 (2018).

26. Claar, D. C., Szostek, L., McDevitt-Irwin, J. M., Schanze, J. J. & Baum, J. K. Global patterns and impacts of El Niño events on coral reefs: a meta-analysis. PLoS ONE 13, e0190957 (2018).

27. Januchowski-Hartley, F. A., Graham, N. A. J., Wilson, S. K., Jennings, S. & Perry, C. T. Drivers and predictions of coral reef carbonate budget trajectories. Proc. R. Soc. B 284, 20162533 (2017).

28. McManus, J. W., Reyes, B. R. & Nañola, C. L. Effects of some destructive fishing methods on coral cover and potential rates of recovery. Environ. Manag. 21, 69–78 (1997).

29. Pollock, F. J. et al. Sediment and turbidity associated with offshore dredging increase coral disease prevalence on nearby reefs. PLoS ONE 9, e102498 (2014).

30. Dixson, D. L., Abrego, D. & Hay, M. E. Chemically mediated behavior of recruiting corals and fishes: a tipping point that may limit reef recovery. Science 345, 892–897 (2014).

31. Costa, O. S., Leão, Z. M. A. N., Nimmo, M. & Attrill, M. J. in Island, Ocean and Deep-Sea Biology (eds Jones, M. B., Azevedo, J. M. N., Neto, A. I., Costa, A. C. & Martins, A. M. F.) 307–315 (Springer, 2000).

32. Cinner, J. How behavioral science can help conservation. Science 362, 889–890 (2018).

33. Bruno, J. F., Côté, I. M. & Toth, L. T. Climate change, coral loss, and the curious case of the parrotfish paradigm: why don’t marine protected areas improve reef resilience? Annu. Rev. Mar. Sci. 11, 307–334 (2019).

34. Strain, E. M. A. et al. A global assessment of the direct and indirect benefits of marine protected areas for coral reef conservation. Divers. Distrib. 25, 9–20 (2019).

35. Madin, J. S. & Connolly, S. R. Ecological consequences of major hydrodynamic disturbances on coral reefs. Nature 444, 477–480 (2006).

36. Robinson, J. P. W. et al. Environmental conditions and herbivore biomass determine coral reef benthic community composition: implications for quantitative baselines. Coral Reefs 37, 1157–1168 (2018).

37. Edmunds, P. et al. Why more comparative approaches are required in time-series analyses of coral reef ecosystems. Mar. Ecol. Prog. Ser. 608, 297–306 (2019).

38. Zawada, K. J. A., Madin, J. S., Baird, A. H., Bridge, T. C. L. & Dornelas, M. Morphological traits can track coral reef responses to the Anthropocene. Funct. Ecol. 33, 962–975 (2019).

39. Skirving, W. J. et al. The relentless march of mass coral bleaching: a global perspective of changing heat stress. Coral Reefs https://doi.org/10.1007/s00338-019-01799-4 (2019).

40. Perry, C. T. et al. Caribbean-wide decline in carbonate production threatens coral reef growth. Nat. Commun. 4, 1402 (2013).

41. Perry, C. T. et al. Remote coral reefs can sustain high growth potential and may match future sea-level trends. Sci. Rep. 5, 18289 (2016).

42. Harvey, B. J., Nash, K. L., Blanchard, J. L. & Edwards, D. P. Ecosystem-based management of coral reefs under climate change.Ecol. Evol. 8, 6354–6368 (2018).

43. Beyer, H. L. et al. Risk-sensitive planning for conserving coral reefs under rapid climate change.Conserv. Lett. 11, e12587 (2018).

44. Hughes, T. P. et al. Coral reefs in the Anthropocene. Nature 546, 82–90 (2017).

45. Van Hooidonk, R. et al. Local-scale projections of coral reef futures and implications of the Paris Agreement. Sci. Rep. 6, 39666 (2016).

46. Fox, H. E. et al. Rebuilding coral reefs: success (and failure) 16 years after low‐cost, low‐tech restoration. Restor. Ecol. https://doi.org/10.1111/rec.12935 (2019).

47. Cinner, J. E. et al. Building adaptive capacity to climate change in tropical coastal communities. Nat. Clim. Change 8, 117–123 (2018).

48. Sen, A. The ends and means of sustainability. J. Hum. Dev. Capab. 14, 6–20 (2013).

49. Bellwood, D. R., Streit, R. P., Brandl, S. J. & Tebbett, S. B. The meaning of the term ‘function’ in ecology: a coral reef perspective. Funct. Ecol. 33, 948–961 (2019).

50. Goatley, C. H. R. & Bellwood, D. R. The roles of dimensionality, canopies and complexity in ecosystem monitoring. PLoS ONE 6, e27307 (2011).

51. Keith, S. A., Baird, A. H., Hughes, T. P., Madin, J. S. & Connolly, S. R. Faunal breaks and species composition of Indo-Pacific corals: the role of plate tectonics, environment and habitat distribution. Proc. R. Soc. B 280, 20130818 (2013).

52. Hijmans, R. J., Phillips, S., Leathwick, J. & Elith, J. dismo: Species distribution modeling. R package version 1.1-4 https://CRAN.R-project.org/package=dismo (2017).

53. Burke, L. M., Reytar, K., Spalding, M. & Perry, A. Reefs at Risk Revisited (World Resources Institute, 2011).

54. Zinke, J. et al. Gradients of disturbance and environmental conditions shape coral community structure for south-eastern Indian Ocean reefs. Divers. Distrib. 24, 605–620 (2018).

55. Madin, J. S. et al. The Coral Trait Database, a curated database of trait information for coral species from the global oceans. Sci. Data 3, 160017 (2016).

56. Ferrari, S. & Cribari-Neto, F. Beta regression for modelling rates and proportions. J. Appl. Stat. 31, 799–815 (2004).

57. Gelman, A. et al. Bayesian Data Analysis (Chapman and Hall/CRC, 2013).

58. Gelman, A., Goodrich, B., Gabry, J. & Ali, I. R-Squared for Bayesian Regression Models (2017); http://www.stat.columbia.edu/~gelman/research/unpublished/bayes_R2.pdf

59. Stan Development Team Stan Modeling Language Users Guide and Reference Manual Version 2.18.0 (2018).

60. Bürkner, P.-C. brms: an R package for Bayesian multilevel models using Stan. J. Stat. Softw. 80, 1–28 (2017).

61. R Core Development Team R: A Language and Environment for Statistical Computing (R Foundation for Statistical Computing, 2018).

62. Lamy, T., Galzin, R., Kulbicki, M., Lison de Loma, T. & Claudet, J. Three decades of recurrent declines and recoveries in corals belie ongoing change in fish assemblages. Coral Reefs 35, 293–302 (2016).

63. Beldade, R., Mills, S. C., Claudet, J. & Côté, I. M. More coral, more fish? Contrasting snapshots from a remote Pacific atoll. PeerJ 3, e745 (2015).

64. Harborne, A. R. et al. Modelling and mapping regional-scale patterns of fishing impact and fish stocks to support coral-reef management in Micronesia. Divers. Distrib. 24, 1729–1743 (2018).