Analyses of coral community change
To estimate the proportion of reef sites containing each coral life history and species group in each time interval, we utilized binomial generalized linear mixed effects models that predicted the proportion of sites containing each life history group as a function of time bin, coral species group, and their interaction as fixed effects and country as a random effect. The interaction term was included to allow for varying temporal trends across individual taxonomic and functional groups. The random effect of country was included to account for uneven geographic sampling across time bins. To ensure equal numbers of surveys were included for each species group within a life history group, only surveys with presence/absence values for the entire complement of coral species within a given life history group were included in each model. Models were fitted using the ‘glmer’ function in the R package ‘lme4’. Mean fitted values and 95% confidence intervals of the proportion of sites with a coral life history group and its constituent species groups were plotted for each time bin using the‘plot_model’ function in the R package ‘sjPlot’. Significant changes in mean fitted values relative to the Pleistocene baseline and subsequent peak values were assessed via a Tukey post-hoc test using the‘emmeans’ function in the R package ‘emmeans’.
To assess the effects of coral community change on regional diversity patterns, we tracked temporal changes in community dissimilarity. We utilized species presence/absence matrices to compute Jaccard’s dissimilarity index [39]. To account for the higher number of reef sites and countries added in the latter part of the time series, we restricted our analysis to change in coral community dissimilarity within individual countries only. Within each time bin, the dissimilarity was computed between all possible combinations of reef sites located within the same country. For each country and time bin combination, a mean dissimilarity value was computed. To equalize the influence of each country and to avoid giving undue influence to countries with a larger number of surveys, mean dissimilarity values were computed for each country prior to computing the overall mean for a time bin. Uncertainty estimates were obtained via a bootstrap procedure that sampled with replacement from the distribution of mean within-country dissimilarity values for each time bin n times (with n = number of countries for that bin). This resampling procedure was performed 1000 times for each time bin; 95% confidence intervals were determined from the 5th and 95th quantiles of the resampled distributions. Significant differences in mean within-country coral community dissimilarity values were determined by pairwise comparisons performed via permutation tests (with 1000 iterations) using the‘pairwise.perm.t.test’ function in the ‘RVAideMemoire’package in R. All statistical analyses were performed using the program Rv3.4 [40], and all P-value corrections for multiple testing were computed using the method outlined in ref 41.