Palau and Yap:
We used a stratified random sampling approach to survey the reefs of Palau and Yap (Fig A, in S1 File, van Woesik and Cacciapaglia, 2018), by randomly selecting 24 study sites at each island using the package 'sp' in R. We stratified the sites in Palau by outer reefs (8), patch reefs in the lagoon (10), and inner reefs (6). In Yap, which does not have an extensive lagoon and only supports a few rare patch reefs, we stratified the sites by outer reefs (10) and inner reefs (14). The allocation of sites per strata was dependent on the reef area. We were particularly interested in determining the potential of shallow-water reef carbonate production and therefore focused our surveys between 2–5 m. At each site we laid six, 10 m long transect tapes, which followed the contours of the reef substrate. The tapes were placed approximately 2 m between the end of one tape and the start of the next tape. Using these transects we applied the line-intercept method to quantify the planar chord length of each benthic component to the nearest centimeter. At each site we also ran six, 10 m transect lines horizontally along the substrate, above the transects that followed the reef contours, which were used to approximate rugosity, by measuring the length difference between the horizontal and the contour-following lines. Fishes were videoed along six, 30 m long by 4 m wide transects. The herbivorous parrotfishes in the videos were subsequently analyzed for size (cm) and identity. A Cannon HD Vixia HFM500 video camera was used to record the fishes. The fish sizes were estimated, using background information of corals as scales, and all fishes in Palau were verified by Geory Mereb from PICRC (Palau International Coral Reef Center, Palau).

For more details please see van Woesik and Cacciapaglia, 2018.

Federated States of Micronesia (FSM):
Twenty-four study sites were randomly selected in each of Pohnpei (6.2°N, 158.2°E) and Kosrae (5.3°N, 162.9°E) FSM using a randomly stratified sampling approach with the package sp in R. In Pohnpei, reefs were stratified as inner reefs, patch reefs, and outer reefs. In Kosrae, we only stratified the reefs as either inner reefs or outer reefs (because of the lack of patch reefs). Sample size of each strata was determined by calculating the geographic area of each reef type, using the area function from the R package raster, and allocating the number of sites in accordance with the area estimates. Reef surveys focused on the 2–5 meters depth contour to estimate shallow-water carbonate production.

Six, 10 m transects, using a modified line-intercept technique that followed the reef substrate, were used to measure the benthic composition for every centimeter, at each site of the 48 sites. A few meters gap was allocated between the ends of the transects to ensure no overlap of substrate between transects. Herbivorous parrotfishes were videoed and identified to species and their estimated length was recorded to the nearest cm along six transects, each of which was 30 m long by 4 m wide. Care was taken to record the fish-transect videos ahead of the other transects to avoid any disturbance to the fishes.

Majuro (Republic of the Marshall Islands) and Kiritimati (Republic of Kiribati):
A stratified random sampling approach was used to survey the reefs of Majuro (7.0667° N, 171.2667° E) and Kiritimati (1.8721° N, 157.4278° W), by randomly selecting 24 study sites at each island using the package 'sp' in R. In both locations, a stratified random sampling approach was used to survey the reefs for carbonate production by randomly selecting 24 sites on each island, with the exception of Kiritimati where only 22 of the 24 sites were surveyed because of inclement weather. At both locations, the sites were stratified as either (i) outer reefs, or (ii) patch reefs in lagoons. The number of sites sampled per habitat varied according to the area of available habitat at each location. The investigators were particularly interested in determining the potential of shallow-water reef carbonate production, and therefore focused surveys between 2–5 m. Majuro was surveyed from 6/17/2019 to 7/6/2019 and Kiritimati was surveyed from 7/10/2019 to 7/22/2019.