We quantified the degree to which urchins have overgrazed Clathromorphum nereostratum across our 700-km study area. To do so, we haphazardly selected a single site at each island for high-resolution study ("habitat.type" = "Barren"), which were of comparable depth (30-40 feet), harbored an abundance of C. nereostratum, and have a known ecological history. We also studied new sites at Ogliuga, Amchitka, Kiska (Rat Islands), Nizki (Semichi Islands), and Attu that met the same depth and benthic composition criteria but were situated adjacent to shallow (15-24 feet depth) remnant kelp stands; detailed study of these barren sites ("habitat.type" = "Barren + kelp subsidy") allowed us to document patterns of bioerosion in the presence of kelp-derived urchin food subsidies. We also visited similar sites at Adak and Tanaga to survey bioerosion, but these survey data were omitted due to sampling error and/or violation of site criteria.

To assess the proportion of C. nereostratum that was overgrazed at each study site, we visually estimated bioerosion using photo quadrat surveys. At each site, a diver descended to the reef and set a random compass bearing, swam in the direction of that bearing for a predetermined number of kicks, and placed a 25 x 25 cm quadrat on the nearest C. nereostratum colony. The diver then took a full frame, high-resolution photo of the quadrat (camera: Canon 5D Mark II DSLR camera with Ikelite DS-150 strobes; lens: Canon 15mm fisheye, mounted on a Kenko 1.4x teleconverter to narrow the field of view and reduce distortion). This process was repeated, photographing C. nereostratum individuals every two body lengths (~4 m distance; n = 10/site). In the lab, photos were corrected for lens barrel distortion, cropped, and edited for brightness, saturation, and contrast in Adobe Photoshop Elements. Using a grid (1 x 1 cm) overlay, we visually estimated C. nereostratum abundance within each quadrat ("Clathromorphum.cover"). We then estimated the proportion of the alga grazed by urchins ("grazed.score"), using a scale of 1-6 (where 1 = 0-5%, 2 = 6-25%, 3 = 26-50%, 4 = 51-75%, 5 = 76-95%, and 6 = 96-100 % cover grazed), as the presence of white perithallus indicates overgrazing to a depth > 250 micrometers, below the meristem layer that is responsible for growth and reproduction. Overgrazing scores were ranked (1-3) because photo quality varied depending on field conditions ("quality.rank"). Low confidence estimates (rank 3 of 3) were removed from the analysis, as were measurements made in excess of n = 10 per site. We assumed all grazing was due to urchins, as they are the only large herbivore in the ecosystem and their bite scars are easy to identify.

To measure the depth (in millimeters) to which urchins grazed C nereostratum ("max.depth.grazed.mm"), a second diver haphazardly removed a small sample of the alga from each photoquadrat (after the photo was taken) with hammer and chisel. In the laboratory, the depth of the most pronounced pentaradial urchin grazing scar on each sample was measured using a microscope with ocular micrometer.

Finally, to estimate the prevalence of larger grazed features (excavation pits) in the field, which represent the cumulative impacts of grazing over decades to centuries, at each interval where photoquadrats were deployed the second diver also measured the dimensions of the nearest excavation pit ("pit.volume.cm^3") generated by grazing (n = 10/site). Each pit was measured with respect to its length, width, and depth (cm). We then approximated the volume of each pit as a half cylinder using the equation V = 1/2[PI]r2h, where r was the depth and h the length of the pit.