**Study site characteristics**

This study was conducted on reef flats within no-take marine protected areas (MPAs) adjacent to Votua, Vatuo-lailai, and Namada villages along the Coral Coast of Viti Levu, Fiji. These reserves are scattered along 11 km of fringing reef and are separated by ~3-8 km. The reserves have high coral cover (38-56%), low macroalgal cover (1-3%), and a high biomass and diversity of herbivorous fishes (Rasher, Hoey, and Hay 2013; Bonaldo and Hay 2014). The reef flats range from ~1-3 m deep at high tide, extend ~500-600 m from shore to the reef crest, and are typical of exposed reef flats occurring throughout Fjii.

Except during low tides in calm weather, waves push water over the reef front, and water then flows laterally across the reef flats to discharge through channels bisecting the flats. This creates a relatively predictable current direction at most locations.

**Distribution surveys**

We characterized the spatial distribution of P. damicornis and S. hystrix in the reef flat MPAs of Namada, Vatuo-lailai, and Votua villages at two scales (August through October 2013). For our larger-scale survey, we mapped each colony within 8 x 8 m plots (N=5, 5, and 10 for Namada, Vatuo-lailai, and Votua, respectively). Each plot was divided into 256 0.5 x 0.5 m cells and each coral >1 cm across mapped into a cell. The location of each survey plot was determined by randomly choosing a point on shore, swimming 100, 200, or 300 kicks directly away from shore at that point, and surveying the closest bommie large enough to fill more than three quarters of an 8 x 8 m plot. In four of 10 surveys at Votua and in all five surveys at Vatuo-lailai and Namada, we also measured the largest diameter of each P. damicornis colony. We did not measure S. hystrix colony size because individual colonies were more frequently discontinuous. To avoid confounding biotically-driven spatial distribution with patterns caused by patchiness of suitable substrate, we also recorded which cells were comprised primarily of unsuitable habitats such as sand-scoured pools or channels and bommie tops covered in rubble.

We analyzed these data using the neighborhood density function O(r) in the point pattern analysis program Programita (Wiegand and Moloney 2004). This analysis identifies distances at which individuals are aggregated, randomly spaced, or overdispersed compared to a specified null model. Unlike the more frequently used Ripley’s K(r) statistic, each distance category is not affected by those inside it; expected aggregation at each distance is compared to the observed value independently of nearer distances. Each concentric ring centered on an individual coral is separately placed on the aggregated-overdispersed continuum and displays the spatial pattern within a different distance category. Ring width was 0.5 m extending up to 4 m. The null model for this analysis was complete spatial randomness (CSR). Because the variance in substrate types violated CSR’s assumption of uniform likelihood of coral placement, we conducted the below analyses once using the entirety of all 8 x 8 m plots and a second time excluding cells of unsuitable habitat (which should better meet CSR’s assumption of uniform likelihood).

To determine whether the observed spatial pattern was random, significantly aggregated, or overdispersed, Programita simulated placement of each plot’s colonies 999 times using CSR, calculated O(r) for each simulation, then combined replicate O(r)’s from each reef and from all three reefs. This generated a distribution of simulated O(r)’s from which we established the significance of the observed spatial patterns. The distance(s) at which significant aggregation or overdispersion occurred were determined by the distances at which the observed pattern fell above or below the 95% simulation envelopes, respectively. This analysis does not parse aggregating and overdispering processes; it shows the net resulting pattern.

In addition to analyzing all P. damicornis and S. hystrix colonies, we analyzed P. damicornis <5 cm, >5 cm, >10 cm, and >15 cm in diameter to see if spatial patterns changed with colony size.

The <5 cm and >5 cm categories were mutually exclusive but because there were not enough colonies between 5 and 10 cm and between 10 and 15 cm to analyze as mutually exclusive groups, larger size categories were subsets of smaller ones.

The 8 x 8 m quadrat surveys could not resolve spatial patterns below the cell size of 0.5 x 0.5 m, meaning that patterns occurring at less than 0.252 m could be undocumented. To determine the spatial distribution of P. damicornis and S. hystrix at smaller scales, we conducted 2 m radius circular surveys around focal P. damicornis and S. hystrix colonies that i) were the largest colony of that species within 4 m (to reduce the effects of conspecifics), and ii) occurred where >75% of the substrate within 2 m was suitable habitat for P. damicornis and S. hystrix, again to equalize the likelihood of colonies occurring everywhere in the survey.

The distance to each surrounding (radial) P. damicornis and S. hystrix colony was the average of the distance to that colony’s near and far sides (N=45 focal colonies for P. damicornis around P. damicornis, 10 for S. hystrix around P. damicornis, and 24 each for P. damicornis and S. hystrix around S. hystrix). We analyzed radial colony counts in 10 cm concentric rings using a generalized linear mixed effects model with Poisson errors and the canonical log link function in R (lme4 package, Bates et al. 2013). Distance was a fixed effect and focal colony with distance nested inside was a random effect, with the log10 of the ring sizes as an offset to control for unequal area sampled at each distance (i.e. ring area increased with distance from the focal colony). We repeated this analysis with just the closest 0.5 m and 1 m of the circles in case radial colonies beyond those distances were masking short-range effects of the focal colonies.

We also analyzed the P. damicornis data from the 8 x 8 m plots in the same manner as we did the circular surveys. To convert the plot data, an R script identified every surveyed P. damicornis colony >2 m from all edges of its plot and equal to or larger than a specified diameter (either 15 or 20 cm) as a focal colony (N=38 and 19 focal colonies, respectively). In order to have an appreciable sample size, we did not restrict focal colonies to those that were the largest within 4 m. The script then calculated the distances to all P. damicornis colonies less than the specified diameter within 2 m and placed them into 10 cm concentric rings as above. We used generalized linear mixed effects models as described for the circular surveys.