*2.5. Statistical Analyses*

We performed a mixed-model ANOVA for all reef fishes and each functional group of fish against structure type as the main effect, with site as a random factor. Since all models indicated a significant effect of site on reef fish counts, we performed a principal component analysis to create orthogonal component scores that characterized the sites by their physical distance from shore, depth, rugosity, algal, soft coral, hard coral, and sponge substrate covers. The three most significant component scores from this analysis accounted for 72.8% of the variation in physical traits (PC 1 = 35.1%, PC 2 = 27.0%, PC 3 = 10.7%) and were included in the ANCOVA as covariates. We then analyzed fishes' use of the structures, using a nested analysis of covariance with structure state (artificial or natural) and structure type (control, soft, boulder, elkhorn, sea rod, diseased, dead, or healthy) nested within structure state as the fixed effects, and fish abundance from the video transect surveys and the three component scores as covariates. The first principal component score was the only covariate positively correlated with either of the main effects, so we included an interaction term of PC1 and structure state in our ANCOVA model. We used Tukey's post-hoc comparisons to estimate differences within structure states.

Observations at each structure (n = 177) were natural log-transformed to meet the assumptions of normality of the residuals and homogeneity of the variances. ANCOVAs were performed separately on the log-transformed counts for all reef fishes together and on the log-transformed counts of each fish feeding guild considered separately (herbivores, omnivores, invertivores, and piscivores). We also conducted ANCOVAs on the five most abundant fish species: bicolor damselfish (*Stegastes partitus*), striped parrotfish (*Scarus iseri*), white grunts (*Haemulon plumierii*), blue-striped grunts (*Haemulon sciurus*), and schoolmaster snapper (*Lutjanus apodus*). Linear regressions were used to relate fish counts to measures of hard coral height and to percent cover of live and diseased tissues, as estimated using JMP Pro 14.1.0 software.
