2.3.1. Relationship of Reef Fish Assemblages to Habitat Structure

For each transect, we estimated diversity, abundance, and biomass. Biomass (g m−2) was calculated using the allometric weight equation:

$$\mathbf{W} = \mathbf{a} \ L^{\mathbf{b}} \tag{1}$$

where L is the weighted mean of the estimated length for each species per transect, and a and b are the constants of length–weight obtained from FishBase [38].

We evaluated diversity using Hill's effective number of species of order 0, 1, and 2 [41], where 0D is species richness, 1D considers all species and their abundance, 2D reflects the most abundant species, and 2/1D reflects their evenness. To explore the relationships of reef fish assemblages to habitat, we performed multiple linear regressions of fish assemblage measures against the main explanatory variables that define habitat structure (benthic cover and rugosity). The preferred models were selected based on the lowest values of Akaike's

Information Criterion (AICc). The models' variables included the average parameters of the models with <2 ΔAICc [42]. The *p*-value and adjusted R<sup>2</sup> of the model with all the explanatory variables and the selected variables were reported. For each model, the validity of the linear models was examined with the normality of the residuals [43].

2.3.2. Differences in Parrotfish Assemblages between Islands (Serranilla and San Andrés)

We evaluated variation in the metrics (0D, biomass, and abundance) and composition (abundance and biomass) of the Scaridae species present between the two islands, Serranilla and San Andrés. We also examined the mean sizes observed for each species at Serranilla and contrasted these with the available information about common and maximum size obtained from FishBase [38].

Two ANOVAs based on permutations (10,000) were performed to test the differences in biomass and abundance using Euclidean matrices from fourth-root transformed data. We used a model with one factor:

$$\mathbf{Y}\_{\text{i}\mathbf{j}} = \mu + \mathbf{I} \text{slard}\_{\text{i}} + \mathbf{e}\_{\text{i}\mathbf{j}} \tag{2}$$

where μ is the general mean; Islandi is the factor with two levels (Serranilla and San Andrés) and 12 replicates per site, and eij is the associated error.

Two permutational multivariate analyses of variance (PERMANOVA) were performed to assess parrotfish assemblage composition differences in biomass and abundance. We used the previous ANOVA model and verified the homogeneity of dispersion with the PERMDISP test and non-metric multidimensional scaling (NMDS) [44]. Similarity percentage analysis (SIMPER) were used to detect the parrotfish responsible for the dissimilarities between the islands. We plotted in the NMDS the small and large parrotfish abundance and biomass to visualize the differences in composition. For PERMANOVA, PERMDISP, SIM-PER, and NMDS, we used a Bray–Curtis similarity matrix with a fourth root transformed data. Statistical analyses were performed in R and Primer v6.1 PERMANOVA+ [45,46], and plots for SIMPER results generated in SigmaPlot v11 software.
