# For every single trait, we made use of the SMA regression mountain between your log

_{ten} trait value (except in the case of maxillary KT, for which we used raw values) and log_{10} body length (outlined above). We then tested for phylogenetic signal in the slopes, treating the slope of each regression as its respective species’ trait value. We estimated Pagel’s lambda (Pagel, 1999) and Blomberg’s K (Blomberg et al., 2003) using the package phytools (Revell, 2012) in R, and we tested the hypothesis that the phylogenetic signal was greater than 0. The phylogenetic tree we used, which contained all species in this study, was pruned from Kazancioglu et al. (Kazancioglu et al., 2009), who used a supermatrix approach to propose relationships between 252 labrid species. For all traits, we found the level of phylogenetic signal to be extremely low, and we were unable to reject the null hypothesis that phylogenetic signal equals 0 (supplementary material Table S13). This implies that the ontogenetic trajectories in the traits we analyzed have been under such strong selection, that the trends in slopes do not follow a Brownian motion model of evolution. While we cannot rule out that the lack of phylogenetic signal may be due to limited power, we were unable to detect phylogenetic signal in any of the traits we analyzed. Therefore, all subsequent analyses were performed using traditional parametric statistical methods.

## Comparisons between facultative products and you can non-cleansers

In each case, the dependent variable meet24 profil Ã¶rnekleri was the log_{10} trait value (except in the case of maxillary KT, for which we used raw values), species identity was the independent variable, and log_{10} body length was used as a covariate. We tested the hypothesis that interactions between the independent variable (species) and the covariates (log_{10} body length) were significantly different from 0. In every case, we found highly significant interactions, indicating that in each analysis, the species-specific slopes were not homogeneous. As this violates a key assumption of ANCOVA, we refrained from comparing least squares means across species.

To check on this new theory that facultative products showcase more extreme allometry in useful characteristics compared with low-products, i performed a series of characteristic-certain a couple-test t-evaluating. For every feature, i analyzed the fresh new equality of the imply of SMA regression mountains toward facultative products up against that of this new low-cleaners. Right here, the brand new null hypothesis was that the mean SMA regression mountain carry out maybe not differ between them organizations. I applied an excellent Sidak correction to reduce the type I mistake likelihood across numerous comparisons (Sidak, 1967).

## To evaluate the connection ranging from for each and every trait and the entire body size across the groups of types, i basic checked having homogeneity out-of mountains because they build independent standard linear habits (GLMs), particular to every characteristic

To identify the morphological correlates of cleaning, we made comparisons of trait magnitudes between facultative cleaners and non-cleaners across the range of body lengths. Given the heterogeneity of slopes, we employed the Wilcox procedure (Wilcox, 1987) to determine regions of the x-axis (log_{10} body length in all cases) in which trait values for non-cleaners were significantly different from those of facultative cleaners. This allowed us to distinguish at what body lengths the differences in trait magnitudes seen between facultative and non-cleaner species were no longer significant, given the error structures of the regressions. We decided to adopt this approach rather than use t-tests to compare regression intercepts because such intercepts represent trait values at a body size of zero, and thus do not constitute trait values that are biologically realistic. The Wilcox procedure is a modification of the Johnson–Neyman method (Johnson and Neyman, 1936) that is adjusted for multiple comparisons. For each trait, we compared the regression line of every non-cleaner species (N=6) with that of each facultative cleaner species (N=5), for a total of 30 comparisons per trait. The Wilcox procedure allowed us to identify the regions where the data in each pairwise comparison begin to overlap, taking into account the spread of data around each regression line. In several cases, regression lines crossed at values of x that represented biologically impossible body lengths for either or both of the species involved. We therefore restricted values of x to those that were covered within our dataset.