## Allometry of traits

Disparate models out-of scaling emerged whenever we checked out the brand new ontogeny from vertical gape point, maxillary kinematic transmission coefficient (KT), jaw protrusion range and you may chew force for Thalassoma wrasses (Fig. 1; discover and additional thing Fig. S1 for types-certain habits). Many Thalassoma wrasses displayed some form of allometry into the this type of useful qualities. Gomphosus varius displayed more consistent pattern out-of allometry across the all the four qualities, indicating negative allometry in per instance. Basically, each feature, only about three variety exhibited isometry.

All wrasses exhibited strong relationships between log_{ten} vertical gape distance and log_{10} body length (R 2 =0.nine4–0.99, all P<0.0001; supplementary material Table S2). The standardized major axis (SMA) regression slopes ranged from 0.51 to 1.58. While non-cleaner taxa exhibited either isometry or negative allometry for vertical gape distance, facultative cleaners almost universally exhibited positive allometry (Fig. 1A). Thalassoma duperrey was the only facultative cleaner to exhibit isometry for this trait.

Scaling of functional traits in all 11 species. The following traits are shown plotted against log_{10} body length: (A) log_{10} vertical gape distance, (B) log_{10} premaxillary protrusion distance, (C) log_{10} total bite force (as estimated by MandibLever 3.3) and (D) maxillary kinematic transmission coefficient (KT). Solid, orange lines indicate regressions for facultative cleaner fishes; blue dashed lines indicate regressions for non-cleaner fishes. Vertical gray lines indicate mean and s.d. of critical x-values indicated by the Wilcox procedure for all comparisons.

Scaling of functional traits in all 11 species. The following traits are shown plotted against log_{10} body length: (A) log_{10} vertical gape distance, (B) log_{10} premaxillary protrusion distance, (C) log_{10} total bite force (as estimated by MandibLever 3.3) and (D) maxillary kinematic transmission coefficient (KT). Solid, orange lines indicate regressions for facultative cleaner fishes; blue dashed lines indicate regressions for non-cleaner fishes. Vertical gray lines indicate mean and s.d. of critical x-values indicated by the Wilcox procedure for all comparisons.

The relationships between log_{10} premaxillary protrusion distance and log_{10} body length (Fig. 1B) were strong and varied substantially (R 2 =0.60–0.98, all P<0.0001; supplementary material Table S3). The SMA regression slopes ranged from 0.62 to 2.46pared with an isometric slope of 1.0, seven species exhibited positive allometry; only three species (two of which were non-cleaners) exhibited isometric trends.

The relationship between log_{10} bite force and log_{10} body length (Fig. 1C) was strong across all species (R 2 =0.92–0.99, all P<0.0001; supplementary material Table S4). The SMA regression slopes ranged from 1.16 to 2.96. All but one of the facultative cleaner species (T. bifasciatum) showed positive allometry for this trait, while only one non-cleaner (T. rueppellii) shared this trend.

Wrasses in this study universally showed strong negative allometry for maxillary KT (Fig. 1D). The SMA regressions yielded slopes that ranged from ?0.38 to ?1.08 (R 2 =0.90–0.98, all P<0.0001; see supplementary material Table S5). All t-tests designed to test the hypothesis that slope was different from 0 (as predicted by isometry) indicated strong, significant deviations from isometry (all P<0.0001).

Through a series of Sidak-corrected two-sample t-tests, we found significant differences in mean slopes between facultative cleaners and non-cleaners in only two traits: log_{10} vertical gape distance and log_{10} bite force (Table 1). Here, we observed that facultative cleaners exhibited steeper slopes for both log_{10} vertical gape distance [t_{9}=4 spiritual singles kullanÄ±cÄ± adÄ±.11 (subscript denotes degrees of freedom), P=0.021; Table 1] and log_{10} bite force (t_{9}=2.66, P=0.046; Table 1).

## Outcome of the new Wilcox processes

We employed the Wilcox procedure to each trait analysis to compare the regression line of each non-cleaner with those of facultative cleaners, allowing us to identify the regions where the data in each pairwise comparison begin to overlap. For log_{10} vertical gape distance, the regression line of each facultative cleaner intersected those of one to four non-cleaner species (Table 2). In 18 cases (out of 30 total comparisons), the Wilcox procedure identified regions of overlap beginning at log_{10} body lengths of 1.81±0.0081 (mean ± s.d.), indicating that overlap of data did not occur until species attained a body length of ± mm. Thus, these results indicate that juvenile facultative cleaners smaller than ± mm exhibited significantly lower vertical gape distances compared with non-cleaners (Fig. 1A).