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Fig. S1. The Two Wrasses Species. Terminal phase males of the warm-water T. pavo (a) and the cool-water C. julis (c). Initial phase individuals of T. pavo (b) and C. julis (d) respectively.

Fig. S2. Details of the experimental design adopted for the field patterns of habitat selection.

Fig. S3. Details of the experimental design adopted for the ‘single species’ experiment.

Fig. S4. Details of the experimental design adopted for the ‘relative dominance’ experiment.

Fig. S5. The two outdoor arenas (in black) used for the manipulative experiments at the IAMC-CNR, Messina (Italy). Both arenas have similar size: 8 m diameter, 1.5 m depth, and ~50 m2 surface.

Table S1. Number of individuals of both species used in the ‘single species’ and the ‘relative dominance’ experiments divided according to colour phases and relative size structure. Note that the same individuals were used for the present-day and the projected SST treatments to avoid excessive collection of fish.

Table S2. anova on the density of the wrasses in two shallow habitats (algae and seagrass) at four latitudes. ns not significant, * P < 0.05, ** P < 0.01, *** P < 0.001. In bold the significant interaction further examined by post-hoc SNK test (Table 1).

Table S3. anova on the habitat selection and habitat permanence of the cool-water fish in the relative dominance experiment. ns not significant, **P < 0.01, ***P < 0.001. In bold the significant interactions further examined by post-hoc SNK tests (Table 1).

Table S4. anova on the searching, interacting with co-specifics (Cj), interacting with T. pavo (Tp) and resting activities of the cool-water fish in the relative dominance experiment. ns not significant, *P < 0.05, **P < 0.01, ***P < 0.001. In bold the significant interactions further examined by post-hoc SNK tests (Table 1).

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