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The biological significance of behavioural predictability (environment-independent within-individual behavioural variation) became accepted recently as an important part of an individual's behavioural strategy besides behavioural type (individual mean behaviour). However, we do not know how behavioural type and predictability evolve. Here, we tested different evolutionary scenarios: (i) the two traits evolve independently (lack of correlations) and (ii) the two traits' evolution is constrained (abundant correlations) due to either (ii/a) proximate constraints (direction of correlations is similar) or (ii/b) local adaptations (direction of correlations is variable). We applied a set of phylogenetic meta-analyses based on 93 effect sizes across 44 vertebrate and invertebrate species, focusing on activity and risk-taking. The general correlation between behavioural type and predictability did not differ from zero. Effect sizes for correlations showed considerable heterogeneity, with both negative and positive correlations occurring. The overall absolute (unsigned) effect size was high (Zr = 0.58), and significantly exceeded the null expectation based on randomized data. Our results support the adaptive scenario: correlations between behavioural type and predictability are abundant in nature, but their direction is variable. We suggest that the evolution of these behavioural components might be constrained in a system-specific way.