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Appendix S1. More complex models of trait evolution.

Appendix S2. Similarity of our simulations to a λ model of trait evolution.

Table S1. Phylogenetic signal indices and tests (a) and related measures (b).

Table S2. Influence of explanatory variables on response variables. (a) Phylogenetic signal indices. (b) Standard deviations of phylo,,genetic signal indices. (c) Phylogenetic signal tests. (d) Standard deviations of phylogenetic signal tests.

Fig. S1. Response of phylogenetic signal tests to increasing strength of Brownian motion for different sample sizes.

Fig. S2. Response of phylogenetic signal tests to polytomies and branch length information.

Fig. S3. Correlation of phylogenetic signal tests for different N.

Fig. S4. Response of phylogenetic signal tests to increasing values of the parameters for different tree transformations.

Fig. S5. Comparison of phylogenetic signal values against increasing strength of Brownian motion for the model of trait evolution applied in this paper (w model) and a λ model of trait evolution.

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