Fig. S1 Inferred DNA substitution rates in the Araceae.

Fig. S2 Results from divergence dating and ancestral area reconstruction (AAR) without fossils.

Fig. S3 Posterior distribution of fossil constraints from the BEAST runs with the simple substitution model (JC+Γ) with either uniform (left column) or gamma-shaped (right column) prior distributions.

Table S1 List of species used in this study with author names, herbarium vouchers and GenBank accession numbers for all sequences

Table S2 Fossils (sorted by age) used as constraints in this study or discussed in the main text

Table S3 Dispersal matrices employed for the maximum likelihood ancestral area reconstructions used in the four-time-slice model (90–60, 60–30), the three-time-slice model (90–30), or both (150–90, 30–0).

Table S4 Divergence age estimates under different molecular clock models in TreeTime, and prior constraint schemes (uniform or gamma) and substitution models (simple, JC+Γ, complex, TPM1uf+Γ for the noncoding region and GTR+Γ for the coding region taking into account the third codon position) in BEAST

Table S5 Results for each node shown in Fig. 3

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