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Figure S1. Log likelihood surface for EFN trait 1 and Binary-2 model on the MCC tree of Simon et al. (2009).

Figure S2. Log-likelihood surface for EFN trait 1 and Precursor-2 model on the MCC tree of Simon et al. (2009).

Figure S3. Log-likelihood surface for EFN trait 1 for the Precursor-2 model on BEAST tree 209 from Simon et al. (2009).

Figure S4. Log-likelihood surface for EFN trait 1 for the Precursor-2 model on BEAST tree 15 from Simon et al. (2009).

Figure S5. Log-likelihood surface for EFN trait 1 for the Precursor-2 model on BEAST tree 123 from Simon et al. (2009).

Figure S6. Maximum-likelihood reconstruction of trait evolution under the Binary-2 model for EFN trait 6.

Figure S7. For EFN trait 1, the inferred location of origins of precursor states (green tick marks) and subsequent gain and loss of EFNs (black filled and open boxes, respectively).

Figure S8. For EFN trait 2, the inferred location of origins of precursor states (green tick marks) and subsequent gain and loss of EFNs (black filled and open boxes, respectively).

Figure S9. For EFN trait 3, the inferred location of origins of precursor states (green tick marks) and subsequent gain and loss of EFNs (black filled and open boxes, respectively).

Figure S10. For EFN trait 4, the inferred location of origins of precursor states (green tick marks) and subsequent gain and loss of EFNs (black filled and open boxes, respectively).

Figure S11. For EFN trait 5, the inferred location of origins of precursor states (green tick marks) and subsequent gain and loss of EFNs (black filled and open boxes, respectively).

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