Genomes evolved at diversity evolutionary rates (Cui et al., 2006; X. Wang et al., 2011). Unfortunately, the divergent evolutionary rates of the selected genomes make the timing of their evolution history is difficult. When timing the evolution history of selected genomes, if we selected different genomes as the reference may result the different results, which may be causing by the nature attribute of different genomes. Here, we employed a pipeline as commonly implemented when comparing angiosperm genomes, such as Fabaceae (Wang et al., 2017), Malvaceae (X. Wang et al., 2015b), durian (Jinpeng Wang et al., 2019c) and Cucurbitaceae ( Wang et al., 2018) and selected the slowest evolved genome as the reference. Therefore, comparing the Ks values of RCT event in three representative Ranunculales genomes, the slowest evolving genome (C. chinensis) was regarded as the reference to accurately correct the times of WGD events and species divergence. To correct the evolutionary rates of duplicated genes generated from WGD events, the maximum likelihood estimates μ from inferred Ks means of RCT-produced duplicated genes were normalized to those of C. chinensis. Supposing that the Ks value of a C. chinensis duplicated gene pair is a random variable and that for a duplicated gene pair in the P. somniferum genome is , we obtained the relative difference:

$$r=({\mu }_p-{\mu }_c)/{\mu }_c$$

To obtain the corrected value:

$$X_{p-correction}:({\mu }_{p-ccorrection},{\sigma }_{p-correction}^2)$$

we defined the correction coefficient as:

$$\frac{{\mu }_{p-ccorrection}}{{\mu }_p}=\frac{{\mu }_c}{{\mu }_p}={\lambda }_p$$

and

$${\mu }_{p-ccorrection}=\frac{{\mu }_c}{{\mu }_p}\times {\mu }_p=\frac{1}{1+r}\times {\mu }_p$$ $${\lambda }_p=\frac{1}{1+r}$$

then,

$$X_{p-correction}:({\lambda }_p{\mu }_p,{\lambda }_p^2{\mu }_p^2)$$

To calculate the Ks of homologous gene pairs between two plants, i and j, suppose that the Ks distribution is

$$X_{ij-correction}:({\lambda }_{ij},{\sigma }_{ij}^2)$$

thus we adopted the algebraic mean of the correction coefficients from two plants,

$${\lambda }_{ij}=({\lambda }_i+{\lambda }_j)/2$$

then,

$$X_{ij-correction}:({\lambda }_{ij}{\mu }_{ij},{\lambda }_{ij}^2{\sigma }_{ij}^2)$$

Therefore, the Ks value between C. chinensis and P. somniferum is

$$X_{cp-correction}:({\lambda }_{cp}{\mu }_{cp},{\lambda }_{cp}^2{\sigma }_{cp}^2)$$

Based on C. chinensis simultaneously separating from V. vinifera and T. sinense, we used the unweighted pair-group method with arithmetic means (UPGMA),

$$d(A,B)=\frac{1}{|A||B|}\sum _{x\in A}\sum _{x\in B}d(x,y)$$

Then, we derived the inferred Ks means from the C. chinensis-V. vinifera and C. chinensis-T. sinense pairs as

$${\mu }_{cv-correction}={\mu }_{ct-correction}=({\mu }_{cv}+{\mu }_{ct})/2$$

The correction coefficients from C. chinensis-V. vinifera and C. chinensis-T. sinense are

$${\lambda }_{cv}={\mu }_{cv-correction}/{\mu }_{cv},{\lambda }_{ct}={\mu }_{ct-correction}/{\mu }_{ct}$$

Therefore, the C. chinensis-V. vinifera and C. chinensis-T. sinense corrected distributions are

$$X_{cv-correction}:({\lambda }_{cv}{\mu }_{cv},{\lambda }_{cv}^2{\sigma }_{cv}^2),X_{ct-correction}:({\lambda }_{ct}{\mu }_{ct},{\lambda }_{ct}^2{\sigma }_{ct}^2)$$

We obtain the correction coefficient of V. vinifera as

$${\lambda }_v={\lambda }_{cv}\times 2-1$$

Similarly, the correction coefficient of T. sinense was

$${\lambda }_t={\lambda }_{ct}\times 2-1$$

Then, we obtained

$$X_{v-correction}:({\lambda }_v{\mu }_v,{\lambda }_v^2{\sigma }_v^2),X_{t-correction}:({\lambda }_t{\mu }_t,{\lambda }_t^2{\sigma }_t^2)$$