Fig. 5.—

Theoretical hierarchical clustering pattern varies with model parameters. (A) Brownian model. (B) Ornstein–Uhlenbeck model. The hierarchical clustering pattern of four cell types, A₁, A₂, B₁, and B₂, is determined by the correlation matrix of their transcriptome profiles (supplementary eq. S2, Supplementary Material online). Homology signal (horizontal axis; $\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{r}(A_0,B_0)$ or $\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{r}({\mu }_A, {\mu }_B$)) and correlated evolution signal (vertical axis; $\gamma$) shape cell type transcriptome similarities together. The phase transition condition between clustering by homology and clustering by species is a straight line (supplementary eqs. S4 and S5, Supplementary Material online). In both models, no clustering by species pattern is observed without correlated evolution ($\gamma =0$). ${\alpha }_B$ and ${\alpha }_{\mathrm{O}\mathrm{U}}$ are parameters that are related to the random walk variance, ${\sigma }^2$, in Brownian and OU model, respectively (see supplementary methods, Supplementary Material online). The dashed arrow indicates how the phase transition boundary changes with parameters ${\alpha }_B$ and ${\alpha }_{\mathrm{O}\mathrm{U}}$. If the random walk variance ${\sigma }^2$ decreases, there is higher chance to see group-by-homology pattern.