Expression evolution across mammalian lineages is accurately modeled by the OU process. (A) Data overview. Phylogenetic tree of all 17 mammals (left) marked by tissue types (colored dots) for which profiles are included. (*) Newly generated data. (B) Expression divergence is not linear. Shown is the pairwise mean squared expression distances (y-axis) between mammals and human for liver samples across evolutionary time, as estimated by substitutions per 100 bp (x-axis). (Error bars) standard deviation of the mean across replicates; (solid line) nonlinear (y = axk) regression fit. (C) OU model. Equation describing OU model (top): (σ) rate of genetic drift; [dB(t)] Brownian motion; (θ) optimal expression level; (α) strength of selection. (Left) Simulated trajectories of expression (y-axis) over evolutionary time (x-axis) under a Brownian motion (top) and OU (bottom) process. Ten example trajectories are shown. (Right) Mean squared distance to initial value (y-axis) across time (x-axis) from 1000 simulated trajectories. (D) Distribution of optimal expression. (Top) Illustration of the change in probability distribution of expression (y-axis) across time (x-axis) under an OU process. The distribution stabilizes as time approaches infinity. (Bottom) Scatter plot of log10TPM values (y-axis) across all liver samples (x-axis) of two example genes with low (NRBP1) and high (APOA4) variance. (Solid and dotted red lines) Estimated mean and variance, respectively, of the asymptotic (optimal) distribution of each gene's expression value estimated using the OU process. Note that mean and variance are calculated in log space.
