Figure 1.

Arboretum. (A) Generative model. Shown are the components of the generative model for a phylogeny with three extant species (X, Y, Z, gray rectangles) and two ancestral species (A, B, white rectangles) with k = 2 modules (heatmaps). The model consists of two parts: module evolution (top) and expression generation (bottom). Module evolution is modeled by transition matrices, one for every branch of the tree (black and white matrices on branches and bottom). The observed expression (heatmaps) is modeled by a mixture of Gaussians—one mixture for each extant species, one mixture component per module. The parameters of each Gaussian are shown on top of each species-specific module. For example, Σ₁^X and μ₁^X denote the covariance and mean of module 1 in species X. (B) Modeling module evolution of a gene family with duplication. (Top) Shown is a gene tree; (star) duplication event. All species after duplication (B, X, and Y) have two copies of the ancestral gene (B1, B2, X1, X2, and Y1, Y2). (Bottom) Module evolution procedure. (C_Aⁱ) Module assignments of the ith orthogroup in species A. Module assignments post-duplication are denoted as, for example, C_X1ⁱ and C_X2ⁱ, for genes X1, X2 in species X. The assignments C_B1ⁱ and C_B2ⁱ are both sampled from the transition matrix of the phylogenetic point right after the duplication (B) and evolved independently down the rest of the subtree.