Fig. 2

Inferring ancestral expression states. a An illustration of how BayesTraits is used to infer the most probable expression states at a given ancestral node on the evolutionary tree. First, evolutionary rates between expression states (defined by quartiles) are randomly assigned. These rates are then use to infer the most probable ancestral states from the observed extant expression values. Finally, the likelihood of the observed extant expression states is evaluated based on the current ancestral states and evolutionary rate and this likelihood is used to update estimations of the evolutionary rate. This process is repeated iteratively to optimize the evolutionary rates across the tree and thus the inferred ancestral states b The observed expression and inferred ancestral expression states of a branch of the AP2 domain family tree for three leaf developmental data sets. The ancestral states of the ancestors of TOE1 and TOE 2 (a β duplication), TOE3 and AP2 (a β duplication), as well as SNZ and SMZ (an α duplication) were inferred using the program described in (a)