Table 2. Notations in our Gibbs sampler.

Symbol	Definition
	Known parameters
m	Number of current species; there are m – 1 ancestral species.
n	Number of genes in one species.
I	Species set. I = {0, 1,..., 2m – 2}.
S	The set of regulatory sequences from all current species.
	Unknown parameters but can be estimated before applying the Gibbs Sampler
	Background site model for species 0.
M0i	Background substitution matrix at the ith branch of the tree, i = 0, 1,..., 2m – 3.
M1i	Motif substitution matrix at the ith branch of the tree, i = 0, 1,..., 2m – 3.
	Unknown parameters that can be estimated from the Gibbs sampling
pi	Probability of a gene containing motif instances in the ith species, i ∈ I.
w	Motif width.
A(i)	Motif instance set in the ith species, i ∈ I.
	The motif instance in the jth gene of ith species, i ∈ I.
	The kth nucleotide in the motif instance in the jth gene of the ith species, i ∈ I.
	Notations that are used for describing the model and no particular interest
	The regulatory sequence of the jth gene in the ith species, i ∈ I.
	Motif model for species 0, the root species.