EREM: Parameter Estimation and Ancestral Reconstruction by Expectation-Maximization Algorithm for a Probabilistic Model of Genomic Binary Characters Evolution

Figure 1

A fragment of a hypothetical input for a 4-species analysis. This is a segment of a multiple alignment of 4 orthologous genes. Notice the gap in one of the genes, designated by * for unknown character. Among the 10 sites in this alignment fragment, there are 6 unique patterns; 𝜔₁=(0,0,0,0)^𝑇,𝜔₂=(0,1,0,1)^𝑇,𝜔₃=(1,1,0,1)^𝑇,𝜔₄=(0,0,1,1)^𝑇,𝜔₅=(0,∗,1,1)^𝑇,and𝜔₆=(0,∗,0,1)^𝑇. This portion of the alignment, therefore, contains 2 copies of 𝜔₁, 2 copies of 𝜔₂, 3 copies of 𝜔₃, and one copy each from 𝜔₄, 𝜔₅, and 𝜔₆.