Fig. 1

Time to most recent substitution \(t_\text{MRS }\). These schematically show the situations that may impact the confidence levels of inferred \(t_{\text {MRS}}\) values. The leaf nodes correspond to the target species are indicated by rectangles. In the left figure, we expect the last substitution occurred between node x and y, and \(t_{\text {MRS}}\) will be around \(t_1\) to \(t_1+t_2\). In the middle figure, the pattern of alignment column is not simple, and the state of node y can be either A or G. Therefore, the inferred \(t_{\text {MRS}}\) will have a large variance between \(t_1\) to \(t_1+t_2+t_3\). In the right figure, there is an ambiguous nucleotide in the column. In such cases, the inferred \(t_{\text {MRS}}\) value is the same as that inferred from only three species, and the confidence will accordingly be lower than when all four nucleotides are known