Computing the minimal number of substitutions to translate a character into another one. (a) depicts the Klein-four group ΣK3ST, which consists of the identity s0and the three substitution types s1,s2,s3from the K3ST model. (b) In order to convert the character GTAGA into ACCTC under ΣK3ST, we need to introduce the operation s:=(s1,s1,s2,s2,s2). As the operation s also translates the constant character AAAAA to GGCCC, converting GTAGA into ACCTC is equivalent to evolving the character state A at the root along the tree to obtain the character GGCCC at the leaves. The Fitch algorithm applied to the latter produces a unique most parsimonious solution of two substitutions as depicted by (c).