On characteristics of ancestral character-state reconstructions under the accelerated transformation optimization Original Research Article

A combinatorial optimization problem regarding assignments of real numbers (called reconstructions) on a tree has been discussed in phylogenetic analysis. Recently, a clear method for finding most-parsimonious reconstructions (MPRs) on a given end-labeled-tree (phylogenetic tree) has been presented by Hanazawa et al. (Discrete Appl. Math. 56 (1995) 245–265, Narushima and Hanazawa, Discrete Appl. Math. 80 (1997) 231–238). In the framework based on the method, we refine and generalize the accelerated transformation (ACCTRAN) reconstruction which originated with Farris (Syst. Zool. 19 (1970) 92) and was defined more explicitly by Swofford and Maddison (Math. Biosci. 87 (1987) 229). This is considered one of the more meaningful and useful of the possible MPRs. We also generalize the MPR-poset of MPRs, which is introduced by Minaka (Forma 8 (1993) 296). Then two theorems on characteristics of ACCTRANs are given. One shows that the ACCTRAN on a rooted e.l.tree T is the unique MPR on T for which the lengths of all subtrees are minimized, that is, the completeness in most-parsimonious properties of ACCTRANs. Another states some conditions for the ACCTRAN to be the greatest element in the MPR-poset.