Estimating Phylogenies from Lacunose Distance Matrices: Additive is Superior to Ultrametric Estimation

Lapointe and Kirsch (1995) have recently explored the possibility of reconstructing phylogenetic trees from lacunose distance matrices. They have shown that missing cells can be estimated using the ultrametric property of distances, and that reliable trees can be derived from such filled matrices. Here, we extend their work by introducing a novel way to estimate distances based on the four-point condition of additive matrices. A simulation study was designed to assess whether the additive procedure is superior to the ultrametric one in recovering distances randomly deleted from complete distance matrices. Our results clearly indicate that the topologies and branch lengths of the trees derived from matrices which were estimated additively are better recovered than those of trees derived from matrices estimated ultrametrically; the original distances are also better recovered with the additive procedure. Except in the case of small matrices with many missing cells for which both methods perform equally well, the additive is generally superior to the ultrametric method for estimating missing cells in distance matrices prior to phylogenetic reconstruction.