Effects of rooting via out-groups on in-group topology in phylogeny

Users of phylogenetic methods require rooted trees, because the direction of time depends on the placement of the root. While phylogenetic trees are typically rooted by using an out-group, this mechanism is inappropriate when the addition of an out-group changes the in-group topology. We perform a formal analysis of phylogenetic algorithms under the inclusion of distant out-groups. It turns out that linkage-based algorithms (including UPGMA) and a class of bisecting methods do not modify the topology of the in-group when an out-group is included. By contrast, the popular neighbour joining algorithm fails this property in a strong sense: every data set can have its structure destroyed by some arbitrarily distant outlier. Furthermore, including multiple outliers can lead to an arbitrary topology on the in-group. The standard rooting approach that uses out-groups may be fundamentally unsuited for neighbour joining.