Maximum likelihood inference of small trees in the presence of long branches

The statistical basis of maximum likelihood (ML), its robustness and the fact that it appears to suffer less from biases lead to it being one of the most popular methods for tree reconstruction. Despite its popularity, very few analytical solutions for ML exist, so biases suffered by ML are not well understood. One possible bias is long branch attraction (LBA), a regularly-cited term generally used to describe a propensity for long branches to be joined together in estimated trees. Although initially mentioned in connection to inconsistency of parsimony, LBA has been claimed to affect all major phylogenetic reconstruction methods, including ML. Despite the widespread use of this term in the literature, exactly what LBA is and what may be causing it is poorly-understood, even for simple evolutionary models and small model trees. Studies looking at LBA have focused on the effect of two long branches on tree reconstruction. However, to understand the effect of two long branches it is also ...