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 with 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 important to understand the effect of just one long branch. If ML struggles to reconstruct one long branch, then this may have an impact on LBA. In this study, we look at the effect of one long branch on three-taxon tree reconstruction. We show that, counterintuitively, long branches are preferentially placed at the tips of the tree. This can be understood through the use of analytical solutions to the ML equation and distance matrix methods. We go on to look at the placement of two long branches on four-taxon trees, showing that there is no attraction between long branches, but that for extreme branch lengths long branches are joined together disproportionally often. These results illustrate that even small model trees are still interesting to help understand how ML phylogenetic reconstruction works, and that LBA is a complicated phenomenon that deserves further study.

Amino acid changes in disease-associated variants differ radically from variants observed in the 1000 genomes project dataset.

The 1000 Genomes Project data provides a natural background dataset for amino acid germline mutations in humans. Since the direction of mutation is known, the amino acid exchange matrix generated from the observed nucleotide variants is asymmetric and the mutabilities of the different amino acids are very different. These differences predominantly reflect preferences for nucleotide mutations in the DNA (especially the high mutation rate of the CpG dinucleotide, which makes arginine mutability very much higher than other amino acids) rather than selection imposed by protein structure constraints, although there is evidence for the latter as well. The variants occur predominantly on the surface of proteins (82%), with a slight preference for sites which are more exposed and less well conserved than random. Mutations to functional residues occur about half as often as expected by chance. The disease-associated amino acid variant distributions in OMIM are radically different from those expected on the basis of the 1000 Genomes dataset. The disease-associated variants preferentially occur in more conserved sites, compared to 1000 Genomes mutations. Many of the amino acid exchange profiles appear to exhibit an anti-correlation, with common exchanges in one dataset being rare in the other. Disease-associated variants exhibit more extreme differences in amino acid size and hydrophobicity. More modelling of the mutational processes at the nucleotide level is needed, but these observations should contribute to an improved prediction of the effects of specific variants in humans.