Supplementary material for: Long branch attraction biases in phylogenetics

Long branch attraction is a prevalent form of bias in phylogenetic
estimation but the reasons for it are only partially understood. We argue
here that it is largely due to differences in the sizes of the model
spaces corresponding to different trees. Trees with long branches together
allow much more flexible internal branch-length parameter estimation.
Consequently, although each tree has the same number of parameters, trees
with long branches together have larger effective model spaces. The
problem of long branch attraction becomes particularly pronounced with
partitioned data. Formulation of tree estimation as model selection leads
us to propose bootstrap bias corrections as cross-checks on estimation
when long branches end up being estimated together.