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.