Data from: Bias in tree searches and its consequences for measuring group supports

When doing a bootstrap analysis with a single tree saved per
pseudoreplicate, biased search algorithms may influence support values
more than actual properties of the data set. Two methods commonly used for
finding phylogenetic trees consist of randomizing the input order of
species in multiple addition sequences followed by branch swapping, or
using random trees as the starting point for branch swapping. The
randomness inherent to such methods is assumed to eliminate any consistent
preferences for some trees or unsupported groups of taxa, but both methods
can be significantly biased. In the case of trees created by sequentially
adding taxa, a bias may occur even if every addition sequence is
equiprobable, and if one of the equally optimal positions for each
terminal to add to the tree is selected equiprobably. In the case of
branch swapping, the bias can happen even when branch swapping
equiprobably selects any of the trees of better score in the
SPR-neighborhood or TBR-neighborhood. Consequently, when the data set is
ambiguous, both random-addition sequences and branch swapping from random
trees may (a) find some of the optimal trees much more frequently than
others, and (b) find some groups with a frequency that differs from their
frequency among all optimal trees. When the data set defines a single
optimal tree, the groups present in that tree may have a different
probability of being found by a search, even if supported by equal amounts
of evidence. This may happen in both parsimony and maximum-likelihood
analyses, and even in small data sets without incongruence.