Using minimum bootstrap support for splits to construct confidence regions for trees

Many of the estimated topologies in phylogenetic studies are presented with the bootstrap support for each of the splits in the topology indicated. If phylogenetic estimation is unbiased, high bootstrap support for a split suggests that there is a good deal of certainty that the split actually is present in the tree and low bootstrap support suggests that one or more of the taxa on one side of the estimated split might in reality be located with taxa on the other side. In the latter case the follow-up questions about how many and which of the taxa could reasonably be incorrectly placed as well as where they might alternatively be placed are not addressed through the presented bootstrap support. We present here an algorithm that finds the set of all trees with minimum bootstrap support for their splits greater than some given value. The output is a ranked list of trees, ranked according to the minimum bootstrap supports for splits in the trees. The number of such trees and their topologies provides useful supplementary information in bootstrap analyses about the reasons for low bootstrap support for splits. We also present ways of quantifying low bootstrap support by considering the set of all topologies with minimum bootstrap greater than some quantity as providing a confidence region of topologies. Using a double bootstrap we are able to choose a cutoff so that the set of topologies with minimum bootstrap support for a split greater than that cutoff gives an approximate 95% confidence region. As with bootstrap support one advantage of the methods is that they are generally applicable to the wide variety of phylogenetic estimation methods.