Bootstrap values are probably the most popular and easiest to understand support values. Bootstrap involves resampling with replacement from one's molecular data with to create fictional datasets, called bootstrap replicates, of the same size.
The bootstrap values belong to a wide category of values called support values. Support values in general are used to give some indication of the degree to which one can be confident that the branch represents some "signal" present in the data.
In particular, bootstrap values show how robust the branches in the tree are, that is, how resistant they are to perturbation in the data. They are obtained by re-sampling columns in the data matrix, building trees from such re-sampled matrices, and looking at the proportion of the obtained trees that contain a given branch. The re-sampling is usually done around 100 or 1000 times.
A low bootstrap value means that if the tree is built using a subset of the data, it is likely that this branch will not appear. A high bootstrap value means that the branch will likely appear on a tree built from such a re-sampled matrix. This does not necessarily mean that the branch is more likely to represent the true historical relationships, though: sometimes, reconstruction artifacts can be robust.
Evolutionary trees are often estimated from DNA or RNA sequence data. In 1985, Felsenstein’s method, which in concept is a straightforward application of the bootstrap, is widely used, but has been criticized as biased in the genetics literature. Felsenstein introduced the use of the bootstrap in the estimation of phylogenetic trees. His technique, which has been widely used, provides assessments of “confidence” for each clade of an observed tree, based on the proportion of bootstrap trees showing that same clade. However Felsenstein’s method has been criticized as biased. Felsenstein’s method provides a reasonable first approximation to the actual confidence levels of the observed clades. More ambitious bootstrap methods can be fashioned to give still better assessments of confidence.
The interpretation of bootstrap values has been both murky and controversial. Felsenstein proposed that bootstrap values of 95% or greater be considered statistically significant and indicate “support” for a clade; alternative nodes can be rejected if they occur in less than 5% of the bootstrap estimates. However, bootstrap confidence levels apply to single nodes, they are not joint confidence statements. Thus, although two clades may each be supported at 95% and are thus not contradictory, the confidence interval that includes both clades may be only 90%, and the joint confidence drops as additional nodes are considered. Joint confidence will thus be necessarily low for a large tree, even if all nodes are strongly supported. A majority-rule consensus tree summarizing all of the bootstrap replicates provides a set of noncontradictory nodes, each interval that contains the phylogeny that would be estimated from repeated sampling of many characters from the underlying set of all characters, NOT the true phylogeny.