Bootstrapping phylogenies: Large deviations and dispersion effects

A large deviation result is established for the bootstrap empirical distribution in a finite sample space, thereby validating both nonparametric and parametric bootstrapping in certain phylogenetic inference problems. The bias previously observed in the bootstrap distribution of the estimated tree topology is shown to stem from dispersion effects in the joint distribution of sample and bootstrap empirical distributions. Both results are examined for maximum likelihood estimation in a three-taxon model having particularly simple geometry. They are also applicable to discrete parameter problems outside of phylogenetic inference.