Weighted bootstrapping: a correction method for assessing the robustness of phylogenetic trees

Abstract Background Non-parametric bootstrapping is a widely-used statistical procedure for assessing confidence of model parameters based on the empirical distribution of the observed data 1 and, as such, it has become a common method for assessing tree confidence in phylogenetics 2. Traditional non-parametric bootstrapping does not weigh each tree inferred from resampled (i.e., pseudo-replicated) sequences. Hence, the quality of these trees is not taken into account when computing bootstrap scores associated with the clades of the original phylogeny. As a consequence, traditionally, the trees with different bootstrap support or those providing a different fit to the corresponding pseudo-replicated sequences (the fit quality can be expressed through the LS, ML or parsimony score) contribute in the same way to the computation of the bootstrap support of the original phylogeny. Results In this article, we discuss the idea of applying weighted bootstrapping to phylogenetic reconstruction by weighting each phylogeny inferred from resampled sequences. Tree weights can be based either on the least-squares (LS) tree estimate or on the average secondary bootstrap score (SBS) associated with each resampled tree. Secondary bootstrapping consists of the estimation of bootstrap scores of the trees inferred from resampled data. The LS and SBS-based bootstrapping procedures were designed to take into account the quality of each "pseudo-replicated" phylogeny in the final tree estimation. A simulation study was carried out to evaluate the performances of the five weighting strategies which are as follows: LS and SBS-based bootstrapping, LS and SBS-based bootstrapping with data normalization and the traditional unweighted bootstrapping. Conclusions The simulations conducted with two real data sets and the five weighting strategies suggest that the SBS-based bootstrapping with the data normalization usually exhibits larger bootstrap scores and a higher robustness compared to the four other competing strategies, including the traditional bootstrapping. The high robustness of the normalized SBS could be particularly useful in situations where observed sequences have been affected by noise or have undergone massive insertion or deletion events. The results provided by the four other strategies were very similar regardless the noise level, thus also demonstrating the stability of the traditional bootstrapping method.