Non-parametric bootstrapping of partitioned datasets

Non-parametric bootstrapping is one of the most commonly used methods for branch support assessment. Unlike Bayesian posterior probability values, which are influenced by a priori data partitioning, non-parametric bootstrapping is usually applied to unpartitioned (combined) datasets. The resulting bootstrap support values are misleading in that they do not measure how well clades are supported by all the partitions, unless all partitions are equal in size (i.e., number of characters). Since most empirical studies include data partitions that are heterogeneous in size, our current bootstrapping approach for partitioned datasets (i.e., bootstrapping the combined dataset) is not adequate. Here I propose a simple modification to non-parametric bootstrapping that takes a priori data partitioning into account by obtaining bootstrap replicates for each partition separately and combining them in such a way that the size (i.e., number of characters) of each partition is taken into account. With this "corrected" bootstrap support value, characters from smaller partitions will have greater influence on final bootstrap values, and those in larger partitions relatively less influence than they would for unpartitioned data.