This could be done using distance matrices of alignments or likelihood scores of topologies. I would like to know if one topology is significantly less likely than another (maximum likelihood) topology.
ML: The Swofford-Olsen-Waddell-Hillis (SOWH) test implemented in the package SOWHAT uses parametric resampling to generate a null distribution of log-likelihoods from the data to be used for hypothesis testing. This seems like a strong approach.
http://sysbio.oxfordjournals.org/content/early/2015/07/30/sysbio.syv055.abstract
BI: Bayes factors are very useful in model testing when applied correctly. However, when testing for a significant difference between the ML tree and an alternative hypothesis, posterior model probabilities are easier to calculate and interpret. Here are two supporting articles:
http://sysbio.oxfordjournals.org/content/early/2013/06/14/sysbio.syt029.full
http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0123301
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