In our lab, we have been using bootstrap statistics and posterior probabilities (in case of Bayesian trees) to assess clade supports in phylogenetic analyses. I was wondering if there were other statistics that we are unaware of.
Thanks in advance for sharing the statistics you have been using.
Here are some phylogenetic support statistics and my thoughts on them:
- Bootstraps are generated from analysing replicate matrices built from the original datasets, taking random characters (= sites, loci, phenotype, etc) and allowing repetition or omission ("resample with replacement"). The bootstrap statistic tells you whether the node is strongly driven by a relatively small number of characters, or if it has general signal support across the dataset. This can be misled by strong but spurious sites, or a model mis-specification which promotes sites without true phylogenetic signal to drive the inference.
- Jack-knife is the same as bootstrap, except it is a sub-sample without replacement; ie, just a (usually) random matrix of the same number of taxa, but fewer characters. Again this provides insight on whether the topology is driven by a minority of the dataset. It isn't very common these days, probably because bootstrap is more statistically reasonable since bias is probably minimised by preserving matrix dimensions. Jack-knife can still be useful though, if interpreted appropriately.
- Bremer values attempt to return statistical support by maximising the homologies of grouped topologies. The method asks if there are alternative ways of grouping homologous characters to create trees which are of a similar length. A statistic of 3 is reasonable support, and 5 is strong support. (I haven't used this method for years, so please correct me if I am wrong about this). It is misled by being fairly naive about the nature of the data and the model.
- Posterior probability in a Bayesian context is an expression of how credible the node is, given the data and the model used to infer the topology. This of course is very fashionable these days, perhaps reasonably so since PPs are more easily interpreted, and integrate a more holistic perspective on both the data and the model. However, PPs can be misled by model-misspecification, leading to the Bayesian process being unable to properly sample the parameter distribution of the model. Even when the model and Markov process is appropriately specified, the nature of the dataset may lead PPs to falsely converge into local maxima of parameter space, so always view with caution. They also tend to be a bit binary - once converging, PPs either tend towards 1, or plummet towards 0. You'll have to think about what this means for yourself, but I find this lack of granularity can hinder interpretation.
- Concordance factors I am less familiar with (so please correct me if I am not right here :) and only applicable to phylogenomic datasets. I believe a gene concordance factor (gCF) sub-partitions the dataset into genes, infers a tree from each, and returns a statistics for the prevalence of that node across the single-gene datasets that are analysed, in the context of the concatenated topology. Site concordance factors (sCF) do the same for sites. Of course, that means applying a model to each gene, so things can get as sophisticated as you like. But I think this is a good things, and can provide powerful insight on the nature of phylogenetic ambiguity, especially in concert with other statistical supports mentioned here.
Preprint New methods to calculate concordance factors for phylogenomic datasets
I am quite fond of the approximate Likelihood Ratio Test (aLRT). which is available in PhyML.
It has very good statistical properties.
I usually label my trees with all three but beware the posterior probability unless you are very knowledgeable about the priors you choose rather than using the defaults (see Yang, 2014, Molecular Evolution: A Statistical Approach).
Here I assume that you are using DNA or proteins. If morphological, then the same principles apply.
An aLRT statistic sounds like a good addition. Thank you, Patrice Showers Corneli for the input.
Here are some phylogenetic support statistics and my thoughts on them:
- Bootstraps are generated from analysing replicate matrices built from the original datasets, taking random characters (= sites, loci, phenotype, etc) and allowing repetition or omission ("resample with replacement"). The bootstrap statistic tells you whether the node is strongly driven by a relatively small number of characters, or if it has general signal support across the dataset. This can be misled by strong but spurious sites, or a model mis-specification which promotes sites without true phylogenetic signal to drive the inference.
- Jack-knife is the same as bootstrap, except it is a sub-sample without replacement; ie, just a (usually) random matrix of the same number of taxa, but fewer characters. Again this provides insight on whether the topology is driven by a minority of the dataset. It isn't very common these days, probably because bootstrap is more statistically reasonable since bias is probably minimised by preserving matrix dimensions. Jack-knife can still be useful though, if interpreted appropriately.
- Bremer values attempt to return statistical support by maximising the homologies of grouped topologies. The method asks if there are alternative ways of grouping homologous characters to create trees which are of a similar length. A statistic of 3 is reasonable support, and 5 is strong support. (I haven't used this method for years, so please correct me if I am wrong about this). It is misled by being fairly naive about the nature of the data and the model.
- Posterior probability in a Bayesian context is an expression of how credible the node is, given the data and the model used to infer the topology. This of course is very fashionable these days, perhaps reasonably so since PPs are more easily interpreted, and integrate a more holistic perspective on both the data and the model. However, PPs can be misled by model-misspecification, leading to the Bayesian process being unable to properly sample the parameter distribution of the model. Even when the model and Markov process is appropriately specified, the nature of the dataset may lead PPs to falsely converge into local maxima of parameter space, so always view with caution. They also tend to be a bit binary - once converging, PPs either tend towards 1, or plummet towards 0. You'll have to think about what this means for yourself, but I find this lack of granularity can hinder interpretation.
- Concordance factors I am less familiar with (so please correct me if I am not right here :) and only applicable to phylogenomic datasets. I believe a gene concordance factor (gCF) sub-partitions the dataset into genes, infers a tree from each, and returns a statistics for the prevalence of that node across the single-gene datasets that are analysed, in the context of the concatenated topology. Site concordance factors (sCF) do the same for sites. Of course, that means applying a model to each gene, so things can get as sophisticated as you like. But I think this is a good things, and can provide powerful insight on the nature of phylogenetic ambiguity, especially in concert with other statistical supports mentioned here.
Preprint New methods to calculate concordance factors for phylogenomic datasets
It is interesting to see how certain statistics are more commonly used than others. It would be nice to know the reasons though.
Madhav
I have used all of Alastair's methods on occasion.
Each of these measures have different purposes because they measure different qualities of the data.Some are customary for parsimony analysis and some for genes and others for everything.
If I remember right, concordance factors are used quite a lot for population genetics.
The jacknife should be faster than a bootstrap because only part of the full sequence is sampled each time. Shorter sequences, faster analysis (except for NJ which is so fast anyway who would notice.
Couldn't agree more about the currently fashionable Bayes world (rather more recent than the more robust ML methods). But with time, maybe the priors controversy will settle as we learn more about effective unbiased priors.
Or maybe not, There is a very strong preference among the untrained for newer methods. Actually Bayes has been around for a very long time in statistics if not trees and has always been controversial primarily because of the difficulty of identifying nice priors.
Dear Alastair R Tanner, it is a wonderful summary. It is greatly appreciated!!
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