different rates and ASR states inferred for identical and near-identical characters

[igoryanovich]

MrBayes strangely outputs very different values for the site rates and ASR states in identical or very similar characters.

What is most worrying here is not the reported rates and ASR states as such, but rather the possibility that this might be indicative of a deeper problem that makes the whole phylogenetic analysis incorrect. If the problem is simply with the reporting rather than e.g. MCMC sampling, that would be a huge relief.

Here in the text, I illustrate the problem. The attachment contains a Readme with a bit more information, .nex files for replicating the issue, and .pstat files from the analyses. I will of course be happy to send logs and other output if that could help.

Two examples (see the attachment for the files to reproduce the issue)

1. Characters 6-7 are both all-1. Yet the rates reported for them and (consistently with that) the ASR states reported differ: char. 6 get a low rate and a high prob of 1 at the constrained node, while char. 7 unexpectedly gets a high rate of change and a low prob. of 1 at the ancestral node of interest.

r(6)	8.146398e-01
r(7)	3.238141e-01

p(1){6@H}	9.999999e-01
p(1){7@H}	1.818785e-03

2. Characters 16-19 all have a single 1, in one of the taxa within the clade with the MRCA for which ASR was requested. Yet the rates differ a lot: character 16 gets a slow rate, while characters 17-19 get fast rates (which is the expected behavior for a character with a single 1). Correspondingly, the ASR state-1 prob-s are close to 1 for character 16, and low for characters 17-19.

r(16)	2.618686e-01	
r(17)	1.858213e+00	
r(18)	1.908333e+00	
r(19)	2.004236e+00	

p(1){16@H}	9.998777e-01
p(1){17@H}	2.413064e-03
p(1){18@H}	4.967924e-03	
p(1){19@H}	6.421850e-03

I have not checked by hand if the rates reported correspond well to the ASR reconstructions, but the two are at least related in the direction in which we'd expect them to if they were in the correct relation.

The behavior appears systematic across runs and insensitive to the random seed, but sensitive to the order of characters in the matrix

The inferences appeared to be the same, modulo small numerical differences, across different identical runs of MrBayes (in the sense of separate analyses, not multiple runs within one analysis), as well as across analyses with different priors (e.g., with a different tree prior than in the attachment) - in the sense that it is the character 7 that gets an unexpectedly low ASR prob. of 1 at the relevant node, and character 16 that gets an unexpectedly high ASR prob. of 1. So there appears to be a systematic component to the issue.

Similarly, explicitly setting two different random seeds did not appear to change much (see .nex and .pstat files with suffixes -seed-100 and seed-700 in the attachment).

However, when I tried to shift the characters' position in the matrix and ran an otherwise identical analysis, the estimates changed (see the attachment). For example, characters 6-7 turned into 5-6, and here are the estimates:

r(5)	3.242324e-01
r(6)	3.290250e-01

p(1){5@H}	9.999999e-01
p(1){6@H}	6.412743e-03

What is the environment that you run MrBayes in?

• Operating system (including variant and release): OS X 10.11
• Version of MrBayes: 3.2.6, with a slight custom change (turned off the prohibition on some coding schemas for standard characters; irrelevant for the current issue)
• If possible, include the output of the Version command in MrBayes below:

   Version                                                                       
                                                                                 
   MrBayes v3.2.6                                                                 `

rates-ASR-problem-example.zip