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– Average Standard Deviation of the Split frequencies: compares the node frequencies between the independent runs (the closer to zero, the better, but it is not clear how small it should be)
– Potential Scale Reduction Factor (PSRF): the closer to one, the better

• By default performs two independent analyses starting from different random trees (mcmc nruns=2)
• Average standard deviation of clade frequencies calculated and presented during the run (mcmc
mcmcdiagn=yes diagnfreq=1000) and written to file
(.mcmc)
• Standard deviation of each clade frequency and potential scale reduction for branch lengths calculated with sumt
• Potential scale reduction calculated for all substitution model parameters with sump

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Model parameter summaries over all 3 runs sampled in files
"Ligia16SCOI28SGulfnoADLGGTRGbygene.nex.run1.p",
"Ligia16SCOI28SGulfnoADLGGTRGbygene.nex.run2.p" etc:
(Summaries are based on a total of 162003 samples from 3 runs)
(Each run produced 60001 samples of which 54001 samples were included)
95% Cred. Interval
----------------------
Parameter Mean Variance Lower Upper Median PSRF *
-------------------------------------------------------------------------------------------
TL{all} 1.578535 0.008255 1.417000 1.771000 1.573000 1.000
r(A<->C){1} 0.036558 0.000133 0.016961 0.061987 0.035555 1.000
r(A<->G){1} 0.405681 0.002305 0.314283 0.502156 0.404811 1.000
r(A<->T){1} 0.044360 0.000120 0.025482 0.068209 0.043489 1.000
r(C<->G){1} 0.022006 0.000120 0.004949 0.047283 0.020532 1.000
r(C<->T){1} 0.472371 0.002269 0.379396 0.565910 0.472279 1.000
r(G<->T){1} 0.019024 0.000079 0.005074 0.039579 0.017873 1.000
pi(A){1} 0.292047 0.000390 0.254211 0.331575 0.291819 1.000
pi(C){1} 0.204875 0.000278 0.173364 0.238514 0.204491 1.000
pi(G){1} 0.214907 0.000324 0.180784 0.251150 0.214522 1.000
pi(T){1} 0.288171 0.000367 0.251355 0.326301 0.287933 1.000
alpha{1} 0.183087 0.000419 0.146653 0.226929 0.181792 1.000
-------------------------------------------------------------------------------------------
* Convergence diagnostic (PSRF = Potential scale reduction factor [Gelman and Rubin, 1992], uncorrected) should approach 1 as runs converge. The values may be unreliable if you have a small number of samples. PSRF should only be used as a rough guide to convergence since all the assumptions that allow one to interpret it as a scale reduction factor are not met in the phylogenetic context.

Nylander, J. A.A. et al. Bioinformatics 2008 24:581-583; doi:10.1093/bioinformatics/btm388
Copyright restrictions may apply.

Empirical Data: two independent runs 300,000,000 generations: complex model with three partitions (by codon): the bad news
Plotted in Tracer

Empirical Data: two independent runs 300,000,000 generations: complex model with three partitions (by codon): the good news; splits were highly correlated between the two runs
Plotted in AWTY: http://ceb.scs.fsu.edu/awty

Empirical Data: two independent runs 300,000,000 generations: complex model with three partitions (by codon): the good news; splits were highly correlated between the two runs
What caused the difference in posterior probabilities? Estimation of particular parameters
Plotted in AWTY: http://ceb.scs.fsu.edu/awty

Yes we have reached convergence:
Do we have a large enough sample of the posterior?
• Long runs are better than short one, but how long?
• Good mixing: “Examine the acceptance rates of the proposal mechanisms used in your
• analysis (output at the end of the run)
• The Metropolis proposals used by MrBayes work best when their acceptance rate is neither too low nor too high. A rough guide is to try to get them within the range of 10 % to 70 %”

Analysis used 2373953.05 seconds of CPU time on processor 0
Likelihood of best state for "cold" chain of run 1 was -9688.70
Likelihood of best state for "cold" chain of run 2 was -9865.21
Likelihood of best state for "cold" chain of run 3 was -9887.59
Likelihood of best state for "cold" chain of run 4 was -9895.35
Acceptance rates for the moves in the "cold" chain of run 1:
With prob. Chain accepted changes to
42.86 % param. 1 (revmat) with Dirichlet proposal
21.42 % param. 2 (revmat) with Dirichlet proposal
55.92 % param. 3 (revmat) with Dirichlet proposal
29.18 % param. 4 (state frequencies) with Dirichlet proposal
12.22 % param. 5 (state frequencies) with Dirichlet proposal
24.61 % param. 6 (state frequencies) with Dirichlet proposal
41.02 % param. 7 (gamma shape) with multiplier
31.74 % param. 8 (gamma shape) with multiplier
79.95 % param. 9 (gamma shape) with multiplier
40.16 % param. 10 (rate multiplier) with Dirichlet proposal
15.80 % param. 11 (topology and branch lengths) with extending TBR
23.62 % param. 11 (topology and branch lengths) with LOCAL

f (

| X )
Posterior probability distribution tree 1 tree 2
Parameter space tree 3


Metropolis-coupled
Markov chain Monte
Carlo a. k. a.
MCMCMC a. k. a.
(MC) 3 cold chain heated chain

cold chain hot chain

cold chain hot chain

cold chain hot chain

cold chain unsuccessful swap hot chain

cold chain hot chain

cold chain hot chain

cold chain successful swap hot chain

cold chain hot chain

cold chain hot chain

cold chain successful swap hot chain

cold chain hot chain

(Only if convergence diagnostics indicate problem!)
• Change tuning parameters of proposals to bring acceptance rate into the range 10 % to 70 %
• Propose changes to ‘difficult’ parameters more often
• Use different proposal mechanisms
• Change heating temperature to bring acceptance rate of swaps between adjacent chains into the range 10 % to
70 %.
• Run the chain longer
• Increase the number of heated chains
• Make the model more realistic

Target distribution
Too modest proposals
Acceptance rate too high
Poor mixing
Too bold proposals
Acceptance rate too low
Poor mixing
Moderately bold proposals
Acceptance rate intermediate
Good mixing