topological.approx.ess()This function calculates the approximate ESS of tree topologies fromall of the chains. It returns a data frame with approximate ESS values,which can be used to decide if the chain has been run for long enoughfor sufficient samples to be collected. The approximate ESS ismathematically similar to the ESS used for continuous parameters, but incertain cases an upper bound will be provided rather than a pointestimate. These are represented by ‘<’, and ‘=’ in the ‘operator’column of the data frame respectively.
approx.ess <- topological.approx.ess(salamanders, burnin = 50)Which gives you a data frame that looks like this:
operator approx.ess chain1 = 243.0683 AMOTL2.run12 = 134.2827 AMOTL2.run23 = 222.0624 LHX2.run14 = 251.0000 LHX2.run25 = 251.0000 TRMT5.run16 = 251.0000 TRMT5.run2RWTY outputs
RWTY outputs a number of useful plots for exploring the performanceof MCMC chains.
Parameter trace plots
If a logfile is provided, RWTY will produce a trace plot of the valueof each column in the log file as a function of position in the chain.If you have multiple chains, the plots will be faceted by chain (you canturn this off usingfacet = FALSE when callinganalyze.rwty(). The title of each plot shows the EffectiveSample Size (ESS) of the parameter. In general, you should aim to haveESS > 200 for all parameters.
salamanders.rwty$pi.C
Parameter correlation plots
If a logfile is provided, RWTY will produce a scatter plot matrixfrom the columns of the log file, along with the topological distancefrom the starting tree. Because the log file output of many MCMCprograms can contain a large number of columns, the default behavior ofmakeplot.pairs is to only plot the topological distance along with thefirst two data columns. In the density plots on the diagonal, red valuesindicate values outside the 95% CI. In the scatter plots in the lowerleft, brighter and more yellow colors indicate samples from later in thechain.
salamanders.rwty$AMOTL2.run1.correlations
If you would like to view correlations between likelihood, topology,and model parameters, you can do so by passing a vector of parameternames or “all” to the params argument of makeplot.pairs oranalyze.rwty.
data(fungus)plotparams <- c("LnL", "pi.A.", "pi.T.")makeplot.pairs(fungus$Fungus.Run1, burnin = 20, params = plotparams)
Tree topology trace plot
RWTY will produce a plot of tree topologies that is similar to thosefor parameters. In these plots, the y-axis represents the distance ofeach tree in the chain from the last tree of the burnin of the firstchain. These plots can reveal whether the MCMC was sampling from astationary distribution of chains (in which case it should be relativestable) or whether it is moving between modes (in which case you mightsee large jumps). They can also show how well the chain is mixing withrespect to tree topologies. Well mixed chains will show the topologytrace jumping rapidly between values. Poorly mixed chains will showchains remaining at similar values in successive samples. Topologytraces can also reveal whether different chains are sampling differentbits of tree space, in which case the stationary distrubtions will showtraces at different y values on the plot. Finally, the topology tracecontains an estimate of the ESS (called the approximate ESS) of treetopologies. Note that this estimate is only useful if the trees aresampled from a stationary distribution.
salamanders.rwty$topology.trace
Autocorrelation plots
These plots demonstrate the change in average tree distance betweentrees at different sampling intervals. A well-mixed chain (in whichsequential samples of tree topologies are effectively independent) willshow flat lines on these plots. In a chain that is mixing poorly withrespect to tree topologies, you will see the plot rising to anasymptote. This reflects the fact that are close to each other in thechain are more similar than trees that are further away, otherwise knownas autocorrelation.
salamanders.rwty$autocorr.plot
Treespace plots
These plots demonstrate the movement of the chain in two dimensionalrepresentations of treespace. The tree space is based on an NMDS scalingof the distances between trees, much like TreeSetViz. The space iscreated using all chains together, so the treespaces represented fordifferent chains are comparable. If all chains are sampling similar treetopolgoies, then the treespace plots will look similar for both chains.In this case, we can see that independent runs of the same gene aresampling from similar regions of tree space. But that chains fromdifferent genes are sampling from different regions of treespace.
salamanders.rwty$treespace.heatmapsalamanders.rwty$treespace.points.plot
Since the salamanders data comes from different genes, and thosegenes are obviously sampling different bits of tree space, it might bemore informative to compare the replicate runs of each geneindividually.
salamanders.treespace = makeplot.treespace(salamanders[1:2], burnin = 50, n.points = 200, fill.color = "LnL")salamanders.treespace$treespace.heatmapsalamanders.treespace$treespace.points.plot
This shows that the replicate analyses of the same gene are samplingvery similar parts of treespace.
Slidingwindow and cumulative split frequency plots
These plots show the split frequencies of clades in the chain, eitheras the frequency within a sliding window or as the frequency calculatedfrom cumulative samples in the chain at various points in analysis. Bydefault they show the 20 clades with the highest standard deviation ofsplit frequencies within each sample (e.g. the standard deviation of thesplit frequencies of a given clade in a given chain, across all slidingwindows). In an analysis that is mixing well, we expect the frequenciesin the sliding window to move around a lot, but the frequencies in thecumulative plot should level off. If the frequencies in the cumulativeplot have not levelled off, it might be necessary to run the chain forlonger. Plots can be produced for single chains, or for multiplechains.
salamanders.rwty$splitfreqs.sliding.plotsalamanders.rwty$splitfreqs.cumulative.plot
For a single chain:
makeplot.splitfreqs.cumulative(salamanders[[1]])makeplot.splitfreqs.sliding(salamanders[[1]])
These plots show the change in split frequencies of clades in thechain, either as the frequency within a sliding window or as thefrequency calculated from cumulative samples in the chain at variouspoints in the analysis. They are analagous to the previous two plots,but instead of showing split frequencies of clades on the y axis, theyshow the change in split frequencies of all clades on the y axis. Thesolid line is the average change in split frequencies (ACSF), and theribbons show the 100%, 95%, and 75% quantiles of the Change in SplitFrequencies (CSF). Ideally, we’d see the sliding window change in splitfrequencies remaining above zero but without big jumps (which wouldindicate the chain being stuck in one region of tree space, then movingto another), and we’d see the cumulative change in split frequenciesapproaching zero (indicating that the chain has settled on sampling froma single reqion of tree space, and that adding additional samples is notmaking any appreciable difference to the estimates of clade posteriorprobabilities one might make from the analysis).
salamanders.rwty$acsf.sliding.plotsalamanders.rwty$acsf.cumulative.plot
Multiple chains only
The following plots are only produced with analyze.rwty() is passedlist of rwty.chain object that contains more than one chain.
This plot shows the ASDSF of all clades that appear in any of thechains, calculated from cumulative samples in the chain at variouspoints in the analysis. The solid line shows the ASDSF, and the ribbonsshow the 75%, 95%, and 100% quantiles of the Standard Deviation of SplitFrequencies (SDSF) across clades. I.e. the upper line of the grey ribbonshows the clade with the 87.5% highest SDSF between chains, and thelower line of the grey ribbon shows the clade with the 12.5% highestSDSF. Each generation in the plot represents the distribution of SDSFsif the chains were all stopped at that point. The lower the ASDSF, themore the chains agree on split frequencies. In general we expect theSDSF to get lower as the chains progress, and to eventually reach anasymptote at some low value once all the chains have been sampling froma stationary distribution for a long time. Because we are usuallyintersted in the right-hand end of this graph, where the ASDSF valuescan be much lower than at the start of the chain, the y axis is plottedon a log10 scale.
Note that the points and line represent the mean, not the median,SDSF. For this reason it is possible for the line to fall outside of theinner ribbons with the distribution of SDSFs is highly skewed.
makeplot.asdsf(salamanders[c(1,2)])
Split frequency scatterplotmatrix
These plots are another way of visualizing the agreement ordisagreement between the regions of tree space that chains have sampled.For each pair of chains, the cumulative final frequency of each clade(which is also our best estimate of that clade’s posterior probability)is plotted against ts frequency in another chain in the lower triangle,and the the correlation (Pearson’s R) and ASDSF of each pair of chainsis shown in the upper triangle.
salamanders.rwty$splitfreq.matrix
ASDSF tree
This plot shows the similarity of split frequencies between chains.Chains with the most similar split frequencies be clustered together inthe tree. This plot can quickly reveal which chains are sampling similarand different regions of tree space.
salamanders.rwty$asdsf.tree
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