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## Using Tracer with LAMARC

LAMARC can produce output readable by the utility program Tracer, written by Andrew Rambaut and Alexei Drummond. We do not distribute Tracer. It can be found at:

http://tree.bio.ed.ac.uk/software/tracer/

We thank the authors for producing this useful program. It is written in Java and runs on most systems as long as a Java runtime environment is available. Tracer is mainly intended for Bayesian runs. For each parameter being estimated, it can display summary statistics (mean, standard deviation, etc) and a graph of the change in that parameter as the run progresses. It can also show the correlation between pairs of parameters. Finally, it produces a statistic, the Effective Sample Size (ESS), meant to indicate the size of a set of independent data points with the same information as our correlated data points. A low ESS means that even though we may have sampled many data points, due to strong correlation between them we have not obtained much real information. This can happen if our search is rejecting most of its proposals, or if the proposals it accepts are all very close together so that it is not moving freely across the surface.

The files that LAMARC outputs for Tracer (as of version 2.1.2) show all values ever sampled by the program, including any chains used prior to the last final chain. This means that the subset of the data used for parameter estimation will be only the final swath of data, and will not include anything before that. We include it in the Tracer output so you can visualize the entire LAMARC run to better see the parameters as they move from their starting values to their final values, and then (hopefully) level off. If you use Tracer to give you estimates, be sure to tell it to not use the initial section, as it will bias your estimates towards the starting values. Other than that, the estimates Tracer produces should be very similar to the estimates LAMARC produces--the two programs use different curve-smoothing algorithms (LAMARC's is described in this article), but should be drawn from the same underlying data.

In both the Bayesian and Likelihood runs of LAMARC, one of the output parameters will be not the estimated parameters, but the data likelihood values for the trees (in the Likelihood run, this is the sole output value, as it does not sample among other parameter values). These data likelihoods are the log of the probability that the data would be produced on the given tree, and will increase from the start of the run and should eventually level off, just like all other parameters.

Tracer is very useful in diagnosing too-short runs. If the trace graph shows a rising line, rather than a line which plateaus and varies around a particular value, the run is too short. Be aware, however, that while a bad-looking trace nearly guarantees a bad run, a good-looking trace cannot guarantee a good run. If there is a favorable region of parameter space which was never found, no examination of the regions which were found can reveal this.

Here is an example of a Bayesian run whose results for the parameter shown (Theta for the first population) are not satisfactory. Note the systematic upward trend through most of the run length. Even though the trace dips back down at the end, the run has clearly not reached a stable state yet, and should be redone with many more steps.

The authors of Tracer red-flag an Effective Sample Size (ESS) statistic under 100 as indicating a run which is definitely too short, but in some of their discussion express doubt about runs with ESS < 200. We distrust runs with ESS < 200 for any parameter. Unfortunately higher ESS is not a guarantee of good results; note that the ESS of the displayed example is 245.

You should check both trace shape and ESS for each parameter, and doubt a run in which either one is unsatisfactory.

Do note that the values reported from within a LAMARC run labelled "Number of unique sampled values for each parameter" are not ESS values, but rather exactly what that title would suggest. In a sense, they could be termed the 'actual sample size', but in addition to this not being a useful statistical measure, nobody wants to make an acronym out of it.

Tracer cannot be used to track parameter estimates in a likelihood run of LAMARC, as likelihood runs don't make running estimates of their parameters (it would be too expensive). The only use of Tracer in a likelihood run is to monitor the fit of the data to the genealogy (the "data likelihood"). Again, a rising line which does not plateau definitely indicates a too-short run, whereas a nice plateau suggests but does not guarantee a good run.

LAMARC automatically writes a file suitable for Tracer for each chromosomal region it analyzes. The files are called "tracefile_regionname_replicate.txt". So the file containing information on the mtDNA region, first replicate, would be named "tracefile_mtDNA_1.txt". This file can be provided to Tracer as-is using the "Import" option in Tracer's menu.

We welcome any input on how to make Tracer more useful with LAMARC, and visa versa.

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