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## LAMARC Tutorial, Conclusion: Analyzing the Rest of Your Data

At this point, you should have been able to coax some of your data through the whole LAMARC process, from the converter to actual estimates of parameters. If not, you should read through the basic tutorial so you can do so. But after having done the work for a subset of your data, you now need to figure out what to do for all your data. While the majority of the tutorial so far has been fairly universal, this is where it must by necessity diverge, since everyone's data are different. But we'll try to keep the advice as generic as possible, and sectioned so that you'll know which bits to skip. Let's start with...

### How much data do I need and/or want?

There are several areas you can focus on to expand your data set. You can collect data from more individuals, you can collect data from new genomic regions, and you can extend your sequencing runs off the end of your current genomic regions. All have their advantages and disadvantages.

#### Individuals

We recommend that you collect data from about 15 to 20 individuals per population. Too many less than that, and you might end up with idiosyncratic results, but as you add more individuals, the increase in power gets smaller and smaller, while the increase in the volume of tree-space you need to search goes up greater than polynomially. So, as you add more and more individuals, LAMARC must work harder and harder for less and less payoff.

#### New genomic regions

If you're bursting at the seams to collect new data, this is probably your best bet. Each new genetic region for which you collect data will contain an essentially identical amount of unique information. In addition, the time it takes to analyze a new genetic region is the same as it takes to analyze any other region. The upshot of this is that as you add regions linearly, your estimates are informed by a linear amount of new information, and it takes a linear amount more time to process. Also note that data collected for new genomic regions need not be from the same individuals for which you collected data for your original genomic regions.

#### Extending the sequences of current genomic regions

In general, the problem with adjacent sequences is that they are very likely to have the same genetic heritage as the sequence you already had. So, while you'll increase the resolution of your picture of your current set of trees, you won't get a whole new set of trees as you would if you had spent the same amount of effort sequencing an entirely new genetic region.

The exception to this rule is when you are interested in estimating the recombination rate. In this case, the longer the sequence, the better. The only practical limit is the size of your computer's memory--as more and more recombinations get added to the trees, the tree itself takes up more and more memory, and your computer might slow down as it has a hard time accessing the whole tree at once, and begins to have to store data in less accessible places.

Also remember that LAMARC's current recombination model is to have a single recombination rate over the entire genome. If your organism has, in truth, recombination 'hot spots', and some of your regions have higher recombination rates than others, the reported joint estimate over all regions may be suspect. LAMARC does report the estimated recombination rates for each region, which should help confirm or deny your suspicions about any such hot spots. We are working on incorporating a hot spot model for recombination into future versions of LAMARC and Recombine.

### So, it looks like I have too many individuals. How about I just pick the interesting ones and use them?

No! Nonononono. Especially if by 'interesting' you mean, 'have unique sequences'. The identical sequences are crucial for accurately determining the population size. If you choose to winnow your data, you should instead pick randomly, otherwise you will hopelessly bias your results.

### OK, what about my populations? Can I have too many?

If you have lots of populations (more than, say, about 5), you will probably have so many parameters to estimate that LAMARC cannot estimate any individual parameter very well. If you can constrain your migration model or population size estimates so that not as many independent parameters need be estimated at once, you can start to relax this restriction. Also, collecting more data from multiple regions can also help (keeping in mind that DNA or SNP data is more informative per region than microsatellite data). As a single data point, we have found that 10 unlinked DNA regions generally contain enough information to get reasonable migration estimates from a suite of 5 populations, all exchanging migrants. You can constrain individual migration rates to be constant (and zero, if you wish), or to be equal to one another. One popular constrained migration models is the stepping-stone model where only adjacent populations exchange migrants. You can use LAMARC's menu to set these; see the 'constraints' section of the menu documentation for more details.

### Can I have too few populations?

The possibility for error here is if there are populations in real life for which you have no samples, that are significant nodes in the overall migration pattern of your species. One way to combat this problem is to assign a 'ghost population'--a population which you include in your analysis, but which has no individuals. In the analysis, then, migrants are free to move through this otherwise unknown population. Peter Beerli, who has worked on LAMARC and is currently working on MIGRATE, has found this technique to have moderate but limited effectiveness (see Beerli, P. "Effect of unsampled populations on the estimation of population sizes and migration rates between sampled populations." Mol Ecol. 2004 Apr;13(4):827-36.) However, we have not had good success with it in LAMARC, and currently it is disallowed. If you feel strongly that you need a 'ghost population' analysis in LAMARC, please let us know; we can re-enable the capability, and consider whether it is a good addition to the program in general.

### What happens if I get assignments wrong?

The most problematic of misassignments is when you have claimed that two groups of individuals come from distinct populations when in reality, they come from a single population. In these cases, the estimated migration rates between the two skyrocket, and the trees become a mass of migrations, making the search very inefficient. If you see LAMARC assign very high migration rates between two populations, you may wish to revisit your data and determine if it's possible that what you classified as two populations is in reality a single interbreeding population. Re-analyzing your data with this assumption may then help your analysis. The program STRUCTURE can also be helpful in diagnosing whether two populations are sufficiently distinct or not. Remember that even if two populations are exchanging no migrants today, if they did so in the fairly recent past, they may be genetically homogenized.

### OK, I think I have my data in a good format. Should I do a Bayesian or likelihood run?

From our initial forays into data analysis, this can highly depend on your particular data set. Some of our simulated data sets have worked well on both types of analysis, some data sets work with one and not the other, and some don't seem to work well no matter how you try to analyze them. General Bayesian vs. likelihood issues are detailed in the Bayes tutorial.

### How do I tell if LAMARC is working, then?

If it gives you accurate results!

### Ha, ha.

OK, OK. Your best test is to track run-to-run variability. One way to do this is to simply run LAMARC more than once and compare the output, making sure to use a different random number seed each time. Another way is to increase the number of replicates you perform. This has the advantage of allowing you to 'save' the effort LAMARC spent on the individual replicates so it can use it for its joint estimate over replicates. (Of course, if you have already determined that you needed replicates, the only way to compare your joint estimate over replicates is to run LAMARC more than once.)

In a likelihood run, you will be able to compare the point estimates of your parameters, plus their confidence intervals (if you have profiling turned on). If LAMARC is succeeding, 95% of your point estimates should fall within each other's confidence intervals. If you didn't turn on profiling, you can at least check the standard deviation of your point estimates, and determine their percentage of the average.

In a Bayesian run, the best way to tell if LAMARC is succeeding is by looking at the produced curvefiles. The simplest way to view the curvefiles is in a spreadsheet program like Excel. There's discussion of what to look for in individual curvefiles in the Bayes tutorial, but in general, multiple peaks generally mean that LAMARC may not have been run long enough.

### How do I view these curvefiles, and how would I compare curvefiles from different runs?

We have included a sample spreadsheet (comparing_curvefiles.xls for the Microsoft Excel version; comparing_curvefiles.sxc for the OpenOffice version) from a run with simulated data. The first three sheets are the original curvefiles, imported into the document using the 'tab' delimiter (seed1005, seed401, and seed17, each from the random number seed used to generate that data). The fourth sheet ('Lined_up') is that exact data, copied and pasted into sequential columns, with inserted cells for two of the pairs of columns such that the data for any given Ln(Theta1) are lined up with each other. Then, in the next sheet ('Combined'), the Ln(Theta1) column is filled out with enough values for all three sets of data, and the extra Ln(Theta1) columns are deleted. Finally, the last sheet ('Graph') shows a graph that was created by highlighting the first four columns, selecting 'add graph', choosing the X-Y Scatter Plot graph type, and filling in the axes labels. As you can see, the resulting graph shows that the estimates of Theta 1 are nicely reproducible.

You can also generate nice plots of curvefiles using the R programming language and environment.

### What do I do if LAMARC is failing?

More detail is given in the Search Strategies for LAMARC article, but in brief, your options are:

- Increase the number of 'Initial' chains that collect data before the 'Final' chain(s).
- Run LAMARC longer in the 'Final' chain by either increasing the number of samples (collecting more trees) or increasing the sampling interval (allowing the trees to evolve more between successive samples).
- Tweak the relative amount of time spent on each of the rearrangers.
- Turn on Replication.
- Turn on Heating.
- Collect more genomic data for your organisms.
- Switch your analysis mode from likelihood to Bayesian, or vice versa.
- Do some/all of the above.

### So, once LAMARC is succeeding, what do I do?

If you have the computational resources for it, once you get a good idea of how long LAMARC will take to crunch your data, we recommend doing one final particularly-long run so you get the best possible estimates. If you've done a likelihood analysis, your estimates will be found at the beginning of the output file. If you've done a Bayesian analysis, your point estimates will be found at the beginning of the output file, but you'll probably want to look at the produced curvefiles, if only because they give you pretty graphs to display. But in general, you're done! Go publish. LAMARC's job is complete.

### Who do I thank for these lovely estimates?

The recommended citation is our announcement paper in Bioinformatics for version 2.0 of LAMARC:

Kuhner, M. K., 2006 "LAMARC 2.0: maximum likelihood and Bayesian estimation of population parameters." Bioinformatics 22(6): 768-770.

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