Stacks

populations

The populations program will analyze a population of individual samples computing a number of population genetics statistics as well as exporting a variety of standard output formats. A population map specifying which individuals belong to which population is submitted to the program and the program will then calculate population genetics statistics such as expected/observed heterozygosity, π, and FIS at each nucleotide position. The populations program will compare all populations pairwise to compute FST. If a set of data is reference aligned, then a kernel-smoothed FST will also be calculated. The populations program can also compute a number of haplotype-based population genetics statistics including haplotype diversity, ΦST, and FST’. For more information on how to specify a population map, see the manual.

The populations program provides strong filtering options to only include loci or variant sites that occur at certain frequencies in each population or in the metapopulation. In addition, the program accepts whitelists and blacklists if you want to include a specific list of loci (or exclude a specific list of loci). For more information on whitelists and blacklists, see the manual.

Program Options

populations -P dir [-O dir] [-M popmap] (filters) [--fstats] [-k [--sigma=150000] [--bootstrap [-N 100]]] (output formats) populations -V vcf -O dir [-M popmap] (filters) [--fstats] [-k [--sigma=150000] [--bootstrap [-N 100]]] (output formats)

Data Filtering:

Locus stats:

Fstats:

Kernel-smoothing algorithm:

File output options:

Genetic map output options (population map must specify a genetic cross):

Additional options:

Kernel-smoothing statistical values along a reference genome

If your data are aligned to a reference genome, then it is possible to ask populations to produce a kernel-smoothed average of your statistical point values along the genome. This translates your point values into a continuous set of values along a chromosome/scaffold. If --smooth is enabled, for each per-population statistical value, including FIS, π, and the haplotype-level measures of π; and for each population-pair value, such as FST, and the haplotype-level values of DXY, φST, etc. will be smoothed along the chromosome.

This is diagrammed in the image to the right. The sliding window is defined by a Gaussian distribution (pictured as a red arc, with f(x) defined in the image). The window is centered over each successive variant site along the chromosome. The size of the window is determined by σ or one standard deviation of the Gaussian distribution. The width of the window, in each direction, then, is 3 x σ, or three standard deviations in length (marked in the figure). The sigma value is by default 150 Kbp in length, giving a window that is 3 x 150 = 450 Kbp on one side, or 900 Kbp in total length (including both tails). This value can be set using the --sigma option to populations.

The smoothed values are calculated by weighting the central value (the variant site the window is centered on), by all of the nearby values — stretching out 3σ in either direction. These nearby values are weighted more heavily when they are closer to the central value. The Gaussian distribution naturally gives the weights for the nearby values.

So, increasing σ (with the --sigma option) will smooth values out further and decreasing it will give a more coarse, or jagged set of values. If your genome is large, it makes sense to increase the size of the window and vice-versa.

Two examples can be seen to the right, one for φST and the other showing the smoothed values for DXY.

Bootstrap resampling

The bootstrap resampling procedure is designed to determine the statistical significance of a particular sliding window value relative to the generated (bootstrapped) empirical distribution. Bootstrap resampling will generate a p-value describing the statistical significance of a particular kernel-smoothed sliding window. Bootstrap resampling allows us to move from single point values being statistically significant (or not), to regions of the genome being statistically significant (or not).

In Stacks v2, bootstrapping is a two stage process that requires the data be aligned to a reference genome. First, the population statistical values must be archived, and then in a subsequent run, this archive of values can be pre-loaded so it is available as a source for the resampling proceedure.

The bootstrap resampling process will center a window on each variable nucleotide position in the population and resample it X times (with replacement), and then calculate a p-value. Bootstrap resampling can be applied to all smoothed values, including the population summary statistics FIS, Π, and haplotype diversity, as well as the calculation of FST and ΦST between pairs of populations. If you have tens of thousands of variable sites (not unusual) and lots of populations, this calculation has to be repeated for every variable site in each population to bootstrap the summary statistics and for all variable sites between each pair of populations for FST and ΦST. So, bootstrap resampling can take a while. The run time can be decreased by enabling multiple threads (--threads) to the populations program.

In Stacks v2, the populations program only loads one chromosome/scaffold at a time into memory. So, when computing smoothed population statistics on chromosome 1, populations has not loaded or computed the corresponding values on chromosome 2, 3, etc. To conduct bootstrapping for sliding windows on chromosome 1, populations must be able to resample from the full set of statistical values (that have not yet been computed). To maintain efficency, bootstrapping is done over two or more runs. During the first run, populations is instructed to archive statistical values with the --bootstrap-archive flag. This flag will cause the file, populations.bsarchive.tsv to be created and populated in the populations output directory. This file contains all the population statistics stored in a very simple and efficient text file. If a particular statistic is not enabled during this stage (e.g. --fstats), than those statistical values will not be available for bootstrap resampling.

Once the archive is created, the user can re-run populations, selecting one of the standard --bootstrap* flags to enable resampling. This can be done as many times as is desired, as long as the archive remains.

Since bootstrapping is so computationally intensive, there are several command line options to the populations program to allow one to turn bootstrapping on for only a subset of the statistics. In addition, a bootstrap "whitelist" is available so you can choose to only bootstrap certain loci (say the loci on a single chromosome). This allows one to take the following strategy for bootstrapping to appropriate levels:

  1. Bootstrap all loci (for example) to 1,000 repetitions.
  2. Identify those loci that are below some p-value threshold (say 0.05).
  3. Add these loci to the bootstrapping whitelist.
  4. Bootstrap again to 10,000 repetitions (now only those loci in the whitelist will be bootstrapped).
  5. Identify those loci that are below some p-value threshold (say 0.005)
  6. Add these loci to the bootstrapping whitelist.
  7. Bootstrap again to 100,000 repetitions (now only those loci in the whitelist will be bootstrapped).
  8. And so on to the desired level of significance...

If instead you are interested in the statistical significance of a particular point estimate of an FST measure, you will want to use the p-value from Fisher's Exact Test, which is calculated for each variable position between pairs of populations and is provided in the FST output files.

Example Usage

  1. Calculate population statistics in a single population and output a Variant Call Format (VCF) SNP file. Run populations on 8 processors:

    ~/% populations -P ./stacks/ --vcf -t 8

  2. Include multiple populations using a population map, and turn on kernel smoothing for π, FIS, and FST (data must be reference aligned for smoothing):

    ~/% populations -P ./stacks/ --popmap ./samples/popmap --smooth -t 8

  3. Filter input so that to process a locus it must be present in 10 of the populations and in 75% of individuals in each population:

    ~/% populations -P ./stacks/ --popmap ./samples/popmap --smooth -p 10 -r 0.75 -t 8

  4. Output data for STRUCTURE and in the GenePop format. Only write the first SNP from any RAD locus, to prevent linked data from being processed by STRUCTURE:

    ~/% populations -P ./stacks/ --popmap ./samples/popmap --smooth -p 10 -r 0.75 -f p_value -t 8 --structure --genepop --write-single-snp

  5. Include a whitelist of 1,000 random loci so that we output a computationally manageable amount of data to STRUCTURE:

    ~/% populations -P ./stacks/ --popmap ./samples/popmap --smooth -p 10 -r 0.75 -f p_value -t 12 --structure --genepop --write-single-snp -W ./wl_1000

    Here is one method to generate a list of random loci from a populations summary statistics file (this command goes all on one line):

    ~/% grep -v "^#" populations.sumstats.tsv | cut -f 1 | sort | uniq | shuf | head -n 1000 | sort -n > whitelist.tsv

    This command does the following at each step:

    1. Grep pulls out all the lines in the sumstats file, minus the commented header lines. The sumstats file contains all the polymorphic loci in the analysis.
    2. cut out the second column, which contains locus IDs
    3. sort those IDs
    4. reduce them to a unique list of IDs (remove duplicate entries)
    5. randomly shuffle those lines
    6. take the first 1000 of the randomly shuffled lines
    7. sort them again and capture them into a file.

  6. Invoke bootstrap resampling to generate p-values reflecting the statistical significance of regions of the genome defined by kernel-smoothed statistics. First, we have to run populations and instruct it to archive our statistical values so they are available for the bootstrapping process:

    ~/% populations -P ./stacks --popmap ../popmap.tsv --fstats --bootstrap-archive -t 14

    Second, once we have generated the archive, we can re-execute populations and tell it to bootstrap resample. Here we also increase the default number of repetitions to 1000. We could also choose one of the --bootstrap-* flags to only bootstrap a particular type of statistic we are interested in to save time:

    ~/% populations -P ./stacks --popmap ../popmap.tsv --fstats --bootstrap --bootstrap-reps 1000 -t 14

Program Outputs

The populations program has a number of standard outputs, besides any particular export that is asked for. The formats of these files are described in detail in the manual.

  1. populations.log: This file contains everything output on the screen, including the version number of Stacks and when it was run. It also includes a lot of useful information describing the data after filters have been applied, including how many loci were discarded/kept, the mean length of loci, and mean number of sites.
  2. populations.log.distribs: This file contains a number of distributions describing the data. The distribution are provided in two forms: prior to filtering and after filtering. You can view the file manually, or you can use the stacks-dist-extract utility we provide to pull out a particular distribution. One distribution that can tell you a lot about your data is the number of samples per locus, pre- and post-filtering. You can extract it like this:

    % stacks-dist-extract populations.log.distribs samples_per_loc_prefilters # Distribution of valid samples matched to a catalog locus prior to filtering. n_samples n_loci 1 17857 2 6103 3 3855 4 4253 5 5591 6 2786 7 3264 8 6518 9 41362 10 40333

    You can see in this data set that more than 40k loci each were found in 9 or 10 samples. But that 17k loci were only found in a single sample -- these loci are likely unreliable.

    When we look at this distribution after filtering, we can see the effect of filtering out the low-value loci:

    % stacks-dist-extract populations.log.distribs samples_per_loc_postfilters # Distribution of valid samples matched to a catalog locus after filtering. n_samples n_loci 8 3040 9 41362 10 40333

  3. populations.sumstats.tsv: This file contains summary statistics describing every SNP found in every population defined in the population map. This includes the frequecy of alleles, expected/observed heterozygosity, π, FIS, and so on.
  4. populations.hapstats.tsv: This file contains summary statistics describing every locus (phased SNPs) found in every population defined in the population map. This includes the frequecy of haplotypes, gene and haplotype diversity.
  5. populations.sumstats_summary.tsv: This file contains population-level, mean summary statistics.
  6. If F-statistics was enabled, populations.fst_X-Y.tsv: This file contains SNP-level measures of FST.
  7. If F-statistics was enabled, populations.phistats_X-Y.tsv: This file contains haplotype-level measures of FST.

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