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 F_{IS} at each
nucleotide position. The populations program will compare all populations pairwise to
compute F_{ST}. If a set of data is reference aligned, then a kernel-smoothed F_{ST} will also be
calculated. The populations program can also compute a number of haplotype-based
population genetics statistics including haplotype diversity, Φ_{ST}, and F_{ST}’. 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.

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:

- -P,--in_path — path to the directory containing the Stacks files.
- -V,--in_vcf — path to an input VCF file.
- -O,--out_path — path to a directory where to white the output files. (Required by -V; otherwise defaults to value of -P.)
- -M,--popmap — path to a population map. (Format is 'SAMPLE1 \t POP1 \n SAMPLE2 ...'.)
- -t,--threads — number of threads to run in parallel sections of code.

- -p,--min-populations [int] — minimum number of populations a locus must be present in to process a locus.
- -r,--min-samples-per-pop [float] — minimum percentage of individuals in a population required to process a locus for that population.
- -R,--min-samples-overall [float] — minimum percentage of individuals across populations required to process a locus.
- -H,--filter-haplotype-wise — apply the above filters haplotype wise (unshared SNPs will be pruned to reduce haplotype-wise missing data).
- --min-maf [float] — specify a minimum minor allele frequency required to process a nucleotide site at a locus (0 < min_maf < 0.5; applied to the metapopulation).
- --min-mac [int] — specify a minimum minor allele count required to process a SNP (applied to the metapopulation).
- --max-obs-het [float] — specify a maximum observed heterozygosity required to process a nucleotide site at a locus (applied to the metapopulation).
- --min-gt-depth [int] — specify a minimum number of reads to include a called SNP (otherwise marked as missing data).
- --write-single-snp — restrict data analysis to only the first SNP per locus.
- --write-random-snp — restrict data analysis to one random SNP per locus.
- -B,--blacklist — path to a file containing Blacklisted markers to be excluded from the export.
- -W,--whitelist — path to a file containing Whitelisted markers to include in the export.

- --hwe — calculate divergence from Hardy-Weinberg equilibrium for each locus.

- --fstats — enable SNP and haplotype-based F statistics.
- --fst_correction — specify a correction to be applied to Fst values: 'p_value'. Default: off.
- --p_value_cutoff [float] — maximum p-value to keep an Fst measurement. Default: 0.05.

- -k,--smooth — enable kernel-smoothed π, F
_{IS}, F_{ST}, F_{ST}', and Φ_{ST}calculations. - --smooth-fstats — enable kernel-smoothed F
_{ST}, F_{ST}', and Φ_{ST}calculations. - --smooth-popstats — enable kernel-smoothed π and F
_{IS}calculations. (Note: turning on smoothing implies --ordered_export.) - --sigma [int] — standard deviation of the kernel smoothing weight distribution. Sliding window size is defined as 3xσ, default σ = 150kbp (3xσ = 450kbp).
- --bootstrap-archive — archive statistical values for use in bootstrap resampling in a subsequent run, statistics must be enabled to be archived.
- --bootstrap — turn on boostrap resampling for all kernel-smoothed statistics.
- -N,--bootstrap-reps [int] — number of bootstrap resamplings to calculate (default 100).
- --bootstrap-pifis — turn on boostrap resampling for smoothed SNP-based π and F
_{IS}calculations. - --bootstrap-fst — turn on boostrap resampling for smoothed F
_{ST}calculations based on pairwise population comparison of SNPs. - --bootstrap-div — turn on boostrap resampling for smoothed haplotype diveristy and gene diversity calculations based on haplotypes.
- --bootstrap-phist — turn on boostrap resampling for smoothed φ
_{ST}calculations based on haplotypes. - --bootstrap-wl [path] — only bootstrap loci contained in this whitelist.

- --ordered-export — if data is reference aligned, exports will be ordered; only a single representative of each overlapping site.
- --fasta-loci — output locus consensus sequences in FASTA format..
- --fasta-samples — output the sequences of the two haplotypes of each (diploid) sample, for each locus, in FASTA format.
- --vcf — output SNPs and haplotypes in Variant Call Format (VCF).
- --vcf-all — output all sites in Variant Call Format (VCF).
- --genepop — output results in GenePop format.
- --structure — output results in Structure format.
- --radpainter — output results in fineRADstructure/RADpainter format.
- --plink — output genotypes in PLINK format.
- --hzar — output genotypes in Hybrid Zone Analysis using R (HZAR) format.
- --phylip — output nucleotides that are fixed-within, and variant among populations in Phylip format for phylogenetic tree construction.
- --phylip-var — include variable sites in the phylip output encoded using IUPAC notation.
- --phylip-var-all — include all sequence as well as variable sites in the phylip output encoded using IUPAC notation.
- --treemix — output SNPs in a format useable for the TreeMix program (Pickrell and Pritchard).
- --no-hap-exports — omit haplotype outputs.
- --fasta-samples-raw — output all haplotypes observed in each sample, for each locus, in FASTA format.

- --map-type — genetic map type to write. 'CP', 'DH', 'F2', and 'BC1' are the currently supported map types.
- --map-format — mapping program format to write, 'joinmap', 'onemap', and 'rqtl' are currently supported.

- -h,--help— display this help messsage.
- -v,--version— print program version.
- --verbose— turn on additional logging.
- --log-fst-comp— log components of F
_{ST}/Φ_{ST}calculations to a file.

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 F_{IS}, π, and the haplotype-level measures of π; and for each population-pair value, such as
F_{ST}, and the haplotype-level values of D_{XY}, φ_{ST}, 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 φ_{ST} and the other showing the smoothed values for D_{XY}.

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 F_{IS}, Π, and haplotype diversity, as well as the calculation of F_{ST}
and Φ_{ST} 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 F_{ST} and Φ_{ST}. 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:

- Bootstrap all loci (for example) to 1,000 repetitions.
- Identify those loci that are below some p-value threshold (say 0.05).
- Add these loci to the bootstrapping whitelist.
- Bootstrap again to 10,000 repetitions (now only those loci in the whitelist will be bootstrapped).
- Identify those loci that are below some p-value threshold (say 0.005)
- Add these loci to the bootstrapping whitelist.
- Bootstrap again to 100,000 repetitions (now only those loci in the whitelist will be bootstrapped).
- 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 F_{ST}
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 F_{ST} output files.

- 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

- Include multiple populations using a population map, and turn on kernel smoothing for π, F
_{IS}, and F_{ST}(data must be reference aligned for smoothing):~/% populations -P ./stacks/ --popmap ./samples/popmap --smooth -t 8

- 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

- 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

- 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:

- 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.
- cut out the second column, which contains locus IDs
- sort those IDs
- reduce them to a unique list of IDs (remove duplicate entries)
- randomly shuffle those lines
- take the first 1000 of the randomly shuffled lines
- sort them again and capture them into a file.

- 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

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.

- 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.
- 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

- 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, F
_{IS}, and so on. - 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.
- populations.sumstats_summary.tsv: This file contains population-level, mean summary statistics.
- If F-statistics was enabled, populations.fst_X-Y.tsv: This file contains SNP-level measures of F
_{ST}. - If F-statistics was enabled, populations.phistats_X-Y.tsv: This file contains haplotype-level measures of F
_{ST}.

## Raw reads |
## Core |
## Execution control |
## Utility programs |