SMC++ infers population history from whole-genome sequence data.
C++ Python C Makefile Shell CMake
Clone or download
Latest commit 9b41e7b May 20, 2018


SMC++ is a program for estimating the size history of populations from whole genome sequence data.

Quick start guide

  1. Follow the installation instructions.

  2. Convert your VCF(s) to the SMC++ input format with vcf2smc:

    $ smc++ vcf2smc out/chr1.smc.gz chr1 Pop1:S1,S2

    This command will parse data for the contig chr1 for samples S1 and S2 which are members of population Pop1. You should run this once for each independent contig in your dataset, producing one SMC++ output file per contig.

  3. Fit the model using estimate:

    $ smc++ estimate -o analysis/ 1.25e-8 out/example.chr*.smc.gz

    The first mandatory argument, 1.25e-8, is the per-generation mutation rate. The remaining arguments are the data files generated in the previous step. Depending on sample size and your machine, the fitting procedure should take between a few minutes and a few hours. The fitted model will be stored in JSON format in analysis/

  4. Visualize the results using plot:

    $ smc++ plot plot.pdf analysis/

SMC++ can also estimate and plot joint demographies from pairs of populations; see split.

Installation instructions

SMC++ is distributed as an Anaconda package. Inside the Anaconda environment, install the precompiled binary using the command:

$ conda install -c terhorst -c bioconda smcpp

This will automatically download all necessary dependencies and create an smc++ executable in the bin/ folder of your Anaconda distribution.

You may also build the software from scratch using the build instructions provided in the next section.

Build instructions

SMC++ requires the following libraries and executables in order compile and run:

  • Python 3.5 or greater.
  • A C++-11 compiler (gcc 4.8 or later, for example).
  • gmp, for some rational field computations.
  • mpfr (at least version 3.0.0), for some extended precision calculations.
  • gsl, the GNU Scientific Library.

On Ubuntu (or Debian) Linux, the library requirements may be installed using the commmand:

$ sudo apt-get install -y libgmp-dev libmpfr-dev libgsl0-dev

On OS X, the easiest way to install them is using Homebrew:

$ brew install mpfr gmp gsl

After installing the requirements, SMC++ may be built by running:

$ pip install git+

(Alternatively, git clone the repository and run the usual python install. You must clone. Downloading the source tarball will not work.)

Note for OS X users

Versions of Clang shipping with Mac OS X do not currently support OpenMP. In order to build SMC++ on OS X you must use a compiler that does, such as gcc:

$ brew install gcc
$ CC=gcc-6 CXX=g++-6 python install

Virtual environment

SMC++ pulls in a fair number of Python dependencies. If you prefer to keep this separate from your main Python installation, or do not have root access on your system, you may wish to install SMC++ inside of a virtual environment. To do so, first create and activate the virtual environment:

$ virtualenv -p python3 <desired location>
$ source <desired location>/bin/activate

Then, install SMC++ as described above.


SMC++ comprises several subcommands which are accessed using the syntax:

$ smc++ <subcommand>

where <subcommand> is one of the following:


This subcommand converts (biallelic, diploid) VCF data to the format used by SMC++.

Required arguments

  1. An indexed VCF file.
  2. An output file. Appending the .gz extension will cause the output to be compressed; the estimate command can read from both compressed and uncompressed data sources.
  3. A contig name. Each call to vcf2smc processes a single contig. VCFs containing multiple contigs should be processed via multiple separate runs.
  4. A list of population(s) and samples. Each population has an id followed by a comma-separated list of sample IDs (column names in the VCF). Up to two populations are supported.

For example, to convert contig chr1 of vcf.gz using samples NA12878 and NA12879 of population CEU, saving to chr1.smc.gz, use:

$ smc++ vcf2smc vcf.gz chr1.smc.gz chr1 CEU:NA12878,NA12879

Optional arguments

  • -d: SMC++ relies crucially on the notion of a pair of distinguished lineages (see paper for details on this terminology). The identity of the distinguished lineages is set using the -d option, which specifies the sample(s) which will form the distinguished pair. -d accepts to sample ids. The first allele will be taken from sample 1 and the second from sample 2. To form the distinguished pair using one haplotype from each of NA1287{8,9} using the above example:

    $ smc++ vcf2smc -d NA12878 NA12879 vcf.gz chr1.smc.gz chr1 CEU:NA12878,NA12879

    Note that "first" and "second" allele have no meaning for unphased data; if your data are not phased, it only makes sense to specify a single individual (e.g. -d NA12878 NA12878).

  • --mask, -m: This specifies a BED-formatted mask file whose positions will be marked as missing data (across all samples) in the outputted SMC++ data set. This can be used to delineate large uncalled regions (e.g. centromeres) which are often omitted in VCF files; without additional information provided by --mask, there is no way to distinguish these missing regions from very long runs of homozygosity. For finer-grained control of missing data, setting individual positions and samples to the missing genotype, ./., also works fine. (The point of --mask is to save the user the trouble of emitting millions of rows of missing observations in the VCF).

  • --missing-cutoff, -c: This is an alternative to --mask which will automatically treat runs of homozgosity longer than -c base pairs as missing. Typically -c should be set high so as not to filter out legitimate long runs of homozyous bases, which are informative about recent demography. This is a fairly crude approach to filtering and is only recommended for use in cases where using --mask is not possible.

Composite likelihood

By varying -d over the same VCF, you can create distinct data sets for estimation. This is useful for forming composite likelihoods. For example, the following command will create three data sets from contig chr1 of myvcf.gz, by varying the identity of the distinguished individual and treating the remaining two samples as "undistinguished":

for i in {7..9};
    do smc++ vcf2smc -d NA1287$i NA1287$i myvcf.gz out.$i.txt chr1 NA12877 NA12878 NA12890;

You can then pass these data sets into estimate:

$ smc++ estimate -o output/ <mutation rate> out.*.txt

SMC++ treats each file out.*.txt as an independently evolving sequence (i.e., a chromosome); the likelihood is simply the product of SMC++ likelihoods over each of the data sets. In the example above where the data sets are generated from the same chromosome but different distinguished individuals (different -d), this independence assumption is violated, leading to a so-called composite likelihood. The advantage of this approach is that it incorporates genealogical information from additional distinguished individuals into the analysis, potentially leading to improved estimates.

Since (a portion of) the computational and memory requirements of SMC++ scale linearly with the total analyzed sequence length, it is generally advisable to composite over a relatively small number of individuals. In practice we generally use 2-10 individuals, depending on genome length, sample size, etc., and have found that this leads to improved estimation without causing significant degeneracy in the likelihood.


vcf2smc targets a common use-case but may not be sufficient for all users. In particular, you should be aware that:

  • The ancestral allele is assumed to be the reference allele.
  • The FILTER and QUAL columns are ignored.
  • Indels, structural variants, and any non-SNP data are ignored.
  • For sites containing multiple entries in the VCF, all but the first entry is ignored.
  • Sites which are not present in the VCF are assumed to be homoyzgous ancestral across all samples. (See masking, above.)

Those wishing to implement their own custom conversion to the SMC++ data format should see the input data format description below.


This command will fit a population size history to data. The basic usage is:

$ smc++ estimate <mutation rate> <data file> [<data file> ...]

Required arguments

  1. The per-generation mutation rate. Scientific notation is acceptable: use e.g. 1e-8 in place of .00000001.
  2. One or more SMC++-formatted data files, generated by vcf2smc, for example.

Optional arguments

  • -o: specifies the directory to store the final estimates as well as all intermediate files and debugging output. Defaults to ., i.e. the current working directory.
  • --polarization-error: if the identity of the ancestral allele is not known, these options can be used to specify a prior over it. With polarization error p, emissions probabilities for entry CSFS(a,b) will be computed as (1-p) CSFS(a,b) + p CSFS(2-a, n-b). The default setting is 0.5, i.e. the identity of the ancestral allele is not known.
  • --unfold is an alias for --polarization-error 0. If the ancestral allele is known (from an outgroup, say) then this option will use the unfolded SFS for computing probabilities. Incorrect usage of this feature may lead to erroneous results.

A number of other arguments concerning technical aspects of the fitting procedure exist. To see them, pass the -h option to estimate.


This command plots fitted size histories. The basic usage is:

$ smc++ plot plot.png model1.json model2.json [...] modeln.json

where model*.json are fitted models produced by estimate.

Required arguments

  1. An output file-name. The output format is determined by the extension (.pdf, .png, .jpeg, etc.)
  2. One or more JSON-formatted SMC++ models (the output from estimate).

Optional arguments

  • -g sets the generation time (in years) used to scale the x-axis. If not given, the plot will be in coalescent units.
  • --logy plots the y-axis on a log scale.
  • -c produces a CSV-formatted table containing the data used to generate the plot.


This command fits two-population clean split models using marginal estimates produced by estimate. To use split, first estimate each population marginally using estimate:

$ smc++ vcf2smc my.vcf.gz data/pop1.smc.gz <contig> pop1:ind1_1,ind1_2
$ smc++ vcf2smc my.vcf.gz data/pop2.smc.gz <contig> pop2:ind2_1,ind2_2
$ smc++ estimate -o pop1/ <mu> data/pop1.smc.gz
$ smc++ estimate -o pop2/ <mu> data/pop2.smc.gz

Next, create datasets containing the joint frequency spectrum for both populations:

$ smc++ vcf2smc my.vcf.gz data/pop12.smc.gz <contig> pop1:ind1_1,ind1_2 pop2:ind2_1,ind2_2
$ smc++ vcf2smc my.vcf.gz data/pop21.smc.gz <contig> pop2:ind2_1,ind2_2 pop1:ind1_1,ind1_2

Finally, run split to refine the marginal estimates into an estimate of the joint demography:

$ smc++ split -o split/ pop1/ pop2/ data/*.smc.gz
$ smc++ plot joint.pdf split/


This command will export (and optionally visualize) the posterior distribution of the time to most recent common ancestor (TMRCA) in the distinguished pair from the given data set.

The output file is the result of:

>>> numpy.savez(output, hidden_states=hs,
                **{'file1'=gamma1, 'file1_sites'=sites1, ...})


  • hs is a vector of length M + 1 indicating the breakpoints used to discretize the hidden TMRCA of the distinguished pair. The breakpoints are chosen such that the probability of coalescence within each interval is uniform with respect to the fitted model.
  • sites1 is the vector of length L containing positions where the decoding is performed for data set file1. Due to the internal archtecture of SMC++, there is one entry per row in the data set.
  • gamma1 is an array of dimension M x L whose entry gamma1[m, ell] gives the average posterior probability of coalescence in interval [hs[m], hs[m + 1]) for each site in the interval {sites1[ell], ..., sites1[ell + 1] - 1}.

There will be a gamma/sites entry for each data set decoded.

Required arguments

  • model: A fitted SMC++ model, i.e. the outputted by estimate.
  • output: A file name to save the posterior decoding arrays, in the format shown above.
  • data: One or more data sets in SMC++ format, i.e. the output of vcf2smc.

Optional arguments

  • --heatmap plot.(png|pdf|jpg): Also produce a heatmap of the posterior decoding. The output format is given by the extension.
  • --start s, --end e: For regions that are much longer than ~1cM, the heatmap will look pretty noisy. These options can be used to narrow in on specific regions of the chromosome.
  • --colorbar: Also add a colorbar showing the scale of the heatmap.


This command prints plain- and BibTex-formatted citation information for the accompanying paper to the console.

Tips for using SMC++

SMC++ has several regularization parameters which affect the quality of the fits obtained using estimate and split. The default settings have proved useful for analyzing high coverage human sequence data from a few hundred individuals. For other types of data, you will likely need to experiment with different values of these parameters in order to obtain good estimates.

  • --thinning: This parameter controls the frequency with which the full CSFS is emitted (see paper for details). Decreasing the value of this parameter will cause the likelihood to depend more strongly on frequency spectrum information in the undistinguished portion of the sample, potentially leading to more accurate results in the recent past. However, decreasing it too much can lead to degeneracy in the likelihood since correlations in the undistinguished portion of the ancestral recombination graph are ignored. The default value for a sample size n is 1000 * log(n) (note that this is different than in versions 1.7.0 and earlier). Empirically, this has worked well for sample sizes on the order of 20 <= n <= 200 but you may need to experiment a bit.
  • --timepoints: This command specifies the starting and ending time points of the model. It accepts either a comma-separated list of two numbers t1,tK specifying the starting and ending time points of the model (in generations), or the default setting h. If h is specified, SMC++ will use an experimental heuristic to calculate the model time points points automatically.
  • --regularization-penalty: This parameter penalizes curvature in the estimated size history. The default value of this parameter is 6.0. Lower values of the penalty shrink the estimated size history towards a line. If your estimates exhibit too much oscillation, try decreasing the value of this parameter. (Note that this behavior is different than in versions 1.7.0 and earlier.)
  • --ftol: This parameter specifies a threshold for stopping the EM algorithm when the relative improvement in log-likelihood becomes small. The default value is 1e-4. If the tolerance is epsilon and x'/x are the new and old estimates, the algorithm will terminate when [loglik(x') - loglik(x)] / loglik(x) < epsilon. Increasing values of epsilon will cause the optimizer to stop earlier, potentially preventing overfitting.
  • --knots: This parameter specifies the number of spline knots used in the underlying representation of the size history. The default value is 32. Using fewer knots can lead to smoother fits, however underspecifying this parameter may smooth out interesting features of the size history.

A useful diagnostic for understanding the final output of SMC++ are the sequence of intermediate estimates .model.iter<k>.json which are saved by --estimate in the --output directory. By plotting these, you can get a sense of whether the optimizer is overfitting and requires additional regularization.

Frequently asked questions

  1. The binary installer dies with the error message:

    ImportError: /lib64/ version `GLIBC_2.14' not found (required by ...).

    How can I fix this?

    This is due to a glibc version mismatch between your system and the build server I use to create the binary installers. Unfortunately, I am unable to create binaries for older versions of glibc. Your options are to either a) upgrade glibc on your system (which would probably require upgrading your operating system); or b) build SMC++ yourself by following the build instructions. Please note that linking a different version of glibc at runtime is not supported, and will likely cause random crashes.

  2. SMC++ claims that my population crashed in the very recent past. What's going on?

    Typically this is due to long runs of homozygosity (ROH) in the data, which can arise for one of several reasons:

    1. The population legitimately experienced a recent crash, leading to inbreeding;
    2. One or more selective sweeps occured; or
    3. Uncalled regions in your VCF were not marked as such before running vcf2smc.

    #1 represents real signal, while #2 and #3 should be filtered out using the -m option of vcf2smc and/or the -c option of estimate.-

  3. How do I get the estimated recombination rate?

    The output file contains fields named rho and N0. rho is the estimated population-scaled recombination rate per base-pair. To convert it to units of generations, multiply by 2 * N0.

What to do if you encounter trouble

SMC++ is under active development and you may encounter difficulties in trying to use it. Always make sure that you have upgraded to the latest version, as the bug you have encountered may have already been fixed. If that does not work, then:

  • If you believe you have encountered a bug in the software

(unexpected crash, high memory usage, etc.) please file an issue in our bug tracker. - If you would like assistance in interpreting the results, please e-mail me directly. I will do my best to try and help, but please understand that I have limited time to respond to such inquiries.

In both cases, you will receive a faster response if you include as much detail as possible about your data set (sample size, # of contigs, etc.), system and, where applicable, the .debug.txt log file saved by SMC++ in the output directory specified to the estimate command.

File formats

Input data format

The data files should be ASCII text and can optionally be gzipped. The format of each line of the data file is as follows:

<span> <d1> <u1> <n1> [<d1> <u2> <n2>]

Explanation of each column:

  • span gives the number of contiguous bases at which this observation occurred. Hence, it will generally be 1 for SNPs and greater than one for a stretch of nonsegregating sites.
  • Then, there are three columns d/u/n for each population:
    o d Gives the genotype (0, 1, or 2) of the
    distinguished individual. If the genotype of the distinguished individual is not known, this should be set to -1.
    o The next column u is the total number of derived alleles found
    in the remainder of the (undistinguished) sample at the site(s).
    o The final column n is the haploid sample size (number of
    non-missing observations) in the undistinguished portion of the sample.

For example, consider the following set of genotypes at a set of 10 contiguous bases on three diploid individuals in one population:

dist.   ..1..N...2

The distinguished individual is row one. A . indicates that the individual is homozygous for the ancestral allele, while an integer indicates that that individual possesses (1,2) copies of the derived allele. An N indicates a missing genotype at that position. Finally, the + in column seven indicates that individual three possessed the ancestral allele on one chromosome, and had a missing observation on the other chromosome (this would be coded as 0/. in a VCF).

The SMC++ format for this input file is:

1   0   2   4
1   0   0   2
1   1   0   4
2   0   0   4
1   -1  0   2
1   0   0   3
2   0   0   4
1   2   1   4

The data files also include a custom metadata header with some additional information about the populations. For this reason, it is advised to please use the included vcf2smc tool in order to translate from the VCF to SMC format.

Output data format

Upon completion, SMC++ will write a JSON-formatted model file into the into the analysis directory. The file is human-readable and contains various parameters related to the fitting procedure.