Please note that demografr is still under active development. Although it’s already being used in ongoing research projects, the interface does occasionally change on rather short notice (function names, function arguments, etc.). I recommend that you keep an eye on the changelog for the list of the most recent updates.


The goal of demografr is to simplify and streamline the development of simulation-based inference pipelines in population genetics, such as Approximate Bayesian Computation (ABC) or parameter grid inferences, and make them more reproducible. demografr also aims to make the inferences orders of magnitude faster and more efficient by leveraging the tree sequences as an internal data structure and computation engine.

Unlike traditional ABC and other simulation-based approaches, which generally involve custom-built pipelines and scripts for population genetic simulation and computation of summary statistics, demografr makes it possible to perform simulation, data analysis, and the inference itself entirely in R within a single reproducible analysis script. By eliminating the need to write custom simulation code and scripting for integration of various population genetic tools for computing summary statistics, it lowers the barrier to entry for new users and facilitates reproducibility for all users regardless of their level of experience by eliminating many common sources of bugs.

How does demografr help with ABC?

demografr streamlines every step of a typical ABC pipeline by leveraging the slendr framework as a building block for simulation and data analysis, making it possible to write complete ABC workflows in R. Specifically:

  1. slendr’s intuitive, interactive interface for definning population genetic models makes it easy to encode even complex demographic models with only bare minimum of R knowledge needed.
  2. demografr makes it possible to encode prior distributions of parameters using familiar R interface resembling standard probabilistic statements, and provides an automated function which simulates ABC replicates drawing parameters from priors in a trivial, one-step manner.
  3. Because slendr’s simulation output is a tree sequence, most population genetic statistics can be computed directly on such tree sequences using R functions which are part of slendr’s statistical library. A tree sequence is never saved to disk and no conversion between file formats is required.
  4. demografr facilitates tight integration with the powerful R package abc by automatically feeding its simulation data to the abc package for inference and analysis.


You can install the development version of demografr from GitHub with:


Note that this requires an R package devtools, which you can obtain simply by running install.packages("devtools").

Because demografr is tightly linked to the slendr simulation package (in fact, new developments in slendr ale currently driven by requirements of demografr), you will also need the development version of slendr itself:


Note on stability

demografr is very much in an experimental stage at this point. Although ABC fitting of “standard” demographic models (i.e. estimating Ne, split times and gene-flow parameters for non-spatial models) already works very nicely, our long-term ambitions for the project are much higher and extend, for instance, towards inferences of spatial models. As such, please be aware that the interface might change on a rather short notice to accomodate features for estimating parameters of much more complex custom models.

If you want to follow updates on demografr, you can do this also on my Mastodon and by checking out the changelog from time to time.

Testing the R package in an online RStudio session

You can open an RStudio session and test examples from the vignettes directly in your web browser by clicking this button (no installation is needed!):


In case the RStudio instance appears to be starting very slowly, please be patient (Binder is a freely available service with limited computational resources provided by the community). If Binder crashes, try reloading the web page, which will restart the cloud session.

Once you get a browser-based RStudio session, you can navigate to the vignettes/ directory and test the examples on your own!

Important pieces missing so far

Tying the results of demografr ABC inference (internally facilitated by the abc package) to various diagnostics features of abc and other tools.

An example ABC analysis

Imagine that we sequenced genomes of individuals from populations “popA”, “popB”, “popC”, and “popD”.

Let’s also assume that we know that the three populations are phylogenetically related in the following way with an indicated gene-flow event at a certain time in the past, but we don’t know anything else (i.e., we have no idea about their Ne or split times):

After sequencing the genomes of individuals from these populations, we computed the nucleotide diversity in these populations as well as their pairwise genetic divergence, and observed the following values which we saved in two standard R data frames:

  1. Nucleotide diversity in each population:
observed_diversity <- read.table(system.file("examples/observed_diversity.tsv", package = "demografr"), header = TRUE)

#>    set    diversity
#> 1 popA 8.037847e-05
#> 2 popB 3.242467e-05
#> 3 popC 1.021123e-04
#> 4 popD 8.968777e-05
  1. Pairwise divergence d_X_Y between populations X and Y:
observed_divergence <- read.table(system.file("examples/observed_divergence.tsv", package = "demografr"), header = TRUE)

#>      x    y   divergence
#> 1 popA popB 0.0002387594
#> 2 popA popC 0.0002391843
#> 3 popA popD 0.0002389617
#> 4 popB popC 0.0001089125
#> 5 popB popD 0.0001155571
#> 6 popC popD 0.0001105323
  1. Value of the following f4-statistic:
observed_f4  <- read.table(system.file("examples/observed_f4.tsv", package = "demografr"), header = TRUE)

#>      W    X    Y    Z            f4
#> 1 popA popB popC popD -3.433205e-06
#> 2 popA popC popB popD -7.125812e-07
#> 3 popA popD popB popC  2.720624e-06

A complete ABC analysis in a single R script

This is how we would use demografr to estimate the Ne and split times for all populations (and the rate of the indicated gene-flow event) with Approximate Bayesian Computation in a single R script:


# set up the internal tskit/msprime environment

# set up parallelization across all CPUs on the current machine
plan(multicore, workers = availableCores())

# bind data frames with empirical summary statistics into a named list
observed <- list(
  diversity  = observed_diversity,
  divergence = observed_divergence,
  f4         = observed_f4

# define a model generating function using the slendr interface
# (each of the function parameters correspond to a parameter we want to infer)

model <- function(Ne_A, Ne_B, Ne_C, Ne_D, T_AB, T_BC, T_CD, gf_BC) {
  # define populations
  popA <- population("popA", time = 1,    N = Ne_A)
  popB <- population("popB", time = T_AB, N = Ne_B, parent = popA)
  popC <- population("popC", time = T_BC, N = Ne_C, parent = popB)
  popD <- population("popD", time = T_CD, N = Ne_D, parent = popC)

  # define gene-flow events
  gf <- gene_flow(from = popB, to = popC, start = 9000, end = 9301, rate = gf_BC)

  # compile a slendr model
  model <- compile_model(
    populations = list(popA, popB, popC, popD), gene_flow = gf,
    generation_time = 1, simulation_length = 10000,
    direction = "forward", serialize = FALSE

  # set up sampling schedule (2 diploid individuals from each population at
  # the end of the simulation) -- this step is optional
  samples <- schedule_sampling(
    model, times = 10000,
    list(popA, 2), list(popB, 2), list(popC, 2), list(popD, 2),
    strict = TRUE

  # a return statement is mandatory!
  # if a sampling schedule is not generated, use return(model)
  return(list(model, samples))

# setup priors for model parameters

priors <- list(
  Ne_A ~ runif(1, 10000),
  Ne_B ~ runif(1, 10000),
  Ne_C ~ runif(1, 10000),
  Ne_D ~ runif(1, 10000),

  T_AB ~ runif(1, 10000),
  T_BC ~ runif(1, 10000),
  T_CD ~ runif(1, 10000),

  gf_BC ~ runif(0, 1)

# define summary functions to be computed on simulated data (must be of the
# same format as the summary statistics computed on empirical data)

compute_diversity <- function(ts) {
  samples <- slendr::ts_names(ts, split = "pop")
  ts_diversity(ts, sample_sets = samples)
compute_divergence <- function(ts) {
  samples <- slendr::ts_names(ts, split = "pop")
  ts_divergence(ts, sample_sets = samples)
compute_f4 <- function(ts) {
  samples <- slendr::ts_names(ts, split = "pop")
        W = list(popA = samples$popA),
        X = list(popB = samples$popB),
        Y = list(popC = samples$popC),
        Z = list(popD = samples$popD))

# the summary functions must be also bound to an R list named in the same
# way as the empirical summary statistics
functions <- list(
  diversity  = compute_diversity,
  divergence = compute_divergence,
  f4         = compute_f4

# validate the individual ABC components for correctness and consistency
validate_abc(model, priors, functions, observed)

# run ABC simulations
data <- simulate_abc(
  model, priors, functions, observed, iterations = 10000,
  sequence_length = 10e6, recombination_rate = 1e-8, mutation_rate = 1e-8

# infer posterior distributions of parameters using the abc R package
abc <- perform_abc(data, engine = "abc", tol = 0.01, method = "neuralnet")

Analysing posterior distributions of parameters

After we run this R script, we end up with an object called abc here. This object contains the complete information about the results of our inference. In particular, it carries the posterior samples for our parameters of interest (Ne of populations and their split times).

For instance, we can get a table of all posterior values with the function extract_summary():

#>                             Ne_A     Ne_B      Ne_C     Ne_D     T_AB     T_BC
#> Min.:                   929.0679 670.3812  2966.659 1790.060 1192.360 4988.493
#> Weighted 2.5 % Perc.:  1201.0043 711.6460  4075.275 2181.297 1561.180 5259.732
#> Weighted Median:       1990.5578 799.0462  7366.514 3714.350 2003.515 5678.190
#> Weighted Mean:         1967.7919 802.3221  7075.016 3578.215 2003.738 5655.562
#> Weighted Mode:         1954.3619 757.0564  7620.487 3809.785 1939.879 5752.531
#> Weighted 97.5 % Perc.: 2837.7028 924.5835 10858.144 4842.347 2326.478 5941.146
#> Max.:                  3144.9674 927.3249 11696.130 5228.341 2569.966 6036.115
#>                            T_CD       gf_BC
#> Min.:                  6863.233 -0.02455945
#> Weighted 2.5 % Perc.:  7294.305  0.02674433
#> Weighted Median:       8127.699  0.16684306
#> Weighted Mean:         8196.626  0.18184086
#> Weighted Mode:         8052.760  0.12030457
#> Weighted 97.5 % Perc.: 9387.034  0.33763567
#> Max.:                  9387.034  0.35898225

We can also specify a subset of model parameters to select, or provide a regular expression for this subsetting:

extract_summary(abc, param = "Ne")
#>                             Ne_A     Ne_B      Ne_C     Ne_D
#> Min.:                   929.0679 670.3812  2966.659 1790.060
#> Weighted 2.5 % Perc.:  1201.0043 711.6460  4075.275 2181.297
#> Weighted Median:       1990.5578 799.0462  7366.514 3714.350
#> Weighted Mean:         1967.7919 802.3221  7075.016 3578.215
#> Weighted Mode:         1954.3619 757.0564  7620.487 3809.785
#> Weighted 97.5 % Perc.: 2837.7028 924.5835 10858.144 4842.347
#> Max.:                  3144.9674 927.3249 11696.130 5228.341

We can also visualize the posterior distributions. Rather than plotting many different distributions at once, let’s first check out the posterior distributions of inferred Ne values:

plot_posterior(abc, param = "Ne")

Similarly, we can take a look at the inferred posteriors of the split times:

plot_posterior(abc, param = "T")

And, finally, the rate of gene flow:

plot_posterior(abc, param = "gf")

Finally, we have the diagnostic functionality of the abc R package at our disposal:

plot(abc, param = "Ne_C")

Additional functionality

demografr also provides a couple of functions designed to make troubleshooting a little easier.

For instance, assuming we have priors set up as above, we can visualize the prior distribution(s) like this:

plot_prior(priors, "Ne")

plot_prior(priors, c("^T", "^gf"), facet = TRUE)