Extracting true ancestry tracts

Please note that the tspop support in slendr implemented in the ts_tracts() function is extremely experimental, only minimally tested, and its functionality is expected to change quite a bit. Please wait for the release of the next major version of slendr (which should include a more developed ts_tracts()) before you use this in your own work.

slendr now includes an experimental, use-it-at-your-own-risk interface to an exciting new algorithm for extracting true tracts of ancestry as implemented in the Python module tspop.

The interface is implemented in an R function ts_tracts() and this vignette describes its use on a simple toy model of Neanderthal and Denisovan introgression into modern humans.

library(ggplot2)
library(dplyr)

library(slendr)
init_env()

Demographic model

Let’s imagine the following demographic model of Neanderthal introgression into the ancestors of all non-Africans (represented by “EUR” and “PAP” populations, approximating European and Papuan people living today), followed by Denisovan introgression into the ancestors of Papuans:

anc_all <- population("ancestor_all", time = 700e3, N = 10000, remove = 640e3)
afr <- population("AFR", parent = anc_all, time = 650e3, N = 10000)
anc_arch <- population("ancestor_archaics", parent = anc_all, time = 650e3, N = 10000, remove = 390e3)
nea <- population("NEA", parent = anc_arch, time = 400e3, N = 2000, remove = 30e3)
den <- population("DEN", parent = anc_arch, time = 400e3, N = 2000, remove = 30e3)
nonafr <- population("nonAFR", parent = afr, time = 100e3, N = 3000, remove = 39e3)
eur <- population("EUR", parent = nonafr, time = 45e3, N = 5000)
pap <- population("PAP", parent = nonafr, time = 45e3, N = 5000)

gf <- list(
  gene_flow(from = nea, to = nonafr, rate = 0.03, start = 55000, end = 50000),
  gene_flow(from = den, to = pap, rate = 0.07, start = 35000, end = 30000)
)

model <- compile_model(
  populations = list(anc_all, afr, anc_arch, nea, den, nonafr, eur, pap),
  gene_flow = gf,
  generation_time = 30,
  serialize = FALSE
)

plot_model(
  model, sizes = FALSE,
  order = c("AFR", "EUR", "nonAFR", "PAP", "ancestor_all", "DEN", "ancestor_archaics", "NEA")
)

Tree sequence simulation

Let’s now simulate a 50Mb tree sequence from this model, recording 50 diploid individuals from EUR and PAP populations:

samples <- schedule_sampling(model, times = 0, list(eur, 50), list(pap, 50))

ts <- msprime(model, sequence_length = 100e6, recombination_rate = 1e-8, samples = samples, random_seed = 42)

Extracting ancestry tracts

In order to extract tracts of Neanderthal and Denisovan ancestry, we can use slendr’s new function ts_tracts() which serves as a simplified R-friendly interface to the Python method tspop.get_pop_ancestry(). An important piece of information used by the function is a so-called “census time”, which records the time of recording of the “ancestral population” identity of each node ancestral to each subsegment in our sample set. Please see the excellent vignette of tspop for more information on the inner workings of the algorithm.

In our case, let’s extract the ancestry tracts corresponding to ancestral nodes present at 55 thousand years ago – this time corresponds to the moment of the start of the archaic introgression:

nea_tracts <- ts_tracts(ts, census = 55000)
den_tracts <- ts_tracts(ts, census = 35000)

tracts <- bind_rows(nea_tracts, den_tracts)

This is what a table with all ancestry tracts looks like. As we would expect, we see a column indicating a name of each individual, the left and right coordinates of each tract in each individual, as well as the population name of the source of each ancestry tract:

tracts

Summaries of ancestral proportions

When we summarise the ancestry proportions in target EUR and PAP populations, we see that the EUR population only carries about ~3% of Neanderthal ancestry and that this is also true for the PAP population. However, we also see that Papuans carry about 7% of Denisovan ancestry. This is consistent with our model, but also with the expectation from empirical data.

summary <- tracts %>%
  group_by(name, node_id, pop, source_pop) %>%
  summarise(prop = sum(length) / 100e6)

summary %>% group_by(pop, source_pop) %>% summarise(mean(prop)) %>% arrange(source_pop, pop)

Let’s visualize these proportions at an individual level:

summary %>%
ggplot(aes(source_pop, prop, color = source_pop, fill = source_pop)) +
  geom_jitter() +
  coord_cartesian(ylim = c(0, 0.2)) +
  geom_hline(yintercept = c(0.03, 0.08), linetype = 2) +
  ylab("ancestry proportion") +
  facet_wrap(~ pop) +
  ggtitle("Ancestry proportions in each individual",
          "(vertical lines represent 3% and 7% baseline expectations")

“Chromosome painting” of ancestry tracts

Because the tracts object contains the coordinates of every single ancestry segment in each of the simulated individuals, we can “paint” each chromosome with each of the two archaic human ancestries:

tracts %>%
mutate(chrom = paste(name, " (node", node_id, ")")) %>%
ggplot(aes(x = left, xend = right, y = chrom, yend = chrom, color = source_pop)) +
  geom_segment(linewidth = 3) +
  theme_minimal() +
  labs(x = "position [bp]", y = "haplotype") +
  ggtitle("True ancestry tracts along each chromosome") +
  theme(axis.text.y = element_blank(), panel.grid = element_blank()) +
  facet_grid(pop ~ ., scales = "free_y")

By lining up NEA & DEN ancestry tracts in both EUR and PAP populations, we can see how the common origin of Neanderthal ancestry in both non-African populations manifests in a significant overlap of NEA tracts between both populations.

Average tract lengths:

Let’s compute simple summaries of tract lengths in the simulated data, and compare them to theoretical expectations.

tracts %>%
  group_by(pop, source_pop) %>%
  summarise(mean(length))

Theoretical expectations (from Racimo and Slatkin 2015, Box 1)

Neanderthal tracts:

m <- 0.03
t <- 52500 / 30
r <- 1e-8

mean_nea <- 1 / ((1 - m) * r * (t - 1))
mean_nea

Denisovan tracts:

m <- 0.07
t <- 37500 / 30
r <- 1e-8

mean_den <- 1 / ((1 - m) * r * (t - 1))
mean_den

As we can see, our simulations are not that far of from the theoretical expectations, giving us confidence that our simulations (and the ancestry tract extraction algorithm) are working as expected.

Distribution of ancestry tract lengths

Finally, let’s plot the distributions of lengths of each of the ancestry tracts. The case of archaic human introgression is very well studied so it’s perhaps not that exciting to look at these figures. That said, in less well studied species, it might be interesting to use these kinds of simulations for inference of introgression times and proportions via Approximate Bayesian Computation or by another method:

expectation_df <- data.frame(
  pop = c("EUR", "PAP", "PAP"),
  source_pop = c("NEA", "NEA", "DEN"),
  length = c(mean_nea, mean_nea, mean_den)
)

p_densities <- tracts %>%
ggplot(aes(length, color = source_pop)) +
  geom_density() +
  geom_vline(data = expectation_df, aes(xintercept = length, color = source_pop),
             linetype = 2) +
  facet_wrap(~ pop) +
  ggtitle("Distribution of tract lengths per different ancestries")

cowplot::plot_grid(p_densities, p_densities + scale_x_log10(), nrow = 2)

Pure msprime tree sequence

Finally, as a sanity check, let’s use the pure msprime simulation example from the official tspop documentation to test that ts_tracts() behaves as expected even on a standard msprime tree-sequence object.

First, let’s run the simulation code exactly as it is:

import msprime

pop_size = 500
sequence_length = 1e7
seed = 98765
rho = 3e-8

# Make the Demography object.
demography = msprime.Demography()
demography.add_population(name="RED", initial_size=pop_size)
demography.add_population(name="BLUE", initial_size=pop_size)
demography.add_population(name="ADMIX", initial_size=pop_size)
demography.add_population(name="ANC", initial_size=pop_size)
demography.add_admixture(
    time=100, derived="ADMIX", ancestral=["RED", "BLUE"], proportions=[0.5, 0.5]
)
demography.add_census(time=100.01) # Census is here!
demography.add_population_split(
    time=1000, derived=["RED", "BLUE"], ancestral="ANC"
)

# Simulate.
ts = msprime.sim_ancestry(
    samples={"RED": 0, "BLUE": 0, "ADMIX" : 2},
    demography=demography,
    random_seed=seed,
    sequence_length=sequence_length,
    recombination_rate=rho
)

Let’s save the msprime tree sequence to disk so that we can load it into R (i.e., approximating what you might want to do should you want to use ts_tracts() without running a slendr simulation first):

import tempfile
path = tempfile.NamedTemporaryFile(suffix=".trees").name

ts.dump(path)

Now let’s move to R again, load the tree sequence into slendr and extract ancestry tracts from it using ts_tracts():

sim_ts <- ts_read(reticulate::py$path)

squashed_tracts <- ts_tracts(sim_ts, census = 100.01, squashed = TRUE)

head(squashed_tracts)
tail(squashed_tracts)

By setting squashed = FALSE, we get the full, un-squashed ancestry segments, each with its appropriate ancestral node ID:

full_tracts <- ts_tracts(sim_ts, census = 100.01, squashed = FALSE)

head(full_tracts)
tail(full_tracts)

By comparing the two tables above to the pandas data frames in the tspop documentation, we can see that we obtained the same results.

- Pure msprime tree sequence