The super admixture framework

The superadmixture R package implements functions for inferring the population coancestry and simulating genotypes according to the super admixture framework. It also has functions for conducting the structured Hardy-Weinberg equilibrium test and estimating admixture proportions using the ALStructure algorithm.

Installation

install.packages("devtools")
devtools::install_github("StoreyLab/superadmixture")

Examples

Input

We created a subset of HGDP datasets by first applying allele frequency filters and then LD-pruning to the HGDP dataset. We then randomly selected 10,000 SNPs out of LD-pruned SNP sets. This subset of genotypes is available in data/X_hgdp.rda. This data has 929 individuals and 10,000 loci. The associated fam file can be found in data/fam_hgdp.rda. These data can be reproduced by scripts data-raw/{hgdp.bash,hgdp.R}.

data("X_hgdp",   package = "superadmixture")
data("fam_hgdp", package = "superadmixture")

Estimating oancestry among individuals

library(popkin)

# estimate kinship coefficients
kinship <- popkin(t(X_hgdp)) 

# map kinship coefficients to coancestry coefficients
coanc_indiv  <- inbr_diag(kinship)

# kinship coefficients and coancestry coefficients are probability, 
# so we truncate at zero to avoid negative probability
coanc_indiv   <- ifelse(coanc_indiv < 0, 0, coanc_indiv)

Estimating admixture proportions

library(superadmixture)

# estimate individual-specific allele frequencies
obj <- est_p_indiv(X_hgdp, k_antepops = 7, loci_on_cols = TRUE)
p_indiv  <- obj$p_indiv
rowspace <- obj$rowspace

# estimate P and Q by decomposing individual-specific allele frequencies
obj <- factor_p_indiv(p_indiv, k_antepops = 7, rowspace = rowspace, verbose = FALSE, max_iters = 200, tol = 1e-2)
Q_hat <- obj$Q_hat

Estimating coancestry among antecedent populations

After obtaining coanc_indiv and Q_hat, we can use the function est_coanc to estimate population coancestry under the super admixture model and under the standard admixture model.

# estimate population coancestry under the super-admixture model
coanc_pops_sup <- est_coanc(coanc_indiv, Q_hat, model = "super")

# estimate population coancestry under the standard admixture model
coanc_pops_std <- est_coanc(coanc_indiv, Q_hat, model = "standard")

Visualizing population-level coancestry and admixture proportions

# order `Q_hat` and `coanc_pops_sup` in the ascending order of coancestry
index <- order(diag(coanc_pops_sup))
coanc_pops_sup <- coanc_pops_sup[index, index]
Q_hat <- Q_hat[index, ]

# use the `fit_tree` function from bnpsd package to create a phylogenetic tree
library(bnpsd)
colnames(coanc_pops_sup) <- rownames(coanc_pops_sup) <- paste0("S", 1:7)
tree <- fit_tree(coanc_pops_sup)

We can visualize tree using the plot_tree function in the superadmixture package. Based on the topology of the tree (see the package vignette for details), we decided to color the populations S1, S2 with light blue and dark blue, S3, S4 with light green and dark green, S5, S6 with light red and dark red, and S7 with purple. We picked a sequence of colors using the get_seq_colors() function. This function returns a sequence of HEX color codes that can be used to specify the coloring scheme for plot_tree() function.

colors <- c(get_seq_colors("Blues", 2), get_seq_colors("Greens", 2), get_seq_colors("Reds", 2), get_seq_colors("Purples", 1))
names(colors) <- paste0("S", 1:7)
plot_tree(tree, colors = colors, font_size = 15)

We can visualize the estimated admixture proportions using the barplot_admix function, which generates the following plot.

barplot_admix(Q_hat, colors = colors, subpops = fam_hgdp$subpop, indiv_on_cols = TRUE)

We also can visualize the coancestry among antecedent populations by heatmaps.

par(xpd = TRUE)
heatmap_coanc_antepops(coanc_pops_sup, tl.offset = 1)

Calculating individual-level coancestry under super admixture and standard admixture

We can obtain the corresponding individual-level coancestry under the super admixture model and under the standard admixture model as follows.

coanc_sup <- t(Q_hat) %*% coanc_pops_sup %*% Q_hat
coanc_std <- t(Q_hat) %*% coanc_pops_std %*% Q_hat

Simulating genotypes from the super-admixture model

# approximate ancestral allele frequencies by average allele frequencies
p_anc <- 0.5 * colMeans(X_amr, na.rm = TRUE)

# simulate genotypes according to the double-admixture method
X_sim_amr <- dbl_admixture(p_anc, coanc_pops_sup, Q_hat, geno_only = TRUE)

Citations

• Danfeng Chen, John D. Storey. 2024. "Coancestry superposed on admixed populations yields measures of relatedness at individual-level resolution." bioRxiv doi: 10.1101/2024.12.29.630632.
• For users of ALStructure for estimating admixture proportions, please cite: Irineo Cabreros, John D. Storey. 2019. "A likelihood-free estimator of population structure bridging admixture models and principal components analysis." doi: 10.1534/genetics.119.302159.
• For users of structured Hardy–Weinberg Equilibrium test, please cite: Wei Hao, John D. Storey. 2019. "Extending tests of Hardy–Weinberg Equilibrium to structured populations." doi: 10.1534/genetics.119.302370.