Last updated: 2019-02-24

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Imports

Lets import some needed packages:

library(ggplot2)
library(tidyr)
library(dplyr)
library(RColorBrewer)
source("../code/viz.R")

Human Origins Global (LD Pruned)

This is the full Human Origins dataset 2068 sampled from around the world. I filtered out rare variants with global minor allele frequency less than 5%, and remove any variants with a missingness level greater than 1%. I then LD pruned the SNPs using standard parameters in plink, resulting in 167178 SNPs.

Greedy

Lets first read the greedy flashier fit

flash_fit = readRDS("../output/flash_greedy/hoa_global_ld/HumanOriginsPublic2068_maf_geno_ldprune.rds")
K = ncol(flash_fit$loadings$normalized.loadings[[1]]) 
n = nrow(flash_fit$loadings$normalized.loadings[[1]])
p = nrow(flash_fit$loadings$normalized.loadings[[2]])
print(K)
[1] 21
print(n)
[1] 2068
print(p)
[1] 167178

Lets now plot the distribution of factors for each drift event

# read factors
delta_df = as.data.frame(flash_fit$loadings$normalized.loadings[[2]])
colnames(delta_df)[1:K] = 1:K 

# gather the data.frame for plotting
delta_gath_df = delta_df %>% 
                gather(K, value) %>%
                filter(K!=1)

# plot the factors
K_ = K
p_fct = ggplot(delta_gath_df, aes(x=value)) + 
        scale_fill_manual(values = getPalette(K_)) +
        geom_histogram() + 
        facet_wrap(~factor(K, levels=2:K_), scales = "free") + 
        labs(fill="K") + 
        scale_x_continuous(breaks = scales::pretty_breaks(n = 3)) +
        scale_y_continuous(breaks = scales::pretty_breaks(n = 3)) + 
        theme_bw()
p_fct

Expand here to see past versions of flash-greedy-ld-viz-factors-1.png:
Version Author Date
f5ef1af jhmarcus 2019-02-15

We can see the later factors tend to get sparser but they still seem to contribute! Here is a plot of the “proportion of variance explained” of each factor:

qplot(2:K, flash_fit$pve[2:K]) + ylab("Proportion of Varaince Explained") + xlab("K") + theme_bw()

print(flash_fit$pve)
 [1] 0.4750002010 0.0221931227 0.0180913971 0.0103143286 0.0025255466
 [6] 0.0015774930 0.0045260494 0.0014121917 0.0012173854 0.0007676335
[11] 0.0006728921 0.0008111508 0.0002212648 0.0003887796 0.0002380212
[16] 0.0002352021 0.0001895606 0.0002282840 0.0002907459 0.0001156450
[21] 0.0001605612

It looks like the PVE drops off at around 11 or so? I setup the flashier run so it estimates a SNP specific precision term. Here is a histogram of fitted variances:

qplot(1/flash_fit$fit$est.tau) + xlab("Estimated Variance") + ylab("Count") + theme_bw()

Lets now look the the fitted means:

qplot(delta_df$`1`) + xlab("Estimated Mean") + ylab("Count") + theme_bw()

The mean seems a bit smaller than I would have expected? These plots looks about reasonable as each of the SNP variances should roughly be interpreted as average heterozygosity \(\approx 2p(1-p)\)? The mean term should roughly be interpreted as the mean allele frequency at the SNP and thus we should see a quadratic relationship with the estimated variance:

p_mv = qplot(delta_df$`1`, 1/flash_fit$fit$est.tau, alpha=.3) + 
       xlab("Estimated Mean") + ylab("Estimated Variance") + 
       scale_alpha(guide = "none") + 
       theme_bw()
p_mv

Lets now take a look at the loadings. First we setup a data.frame that we can work with:

# read the meta data
meta_df = read.table("../data/meta/HumanOriginsPublic2068_maf_geno_ldprune.meta", sep=" ", header=T)

# setup loadings data.frame
l_df = as.data.frame(flash_fit$loadings$normalized.loadings[[1]])
K = ncol(l_df)
l_df$iid = as.vector(meta_df$iid) # individual ids
l_df$clst = meta_df$clst # population labels
pops = unique(l_df$clst) # all unique pop labels

# join with the meta data
l_df = l_df %>% inner_join(meta_df, on="clst")
l_df = l_df %>% arrange(region, clst) # sort by region then by population
l_df$iid = factor(l_df$iid, levels = l_df$iid) # make sure the ids are sorted
colnames(l_df)[1:K] = 1:K

head(l_df)
           1           2            3          4            5          6
1 0.02198997 0.009454832 4.485180e-06 0.02211841 3.303098e-05 0.01764253
2 0.02198997 0.009511229 4.406670e-06 0.02247997 4.952488e-05 0.01608845
3 0.02198997 0.006147078 4.086449e-06 0.02482062 2.726321e-05 0.01692735
4 0.02198997 0.009103984 4.338176e-06 0.02293795 2.797966e-05 0.01742585
5 0.02198997 0.009529573 4.394827e-06 0.02267025 3.845100e-05 0.01450389
6 0.02198997 0.009243629 4.460459e-06 0.02215776 2.795106e-05 0.01760249
            7            8            9           10           11
1 0.004374536 1.089539e-03 2.812993e-05 3.470028e-05 3.866924e-05
2 0.003241962 4.231122e-04 2.932860e-05 3.615817e-05 3.888100e-05
3 0.004951296 9.893482e-05 2.583221e-05 3.555401e-05 3.744459e-05
4 0.004661258 1.784788e-04 2.702595e-05 3.411185e-05 3.742829e-05
5 0.004437185 8.043608e-04 2.643633e-05 3.423255e-05 3.784264e-05
6 0.005064440 8.324509e-05 2.791866e-05 3.363985e-05 3.856931e-05
          12           13           14         15           16
1 0.05017069 8.140998e-05 4.952727e-05 0.08068407 7.771326e-05
2 0.04589132 8.638569e-05 5.161609e-05 0.05897009 7.994484e-05
3 0.05074213 8.358567e-05 5.114096e-05 0.08024062 7.892103e-05
4 0.05519966 7.798145e-05 4.992192e-05 0.09129734 8.299529e-05
5 0.05242051 7.961690e-05 4.865967e-05 0.09571542 8.121683e-05
6 0.05152888 8.057720e-05 5.030271e-05 0.07831456 7.913664e-05
            17           18           19           20           21
1 7.842225e-05 1.019054e-04 2.147227e-04 8.793061e-05 8.502300e-05
2 8.227041e-05 8.412758e-05 1.665734e-04 8.801740e-05 1.154576e-04
3 9.672675e-05 8.794415e-05 1.557965e-04 8.469595e-05 2.321882e-04
4 8.006631e-05 1.754711e-04 9.898022e-05 8.627449e-05 3.734673e-04
5 7.616521e-05 8.802899e-05 1.127468e-04 8.540387e-05 6.950001e-03
6 8.043370e-05 8.734172e-05 2.415143e-04 8.651963e-05 8.910156e-05
            iid     clst region country  lat lon    clst2
1 Algerian43A22 Algerian Africa Algeria 36.8   3 Algerian
2 Algerian43A21 Algerian Africa Algeria 36.8   3 Algerian
3 Algerian43A34 Algerian Africa Algeria 36.8   3 Algerian
4 Algerian43A13 Algerian Africa Algeria 36.8   3 Algerian
5 Algerian43A24 Algerian Africa Algeria 36.8   3 Algerian
6 Algerian43A32 Algerian Africa Algeria 36.8   3 Algerian

Its hard to find a color scale that can sufficiently visualize all of the loadings in a single plot. Instead I just split the loadings up into two plots (K=2,…,11) and (K=12,…,21). Lets first visualize loadings 2 through 12:

# gather the data.frame for plotting
l_gath_df = l_df %>% 
            gather(K, value, -iid, -clst, -region, -country, -lat, -lon, -clst2) %>% 
            filter(K %in% paste0(2:11))

# Africa
africa_pops = get_pops(meta_df, "Africa")
p_africa = positive_structure_plot(l_gath_df %>% filter(region == "Africa"), 
                                   africa_pops, colset="Set3", label_size=5) +
           ggtitle("Africa") + theme(plot.title = element_text(size=6))

# America
america_pops = get_pops(meta_df, "America")
p_america = positive_structure_plot(l_gath_df %>% filter(region == "America"), 
                                    america_pops, colset="Set3", label_size=5) + 
            ggtitle("America") + theme(plot.title = element_text(size=6))

# Central Asia Siberia
central_asia_siberia_pops = get_pops(meta_df, "CentralAsiaSiberia")
p_central_asia_siberia = positive_structure_plot(l_gath_df %>% filter(region == "CentralAsiaSiberia"), 
                                                 central_asia_siberia_pops, colset="Set3", label_size=5) + 
                         ggtitle("CentralAsiaSiberia") + theme(plot.title = element_text(size=6))

# East Asia
east_asia_pops = get_pops(meta_df, "EastAsia")
p_east_asia = positive_structure_plot(l_gath_df %>% filter(region == "EastAsia"), 
                                      east_asia_pops, colset="Set3", label_size=5) + 
              ggtitle("EastAsia") + theme(plot.title = element_text(size=6))

# South Asia
south_asia_pops = get_pops(meta_df, "SouthAsia")
p_south_asia= positive_structure_plot(l_gath_df %>% filter(region == "SouthAsia"),
                                      south_asia_pops, colset="Set3", label_size=5) + 
              ggtitle("SouthAsia") + theme(plot.title = element_text(size=6))

# West Eurasia
west_eurasia_pops = get_pops(meta_df, "WestEurasia")
p_west_eurasia = positive_structure_plot(l_gath_df %>% filter(region == "WestEurasia"), 
                                         west_eurasia_pops, colset="Set3", label_size=5) + 
                 ggtitle("WestEurasia") + theme(plot.title = element_text(size=6))

# Oceania
oceania_pops = get_pops(meta_df, "Oceania")
p_oceania = positive_structure_plot(l_gath_df %>% filter(region == "Oceania"), 
                                    oceania_pops, colset="Set3", label_size=5) + 
            ggtitle("Oceania") + theme(plot.title = element_text(size=6))

# Global
p = cowplot::plot_grid(p_africa, p_west_eurasia, p_central_asia_siberia, p_america, p_east_asia, p_south_asia, p_oceania, 
                       rel_heights = c(1.2, 1.3, 1, 1, 1, 1, 1.1),
                       nrow = 7, align = "v") 
p

Lets now visualize loadings 12 to 21 (be careful: there is no connection to the colors in the last plot):

# gather the data.frame for plotting
l_gath_df = l_df %>% 
            gather(K, value, -iid, -clst, -region, -country, -lat, -lon, -clst2) %>% 
            filter(K %in% paste0(12:21))

# Africa
africa_pops = get_pops(meta_df, "Africa")
p_africa = positive_structure_plot(l_gath_df %>% filter(region == "Africa"), 
                                   africa_pops, colset="Set3", label_size=5) +
           ggtitle("Africa") + theme(plot.title = element_text(size=6))

# America
america_pops = get_pops(meta_df, "America")
p_america = positive_structure_plot(l_gath_df %>% filter(region == "America"), 
                                    america_pops, colset="Set3", label_size=5) + 
            ggtitle("America") + theme(plot.title = element_text(size=6))

# Central Asia Siberia
central_asia_siberia_pops = get_pops(meta_df, "CentralAsiaSiberia")
p_central_asia_siberia = positive_structure_plot(l_gath_df %>% filter(region == "CentralAsiaSiberia"), 
                                                 central_asia_siberia_pops, colset="Set3", label_size=5) + 
                         ggtitle("CentralAsiaSiberia") + theme(plot.title = element_text(size=6))

# East Asia
east_asia_pops = get_pops(meta_df, "EastAsia")
p_east_asia = positive_structure_plot(l_gath_df %>% filter(region == "EastAsia"), 
                                      east_asia_pops, colset="Set3", label_size=5) + 
              ggtitle("EastAsia") + theme(plot.title = element_text(size=6))

# South Asia
south_asia_pops = get_pops(meta_df, "SouthAsia")
p_south_asia= positive_structure_plot(l_gath_df %>% filter(region == "SouthAsia"),
                                      south_asia_pops, colset="Set3", label_size=5) + 
              ggtitle("SouthAsia") + theme(plot.title = element_text(size=6))

# West Eurasia
west_eurasia_pops = get_pops(meta_df, "WestEurasia")
p_west_eurasia = positive_structure_plot(l_gath_df %>% filter(region == "WestEurasia"), 
                                         west_eurasia_pops, colset="Set3", label_size=5) + 
                 ggtitle("WestEurasia") + theme(plot.title = element_text(size=6))

# Oceania
oceania_pops = get_pops(meta_df, "Oceania")
p_oceania = positive_structure_plot(l_gath_df %>% filter(region == "Oceania"), 
                                    oceania_pops, colset="Set3", label_size=5) + 
            ggtitle("Oceania") + theme(plot.title = element_text(size=6))

# Global
p = cowplot::plot_grid(p_africa, p_west_eurasia, p_central_asia_siberia, p_america, p_east_asia, p_south_asia, p_oceania, 
                       rel_heights = c(1.2, 1.3, 1, 1, 1, 1, 1.1),
                       nrow = 7, align = "v") 
p

Its kinda interesting to see that some populations have zero loading on later factors. This would be difficult to visualize see if using a single plot for all the factors.

ADMIXTURE

Lets visualize ADMIXTURE with 9 factors which should roughly align to the first plot i.e. FLASH with 2,…,11 (be careful: there is no connection to the colors in the last plot):

l_df = read.table("../output/admixture/hoa_global_ld/HumanOriginsPublic2068_maf_geno_ldprune.K9r1.Q", sep=" ", header=F)
K = ncol(l_df)

l_df$iid = as.vector(meta_df$iid) # individual ids
l_df$clst = meta_df$clst # population labels

# join with the meta data
l_df = l_df %>% inner_join(meta_df, on="clst")
l_df = l_df %>% arrange(region, clst) # sort by region then by population
l_df$iid = factor(l_df$iid, levels = l_df$iid) # make sure the ids are sorted
colnames(l_df)[1:K] = 1:K

# gather the data.frame for plotting
l_gath_df = l_df %>% 
            gather(K, value, -iid, -clst, -region, -country, -lat, -lon, -clst2)

# Africa
africa_pops = get_pops(meta_df, "Africa")
p_africa = positive_structure_plot(l_gath_df %>% filter(region == "Africa"), 
                                   africa_pops, colset="Set3", label_size=5) +
           ggtitle("Africa") + theme(plot.title = element_text(size=6))

# America
america_pops = get_pops(meta_df, "America")
p_america = positive_structure_plot(l_gath_df %>% filter(region == "America"), 
                                    america_pops, colset="Set3", label_size=5) + 
            ggtitle("America") + theme(plot.title = element_text(size=6))

# Central Asia Siberia
central_asia_siberia_pops = get_pops(meta_df, "CentralAsiaSiberia")
p_central_asia_siberia = positive_structure_plot(l_gath_df %>% filter(region == "CentralAsiaSiberia"), 
                                                 central_asia_siberia_pops, colset="Set3", label_size=5) + 
                         ggtitle("CentralAsiaSiberia") + theme(plot.title = element_text(size=6))

# East Asia
east_asia_pops = get_pops(meta_df, "EastAsia")
p_east_asia = positive_structure_plot(l_gath_df %>% filter(region == "EastAsia"), 
                                      east_asia_pops, colset="Set3", label_size=5) + 
              ggtitle("EastAsia") + theme(plot.title = element_text(size=6))

# South Asia
south_asia_pops = get_pops(meta_df, "SouthAsia")
p_south_asia= positive_structure_plot(l_gath_df %>% filter(region == "SouthAsia"),
                                      south_asia_pops, colset="Set3", label_size=5) + 
              ggtitle("SouthAsia") + theme(plot.title = element_text(size=6))

# West Eurasia
west_eurasia_pops = get_pops(meta_df, "WestEurasia")
p_west_eurasia = positive_structure_plot(l_gath_df %>% filter(region == "WestEurasia"), 
                                         west_eurasia_pops, colset="Set3", label_size=5) + 
                 ggtitle("WestEurasia") + theme(plot.title = element_text(size=6))

# Oceania
oceania_pops = get_pops(meta_df, "Oceania")
p_oceania = positive_structure_plot(l_gath_df %>% filter(region == "Oceania"), 
                                    oceania_pops, colset="Set3", label_size=5) + 
            ggtitle("Oceania") + theme(plot.title = element_text(size=6))

# Global
p = cowplot::plot_grid(p_africa, p_west_eurasia, p_central_asia_siberia, p_america, p_east_asia, p_south_asia, p_oceania, 
                       rel_heights = c(1.2, 1.3, 1, 1, 1, 1, 1.1),
                       nrow = 7, align = "v") 
p

There is a lot that one can compare between the ADMIXTURE and FLASH results. A high level observation seems that the ADMIXTURE results look a bit more clustered i.e. the Americas and East Asia look like they are explained mostly by 1 or 2 factors whereas FLASH uses 3-4. Its hard to tell be it seems that this is true in many of the super regions … ADMIXTURE tends use fewer factors to explain population structure in each region, leaing to a more clustered result?

Session information

sessionInfo()
R version 3.5.1 (2018-07-02)
Platform: x86_64-apple-darwin13.4.0 (64-bit)
Running under: macOS  10.14.2

Matrix products: default
BLAS/LAPACK: /Users/jhmarcus/miniconda3/lib/R/lib/libRblas.dylib

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] bindrcpp_0.2.2     RColorBrewer_1.1-2 dplyr_0.7.6       
[4] tidyr_0.8.1        ggplot2_3.0.0     

loaded via a namespace (and not attached):
 [1] Rcpp_1.0.0        compiler_3.5.1    pillar_1.3.0     
 [4] git2r_0.23.0      plyr_1.8.4        workflowr_1.1.1  
 [7] bindr_0.1.1       R.methodsS3_1.7.1 R.utils_2.7.0    
[10] tools_3.5.1       digest_0.6.18     evaluate_0.12    
[13] tibble_1.4.2      gtable_0.2.0      pkgconfig_2.0.1  
[16] rlang_0.3.1       yaml_2.2.0        xfun_0.4         
[19] flashier_0.1.0    withr_2.1.2       stringr_1.3.1    
[22] knitr_1.21        cowplot_0.9.4     rprojroot_1.3-2  
[25] grid_3.5.1        tidyselect_0.2.4  glue_1.3.0       
[28] R6_2.3.0          rmarkdown_1.11    reshape2_1.4.3   
[31] purrr_0.2.5       magrittr_1.5      whisker_0.3-2    
[34] backports_1.1.2   scales_0.5.0      htmltools_0.3.6  
[37] assertthat_0.2.0  colorspace_1.3-2  labeling_0.3     
[40] stringi_1.2.4     lazyeval_0.2.1    munsell_0.5.0    
[43] crayon_1.3.4      R.oo_1.22.0

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