Last updated: 2020-06-01

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Knit directory: drift-workflow/analysis/

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These are the previous versions of the repository in which changes were made to the R Markdown (analysis/OutOfAfrica_3G09_fix.Rmd) and HTML (docs/OutOfAfrica_3G09_fix.html) files. If you’ve configured a remote Git repository (see ?wflow_git_remote), click on the hyperlinks in the table below to view the files as they were in that past version.

File Version Author Date Message
Rmd 5b4cd63 Joseph Marcus 2020-06-01 updated to larger sample size for ooa fixed sim
html cb9009e Joseph Marcus 2020-05-21 Build site.
Rmd 3549c6d Joseph Marcus 2020-05-21 wflow_publish(“index.Rmd”)
html f66648a Joseph Marcus 2020-05-20 Build site.
Rmd e4cdfd8 Joseph Marcus 2020-05-20 wflow_publish(“OutOfAfrica_3G09_fix.Rmd”)
html 1dde8eb Joseph Marcus 2020-05-20 Build site.
Rmd e42d06d Joseph Marcus 2020-05-20 wflow_publish(“OutOfAfrica_3G09_fix.Rmd”)
html 5f94116 Joseph Marcus 2020-05-18 Build site.
Rmd 59c3de9 Joseph Marcus 2020-05-18 wflow_publish(“OutOfAfrica_3G09_fix.Rmd”)
html 484ce56 Joseph Marcus 2020-05-18 Build site.
Rmd 36c05dd Joseph Marcus 2020-05-18 wflow_publish(“analysis/OutOfAfrica_3G09_fix.Rmd”)
Rmd 865cef4 Joseph Marcus 2020-05-18 added fixed shared factor
html 865cef4 Joseph Marcus 2020-05-18 added fixed shared factor

Here I visualize population structure with simulated data from the OutOfAfrica_3G09 scenario. See Figure 2. from Gutenkunst et al. 2009.

Below, I show a number of EBMF solutions and in each of them I don’t display the first shared factor which is prefixed to the one-vector and scale the loadings by the prior variance. I only describe the loadings that remain after the shared factor.

Imports

Import the required libraries and scripts:

suppressMessages({
  library(lfa)
  library(flashier)
  library(drift.alpha)
  library(ggplot2)
  library(RColorBrewer)
  library(reshape2)
  library(tidyverse)
  library(alstructure)
  source("../code/structure_plot.R")
})

Data

data_path <- "../output/simulations/OutOfAfrica_3G09/rep1.txt"
G <- t(as.matrix(read.table(data_path, sep=" ")))
colnames(G) <- NULL
rownames(G) <- NULL
n <- nrow(G)
daf <- colSums(G) / (2 * n)
colors <- brewer.pal(8, "Set2")

# filter out too rare and too common SNPs
Y <- G[,((daf>=.05) & (daf <=.95))]
p <- ncol(Y)
print(n)
[1] 300
print(p)
[1] 21492
# sub-population labels from stdpop
labs <- rep(c("YRI", "CEU", "HAN"), each=100)

we end up with 300 individuals and ~20000 SNPs. View fitted the sample covariance matrix:

plot_cov((1.0 / p) * Y %*% t(Y), as.is=T) + 
  scale_fill_viridis_c() + 
  labs(fill="Cov")
Scale for 'fill' is already present. Adding another scale for 'fill',
which will replace the existing scale.

Version Author Date
1dde8eb Joseph Marcus 2020-05-20
865cef4 Joseph Marcus 2020-05-18

plot allele frequencies of Africa vs OOA populations:

daf_afr <- colSums(G[1:100,]) / (2*100)
daf_ooa <- colSums(G[101:300,]) / (2*200)
qplot(daf_ooa, daf_afr, alpha=.1)

Version Author Date
1dde8eb Joseph Marcus 2020-05-20
484ce56 Joseph Marcus 2020-05-18
865cef4 Joseph Marcus 2020-05-18
hist(daf_afr)

Version Author Date
1dde8eb Joseph Marcus 2020-05-20
484ce56 Joseph Marcus 2020-05-18
hist(daf_ooa)

Version Author Date
1dde8eb Joseph Marcus 2020-05-20
484ce56 Joseph Marcus 2020-05-18

flash [greedy]

Run the greedy algorithm:

ones <- matrix(1, nrow = n, ncol = 1)
ls.soln <- t(solve(crossprod(ones), crossprod(ones, Y)))
fl <- flash.init(Y) %>%
  flash.init.factors(EF = list(ones, ls.soln), 
                     prior.family=c(prior.bimodal(), prior.normal())) %>%
  flash.fix.loadings(kset = 1, mode = 1L) %>%
  flash.backfit() %>%
  flash.add.greedy(Kmax=6, prior.family=c(prior.bimodal(), prior.normal()))
Backfitting 1 factors (tolerance: 9.61e-02)...
Wrapping up...
Done.
Adding factor 2 to flash object...
Adding factor 3 to flash object...
Adding factor 4 to flash object...
Adding factor 5 to flash object...
Factor doesn't significantly increase objective and won't be added.
Wrapping up...
Done.
sd <- unlist(lapply(fl$fitted.g[[2]], '[[', 3))
L <- fl$flash.fit$EF[[1]]
s2 <- fl$residuals.sd^2
LDsqrt <- L %*% diag(sd)
K <- ncol(LDsqrt)
plot_loadings(LDsqrt[,2:K], labs) + scale_color_brewer(palette="Set2")

Version Author Date
1dde8eb Joseph Marcus 2020-05-20
484ce56 Joseph Marcus 2020-05-18
865cef4 Joseph Marcus 2020-05-18

view structure plot:

create_structure_plot(L=LDsqrt[,2:K], labels=labs, colors=colors)

Version Author Date
1dde8eb Joseph Marcus 2020-05-20
484ce56 Joseph Marcus 2020-05-18
865cef4 Joseph Marcus 2020-05-18

view fitted covariance matrix:

plot_cov(LDsqrt %*% t(LDsqrt) + s2*diag(n), as.is=T) + 
  scale_fill_viridis_c() +
  labs(fill="Cov") 
Scale for 'fill' is already present. Adding another scale for 'fill',
which will replace the existing scale.

Version Author Date
1dde8eb Joseph Marcus 2020-05-20
484ce56 Joseph Marcus 2020-05-18
865cef4 Joseph Marcus 2020-05-18

the greedy algorithm finds 3 population specific factors.

flash [backfit]

Run flash [backfit] initializing from the greedy solution:

flbf <- fl %>% 
  flash.backfit() %>% 
  flash.nullcheck(remove=TRUE)
Backfitting 4 factors (tolerance: 9.61e-02)...
  Difference between iterations is within 1.0e+02...
  Difference between iterations is within 1.0e+01...
  Difference between iterations is within 1.0e+00...
  Difference between iterations is within 1.0e-01...
Wrapping up...
Done.
Nullchecking 4 factors...
Factor 2 removed, increasing objective by 5.814e-05.
Wrapping up...
Done.
sd <- unlist(lapply(flbf$fitted.g[[2]], '[[', 3))
s2 <- flbf$residuals.sd^2
L <- flbf$flash.fit$EF[[1]]
LDsqrt <- L %*% diag(sd)
K <- ncol(LDsqrt)
plot_loadings(LDsqrt[,2:K], labs) + scale_color_brewer(palette="Set2")

Version Author Date
1dde8eb Joseph Marcus 2020-05-20
484ce56 Joseph Marcus 2020-05-18
865cef4 Joseph Marcus 2020-05-18

view structure plot:

create_structure_plot(L=LDsqrt[,2:K], labels=labs, colors=colors)

Version Author Date
1dde8eb Joseph Marcus 2020-05-20
484ce56 Joseph Marcus 2020-05-18
865cef4 Joseph Marcus 2020-05-18

view fitted covariance matrix:

plot_cov(LDsqrt %*% t(LDsqrt) + s2*diag(n), as.is=T) + 
  scale_fill_viridis_c() +
  labs(fill="Cov")
Scale for 'fill' is already present. Adding another scale for 'fill',
which will replace the existing scale.

Version Author Date
1dde8eb Joseph Marcus 2020-05-20
484ce56 Joseph Marcus 2020-05-18
865cef4 Joseph Marcus 2020-05-18

the backfitting algorithm represents the data with a sparser solution and finds a factor represented by YRI and a small loading from Han and

drift

Run drift initializing from the greedy solution:

init <- init_from_data(Y, Kmax=6)
dr <- drift(init, miniter=2, 
            maxiter=1000, 
            tol=1e-5, 
            verbose=FALSE) 

sd <- sqrt(dr$prior_s2)
L <- dr$EL
LDsqrt <- L %*% diag(sd)
s2 <- dr$resid_s2
K <- ncol(LDsqrt)
plot_loadings(LDsqrt[,2:K], labs) + scale_color_brewer(palette="Set2")

Version Author Date
1dde8eb Joseph Marcus 2020-05-20
484ce56 Joseph Marcus 2020-05-18
865cef4 Joseph Marcus 2020-05-18

view structure plot:

create_structure_plot(L=LDsqrt[,2:K], labels=labs, colors=colors)

Version Author Date
1dde8eb Joseph Marcus 2020-05-20
484ce56 Joseph Marcus 2020-05-18
865cef4 Joseph Marcus 2020-05-18

view fitted covariance matrix:

plot_cov(LDsqrt %*% t(LDsqrt) + s2*diag(n), as.is=T) + 
  scale_fill_viridis_c() +
  labs(fill="Cov")
Scale for 'fill' is already present. Adding another scale for 'fill',
which will replace the existing scale.

Version Author Date
1dde8eb Joseph Marcus 2020-05-20
484ce56 Joseph Marcus 2020-05-18

the drift algorithm converges quickly and maintains the greedy solution. Lets try adding a factor:

dr2 <- drift(add_factor(dr), 
             miniter=2, 
             maxiter=1000, 
             tol=1e-5, 
             verbose=FALSE) 

sd <- sqrt(dr2$prior_s2)
L <- dr2$EL
LDsqrt <- L %*% diag(sd)
s2 <- dr2$resid_s2
K <- ncol(LDsqrt)
plot_loadings(LDsqrt[,2:K], labs) + scale_color_brewer(palette="Set2")

The additional factor does seem to capture much interesting structure.


sessionInfo()
R version 3.5.1 (2018-07-02)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Scientific Linux 7.4 (Nitrogen)

Matrix products: default
BLAS/LAPACK: /software/openblas-0.2.19-el7-x86_64/lib/libopenblas_haswellp-r0.2.19.so

locale:
 [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
 [3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8    
 [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
 [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 
 [9] LC_ADDRESS=C               LC_TELEPHONE=C            
[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       

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

other attached packages:
 [1] alstructure_0.1.0  forcats_0.5.0      stringr_1.4.0     
 [4] dplyr_0.8.5        purrr_0.3.4        readr_1.3.1       
 [7] tidyr_1.0.2        tibble_3.0.1       tidyverse_1.3.0   
[10] reshape2_1.4.3     RColorBrewer_1.1-2 ggplot2_3.3.0     
[13] drift.alpha_0.0.9  flashier_0.2.4     lfa_1.9.0         

loaded via a namespace (and not attached):
 [1] httr_1.4.1        viridisLite_0.3.0 jsonlite_1.6     
 [4] modelr_0.1.6      assertthat_0.2.1  mixsqp_0.3-43    
 [7] cellranger_1.1.0  yaml_2.2.0        ebnm_0.1-24      
[10] pillar_1.4.3      backports_1.1.6   lattice_0.20-38  
[13] glue_1.4.0        digest_0.6.25     promises_1.0.1   
[16] rvest_0.3.5       colorspace_1.4-1  htmltools_0.3.6  
[19] httpuv_1.4.5      Matrix_1.2-15     plyr_1.8.4       
[22] pkgconfig_2.0.3   invgamma_1.1      broom_0.5.6      
[25] haven_2.2.0       corpcor_1.6.9     scales_1.1.0     
[28] whisker_0.3-2     later_0.7.5       git2r_0.26.1     
[31] farver_2.0.3      generics_0.0.2    ellipsis_0.3.0   
[34] withr_2.2.0       ashr_2.2-50       cli_2.0.2        
[37] magrittr_1.5      crayon_1.3.4      readxl_1.3.1     
[40] evaluate_0.14     fansi_0.4.1       fs_1.3.1         
[43] nlme_3.1-137      xml2_1.3.2        truncnorm_1.0-8  
[46] tools_3.5.1       hms_0.5.3         lifecycle_0.2.0  
[49] munsell_0.5.0     reprex_0.3.0      irlba_2.3.3      
[52] compiler_3.5.1    rlang_0.4.5       grid_3.5.1       
[55] rstudioapi_0.11   labeling_0.3      rmarkdown_1.10   
[58] gtable_0.3.0      DBI_1.0.0         R6_2.4.1         
[61] lubridate_1.7.4   knitr_1.20        workflowr_1.6.1  
[64] rprojroot_1.3-2   stringi_1.4.6     parallel_3.5.1   
[67] SQUAREM_2020.2    Rcpp_1.0.4.6      vctrs_0.2.4      
[70] dbplyr_1.4.3      tidyselect_1.0.0