Last updated: 2020-04-24

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Rmd b426ca9 jgblanc 2020-04-24 added supplemental stuff 
get_cm <- function(Ve) {
## Kinship Matrix for all LMAD lines 
myF <- read.table('../data/Kinship_matrices/F_Kern.txt')

## Set Parameters for Simulated data 
means <- rep(0,nrow(myF))
Va <- 1 
Ve <- Ve
I <- diag(nrow(myF))
sig <- as.matrix((myF * 2 * Va) + (Ve * I))

## Simulate n number of random draws 
dat1 <- mvrnorm(n = 500, mu = means, Sigma = sig)
## Transpose simulated data to get in the correct form 
df1 <- t(dat1)

## Mean center the data 
for (i in 1:ncol(df1)){
  df1[,i] <- scale(df1[,i], scale = FALSE)
}

## Get Eigen Values and Vectors 
myE <- eigen(myF)
E_vectors <- myE$vectors
E_values <- myE$values

## Make new matrix to collect Z values
df2 <- data.frame(matrix(ncol=ncol(df1), nrow=nrow(df1)))
colnames(df2) <- colnames(df1[1:ncol(df1)])
rownames(df2) <- rownames(df1)

## Calculate Q values by multiplying the mean-centered expression value by each eigen vector 
for (i in 1:ncol(df2)) {
  #print(i)
  mean_centered_data <- t(as.matrix(as.numeric(df1[,i])))
  for (k in 1:nrow(df2)){
    u <- as.matrix(as.numeric(E_vectors[,k]))
    value <- mean_centered_data %*% u
    df2[k,i] <- value
  }
}


## Get the square root of the Eigen values   
de <- data.frame(matrix(nrow = nrow(myF),ncol = 2))
de$Egien_values <- E_values 
de$Sqrt_EV <- sqrt((de$Egien_values))

## Calculate C-values by dividing Q values by the square root of the eigen values
df4 <- data.frame(matrix(ncol=ncol(df2),nrow=nrow(df2)))
for (i in 1:ncol(df2)){
  df4[,i] <- (df2[,i] / de$Sqrt_EV)
}

for (i in 1:ncol(df4)) {
  df4[,i] <- scale(df4[,i])
}

cvar_sim <- data.frame(matrix(ncol=1, nrow = nrow(myF)))
for (i in 1:nrow(myF)) {
  val <- t(df4[i,])
  val <- var(val[,1])
  cvar_sim[i,1] <- val 
}
return(cvar_sim)
}
zero <- get_cm(Ve = 0)
one <- get_cm(Ve = 0.25)
two <- get_cm(Ve = 0.5)

dat <- cbind(zero, one, two)
colnames(dat) <- c("zero", "one", "two")
dat$PC <- seq(from = 1, to= 207, by =1)

dat2 <- dat[1:200,]

dat3 <- melt(dat2, id.vars = "PC")


col <- c("darkblue", "darkgreen", "deeppink")

pl1 <- ggplot(dat3, aes(x = PC, y = value, color = variable)) + geom_point(alpha = 0.5) + scale_color_manual(values = col, labels = c("Ve = 0", "Ve = Va/4", "Ve = Va/2")) + theme_classic() +  theme(legend.position=c(0.1,0.85)) + theme(legend.title=element_blank()) + ylab("Var(Cm)") + ggtitle("Variance in Cm: Neutral Simulations") + theme(plot.title = element_text(hjust = 0.5)) + theme(legend.background = element_rect(size=0.5, linetype="solid", fill = "lightgray",
                                  colour ="black"))

pl1

get_cm_real <- function(myTissue){
  print(myTissue)
  # Read in mean-centered expression values
  df1 <- read.table(paste("../data/Mean_centered_expression/",myTissue,".txt",sep=""))
  geneNames = names(df1)
  # Read in tissue specific kinship matrix 
  myF <- read.table(paste('../data/Kinship_matrices/F_',myTissue,'.txt',sep=""))

  ## Get Eigen Values and Vectors 
  myE <- eigen(myF)
  E_vectors <- myE$vectors
  E_values <- myE$values

  ## Testing for selection on first 5 PCs
  myM = 1:nrow(myF)

  ## Using the last 1/2 of PCs to estimate Va
  myL = 6:dim(myF)[1]

  # # test for selection on each gene
  allGeneOutput <- matrix(nrow=nrow(myF), ncol=ncol(df1))
  for (i in 1:ncol(df1)) {
    myQpc = calcQpc(myZ = df1[,i], myU = E_vectors, myLambdas = E_values, myL = myL, myM = myM)
    allGeneOutput[,i] <- myQpc$cm[1,]
  }

  return(allGeneOutput)
}
C_kern <- get_cm_real("Kern")
[1] "Kern"
for (i in 1:ncol(C_kern)) {
  C_kern[,i] <- scale(C_kern[,i])
}

cvar_kern <- data.frame(matrix(ncol=1, nrow = 207))
for (i in 1:207) {
  val <- C_kern[i,]
  val <- var(val)
  cvar_kern[i,1] <- val 
}

plot(cvar_kern[,1])

C_gshoot <- get_cm_real("Gshoot")
[1] "Gshoot"
for (i in 1:ncol(C_gshoot)) {
  C_gshoot[,i] <- scale(C_gshoot[,i])
}

cvar_gshoot <- data.frame(matrix(ncol=1, nrow = 239))
for (i in 1:239) {
  val <- C_gshoot[i,]
  val <- var(val, na.rm = T)
  cvar_gshoot[i,1] <- val 
}

plot(cvar_gshoot[,1])

C_groot <- get_cm_real("GRoot")
[1] "GRoot"
for (i in 1:ncol(C_groot)) {
  C_groot[,i] <- scale(C_groot[,i])
}

cvar_groot <- data.frame(matrix(ncol=1, nrow = 232))
for (i in 1:232) {
  val <- C_groot[i,]
  val <- var(val, na.rm = T)
  cvar_groot[i,1] <- val 
}

plot(cvar_groot[,1])

cvar_kern2 <- cvar_kern[1:200,]
cvar_gshoot2 <- cvar_gshoot[1:200,]
cvar_groot2 <- cvar_groot[1:200,]
PC <- seq(1,200)
data_plot <- cbind(PC, cvar_kern2, cvar_gshoot2, cvar_groot2)
colnames(data_plot) <- c("PC", "Kern", "GShoot", "GRoot")


data_plot2 <- melt(data_plot, id.vars = "PC")
data_plot2 <- data_plot2[-c(1:200), ]

col <- c("darkblue", "darkgreen", "deeppink")

pl2 <- ggplot(dat = data_plot2, aes(x = Var1, y = value, color = Var2)) + geom_point(alpha = 0.5) +  ylab("Var(Cm)") + ggtitle("Kernel Data") + scale_color_manual(values = col) + theme_classic() + theme(plot.title = element_text(hjust = 0.5))  +  theme(legend.position=c(0.1,0.85)) + theme(legend.title=element_blank()) + ylab("Var(Cm)") + ggtitle("Variance in Cm: Real Data") +  theme(legend.background = element_rect(size=0.5, linetype="solid", fill = "lightgray",colour ="black")) + geom_rect(mapping=aes(xmin=101, xmax=200, ymin=-Inf, ymax=Inf),fill = "lightyellow", inherit.aes= F, alpha = 0.0138)
pl2

library(ggpubr)
Loading required package: magrittr
pl <- ggarrange(pl1, pl2,  labels = c("A", "B"))

pl

ggsave("../figures/Supplement_Ve.png", pl, width = 13, height = 6)

sessionInfo()
R version 3.6.2 (2019-12-12)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS High Sierra 10.13.6

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.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] ggpubr_0.2.5      magrittr_1.5      quaint_0.0.0.9000 dplyr_0.8.4      
[5] ggplot2_3.2.1     reshape2_1.4.3    MASS_7.3-51.4     workflowr_1.6.0  

loaded via a namespace (and not attached):
 [1] Rcpp_1.0.3       compiler_3.6.2   pillar_1.4.3     later_1.0.0     
 [5] git2r_0.26.1     plyr_1.8.5       tools_3.6.2      digest_0.6.25   
 [9] evaluate_0.14    lifecycle_0.1.0  tibble_2.1.3     gtable_0.3.0    
[13] pkgconfig_2.0.3  rlang_0.4.4      yaml_2.2.1       xfun_0.12       
[17] withr_2.1.2      stringr_1.4.0    knitr_1.28       fs_1.3.1        
[21] cowplot_1.0.0    rprojroot_1.3-2  grid_3.6.2       tidyselect_1.0.0
[25] glue_1.3.1       R6_2.4.1         rmarkdown_2.1    farver_2.0.3    
[29] purrr_0.3.3      whisker_0.4      backports_1.1.5  scales_1.1.0    
[33] promises_1.1.0   htmltools_0.4.0  assertthat_0.2.1 colorspace_1.4-1
[37] ggsignif_0.6.0   httpuv_1.5.2     labeling_0.3     stringi_1.4.6   
[41] lazyeval_0.2.2   munsell_0.5.0    crayon_1.3.4