Meta-analysis of genome-wide predictions- part 2

Introduction

This is an extension to the previous report titled “Individual and meta-analysis of genomide-wide predictions”. Here, we further show some relationships and estimated breeding values using meta-SNP effects across populations. Note, this document (as well as the previous) uses the same ‘ultimate meat pH’ as the phenotypic variable.

Load Libraries

library(data.table)
library(gwaR)
library(regress)
library(Matrix)
library(knitr)
library(magrittr)
library(ggplot2)
library(kableExtra)
library(qqman)

Load Necessary Functions and datasets

Basically, the gwaR package was used in computing these functions to perform the genome-wide prediction from genomic best linear unbiased prediction (GBLUP).

source("Toolkit_function.R")
source("toolkit_function_Meta_v2.R")
load("Pop1.Rdata")
load("comm_g_var.Rdata")
load("Pop2.Rdata")
load("msu_g_var.Rdata")
load("Pop3.Rdata")
load("marc_g_var.Rdata")

#Required population datasets were loaded as in part1

Meta-Analysis

• The table shows parameters such as meta-fixed effect (\(\hat\beta\)) and meta-SNP effect \(\hat{g}\) obtained using the meta-fixed effect. The meta-analysis is based on the SNP-centric model.
• Also, the additive genetic variance, fixed effect, Z_score, and p_value for each population can be accessed using the \(result\) list in the meta object.

meta <- meta_gp(N = c(1857, 904, 530), comm_g_var, Pop1, msu_g_var, Pop2,
              marc_g_var, Pop3)
#Summary of meta-analysis
meta$table

Meta analysis table (First 6 rows)

SE_Meta	Z_Meta	p_Meta	\(\beta_Meta\)	\(\hat{g}_Meta\)
0.5691040	-2.1916848	0.0284023	-1.2472965	-0.0280941
0.6373828	-0.1952363	0.8452079	-0.1244403	-0.0022345
0.5696505	1.5758466	0.1150612	0.8976818	0.0201806
0.5838699	0.7643431	0.4446628	0.4462769	0.0095500
0.5826945	0.7308853	0.4648492	0.4258828	0.0091503
0.6059635	-1.6794179	0.0930706	-1.0176659	-0.0202182

Output for Estimated genetic variance

kable(x1, caption="Estimated genetic variance", col.names = c("Pop1", "Pop2", "Pop3", "Meta"))%>%kable_styling(latex_options = "scale down")

Estimated genetic variance

Pop1	Pop2	Pop3	Meta
0.0097099	0.0030214	0.0061176	0.0072951

Output for Meta-\(\hat{g}\) using population variances and Meta-\(\hat{g}\)

kable(x2, col.names = c("Pop1", "Pop2", "Pop3", "Meta"))%>%kable_styling(latex_options = "scale down")

Pop1	Pop2	Pop3	Meta
-0.0373941	-0.0116356	-0.0235597	-0.0280941
-0.0029742	-0.0009255	-0.0018739	-0.0022345
0.0268610	0.0083581	0.0169234	0.0201806
0.0127113	0.0039553	0.0080086	0.0095500
0.0121794	0.0037898	0.0076735	0.0091503
-0.0269110	-0.0083737	-0.0169549	-0.0202182

Comparing Individual Estimated \(\hat{g}\) with meta \(\hat{g}\)

par(mfrow= c(1, 3))
par(mar=c(6,5,6,0))
plot(p1, mt, xlab = expression(hat(g)[POP1]), 
     ylab = expression(hat(g)[Meta]), cex.lab= 1.5, col="orangered3")
plot(p2, mt, xlab = expression(hat(g)[POP2]), 
     ylab = expression(hat(g)[Meta]), cex.lab= 1.5, col="gold3")
plot(p3, mt, xlab = expression(hat(g)[POP3]), 
     ylab = expression(hat(g)[Meta]), cex.lab= 1.5, col="forestgreen")
mtext("Individual Estimated SNP effect vs Meta-SNP effect", side =3, line= -4, outer = TRUE)

Comparing Individual Estimated \(\hat{g}\) vs Meta \(\hat{g}\) using population variance

par(mfrow= c(1, 3))
par(mar=c(6,5,6,0))
plot(p1, g1, xlab = expression(hat(g)[POP1]), 
     ylab = expression(hat(g)[Meta]), cex.lab= 1.5, col="skyblue3")
plot(p2, g2, xlab = expression(hat(g)[POP2]), 
     ylab = expression(hat(g)[Meta]), cex.lab= 1.5, col="burlywood3")
plot(p3, g3, xlab = expression(hat(g)[POP3]), 
     ylab = expression(hat(g)[Meta]), cex.lab= 1.5, col="brown3")
mtext("Individual Estimated SNP effect vs Meta-SNP effect using population variance", side =3, line= -4, outer = TRUE)

Breeding values estimated using meta-SNP effect

Pop1 <- read_poly(com_filter$geno, meta$ghat)

## ......................................... 
## Estimated breeding value showing first 6 animals of 1857 : 
##             [,1]
## [1,]  0.02973056
## [2,]  0.01937412
## [3,]  0.05259549
## [4,]  0.03154981
## [5,] -0.01356126
## [6,]  0.04172895
## .........................................

Pop2 <- read_poly(msu_filter$geno, meta$ghat)

## ......................................... 
## Estimated breeding value showing first 6 animals of 904 : 
##             [,1]
## [1,]  0.04290191
## [2,]  0.03637714
## [3,] -0.12191415
## [4,]  0.04274640
## [5,]  0.10285873
## [6,] -0.03380150
## .........................................

Pop3 <- read_poly(mac_filter$geno, meta$ghat)

## ......................................... 
## Estimated breeding value showing first 6 animals of 530 : 
##             [,1]
## [1,]  0.05680378
## [2,] -0.03529593
## [3,] -0.02191941
## [4,] -0.07912480
## [5,] -0.08487892
## [6,] -0.01974606
## .........................................