In charlotte-ngs/lbgfs2021: Livestock Breeding and Genomics (ETHZ) - Fall Semester 2021

knitr::opts_chunk$set(echo = TRUE)

Data

nr_animal <- 5
tbl_decomp <- tibble::tibble(Animal = c(1:nr_animal),
                             Sire = c(NA, NA, NA, 1, 4),
                             Dam = c(NA, NA, NA, 2, 3),
                             Trait = c(4.5, 2.9, 3.9, 3.5, 5.0))
tbl_decomp

Model

$$y = X\mu + Zu + e$$

Components

X = matrix(1, nrow = nr_animal, ncol = 1)
X

Z = diag(1, nrow = nr_animal)
Z

Pedigree

ped = pedigreemm::pedigree(sire = tbl_decomp$Sire, 
                           dam = tbl_decomp$Dam,
                           label = as.character(1:nr_animal))
Ainv <- as.matrix(pedigreemm::getAInv(ped = ped))
Ainv

MME

xtx <- crossprod(X)
xtx

xtz <- crossprod(X, Z)
xtz

ztx <- crossprod(Z, X)
ztx

ztz <- crossprod(Z)
ztz

sigmae2 <- 40
sigmau2 <- 20
lambda <- sigmae2/sigmau2
lambda

ztzainvlambda <- ztz + Ainv * lambda
ztzainvlambda

coef_mat <- rbind(cbind(xtx, xtz), cbind(ztx, ztzainvlambda))
coef_mat

y <- tbl_decomp$Trait
xty <- crossprod(X,y)
zty <- crossprod(Z,y)
rhs <- rbind(xty, zty)
rhs 

Solutions

sol <- solve(coef_mat, rhs)
sol

Problem 1: Decomposition

From the lecture, we know how the predicted breeding value of animal $4 can be decomposed into different components. Verify this decomposition based on the solutions obtained above.

Solution

Problem 2: Reliabilities

Compute the reliabilities of all the predicted breeding values.

Solution

charlotte-ngs/lbgfs2021 documentation built on Dec. 19, 2021, 3:01 p.m.