Question 1.1

Compute the pairwise relatedness of Ritland (1996) between the first three individuals (i.e.., ID1-ID2, ID1-ID3, and ID2-ID3) based on the first five SNPs in mice.X. Hint: compute a locus specific relaitonship and then average them over loci.

X35 <- mice.X[1:3, 1:5]
n <- nrow(X35)
m <- ncol(X35)
G35 <- matrix(NA, ncol=n, nrow=n)

Question 1.2

Read Pew et al. (2015) paper and download the related R package from here. Verify your results from Question 1.1 using the conancestry() function with the ritland=1 argument. Note that you have to recode your genotype matrix in order to use this function.

library(related)

## Loading required package: tools
## Loading required package: ggplot2

Question 1.3

Write a function that returns the total allelic (TA) relationship of Nejati-Javaremi et al. (1997). Apply your function to the first three individuals and the first five SNPs in mice.X.

Question 1.4

Compute the first genomic relationship matrix of VanRaden (2008) using the entire markers. Report the median of the lower triangular part of G matrix.

Question 1.5

Compute the second genomic relationship matrix of VanRaden (2008) using the entire markers. Report the median of the lower triangular part of G matrix. What is the correlation of lower triangular parts of two VanRaden’s (2008) G matrices?

Question 1.6

Compute the dominant genomic relationship matrix of Su et al. (2012) using the entire markers. Report the median of the lower triangular part of D matrix.

Question 1.7

Compute the dominant genomic relationship matrix of Vitezica et al. (2013) using the entire markers. Report the median of the lower triangular part of D matrix. What is the correlation of lower triangular parts of two D matrices?