Numerator Relationship Matrix

Given is the following pedigree

In [1]:

s_data_root <- "https://charlotte-ngs.github.io/lbgfs2024/data"
s_ped_p01 <- file.path(s_data_root, "aural_exam_pedigree_p01.csv")
tbl_ped_p01 <- readr::read_delim(s_ped_p01, 
                                 delim = ",", 
                                 show_col_types = FALSE)

Pedigree shown as table

In [2]:

knitr::kable(tbl_ped_p01)

Animal	Sire	Dam
6	2	1
7	2	3
8	6	4
9	7	5
10	8	9
11	10	5

Use the above pedigree to compute

1. the numerator relationship matrix \(A\) and
2. the inbreeding coefficients of each animal
3. the expected inbreeding coefficients of potential offspring of animal 1 when mated to all possible mates in the pedigree

Given a numerator relationship \(A\), how can be determined which animals has which parents?