4.4 Calculating relationship and inbreeding coefficients by the tabular method - and matrix inversion

Link other applications of the Matrix: Estimating animal model breeding values and calculating selection index. The matrix nversion is done by a program made by Andrew to be found at the folowing location Andrew Ippoliti's Blog.

... Input aera ....                    ....Output area ....
Set digit for print ->

For larger sets of data use notepad or any other editor. Move the data to the input area (left field) by means of the clip board using ctrl-ins (copy) and shift-ins (insert).
The oldest animals should appear first, any numbers can be applied.
The Invert botton can only be run after an inbreeding run, or you put a matrix to be inverted in the output area!

Example:
Example of calculating inbreeding where the columns in the matrix shown below are animal, sire and dam, where the oldest animals should appear first. The pedigree are converted in a matrix as done below (0 means unknown parent): 
animal sire dam
---------------
 1     0   0
 2     1   0
 3     1   0
 4     1   0
 5     2   3
 6     4   3
 7     5   6

Take these data including in the clip board and transfer them to left window and there after press the 'Inbreeding' button and the inbreeding and relationship matrix should appear in the right window.
There after use in the input window: and press the 'Inbreeding' button

The relationship matrix will appear in the result window and will look as shown below. 

        Animal   F (inbreeding)

        1.000    0.000
        2.000    0.000
        3.000    0.000
        4.000    0.000
        5.000    0.125
        6.000    0.125
        7.000    0.218

        Relationship matrix  1+F (inbreeding) in the diagonal

             1.000    0.500   0.500   0.500   0.500   0.500   0.500
             0.500    1.000   0.250   0.250   0.625   0.250   0.437
             0.500    0.250   1.000   0.250   0.625   0.625   0.625
             0.500    0.250   0.250   1.000   0.250   0.625   0.437
             0.500    0.625   0.625   0.250   1.125   0.437   0.781
             0.500    0.250   0.625   0.625   0.437   1.125   0.781
             0.500    0.437   0.625   0.437   0.781   0.781   1.218
The inbreeding for each animal is given by its diagonal element minus one, i.e. the last three animals are inbred with an inbreeding coefficient of 0.125, 0.125 and 0.218 respectively.
The identifying numbers of each animal can be any number, as long as the oldest animals appear first in the list. When defining the base (oldest) generation both parents are set as zeros (0 = unknown).

Below is shown a hand calculated example with the two general formula in use.
The relationship between two animals is the average relationship between the oldest and the others two parents.
and the inbreeding of an individual is half the relationship between the two parents.

For your own data put them in the matrix 'Animal sire dam' and repeat the process:

Questions:
In the pedigree shown below the individuals have been assigned the numbers from 1 to 11.
...... 
Animal Sire Dam  , where 0 means unknown
-------------------
    1     0   0
    2     0   0
    3     0   0
    4     0   0
    5     0   0
    6     2   1
    7     5   4
    8     7   3
    9     7   6
   10     7   8
   11     10  9

Calculate the inbreeding coefficient for the individuals No 10 and 11, and calculate the additive relationship coefficient between individual 11 and all others in the pedigree. The data set to be used for the calculations is given above.

What would be the inbreeding coefficient after 5 generation of full sib mating?

Back to the other programs or back to inbreeding theory. back to inbreeding theory (danish).