LBG - FS2024 – Solution 11

Author

Peter von Rohr

Problem 1: Marker Effect Model

We are given the dataset that is shown in the table below. This dataset contains gentyping results of 10 animals for 2 SNP loci.

Task

  • The goal of this problem is to estimate SNP marker effects using a marker effect model. Because we have just 2 SNP loci, you can use a fixed effects linear model with the 2 loci as fixed effects. Furthermore you can also include a fixed intercept into the model.
  • You can use the R-function lm() to get the solutions for estimates of the unknown SNP effects.
  • Compute genomic breeding values for all animals with genotypic data

Solution

  • Use a regression model for the SNP-effects
  • Use marker effects to compute genomic breeding values, start by extracting estimates of marker effects
  • Compute direct genomic breeding values
  • Rank animals according to genomic breeding values

Problem 2: Breeding Value Model

Use the same data as in Problem 1 to estimate genomic breeding values using a breeding value model.

Hints

  • The only fixed effect in this model is the mean \(\mu\) which is the same for all observations.
  • You can use the following function to compute the inverse genomic relationship matrix

Solution

  • Design matrix \(X\) for fixed effects
  • Design matrix \(W\) for random genomic breeding values
  • Get genomic relationship matrix
  • Set up coefficient matrix assuming a value of \(\lambda = \sigma_e^2 / \sigma_u^2 = 3\)
  • Get list of genomic breeding values
  • Ranking animals according to their genomic breeding values