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Problem 1: Parent Offspring Breeding Values

As shown in the course notes, the breeding value ui of animal i can be decomposed into the average of the parent breeding values plus a mendelian sampling term (mi). This means

ui=12us+12ud+mi

where animal i has parents s and d. The mendelian sampling term mi is the deviation of the single breeding value ui from the parent average breeding value. Because mi is modelled as a deviation, it follows that for a large number (N) of offspring from parents s and d, the average over all mendelian sampling terms must be 0.

Your Task

Show that the average mendelian sampling term over a large number of offspring is 0 using a single locus model for the following cases.

Case 1: Homozygous and Heterozygous Parents

Parent s with genotype G1G1 and parent d with genotype G1G2

Case 2: Homozygous and Heterozygous Parents

Parent s with genotype G2G2 and parent d with genotype G1G2

Case 3: Heterozygous Parents

Both parents s and d have genotype G1G2

Your Solution

  • For each of the following cases compute the parent average of breeding values.
  • Compute the difference between the breeding values of every possible offspring and the parent average
  • Compute the average over all mendelian sampling terms

Case 1: Homozygous and Heterozygous Parents

Case 2: Homozygous and Heterozygous Parents

Case 3: Heterozygous Parents


Latest Changes: 2023-11-10 07:36:54 (pvr)

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