AGB 121: Principles of Animal Genetics and Population Genetics (2+1)

Genotypic variance

GENOTYPE VARIANCE

• The variances are obtained by squaring the values multiplying by the frequency of the genotypes concerned and summing over the all genotypes.
• Genotypic variance is due to additive effects of genes and non-additive effects of genes.
• Additive effects are connected with breeding values of the individual because parents pass their genes to their offspring not their genotype.

Additive and Dominace variance

• Variance is obtained by squaring the values then multiplying by the frequency of the genotype concerned, and summing the three genotypes.

Genotype	A1 A1	A1 A2	A2 A2
Frequencies	p2	2pq	q2
Assigned values	a	d	-a
Breeding values	2q a	(q-p) a	-2p a
Dominance deviation	-2q2 d	2pqd	-2p2 d

• The additive variance which is the variance of breeding value is obtained as follows
  • V_A = (2q a )²p² + [(q-p) a ]²2pq + (-2p a )q²
  • V_A = 4p²q² a ² + (q²-2pq+p²) a ² 2pq + 4p²q² a ²
  • V_A = 2pq a ² (2pq + q² - 2pq +p² + 2pq)
  • V_A = 2pq a ² (1)
  • V_A = 2pq [a + d (q-p)] ²
• The variance of dominance deviation is
  • V_D = (-2q²d) ² + (2pqd) ² + (-2p²d) ²
  • V_D = (2pqd) ²
• Total genetic variance
  • V_G = V_A + V_D
  • V_G = 2pq [a + d (q-p)] ² + (2pqd) ²
  • V_G = 2pq a ² + (2pqd) ²

• In general the genes contribute much more variance when at intermediate frequencies than when at high or low frequencies, recessives at low frequency, in particular, contribute very little variance.

Interaction variance

• When more than one locus is under consideration then the interaction deviations give rise to the interaction variance.
• It is the variation of the interaction deviations brought about by the epistatic interactions at different loci.
• Two factor interactions arise from interaction of two loci three factor from three loci etc.
• In two factor interaction

  • V_I = V_AA + V_AD + V_DD + etc