Estimated Breeding Value (EBV) Calculation
Question:
A boar has sired 20 litters averaging 7.8 weaned pigs each. Postweaning average daily gains of his progeny average
(a) Estimate the boar’s breeding value (EBV) for postweaning average daily gain.
(b) Estimate the EBV assuming no environmental covariation among littermates (
(c) Explain why the EBV increases when
A boar has sired 20 litters averaging 7.8 weaned pigs each. Postweaning average daily gains of his progeny average
0.06 lb/day above the contemporary group means. The heritability (h²) of postweaning gain is 0.28, and the common environmental effect (c²) is 0.07.
(a) Estimate the boar’s breeding value (EBV) for postweaning average daily gain.
(b) Estimate the EBV assuming no environmental covariation among littermates (
c² = 0).(c) Explain why the EBV increases when
c² is assumed to be zero.
🔢 Step-by-Step Solution:
Total number of progeny:
n = 20 litters × 7.8 pigs = 156 pigs
EBV Formula (with environmental effect):
Where:
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EBV = [n × k × h²] / [1 + (k − 1)(c² + ¼h²)] × PWhere:
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k = 7.8•
k − 1 = 6.8•
¼h² = 0.25 × 0.28 = 0.07•
c² + ¼h² = 0.07 + 0.07 = 0.14•
Denominator = 1 + 6.8 × 0.14 = 1.952•
Numerator = 156 × 0.28 = 43.68•
P = 0.06
EBV Calculation (with c²):
EBV = (43.68 / 1.952) × 0.06 ≈ 22.37 × 0.06 = 1.34 lb/day
EBV Calculation (assuming c² = 0):
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Denominator = 1 + (k − 1) × ¼h² = 1 + 6.8 × 0.07 = 1.476•
Numerator = 43.68EBV = (43.68 / 1.476) × 0.06 ≈ 29.60 × 0.06 = 1.78 lb/day
Explanation:
When
When
c² is removed, the denominator becomes smaller, increasing the EBV. This is because without accounting for shared environmental influence, all variance in progeny performance is attributed to genetics, resulting in a higher estimate of breeding value.
✅ Final Answers:
(a) EBV with
(b) EBV with
(c) The EBV increased when
(a) EBV with
c² = 0.07: 1.34 lb/day(b) EBV with
c² = 0: 1.78 lb/day(c) The EBV increased when
c² was removed because the adjustment for common environmental effect was eliminated, attributing more variation to genetics.