Question 2 (5 pts). The phenotypic variance or components of phenotypic variance
ID: 3166582 • Letter: Q
Question
Question 2 (5 pts). The phenotypic variance or components of phenotypic variance were estimated for the same trait in each of two herds of cattle.
Phenotypic
Variation
Components of Phenotypic Variation
VP
VG
VA
VD
VI
VGxE
VE
herd 1
124
33
6
27
89
herd 2
93
15
5
12
65
a. What is VP for herd 1?
b. What is VA for herd 1?
c. What is VG for herd 2?
d. Which herd has the largest broad-sense heritability for this trait? What is the heritability? Show calculations!!!
e. Which herd has the smallest narrow-sense heritability for this trait? What is the heritability? Show calculations!!!
Phenotypic
Variation
Components of Phenotypic Variation
VP
VG
VA
VD
VI
VGxE
VE
herd 1
124
33
6
27
89
herd 2
93
15
5
12
65
Explanation / Answer
Q.a calculation for VP of herd 1.
Formula used VP= VG+ VE
VP= 124 + 89 = 213
VP for herd 1 is 213.
Q .b VA for herd 1
VG = VA + VD + VI
124 = VA +33 +6
124 = VA + 39
124 – 39 = VA
VA for herd 1 = 85
Q.c VG for herd 2
VG = VA + VD +VI
VG = 93 +15+5
VG = 113
VG for herd 2 is 113.
Q.d Broad sense heritability is the total proportion of variation which comes due to heritability.
Calculation for broad sense heritability –
For herd 1
H2 = VG / VP
H2 = 124 / 213
H2 = 0.58
For herd 2 = H2 = 113 /178 = 0.63
VP for herd is calculated using formula VP = VG+ VE
Broad sense heritability for herd 1 is 0.58 and herd 2 is 0.63. so herd 2 is having largest broad sense heritability.
Q. e Narrow sense heritability is proportion of total variation which comes due to additive effect.
Calculation for narrow sense heritability-
For herd 1
h2 = VA / VP
h2 = 85 / 124
h2 = 0.68
For herd 2
h2 = VA / VP = 93 /178
h2 = 0.52
Narroe sense heritability for herd 1 is 0.68 and for herd 2 is 0.52.so herd 2 have smallest narrow sense heritability.
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