在一群非近親的約克夏豬群中,逢機選擇五隻公豬,每一隻公豬配種兩隻母豬,且每隻母豬個別紀錄兩隻小公豬平均日增重,所獲得資料如下表;請分別估算該豬群平均日增重的遺傳變方(genetic variance)、遺傳變異率(heritability, h2)與機差(Standard Deviation)。
Sire |
Dam |
Pig gains |
|
1 |
1 |
3.80 |
2.42 |
|
2 |
2.76 |
2.40 |
2 |
3 |
4.32 |
4.74 |
|
4 |
4.24 |
4.44 |
3 |
5 |
4.70 |
2.16 |
|
6 |
4.48 |
2.50 |
4 |
7 |
2.92 |
4.88 |
|
8 |
2.84 |
4.30 |
5 |
9 |
4.04 |
3.82 |
|
10 |
4.06 |
4.92 |
Pig_gains數據來源:
使用R語言製造變數
> pig<-seq(2,5,by=0.02)
> sample(pig,20)
[1] 3.80 4.32 4.70 2.92 4.04 2.42 4.74 2.16 4.88 3.82 2.76 4.24 4.48 2.84 4.06 2.40 4.44 2.50 4.30 4.92
data nested_design;
do sire = 1 to 5;
input dam pig_gains @@ ;
output;
end;
cards;
1 3.80 3 4.32 5 4.70 7 2.92 9 4.04
1 2.42 3 4.74 5 2.16 7 4.88 9 3.82
2 2.76 4 4.24 6 4.48 8 2.84 10 4.06
2 2.40 4 4.44 6 2.50 8 4.30 10 4.92
;
proc sort; by dam;
proc print;
proc varcomp method=type1;
class sire dam ;
model pig_gains= sire dam(sire);
run;
The SAS System
Variance Components Estimation Procedure
Class Level Information |
|
|
Class |
Levels |
Values |
sire |
5 |
1 2 3 4 5 |
dam |
10 |
1 2 3 4 5 6 7 8 9 10 |
Number of Observations Read |
20 |
Number of Observations Used |
20 |
Dependent Variable: |
pig_gains |
Type 1 Analysis of Variance |
|
|
|
|
Source |
DF |
Sum of Squares |
Mean Square |
Expected Mean Square |
sire |
4 |
6.333320 |
1.583330 |
Var(Error) + 2 Var(dam(sire)) + 4 Var(sire) |
dam(sire) |
5 |
0.743100 |
0.148620 |
Var(Error) + 2 Var(dam(sire)) |
Error |
10 |
9.691800 |
0.969180 |
Var(Error) |
Corrected Total |
19 |
16.768220 |
|
|
Type 1 Estimates |
|
Variance Component |
Estimate |
Var(sire) |
0.35868 |
Var(dam(sire)) |
-0.41028 |
Var(Error) |
0.96918 |
- 遺傳變方(genetic variance)
父方: 0.35868
母方: -0.41028 (由於變方為平方和,所以計算遺傳變異率時須以0計算)
- 遺傳變異率(heritability, h2)
0.35868+0)/( 0.35868+0+0.96918)= 0.2701188
- 機差(Standard Deviation)
0.96918