Example 32.1: Monoecious Population Analysis
The following example shows a covariance analysis within
nonoverlapping generations for a monoecious population.
Parents of generation 1 are unknown
and therefore assumed to be unrelated.
The result appears in Output 32.1.1.
data Monoecious;
input Generation Individual Parent1 Parent2 Covariance @@;
datalines;
1 1 . . . 1 2 . . . 1 3 . . .
2 1 1 1 . 2 2 1 2 . 2 3 2 3 .
3 1 1 2 . 3 2 1 3 . 3 3 2 1 .
3 4 1 3 . 3 . 2 3 0.50 3 . 4 3 1.135
;
title 'Inbreeding within Nonoverlapping Generations';
proc inbreed ind covar matrix data=Monoecious;
class Generation;
run;
Output 32.1.1: Monoecious Population Analysis
|
| Inbreeding within Nonoverlapping Generations |
| The INBREED Procedure |
| Generation = 1 |
| Covariance Coefficients |
| Individual |
Parent1 |
Parent2 |
1 |
2 |
3 |
| 1 |
|
|
1.0000 |
. |
. |
| 2 |
|
|
. |
1.0000 |
. |
| 3 |
|
|
. |
. |
1.0000 |
| Inbreeding within Nonoverlapping Generations |
| The INBREED Procedure |
| Generation = 1 |
Covariance Coefficients
of Individuals |
| Individual |
Parent1 |
Parent2 |
Coefficient |
| 1 |
|
|
1.0000 |
| 2 |
|
|
1.0000 |
| 3 |
|
|
1.0000 |
| Inbreeding within Nonoverlapping Generations |
| The INBREED Procedure |
| Generation = 2 |
| Covariance Coefficients |
| Individual |
Parent1 |
Parent2 |
1 |
2 |
3 |
| 1 |
1 |
1 |
1.5000 |
0.5000 |
. |
| 2 |
1 |
2 |
0.5000 |
1.0000 |
0.2500 |
| 3 |
2 |
3 |
. |
0.2500 |
1.0000 |
| Inbreeding within Nonoverlapping Generations |
| The INBREED Procedure |
| Generation = 2 |
Covariance Coefficients
of Individuals |
| Individual |
Parent1 |
Parent2 |
Coefficient |
| 1 |
1 |
1 |
1.5000 |
| 2 |
1 |
2 |
1.0000 |
| 3 |
2 |
3 |
1.0000 |
| Inbreeding within Nonoverlapping Generations |
| The INBREED Procedure |
| Generation = 3 |
| Covariance Coefficients |
| Individual |
Parent1 |
Parent2 |
1 |
2 |
3 |
4 |
| 1 |
1 |
2 |
1.2500 |
0.5625 |
0.8750 |
0.5625 |
| 2 |
1 |
3 |
0.5625 |
1.0000 |
1.1349 |
0.6250 |
| 3 |
2 |
1 |
0.8750 |
1.1349 |
1.2500 |
1.1349 |
| 4 |
1 |
3 |
0.5625 |
0.6250 |
1.1349 |
1.0000 |
| Inbreeding within Nonoverlapping Generations |
| The INBREED Procedure |
| Generation = 3 |
Covariance Coefficients
of Individuals |
| Individual |
Parent1 |
Parent2 |
Coefficient |
| 1 |
1 |
2 |
1.2500 |
| 2 |
1 |
3 |
1.0000 |
| 3 |
2 |
1 |
1.2500 |
| 4 |
1 |
3 |
1.0000 |
|
Note that, since the parents of the first generation
are unknown, off-diagonal elements of the covariance
matrix are all 0s and on-diagonal elements are all 1s.
If there is an INIT=cov value, then the off-diagonal
elements would be equal to cov, while on-diagonal
elements would be equal to 1 + cov/2.
In the third generation, individuals 2 and 4 are
full siblings, so they belong to the same family.
Since PROC INBREED computes covariance coefficients
between families, the second and fourth columns of
inbreeding coefficients are the same, except that their
intersections with the second and fourth rows are reordered.
Notice that, even though there is an observation to
assign a covariance of 0.50 between individuals 2 and 3
in the third generation, the covariance between 2 and 3
is set to 1.135, the same value assigned between 4 and 3.
This is because families get the same covariances,
and later specifications override previous ones.
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.
