Performing the Analysis
To compute the covariance coefficients for the
overlapping generation mode, use the following statements:
proc inbreed data=Population covar matrix init=0.25;
run;
Here, the DATA= option names the SAS data set to be
analyzed, and the COVAR and MATRIX options tell the
procedure to output the covariance coefficients matrix.
If you omit the COVAR option, the inbreeding coefficients
are output instead of the covariance coefficients.
Note that the PROC INBREED statement
also contains the INIT= option.
This option gives an initial covariance
between any individual and unknown individuals.
For example, the covariance between any individual and
`JANE' would be 0.25, since `JANE' is unknown, except
when `JANE' appears as a parent (see Figure 32.1).
Covariance Coefficients |
Individual |
Parent1 |
Parent2 |
GEORGE |
LISA |
MARK |
SCOTT |
KELLY |
AMY |
MIKE |
DAVID |
JANE |
MERLE |
JIM |
GEORGE |
|
|
1.1250 |
0.2500 |
0.6875 |
0.2500 |
0.2500 |
0.2500 |
0.6875 |
0.4688 |
0.2500 |
0.4688 |
0.4688 |
LISA |
|
|
0.2500 |
1.1250 |
0.6875 |
0.2500 |
0.6875 |
0.2500 |
0.2500 |
0.6875 |
0.2500 |
0.2500 |
0.6875 |
MARK |
GEORGE |
LISA |
0.6875 |
0.6875 |
1.1250 |
0.2500 |
0.5000 |
0.2500 |
0.4688 |
0.8125 |
0.2500 |
0.3594 |
0.8125 |
SCOTT |
|
|
0.2500 |
0.2500 |
0.2500 |
1.1250 |
0.6875 |
0.2500 |
0.2500 |
0.4688 |
0.2500 |
0.2500 |
0.4688 |
KELLY |
SCOTT |
LISA |
0.2500 |
0.6875 |
0.5000 |
0.6875 |
1.1250 |
0.2500 |
0.2500 |
0.8125 |
0.2500 |
0.2500 |
0.8125 |
AMY |
|
|
0.2500 |
0.2500 |
0.2500 |
0.2500 |
0.2500 |
1.1250 |
0.6875 |
0.2500 |
0.2500 |
0.4688 |
0.2500 |
MIKE |
GEORGE |
AMY |
0.6875 |
0.2500 |
0.4688 |
0.2500 |
0.2500 |
0.6875 |
1.1250 |
0.3594 |
0.2500 |
0.6875 |
0.3594 |
DAVID |
MARK |
KELLY |
0.4688 |
0.6875 |
0.8125 |
0.4688 |
0.8125 |
0.2500 |
0.3594 |
1.2500 |
0.2500 |
0.3047 |
0.8125 |
JANE |
|
|
0.2500 |
0.2500 |
0.2500 |
0.2500 |
0.2500 |
0.2500 |
0.2500 |
0.2500 |
1.1250 |
0.6875 |
0.2500 |
MERLE |
MIKE |
JANE |
0.4688 |
0.2500 |
0.3594 |
0.2500 |
0.2500 |
0.4688 |
0.6875 |
0.3047 |
0.6875 |
1.1250 |
0.3047 |
JIM |
MARK |
KELLY |
0.4688 |
0.6875 |
0.8125 |
0.4688 |
0.8125 |
0.2500 |
0.3594 |
0.8125 |
0.2500 |
0.3047 |
1.2500 |
|
Figure 32.1: Analysis for an Overlapping Population
In the previous example, PROC INBREED treats
the population as a single generation.
However, you may want to process the population with
respect to distinct, nonoverlapping generations.
To accomplish this, you need to identify the generation variable
in a CLASS statement, as shown by the following statements.
proc inbreed data=Population covar matrix init=0.25;
class Generation;
run;
Note that, in this case, the covariance matrix is displayed
separately for each generation (see Figure 32.2).
The INBREED Procedure |
Generation = 1 |
Covariance Coefficients |
Individual |
Parent1 |
Parent2 |
MARK |
KELLY |
MIKE |
MARK |
GEORGE |
LISA |
1.1250 |
0.5000 |
0.4688 |
KELLY |
SCOTT |
LISA |
0.5000 |
1.1250 |
0.2500 |
MIKE |
GEORGE |
AMY |
0.4688 |
0.2500 |
1.1250 |
The INBREED Procedure |
Generation = 2 |
Covariance Coefficients |
Individual |
Parent1 |
Parent2 |
DAVID |
MERLE |
JIM |
MARK |
DAVID |
MARK |
KELLY |
1.2500 |
0.3047 |
0.8125 |
0.5859 |
MERLE |
MIKE |
JANE |
0.3047 |
1.1250 |
0.3047 |
0.4688 |
JIM |
MARK |
KELLY |
0.8125 |
0.3047 |
1.2500 |
0.5859 |
MARK |
MIKE |
KELLY |
0.5859 |
0.4688 |
0.5859 |
1.1250 |
|
Figure 32.2: Analysis for a Nonoverlapping Population
You may also want to see covariance
coefficient averages within sex categories.
This is accomplished by indicating the
variable defining the gender of individuals
in a GENDER statement and by adding the
AVERAGE option to the PROC INBREED statement.
For example, the following statements produce the
covariance coefficient averages shown in Figure 32.3.
proc inbreed data=Population covar average init=0.25;
class Generation;
gender Sex;
run;
The INBREED Procedure |
Generation = 1 |
Averages of Covariance Coefficient Matrix in Generation 1 |
|
On Diagonal |
Below Diagonal |
Male X Male |
1.1250 |
0.4688 |
Male X Female |
. |
0.3750 |
Female X Female |
1.1250 |
0.0000 |
Over Sex |
1.1250 |
0.4063 |
Number of Males |
2 |
Number of Females |
1 |
Number of Individuals |
3 |
The INBREED Procedure |
Generation = 2 |
Averages of Covariance Coefficient Matrix in Generation 2 |
|
On Diagonal |
Below Diagonal |
Male X Male |
1.2083 |
0.6615 |
Male X Female |
. |
0.3594 |
Female X Female |
1.1250 |
0.0000 |
Over Sex |
1.1875 |
0.5104 |
Number of Males |
3 |
Number of Females |
1 |
Number of Individuals |
4 |
|
Figure 32.3: Averages within Sex Categories for a Nonoverlapping Generation
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.