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 The INBREED Procedure

## 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).

 The INBREED Procedure

 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

 Number of Individuals 11

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

 Number of Individuals 3

 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

 Number of Individuals 4

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 inGeneration 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 inGeneration 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

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