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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 44.4).

Figure 44.1 Analysis for an Overlapping Population
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

In the previous example, PROC INBREED treats the population as a single generation. However, you might 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 44.5).

Figure 44.2 Analysis for a Nonoverlapping Population
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

You might 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 44.3:

```proc inbreed data=Population covar average init=0.25;
class Generation;
gender Sex;
run;
```

Figure 44.3 Averages within Sex Categories for a Nonoverlapping Generation
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 1 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 1 4

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