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 65.4).

Figure 65.1: Analysis for an Overlapping Population

The INBREED Procedure

Covariance Coefficients
IndividualParent1Parent2GeorgeLisaMarkScottKellyAmyMikeDavidJaneMerleJim
George  1.12500.25000.68750.25000.25000.25000.68750.46880.25000.46880.4688
Lisa  0.25001.12500.68750.25000.68750.25000.25000.68750.25000.25000.6875
MarkGeorgeLisa0.68750.68751.12500.25000.50000.25000.46880.81250.25000.35940.8125
Scott  0.25000.25000.25001.12500.68750.25000.25000.46880.25000.25000.4688
KellyScottLisa0.25000.68750.50000.68751.12500.25000.25000.81250.25000.25000.8125
Amy  0.25000.25000.25000.25000.25001.12500.68750.25000.25000.46880.2500
MikeGeorgeAmy0.68750.25000.46880.25000.25000.68751.12500.35940.25000.68750.3594
DavidMarkKelly0.46880.68750.81250.46880.81250.25000.35941.25000.25000.30470.8125
Jane  0.25000.25000.25000.25000.25000.25000.25000.25001.12500.68750.2500
MerleMikeJane0.46880.25000.35940.25000.25000.46880.68750.30470.68751.12500.3047
JimMarkKelly0.46880.68750.81250.46880.81250.25000.35940.81250.25000.30471.2500

Number of Individuals11


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 65.5).

Figure 65.2: Analysis for a Nonoverlapping Population

The INBREED Procedure
 
Generation = 1

Covariance Coefficients
IndividualParent1Parent2MarkKellyMike
MarkGeorgeLisa1.12500.50000.4688
KellyScottLisa0.50001.12500.2500
MikeGeorgeAmy0.46880.25001.1250

Number of Individuals3

The INBREED Procedure
 
Generation = 2

Covariance Coefficients
IndividualParent1Parent2DavidMerleJimMark
DavidMarkKelly1.25000.30470.81250.5859
MerleMikeJane0.30471.12500.30470.4688
JimMarkKelly0.81250.30471.25000.5859
MarkMikeKelly0.58590.46880.58591.1250

Number of Individuals4


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 65.3:

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

Figure 65.3: Averages within Sex Categories for a Nonoverlapping Generation

The INBREED Procedure
 
Generation = 1

Averages of Covariance Coefficient Matrix in
Generation 1
 On DiagonalBelow Diagonal
Male X Male1.12500.4688
Male X Female.0.3750
Female X Female1.12500.0000
Over Sex1.12500.4063

Number of Males2
Number of Females1
Number of Individuals3

The INBREED Procedure
 
Generation = 2

Averages of Covariance Coefficient Matrix in
Generation 2
 On DiagonalBelow Diagonal
Male X Male1.20830.6615
Male X Female.0.3594
Female X Female1.12500.0000
Over Sex1.18750.5104

Number of Males3
Number of Females1
Number of Individuals4