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 46.4).

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 46.5).

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 46.3:

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 |