Examples
Example 35.1. Monoecious Population Analysis
The following example shows a covariance analysis within nonoverlapping generations for a monoecious population. Parents of generation 1 are unknown and therefore assumed to be unrelated. The result appears in Output 35.1.1.
data Monoecious; input Generation Individual Parent1 Parent2 Covariance @@; datalines; 1 1 . . . 1 2 . . . 1 3 . . . 2 1 1 1 . 2 2 1 2 . 2 3 2 3 . 3 1 1 2 . 3 2 1 3 . 3 3 2 1 . 3 4 1 3 . 3 . 2 3 0.50 3 . 4 3 1.135 ; title 'Inbreeding within Nonoverlapping Generations'; proc inbreed ind covar matrix data=Monoecious; class Generation; run;
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Inbreeding within Nonoverlapping Generations The INBREED Procedure Generation = 1 Covariance Coefficients Individual Parent1 Parent2 1 2 3 1 1.0000 . . 2 . 1.0000 . 3 . . 1.0000 Inbreeding within Nonoverlapping Generations The INBREED Procedure Generation = 1 Covariance Coefficients of Individuals Individual Parent1 Parent2 Coefficient 1 1.0000 2 1.0000 3 1.0000 Number of Individuals 3
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Inbreeding within Nonoverlapping Generations The INBREED Procedure Generation = 2 Covariance Coefficients Individual Parent1 Parent2 1 2 3 1 1 1 1.5000 0.5000 . 2 1 2 0.5000 1.0000 0.2500 3 2 3 . 0.2500 1.0000 Inbreeding within Nonoverlapping Generations The INBREED Procedure Generation = 2 Covariance Coefficients of Individuals Individual Parent1 Parent2 Coefficient 1 1 1 1.5000 2 1 2 1.0000 3 2 3 1.0000 Number of Individuals 3
Inbreeding within Nonoverlapping Generations The INBREED Procedure Generation = 3 Covariance Coefficients Individual Parent1 Parent2 1 2 3 4 1 1 2 1.2500 0.5625 0.8750 0.5625 2 1 3 0.5625 1.0000 1.1349 0.6250 3 2 1 0.8750 1.1349 1.2500 1.1349 4 1 3 0.5625 0.6250 1.1349 1.0000 Inbreeding within Nonoverlapping Generations The INBREED Procedure Generation = 3 Covariance Coefficients of Individuals Individual Parent1 Parent2 Coefficient 1 1 2 1.2500 2 1 3 1.0000 3 2 1 1.2500 4 1 3 1.0000 Number of Individuals 4
Note that, since the parents of the first generation are unknown, off-diagonal elements of the covariance matrix are all 0s and on-diagonal elements are all 1s. If there is an INIT= cov value, then the off-diagonal elements would be equal to cov , while on-diagonal elements would be equal to 1 + cov/ 2.
In the third generation, individuals 2 and 4 are full siblings, so they belong to the same family. Since PROC INBREED computes covariance coefficients between families, the second and fourth columns of inbreeding coefficients are the same, except that their intersections with the second and fourth rows are reordered. Notice that, even though there is an observation to assign a covariance of 0.50 between individuals 2 and 3 in the third generation, the covariance between 2 and 3 is set to 1.135, the same value assigned between 4 and 3. This is because families get the same covariances, and later specifications override previous ones.
Example 35.2. Pedigree Analysis
In the following example, an inbreeding analysis is performed for a complicated pedigree. This analysis includes computing selective matings of some individuals and inbreeding coefficients of all individuals. Also, inbreeding coefficients are averaged within sex categories. The result appears in Output 35.2.1.
data Swine; input Swine_Number $ Sire $ Dam $ Sex $; datalines; 3504 2200 2501 M 3514 2521 3112 F 3519 2521 2501 F 2501 2200 3112 M 2789 3504 3514 F 3501 2521 3514 M 3712 3504 3514 F 3121 2200 3501 F ; title 'Least Related Matings'; proc inbreed data=Swine ind average; var Swine_Number Sire Dam; matings 2501 / 3501 3504 , 3712 / 3121; gender Sex; run;
Note the following from Output 35.2.1:
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Observation 4, which defines Swine_ Number =2501, should precede the first and third observations where the progeny for 2501 are given. PROC INBREED ignores observation 4 since it is given out of order. As a result, the parents of 2501 are missing or unknown.
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The first column in the Inbreeding Averages table corresponds to the averages taken over the on-diagonal elements of the inbreeding coefficients matrix, and the second column gives averages over the off-diagonal elements.
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Least Related Matings The INBREED Procedure Inbreeding Coefficients of Individuals Swine_ Number Sire Dam Coefficient 2200 . 2501 . 3504 2200 2501 . 2521 . 3112 . 3514 2521 3112 . 3519 2521 2501 . 2789 3504 3514 . 3501 2521 3514 0.2500 3712 3504 3514 . 3121 2200 3501 . Least Related Matings The INBREED Procedure Inbreeding Coefficients of Matings Sire Dam Coefficient 2501 3501 . 2501 3504 0.2500 3712 3121 0.1563 Averages of Inbreeding Coefficient Matrix Inbreeding Coancestry Male X Male 0.0625 0.1042 Male X Female . 0.1362 Female X Female 0.0000 0.1324 Over Sex 0.0227 0.1313 Number of Males 4 Number of Females 7 Number of Individuals 11
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Example 35.3. Pedigree Analysis with BY Groups
This example demonstrates the structure of the OUTCOV= data set created by PROC INBREED. Note that the first BY group has three individuals, while the second has five. Therefore, the covariance matrix for the second BY group is broken up into two panels, as shown in Output 35.3.1.
data Swine; input Group Swine_Number $ Sire $ Dam $ Sex $; datalines; 1 2789 3504 3514 F 2 2501 2200 3112 . 2 3504 2501 3782 M ; proc inbreed data=Swine covar noprint outcov=Covariance init=0.4; var Swine_Number Sire Dam; gender Sex; by Group; run; title 'Printout of OUTCOV= data set'; proc print data=Covariance; format Col1-Col3 4.2; run;
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Printout of OUTCOV= data set Swine_ OBS Group Sex _TYPE_ _PANEL_ _COL_ Number Sire Dam COL1 COL2 COL3 1 1 M COV 1 COL1 3504 1.20 0.40 0.80 2 1 F COV 1 COL2 3514 0.40 1.20 0.80 3 1 F COV 1 COL3 2789 3504 3514 0.80 0.80 1.20 4 2 M COV 1 COL1 2200 1.20 0.40 0.80 5 2 F COV 1 COL2 3112 0.40 1.20 0.80 6 2 M COV 1 COL3 2501 2200 3112 0.80 0.80 1.20 7 2 F COV 1 3782 0.40 0.40 0.40 8 2 M COV 1 3504 2501 3782 0.60 0.60 0.80 9 2 M COV 2 2200 0.40 0.60 . 10 2 F COV 2 3112 0.40 0.60 . 11 2 M COV 2 2501 2200 3112 0.40 0.80 . 12 2 F COV 2 COL1 3782 1.20 0.80 . 13 2 M COV 2 COL2 3504 2501 3782 0.80 1.20 .
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