linkage user's guide (version 5.2)

2.8 Consanguinity and Marriage Loops

One or more inbreeding or marriage loops can be accommodated by the present version of LINKAGE. (A marriage loop is created when relatives marry relatives, e.g. two brothers marry two sisters.) For simplicity, this section covers the case of a single loop. In order to calculate the likelihood, we must break the loop by duplicating an individual who has both parents and children included in the pedigree. In one of the duplicated records the parental and sib pointers are unmodified, but the first offspring pointer is set to 0. In the second of the records the first offspring pointer is maintained, but the parental and sib pointers are set to 0. A new id number is introduced for one of the duplicated individuals. The duplicates should have exactly the same phenotypes and genotypes. They are distinguished from other members of the pedigree by a 2 in the proband field.

Example

Figure 3 shows a modification of the first example in section 2.7. 


                       [1]--.--(2)
                        a   |
                        22  |   12
                        12  |   12
         Figure 3           |
                     .------+------.
                     |      |      |
            (6)--.--[3]    [4]     |
                 |   a             |
             13  |   12     22     |
             12  |   22     12     |
                 |                 |
             .-------.             |
             |       |             |
            [7]     (8)-----.-----(5)
             a              |      a
             13      u      |      12
             22      u      |      22
                            |
                           (9)
                            a
                            11
                            12
If we choose to break the loop at individual 5 in figure 3, we replace that pedigree with the one shown in figure 4, where 10 is the duplicate of 5. 

                       [1]--.--(2)
                        a   |
                        22  |   12
                        12  |   12
         Figure 4           |
                     .------+------.
                     |      |      |
            (6)--.--[3]    [4]    (10)
                 |   a             a
             13  |   12     22     12
             12  |   22     12     22
                 |
             .-------.
             |       |
            [7]     (8)-----.-----(5)
             a              |      a
             13      u      |      12
             22      u      |      22
                            |
                           (9)
                            a
                            11
                            12
The PEDFILE then becomes: 
  1   1  0   0  3  0  0  1  1  2  0  1  0  1  1  Ped: 1  Per:  1
  1   2  0   0  3  0  0  2  0  1  1  1  0  1  1  Ped: 1  Per:  2
  1   3  1   2  7  4  4  1  0  2  1  1  0  0  1  Ped: 1  Per:  3
  1   4  1   2  0  5  5  1  0  1  0  1  0  1  1  Ped: 1  Per:  4
  1   5  0   0  9  0  0  2  2  2  1  1  0  0  1  Ped: 1  Per:  5
  1  10  1   2  0  0  0  2  2  2  1  1  0  0  1  Ped: 1  Per:  5
  1   6  0   0  7  0  0  2  0  1  1  0  1  1  1  Ped: 1  Per:  6
  1   7  3   6  0  8  8  1  0  2  1  0  1  0  1  Ped: 1  Per:  7
  1   8  3   6  9  0  0  1  0  1  0  0  0  0  0  Ped: 1  Per:  8
  1   9  8   5  0  0  0  2  0  2  1  0  0  1  1  Ped: 1  Per:  9
where 2 is entered into the proband field for both 5 and 10. When the loop is broken at the "proband," a 1 is entered into the proband field for one of the duplicates, e.g.: 
  1   1  0   0  3  0  0  1  0  2  0  1  0  1  1  Ped: 1  Per:  1
  1   2  0   0  3  0  0  2  0  1  1  1  0  1  1  Ped: 1  Per:  2
  1   3  1   2  7  4  4  1  0  2  1  1  0  0  1  Ped: 1  Per:  3
  1   4  1   2  0  5  5  1  0  1  0  1  0  1  1  Ped: 1  Per:  4
  1   5  0   0  9  0  0  2  1  2  1  1  0  0  1  Ped: 1  Per:  5
  1  10  1   2  0  0  0  2  2  2  1  1  0  0  1  Ped: 1  Per:  5
  1   6  0   0  7  0  0  2  0  1  1  0  1  1  1  Ped: 1  Per:  6
  1   7  3   6  0  8  8  1  0  2  1  0  1  0  1  Ped: 1  Per:  7
  1   8  3   6  9  0  0  1  0  1  0  0  0  0  0  Ped: 1  Per:  8
  1   9  8   5  0  0  0  2  0  2  1  0  0  1  1  Ped: 1  Per:  9
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