Figure 1: Pedigree 1
In this section we show four sample pedigrees. In each case, we selected the proband to be the leftmost individual at the topmost generation. This would be the typical choice that most users make.
For each pedigree, we show a picture of the pedigree, the corresponding nuclear family graph, and a transcript of how the traversal goes. In the nuclear family graph, each nuclear family is labeled with the number of its leftmost child.
The first pedigree shows the simple case, where all the updates go upward.
Figure 2: Nuclear family graph for Pedigree 1
Here is a partial transcript of the traversal on pedigree 1.
Start at nuclear family 205 Visit nuclear family 304 Update person 205 conditioned on 204 and 304 going up Backup to nuclear family 205 Visit nuclear family 302 Update person 202 conditioned on 203, 302, and 303 going up Backup to nuclear family 205 Visit nuclear family 300 Visit nuclear family 400 Update person 300 conditioned on 301 and 400 going up Back up to 300 Update person 200 conditioned on 201 and 300 going up Backup to nuclear family 205 Update person 100 conditioned on 101 and 205, 202, and 200 going up
Here is the second sample pedigree. It illustrates going down instead of going up.
Figure 4: Nuclear family graph for Pedigree 2
Start at nuclear family 201 Visit nuclear family 304 Visit nuclear family 203 Update person 203 conditioned on 102 and 103, going down Back to nuclear family 304 Visit nuclear family 404 Update person 304 conditioned on 305, 404, and 405, going up Backup to nuclear family 304 Visit nuclear family 403 Update person 302, conditioned on 303 and 403, going up Backup to nuclear family 304 Visit nuclear family 400 Update person 300, conditioned on 301, 400, 401, and 402, going up Backup to nuclear family 304 Update person 202 conditioned on 203, 304, 302, and 300, going up Backup to nuclear family 201 Update person 100, conditioned on 101, 201, and 202, going up
Here is a third sample pedigree. It illustrates n-multiple marriages (individual 205). It can also be used to illustrate how LINKAGE deviates from the Elston-Stewart algorithm in an algorithmically fundamental way. The Elston-Stewart algorithm would allow a traversal order in which the nuclear families are updated in the order 402, 403, 404, 406, 307, 314, 310, 316. LINKAGE would never use this order no matter how the siblings in each nuclear family are arranged.
Figure 6: Nuclear family graph for pedigree 3
Here is the transcript for the third pedigree:
Start at nuclear family 202 Visit nuclear family 307 Visit nuclear family 402 Update person 307, conditioned on 306 and 402, going up Backup to 307 Visit nuclear family 403 Update person 308, conditioned on 309 and 403, going up Backup to 307 Update person 202, conditioned on 203, 307, and 308, going up Backup to 202 Visit nuclear family 314 Update person 205, conditioned on 206 and 314, going up Backup to 202 Visit nuclear family 310 Visit nuclear family 404 Update person 312, conditioned on 313 and 404, going up Backup to 310 Update person 205, conditioned on 204, 310, 311, and 312, going up Backup to 202 Visit nuclear family 316 Visit nuclear family 406 Update person 316, conditioned on 315, 406, and 405, going up Backup to 316 Update person 207, conditioned on 208 and 316, going up Backup to 202 Update person 101, conditioned on 102, 202, 205, and 207, going up
The fourth pedigree illustrates the distinction between f-multiple marriages (individual 4) and n-multiple marriages (individual 20). It has the advantage of being in marriage graph format, which is much closer to what the nuclear family graph looks like. In particular there is a one-to-one correspondence between the filled in dots in the marriage graph and the vertices in the nuclear family graph.
Figure 7: Pedigree 4, marriage graph format
Figure 8: Nuclear family graph for pedigree 4
Here is the traversal transcript for pedigree 4:
Start at nuclear family 13 Visit nuclear family 21 Update person 13, conditioned on 16 and 21, going up Backup to 13 Visit nuclear family 19 Visit nuclear family 11 Visit nuclear family 10 Visit nuclear family 18 Visit nuclear family 24 Visit nuclear family 17 Visit nuclear family 8 Update person 8, conditioned on 1,2, and 9, going down Back to nuclear family 17 Update person 17, conditioned on 8 and 14, going down Back to nuclear family 24 Update person 18, conditioned on 17. 24, and 25 going up Backup to nuclear family 18 Update person 10 conditioned on 15, and 18, going up Backup to nuclear family 10 Update person 4, conditioned on 3 and 10, going up Backup to nuclear family 11 Update person 11 conditioned on 4 and 5, going down Back to nuclear family 19 Visit nuclear family 28 Update person 20, conditioned on 23 and 28, going up Backup to nuclear family 19 Visit nuclear family 26 Update person 20, conditioned on 22 and 26, going up Backup to nuclear family 19 Update person 12, conditioned on 11, 19, and 20, going up Backup to nuclear family 13 Update person 7, conditioned on 6, 13, and 12, going up
