## Trio analysis for Nagasaki poster

#### using the Symbolic Kinship Program ### Family tree and DQa types for a complicated cousin case ### Is A the father of B?

For the locus DQa, the information shown in the figure is encoded for the program as follows
```; c=3 d=4 fgh=1.1, 1.2, 1.3  Comment line. Explains the letters used for alleles.
IIA, IIB, IIC   : ?   + ?       ; siblings of the grandparental generation
C       h       : ?   + IIA     ; Mrs. C's genotype (h=1.3) and her parents
B       h       : C   + A/?     ; B has two possible fathers, A and ?.
E       cd      : D   + A       ; E is the known child of A.
D,F     cd      : ?   + IIB     ; D and F are siblings.
H       c       : IID + ?       ; H shares one parent with A.
G       gc      : ?   + IIC     ; G shares A's other parent.
A               : IID + IIC     ; A's genotype is not known.
```

After some considerable amount of time -- this problem is far more complicated than most -- the computer announces the following formula:

(2+18c+5d+10h+16cc+48cd+66ch+23dh+48ccd+42cch+114cdh+64ccdh) / (48h+400ch+120dh+296cch+840cdh+640ccdh)

In this formula the letters c, d, and h now stand for the frequencies of the alleles 3, 4, and 1.3.

Substituting the approximate allele frequencies for the Japanese population: c=0.3903 d=0.1278 h=0.2167
we obtain the numeric result that the likelihood ratio = 0.386.

Similar calculations using phenotypic data for various systems lead to the following results:
SystemLRfrequenciesformula
ABO1 / 5.4a=0.2774 o=0.5519 (8a2+8ao+72a3+316a2o+308ao2+ 80o3+8a4+484a3o+1224a2o2+ 456ao3-20o4-64a5-536a4o- 1132a3o2-876a2o3-560ao4- 60o5-24a6-440a5o- 1892a4o2-3100a3o3-1944a2o4-352ao5-32a6o-224a5o2-576a4o3- 640a3o4-256a2o5) / (32a2+32ao+336a3+1576a2o+1544ao2+368o3+ 64a4+2576a3o+6624a2o2+2656ao3-80o4- 304a5-2361a4o-4520a3o2-3192a2o3-2808ao4-288o5-128a6-2461a5o-10637a4o2-17312a3o3-10768a2o4-2080ao5-323a6o-2246a5o2-5763a4o3-6400a3o4-2568a2o5+a7o+3a6o2+3a5o3+a4o4+8a3o5+8a2o6)
Gc 0.814 b=0.23 s=0.77 (4s+22b2+102bs+20s2+73b3+582b2s+417bs2+8s3+22b4+920b3s+1588b2s2+130bs3+172b4s+1464b3s2+332b2s3+128b4s2+128b3s3) / (8bs+8s2+44b3+240b2s+228bs2+32s3+104b4+1032b3s+1520b2s2+592bs3+1040b4s+2912b3s2+1872b2s3+1280b4s2+1280b3s3)
Hp 1.22 b=0.75 (6+97b+167b2-42b3-162b4-62b5-4b6) / (8b+124b2+182b3-98b4-176b5-40b6)
Bf 1.16 s=0.7945 (6+97s+167s2-42s3-162s4-62s5-4s6) / (8s+124s2+182s3-98s4-176s5-40s6)
Esd 1.14 a=0.64 (4+41a-26a2-71a3+50a4+6a5-4a6) / (8+76a-106a2-136a3+206a4-8a5-40a6)
6-PGD 1 / 5.22 a=0.9042 (2+25a+46a2+22a3+2a4) / (8+116a+234a2+134a3+20a4)
HLA-A 1.05 b=0.3 d=0.1 (6+31b+156d+19b2+576bd+650d2+294b2d+1800bd2+440d3+696b2d2+1000bd3+256b2d3) / (32b+80b2+696bd+1424b2d+2456bd2+4256b2d2+1696bd3+2560b2d3)
dqa 0.386 c=0.3903 d=0.1278 h=0.2167 (2+18c+5d+10h+16c2+48cd+66ch+23dh+48c2d+42c2h+114cdh+64c2dh) / (48h+400ch+120dh+296c2h+840cdh+640c2dh)
D1S80 0.305 a=0.157 b=0.0165 e=0.0041 z=0.1157 i=0.0537 (4e+4a2+38ae+8e2+8ez+42a2e+32a2z+58ae2+84aez+32e2z+48a2e2+296a2ez+256ae2z+384a2e2z+a4bi+5a3bei) / (16a2+16ae+256a2e+128a2z+32ae2+64aez+320a2e2+1376a2ez+224ae2z+2048a2e2z)
cumulative LR 1 / 174