Table II.

Multinomial probabilities for genotype combinations in case/parent trios

Column index
1	2	3	4	5	6	7	8	9	10
Cell (row) index	Genotypesagmgfgc	Index of parental mating type	P(dis|gm, gf, gc)bc	P(gc|gm, gf)c	P(gm, gf)cd assuming random mating and HWE	P(gm, gf)c assuming only exchangeable parental mating types	P(gm, gf, gc|dis)bce assuming only exchangeable parental mating types	P(gm, gf, gc|dis)bce with reparameterization Σ = K/α µ1 = /Σ µ2 = 0.5/Σ µ3 = /Σ µ4 = 0.25/Σ µ5 = 0.5/Σ µ6 = /Σ	P(gm, gf, gc|dis)bc with reparameterization Ip
1	22 22 22	1	αR2S2ImIpγ22	1				R2S2ImIpγ22µ1
2	22 12 22	2	αR2S2ImIpγ22	0.5	2A1			R2S2ImIpγ22µ2
3	22 12 21	2	αR1S2Imγ21	0.5	2A1			R1S2Imγ21µ2
4	12 22 22	2	αR2S1ImIpγ12	0.5	2A1			R2S1ImIpγ12µ2
5	12 22 12	2	αR1S1Ipγ11	0.5	2A1			R1S1Ipγ11µ2
6	22 11 21	3	αR1S2Imγ21	1				R1S2Imγ21µ3
7	11 22 12	3	αR1Ip	1				R1Ipµ3
8	12 12 22	4	αR2S1ImIpγ12	0.25				R2S1ImIpγ12µ4
9a	12 12 12	4	αR1S1Ipγ11	0.25				R1S1Ipγ11µ4
9b	12 12 21	4	αR1S1Imγ11	0.25				R1S1Imγ11µ4
10	12 12 11	4	αS1	0.25				S1µ4
11	12 11 21	5	αR1S1Imγ11	0.5				R1S1Imγ11µ5
12	12 11 11	5	αS1	0.5				S1µ5
13	11 12 12	5	αR1Ip	0.5				R1Ipµ5
14	11 12 11	5	α	0.5				µ5	µ5
15	11 11 11	6	α	1				µ6	µ6

^ag_m and g_f refer to the unordered alleles in the mother and father respectively. g_c refers to the ordered alleles (maternal/paternal) in the child.

^bdis indicates the event that the child is affected with disease.

^c(g_m, g_f) refer to the ordered parental genotypes (maternal, paternal).

^dA₁ and A₂ are the allele frequencies of allele 1 and 2, respectively.

^eFormulae for K and Σ are given in the Appendix.