Mating type = i

Pr(Mating type = iD, pop = k)

Child genotype

Notation

Pr(Child genotypeD, Mating type = i, pop = k) (t= 1/2 when k= 2)

Pr(x_{
abc
}D, pop = k)


MM × MM (i = 1)

μ
_{k,1}

MM

x
_{222}

1

μ
_{k,1}

MM × MNC(i = 2)

μ
_{k,2}

MM

x
_{212}

t

μ
_{k,2}
t

MM × MNC(i = 2)

μ
_{k,2}

MN

x
_{211}

(1  t)

μ_{k,2}(1  t)

MM × NN(i = 3)

μ
_{k,3}

MN

x
_{201}

1

μ
_{k,3}

MN × MN(i = 4)

μ
_{k,4}

MM

x
_{112}

t
^{2}

μ
_{k,4}
t
^{2}

MN × MN(i = 4)

μ
_{k,4}

MN

x
_{111}

2t(1  t)

2 μ_{k, 4}t(1  t)

MN × MN(i = 4)

μ
_{k,4}

NN

x
_{110}

(1  t)^{2}

μ_{k,4}(1  t)^{2}

MN × NN(i = 5)

μ
_{k,5}

MN

x
_{101}

t

μ
_{k,5}
t

MN × NN(i = 5)

μ
_{k,5}

NN

x
_{100}

(1  t)

μ_{
k,5
}(1  t)

NN × NN(i = 6)

μ
_{k,6}

NN

x
_{000}

1

μ
_{k, 6}

 In this table, the high risk allele is M. Also, we define D to be the event that the child is affected. Note that 1 ≤ k ≤ 2. The last column is computed using the definition of conditional probability. Schaid and Sommer [63] also demonstrated this calculation. Note that \text{Pr}\left({x}_{abc}D,\text{pop}=k\right)={f}_{B}\left({x}_{abc};{\overrightarrow{\theta}}_{k}\right). Finally, t = Pr(heterozygous parent transmits an M allele to an affected child).