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Formulas for sibship Paternity and mutation Go to home page of Charles H. Brenner |
Each row of the table lists a possible pattern of gene sharing among child, [mother], and alleged father (on the left) and paternity index formulas (on the right). The paternity index formulas were derived automatically by the Symbolic Kinship Program.
The letters
o,
p,
q,
r,
s
in the "Child, Mother, Alleged Father" columns represent
alleles.
and
The letters
p,
q,
o
in the likelihood ratio columns
represent the allele frequency of the corresponding allele.
| If the possibility of an undetected allele changes the formula,
the more general form is listed in the
"Silent allele" or null allele of course includes the possibility of RFLP bands that are not visible for whatever reason, and of PCR primer dropout. The only caveat is that one must somehow estimate the frequency o with which alleles are unobserved. | ||||
Child | Mother | Alleged father | Likelihood ratio for paternity vs. non-paternity | ||
Co-dominant system | With silent allele o | Notes | |||
q | pq | q | 1/q | 1 / q' | |
q | p | q | impossible | (q'/q") / q | (1) |
pq | p or pr | q | 1/q | (q'/q") / q | (1) |
q | q | q | 1/q | 1 / (q'-o3/q'(q+3o)) | (1*) |
pq | p or pr or ps | qr (or pq) | 1/2q | ||
q | p | qr | impossible | 1 / 2q | (2) |
q | pq | qr (or pq) | 1/2q | 1 / 2q' | (2) |
q | q | qr | 1/2q | 1 / 2(q'-o²/q") | (2*) |
pq | pq | pq | 1/(p+q) | ||
pq | pq | q | 1/(p+q) | (q'/q") / (p+q) | |
pq | pq | qr | 1/(2p+2q) | ||
q | pq | r | 0 | o / q'r" | (3) |
q | q | r | 0 | o / (q'r" + oqr"/q') | (3*) |
q | p | r | impossible | 0 | |
q | Mother not tested | q | 1/q | (1 + o(1-o/q")/q) / q" | (4*) |
pq | Mother not tested | q | 1/2q | (q'/q") / 2q | |
q | Mother not tested | qr | 1/2q | (q'/q") / 2q | |
pq | Mother not tested | pq | (p+q) / 4pq | ||
pq | Mother not tested | qr | 1/4q | ||
q | Mother not tested | r | 0 | o / q"r" | (3*) |