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Immigration example – daughter or sister?

Resident
Mother

Reference
Child

Applicant
M C D
THO16,76,9.36,9.3
TPOX888
CSF1PO1110,1110,11
D3S135815,1614,1614,15
VWA14,191414,19
FGA21,2524,2521,24
D8S117914,1510,1510,14
D21S1121,31.230,31.230,31.2
D18S51141410,14
D5S81811,121211,12
D13S31711,121211,12
D7S8208,118,118,12
D16S5399,1010,139,13
Resident claims Applicant as a daughter (H0, left diagram), but might she instead be a sister (H1, right diagram)?

Sisters get much lower priority to immigrate.

The DNA types for Applicant and the two references, shown in the box at left, are entered into DNAVIEW and a "case" is defined consisting of the three people – M, C, and D.

Using the automated Kinship facility (called Immigration – available in DNAVIEW but not in PATER or in Abridged DNAVIEW), the problem of the diagrams above is coded as follows: 

; D=daughter or sister of M
  C, D/? : M      + Fred
  M, ?/D : Granny + Gramps

Immigration determines the genotype patterns –

THO1 TPOX CSF1PO D3S1358 VWA FGA D8S1179 D21S11 D18S51 D5S818 D13S317 D7S820 D16S539
M pq M p M q M qr M pq M pr M qr M pr M q M pq M pq M pq M pq
C pr C p C pq C pr C p C qr C pr C qr C q C q C q C pq C qr
D pr D p D pq D pq D pq D pq D pq D qr D pq D pq D pq D pr D pr
then, locus by locus, deduces the algebraic likelihood ratio formulas (in terms of genotype frequencies p, q, etc.), looks up the frequencies, and evaluates the expressions. It takes about one minute of computation, with no human intervention necessary, to produce the report in the box below.

Locus Likelihood ratio Frequencies
numericsymbolic
THO1 2.73 (1+r) / (r+2pr) p=0.237 r=0.331
TPOX 1.31 2 / (1+p) p=0.528
CSF1PO 3.8 (1+p) / (p+pq) p=0.251 q=0.309
D3S1358 5.89 (1+p) / (p+2pq) p=0.126 q=0.256
VWA 0.982 (1+p+q) / (1+p+q+2pq) p=0.131 q=0.0869
FGA 6.28 (1+q) / (q+2pq) p=0.171 q=0.135
D8S1179 9.81 (1+p) / (p+2pq) p=0.0761 q=0.221
D21S11 4.21 (1+q) / (q+2qr) q=0.252 r=0.0894
D18S51 0.857 1 / (1+q) q=0.167
D5S818 0.869 (1+p+q) / (1+p+q+2pq) p=0.369 q=0.35
D13S317 0.896 (1+p+q) / (1+p+q+2pq) p=0.305 q=0.307
D7S820 0.764 1 / (1+2p) p=0.155
D16S539 5.76 (1+r) / (r+2pr) p=0.107 r =0.167

cumulative LR=59900
The likelihood ratio of about 60000 favoring the "daughter" hypothesis ( H0) corresponds to a posterior probability (assuming a 50% a priori probability) of 99.99+%, or practical proof.

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