Likelihood ratios with X examples. - Familias · Likelihood ratios with X examples. Workshop...
Transcript of Likelihood ratios with X examples. - Familias · Likelihood ratios with X examples. Workshop...
Likelihood ratios with X examples.
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Nádia Pinto IPATIMUP/i3S, Porto, Portugal [email protected]
Human Karyotype
Female Male
2 copies 1 copy
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
M F
X Chromosomal markers
M F
Autosomal markers
C
Chromosomal Transmission
C
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
M F
1 1/2
D
M F
Autosomal markers
1/2 1/2
D
Chromosomal Transmission
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
X & Y Chromosomal markers
M F
X & Y Chromosomal markers
1 1/2
M F
Autosomal markers
1/2 1/2
S S
Chromosomal Transmission
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
2. FORMALIZING GENEALOGIES UNDER THE PERSPECTIVE OF X-CHROMOSOMAL MARKERS
Autosomal
X X X X X
X X
X X X
X
X
Y Y
Y
Y
Heterosomal
Grandparents
Parents
Grandchildren
Chromosomal Transmission
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
2. FORMALIZING GENEALOGIES UNDER THE PERSPECTIVE OF X-CHROMOSOMAL MARKERS
Chromosomal Transmission
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Autosomal
X X X X X
X X
X X X
X
X
Y Y
Y
Y
Heterosomal
Grandparents
Parents
Grandchildren
M F
X Chromosomal markers
1
D
M F
Autosomal markers
1/4≤P≤1/2 0 ≤P≤1/4
C
1/4≤P≤1/2
Chromosomal Transmission
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
M F
X Chromosomal markers
1
D
M F
Autosomal markers
1/4≤P≤1/2 0 ≤P≤1/4
C
0≤P≤1/4
Chromosomal Transmission
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
F
1
D
F
1
S
.
.
. X
.
.
. X
Paternal X & Y Chromosomal Transmission
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Verbally:
Posterior odds = Prior odds × LR
Mathematically (the proof follows from Bayes theorem):
2
1
2
1
02
01
|
|
|
|
HGP
HGP
HP
HP
GHP
GHP
O
O
genetic configuration observed :OG
individuals linked by genetic relationship R1 :1H
:2H individuals linked by genetic relationship R2
Statistical Analyses
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Assuming the hypotheses as a priori equally likely…
2
1
2
1
02
01
|
|
|
|
HGP
HGP
HP
HP
GHP
GHP
O
O
genetic configuration observed :OG
individuals linked by genetic relationship R1 :1H
:2H individuals linked by genetic relationship R2
= 1
Statistical Analyses
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Assuming the hypotheses as a priori equally likely…
2
1
02
01
|
|
|
|
HGP
HGP
GHP
GHP
O
O
genetic configuration observed :OG
individuals linked by genetic relationship R1 :1H
:2H individuals linked by genetic relationship R2
Numerically: Posterior odds = LR
Statistical Analyses
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
2
1
|
|
HGP
HGPLR
O
O
Genetic configuration observed :OG
individuals linked by genetic relationship R1 :1H
:2H individuals linked by genetic relationship R2
R1 and R2 are mutually exclusive and exhaustive
n
k
kfinal LRLR1
n: number of analyzed unassociated loci/set of loci
likelihood ratio associated with locus/set of loci k :kLR
Assuming independent alleles/haplotypes in different markers:
Statistical Analyses
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Alleles IBD IBS
No Yes
No No
Yes Yes
No Yes
Two alleles are called identical-by-descent (or IBD) if they have descended from a single ancestral allele.
Example:
M
C
1 2 1 3
F
1
Note that IBD is always measured with respect to some “founding” group of ancestors that are assumed to be unrelated.
2
1 F
1
1
1
C
1 F
1
2
1
F
F
C
C
C
Identity-by-descent (IBD) ≠ Identity-by-state (IBS)
IBD
IBS IBD
IBS , unless mutation
Two individuals are said to be related if the allele of one can be IBD to that of the other.
AUTOSOMAL REVIEW
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Patterns of IBD for two individuals
Δ4 I1:
I2:
Δ5 I1:
I2:
Δ6 I1:
I2:
Δ2 I1:
I2:
Δ3 I1:
I2:
Δ1 I1:
I2:
Δ7 I1:
I2:
Δ9 I1:
I2:
Δ8 I1:
I2:
Jacquard’s coefficients (1970)
AUTOSOMAL REVIEW
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Inbred individual C (Example):
A and B First Cousins
B
C
A
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Inbred individual C (Example):
B
C
A
A and B First Cousins
Alleles:
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Inbred individual C (Example):
... ...
B
C
A
A and B First Cousins
Alleles:
... ...
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Inbred individual C (Example):
... ...
1/2 1/2
1/2 1/2
1/2 1/2 B
C
A
A and B First Cousins
Alleles:
... ...
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Inbred individual C (Example):
... ...
1/2 1/2
1/2 1/2
1/2 1/2 B
C
A
A and B First Cousins
Alleles:
42
16
P(C is inbred) =
... ...
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Inbred individual C (Example):
... ...
1/2 1/2
1/2 1/2
1/2 1/2 B
C
A
A and B First Cousins
Alleles:
42
16
P(C is inbred) =
... ...
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Inbred individual C (Example):
... ...
1/2 1/2
1/2 1/2
1/2 1/2 B
C
A
A and B First Cousins
Alleles:
42
16
P(C is inbred) =
= %25,62
14
... ...
P(C being autozygous) = 6.25%
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Δ4 I1:
I2:
Δ5 I1:
I2:
Δ6 I1:
I2:
Δ2 I1:
I2:
Δ3 I1:
I2:
Δ1 I1:
I2:
k2 I1:
I2:
k0 I1:
I2:
k1 I1:
I2:
Jacquard’s coefficients (1970)
Patterns of IBD for two individuals
AUTOSOMAL REVIEW
An individual is called inbred if he / she can carry
two identical-by-descent alleles at a locus.
An individual is called (autosomally) inbred if her
/ his parents are related.
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
k2 I1:
I2:
k0 I1:
I2:
k1 I1:
I2:
M F
MT1 MT2
Identical Twins
k2=1; k1=0; k0=0;
M F
C
Parent - Child
k2=0; k1=1; k0=0;
M F
C
Unrelated
k2=0; k1=0; k0=1;
Patterns of IBD for two individuals
AUTOSOMAL REVIEW
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
M F
C1 C2
M F
C1 C2
M F
C1 C2
C1:
C2:
C1:
C2:
C1:
C2:
IBD patterns: Example
k2=1/4 k1=1/2 k0=1/4
AUTOSOMAL REVIEW
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Joint Genotypic Probabilities
AUTOSOMAL REVIEW
Workshop program: Familial testing, X-files, FamLinkX
Joint Genotypic Probabilities
AUTOSOMAL REVIEW
Workshop program: Familial testing, X-files, FamLinkX
Sample 1: AiAk
Sample 2: AiAk
H0 k2 k1 k0 P(G=AiAk,AiAk|H0)
Identical twins 1 0 0
Parent-child 0 1 0
Unrelated 0 0 1
Full-siblings 1/4 1/2 1/4
Joint Genotypic Probabilities: Example
AUTOSOMAL REVIEW
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
JACQUARD’S COEFFICIENTS (1970)
DESAFIO TEÓRICO DE PARENTESCO – GHEP 2016
P3
P1
P4
P2
M1
F1 F2
M2
M4
M3
Δ9 = 12/64
Δ4 I1:
I2:
Δ5 I1:
I2:
Δ6 I1:
I2:
Δ2 I1:
I2:
Δ3 I1:
I2:
Δ1 I1:
I2:
Δ7 I1:
I2:
Δ9 I1:
I2:
Δ8 I1:
I2:
Δ8 = 30/64 Δ7 = 15/64
Δ6 = 1/64 Δ5 = 2/64 Δ4 = 1/64
Δ3 = 2/64 Δ2 = 0 Δ1 = 1/64
JACQUARD’S COEFFICIENTS (1970)
DESAFIO TEÓRICO DE PARENTESCO – GHEP 2016
Δ9 = 28/64
Δ4 I1:
I2:
Δ5 I1:
I2:
Δ6 I1:
I2:
Δ2 I1:
I2:
Δ3 I1:
I2:
Δ1 I1:
I2:
Δ7 I1:
I2:
Δ9 I1:
I2:
Δ8 I1:
I2:
Δ8 = 32/64 Δ7 = 0
Δ6 = 0 Δ5 = 0 Δ4 = 2/64
Δ3 = 2/64 Δ2 = 0 Δ1 = 0
H2 H1
H2 H1 H1 H2
H0 H1 Δ1= 0
Δ2= 0
Δ3= 2/64
Δ4= 2/64
Δ5= 0
Δ6= 0
Δ7= 0
Δ8= 32/64
Δ9= 28/64
JOINT GENOTYPIC PROBABILITIES - WEIR ET AL., NATURE REVIEWS GENETICS 2006, 7:775
DESAFIO TEÓRICO DE PARENTESCO – GHEP 2016
Δ1= 1/64
Δ2= 0
Δ3= 2/64
Δ4= 1/64
Δ5= 2/64
Δ6= 1/64
Δ7= 15/64
Δ8= 30/64
Δ9= 12/64
Relationships k2 k1 k0
Identical twins 1 0 0
Parent-child 0 1 0
Full-siblings 1/4 1/2 1/4
Half-siblings Avuncular
Grandparent-Grandchild 0 1/2 1/2
First Cousins Great-grandparent / Great-grandchild
0 1/4 3/4
Unrelated 0 0 1
IBD partitions: Examples
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Relationships k2 k1 k0
Identical twins 1 0 0
Parent-child 0 1 0
Full-siblings 1/4 1/2 1/4
Half-siblings Avuncular
Grandparent-Grandchild 0 1/2 1/2
First Cousins Great-grandparent / Great-grandchild
0 1/4 3/4
Unrelated 0 0 1
IBD partitions: Examples
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Joint Genotypic Probabilities
Workshop program: Familial testing, X-files, FamLinkX
Joint Genotypic Probabilities
Workshop program: Familial testing, X-files, FamLinkX
Autosomal kinship classes: Example
A
B
H1: Avuncular H2: Half-siblings
A
B
H3: Grandparent / Grandchild
B A
≡ ≡
k0 = k1 = 1/2; k2=0
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Autosomal kinship classes: Example
A
B
H1: Avuncular H2: Half-siblings
A
B
H3: Grandparent / Grandchild
B A ≡ ≡
k0 = k1 = 1/2; k2=0
G k2 k1 k0 P(G|H)
AiAi, AiAi
1/4 1/2 1/4 AiAi, AkAk
AiAk,AiAk
… …
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Autosomal kinship classes: Example
A
B
H1: Avuncular H2: Half-siblings
A
B
H3: Grandparent / Grandchild
B A ≡ ≡
k0 = k1 = 1/2; k2=0
For any genotypic configuration G and alternative hypotheses:
The hypotheses are equally likely and, therefore, theorectically indistinguishable.
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Autosomal kinship classes: (Sub-)Example
Inheritance claiming
W
M ?
$
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Autosomal kinship classes: (Sub-)Example
Inheritance claiming
W
M ?
$
M W
vs M
W
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Autosomal kinship classes: (Sub-)Example
Inheritance claiming
W
M ?
$
M W
vs M
W
Theorectically indistinguishable by unlinked autosomal markers (despite the number of analysed markers)
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
F2
F1
X X
X X
1/2
X X
X
X X
F1
F2
X X
X
X X
F1
F2
X
1/2 1/2
IBD X-patterns among two females
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
F2
X
F1
X
X
X X
1 1
F1 F2
X X X
X X X X
1/2
1/2 1 1
1 1/2
F1
X X X
F2
X X X
X X
1
1/2 1/2
F1 F2
X X X
X X X X
1/2
1/2 1 1
4.2 HIPÓTESIS - INDIQUE LAS DOS HIPÓTESIS EMPLEADAS
DESAFIO TEÓRICO DE PARENTESCO – GHEP 2016
Total de respostas: 54 labs
23 labs
H0: H1 y H2 son hermanas de padre y madre H1: H1 y H2 son hermanas de madre
H0: Daughter 1 and Daughter 2 are half sisters H1: Daughter 1 and Daughter 2 are full sisters
Vs.
X X X
5 Labs H0: Hija1 e Hija2 comparten el mismo padre biológico H1: Hija1 e Hija2 tienen diferente padre biológico H0: Probabilidad de que la hija 1 y la hija 2 sean hijas de diferente padre H1: Probabilidad de que la hija 1 y la hija 2 sean hijas del mismo padre
Vs.
H0: Filha 1 e Filha 2 são filhas da mesma mãe e do mesmo pai (Full siblings) H1: Filha 1 e Filha 2 são filhas da mesma mãe mas não do mesmo pai (Half siblings)
4.2 HIPÓTESIS - INDIQUE LAS DOS HIPÓTESIS EMPLEADAS
DESAFIO TEÓRICO DE PARENTESCO – GHEP 2016
Total de laboratórios que indicam existir parentesco entre mãe/pai: 26 labs
H1 H2
H2 H1
3 labs: Ho primos / H1 primos 2 labs: Ho/H1 primos
H0: La hija 1 y la hija 2 son hermanas de padre y madre, y estos son primos H1: La hija 1 y la hija 2 son hermanas de la misma madre y distinto padre
8 labs: Ho primos en primer grado 9 labs: Ho/H1 primos en primer grado
H0: Daughter 1 and Daughter 2 are full sisters (mother and first-degree cousin are the parents) H1: Daughter 1 and Daughter 2 are half sisters (mother and first-degree cousin are the parents of Daughter 1)
1 lab: Ho primos en primer grado via materna 1 lab: Ho/H1 primos en primer grado via materna
Una mujer ha tenido una hija (Hija 1) de un primer matrimonio con un primo en primer grado (hijo de su tío materno, hermano de su madre).
4.2 HIPÓTESIS - INDIQUE LAS DOS HIPÓTESIS EMPLEADAS
H0 - Hija 1 e Hija 2 são irmãs inteiras e a avó materna é irmã inteira do avô paterno. H1 – Hija 1 e Hija 2 são meias-irmãs por via materna e a avó materna é irmã inteira do avô paterno de Hija 1 e o pai de Hija 2 é não aparentado.
H0 - Hija1 e Hija2 son hermanas biológicas por linea paterna, siendo ambas hermanas por linea materna y padre hijo del tío materno de madre. H1 – Hija2 NO es hermana por linea paterna de hija1, siendo ambas hermanas por linea materna, hija1 hija de P y P hijo del tío materno de madre.
H2 H1 H1 H2
DESAFIO TEÓRICO DE PARENTESCO – GHEP 2016
Labs. 575389 y 575456
F1:
F2:
F1:
F2:
F1:
F2:
F1:
F2:
F1:
F2:
ΛFF1 F1:
F2:
F1:
F2:
F1:
F2:
F1:
F2:
ΛFF2 ΛFF
3
ΛFF4 ΛFF
5 ΛFF6
ΛFF7 ΛFF
8 ΛFF9
Patterns of IBD for X Chromosome markers and two females
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
F1:
F2:
F1:
F2:
F1:
F2:
F1:
F2:
F1:
F2:
ΛFF1 F1:
F2:
F1:
F2:
F1:
F2:
F1:
F2:
ΛFF2 ΛFF
3
ΛFF4 ΛFF
5 ΛFF6
ΛFF7 ΛFF
8 ΛFF9
A female is called X inbred if she can carry two
identical-by-descent X alleles at a locus.
Patterns of IBD for X Chromosome markers and two females
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
... ...
1/2 1/2
1/2 1/2
1/2 1/2 B A
A and B First Cousins
Alleles:
42
16
P(C is inbred) =
= %25,62
14
... ...
P(C is autozygous) = 6.25%
Inbreeding from Autosomal and X-Chromosomal perspective
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Autosomal Transmission
C
X ...
1 1
1/2 1
1/2 1 B A
A and B First Cousins
Y Alleles:
X
Inbreeding from Autosomal and X-Chromosomal perspective
Workshop program: Familial testing, X-files, FamLinkX
X-Chromosomal Transmission
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Y ...
Y X
X
X
X X X
X
1/2 1
1/2 1 B A
Y Alleles:
X
Y
Y X
X
X
X X X
X
1/2
X
1/2
P(inbreeding) = 0
C C
X X
Patterns of IBD for X Chromosome markers and two females
F1:
F2:
F1:
F2:
F1:
F2:
xFF2 xFF
1 xFF0
M F
Identical Twins
k2=1; k1=0; k0=0;
AUTOSOMAL REVIEW
Workshop program: Familial testing, X-files, FamLinkX
Patterns of IBD for X Chromosome markers and two females
F1:
F2:
F1:
F2:
F1:
F2:
xFF2 xFF
1 xFF0
M
X X X
F
X X X X
Female Identical Twins
x2=1; x1=0; x0=0;
X CHROMOSOMAL
M F
Identical Twins
k2=1; k1=0; k0=0;
AUTOSOMAL REVIEW
Workshop program: Familial testing, X-files, FamLinkX
Patterns of IBD for X Chromosome markers and two females
F1:
F2:
F1:
F2:
F1:
F2:
xFF2 xFF
1 xFF0
AUTOSOMAL REVIEW
Parent - Child
k2=0; k1=1; k0=0;
P
C
Workshop program: Familial testing, X-files, FamLinkX
X Chromosomal markers – Alleged father unavailable for testing
AF
F1
F2
X X
X
X
1/2
1 P(F1 & F2 sharing one IBD X-allele) = 1
AF
F2
X
X
1 F1
X
1
Mendelian incompatibilities can be found
Ex. Ex.
X X
X
X Chromosomal markers in kinship testing
Formalizing relatedness through X Chromosomal perspective
Note that in autosomal transmission among non-inbred individuals the sharing of IBD alleles is only mandatory in the cases parent/child and identical twins.
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
X Chromosomal markers – Alleged father unavailable for testing
AF
F1
F2 P(F1 & F2 sharing one IBD X-allele) = 1
AF
F2 F1
X
Ex. Ex.
X X
X Chromosomal markers in kinship testing
Formalizing relatedness through X Chromosomal perspective
X
MUTATION? ABSENCE OF RELATEDNESS?
Mendelian incompatibilities can be found
X X
X X
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Patterns of IBD for X Chromosome markers and two females
F1:
F2:
F1:
F2:
F1:
F2:
xFF2 xFF
1 xFF0
x2=0; x1=1; x0=0;
X CHROMOSOMAL AUTOSOMAL REVIEW
Parent - Child
k2=0; k1=1; k0=0;
P
C
Mother - Daughter
D
M
X X
X X
AF
F2
X
F1
X
X
X X
Paternal Half-Sisters
AF
X X
X
X X
F1
F2
Paternal Grandmother-Granddaughter
Workshop program: Familial testing, X-files, FamLinkX
Patterns of IBD for X Chromosome markers and two females
F1:
F2:
F1:
F2:
F1:
F2:
xFF2 xFF
1 xFF0
AUTOSOMAL REVIEW
Unrelated
k2=0; k1=0; k0=1;
M F
B
M F
A
Workshop program: Familial testing, X-files, FamLinkX
Patterns of IBD for X Chromosome markers and two females
F1:
F2:
F1:
F2:
F1:
F2:
xFF2 xFF
1 xFF0
x2=0; x1=0; x0=1;
X CHROMOSOMAL AUTOSOMAL REVIEW
Unrelated
k2=0; k1=0; k0=1;
Unrelated
M F
B
M F
A
F1
X
F2
X X X
B
A X
X
X X
Y
X X
X X
Workshop program: Familial testing, X-files, FamLinkX
C1:
C2:
C1:
C2:
C1:
C2:
X IBD patterns: Example – Full-sisters
x2 = 1/2 x1 = 1/2 x0 = 0
M F
X X
A
X X
B
M F
X X
A
X X
B
M F
X X
A
X X
B
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
C1:
C2:
C1:
C2:
C1:
C2:
X IBD patterns: Example – Paternal Aunt - Niece
x2 = 0 x1 = 1/2 x0 = 1/2
M F
X X
N
A
X X
M F
X X
N
A
X X
M F
X X
N
A
X X
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Joint X Chromosomal Genotypic Probabilities (Female-Female pair)
Genotypes Joint Genotypic Probabilities for X-markers and two females
General Non-inbred females
AiAi, AiAi Λ1
FFpi + (Λ2FF+ Λ3
FF+ Λ5FF+ Λ7
FF)pi2+(Λ4
FF+
Λ6FF+ Λ8
FF)pi3+ Λ9
FFpi4
x2FFpi
2 + x1FFpi
3+ x0FFpi
4
AiAi, AjAj Λ2FFpipj + Λ4
FFpipj2+ Λ6
FFpi2pj + Λ9
FFpi2pj
2 x0FFpi
2pj2
AiAi, AiAj Λ3FFpipj +(2 Λ4
FF + Λ8FF)pi
2pj+ 2Λ9FFpi
3pj x1FFpi
2pj+ 2x0FFpi
3pj
AiAj, AiAi Λ5FFpipj +(2 Λ6
FF + Λ8FF)pi
2pj+ 2Λ9FFpi
3pj x1FFpi
2pj+ 2x0FFpi
3pj
AiAi, AjAl 2Λ4FFpipjpl + 2Λ9
FFpi2pjpl 2x0
FFpi2pjpl
AjAl, AiAi 2Λ6FFpipjpl + 2Λ9
FFpi2pjpl 2x0
FFpi2pjpl
AiAj, AiAj 2Λ7FFpipj + Λ8
FFpipj(pi + pj) + 4Λ9FFpi
2pj2
2x2FFpipj + x1
FFpipj(pi + pj) +
4x0FFpi
2pj2
AiAj, AiAk Λ8FFpipjpk + 4Λ9
FFpi2pjpk x1
FFpipjpk + 4x0FFpi
2pjpk
AiAj, AkAl 4Λ9FFpipjpkpl 4x0
FFpipjpkpl
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Patterns of IBD for X Chromosome markers and a pair female/male
ΛFM1 F:
M:
F:
M:
ΛFM2
ΛFM3 F:
M:
ΛFM4 F:
M:
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Patterns of IBD for X Chromosome markers and a pair female/male
ΛFM1 F:
M:
F:
M:
ΛFM2
xFM1 F:
M:
xFM0 F:
M:
Assuming non-inbred female:
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Joint X Chromosomal Genotypic Probabilities (Female-Male pair)
Genotypes Joint Genotypic Probabilities for X-markers and a pair Female / Male
General Pair Female / Male Non-inbred Female
AiAi, Ai Λ1FMpi + (Λ2
FM+ Λ3FM)pi
2 + Λ4FMpi
3 x1FM pi
2+ x0FM pi
3
AiAi, Aj Λ2FMpipj + Λ4
FMpi2pj x0
FM pi2pj
AiAj, Ai Λ3FMpipj + 2Λ4
FM pi2pj x1
FM pipj + 2x0FM pi
2pj
AiAj, Ak 2Λ4FMpipjpk 2x0
FM pipjpk
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Examples (considering a non-inbred female):
paternal uncle - niece
x0FM = 1/2
x1FM = 1/2
unrelated
x0FM = 1
x1FM = 0
Genotypes
Joint Genotypic Probabilities for X-markers and a
female (non-inbred) / male pair
General paternal uncle - niece unrelated
AiAi, Ai x1FM pi
2+ x0FM pi
3 1/2pi2+ x0
FM 1/2pi3 pi
3
AiAi, Aj x0FM pi
2pj 1/2pi2pj pi
2pj
AiAj, Ai x1
FM pipj + 2x0FM
pi2pj
1/2pipj + pi2pj 2pi
2pj
AiAj, Ak 2x0FM pipjpk pipjpk 2pipjpk
Joint X Chromosomal Genotypic Probabilities (Female-Male pair)
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
xMM1 M1:
M2:
xMM0 M1:
M2:
Joint Genotypic Probabilities
Genotypes Joint Genotypic Probabilities for X-chromosome
markers and two males
Ai, Ai x1MMpi + x0
MMpi2
Ai, Aj x0MMpipj
Joint X Chromosomal Genotypic Probabilities (Male-Male pair)
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Examples:
maternal uncle - nephew
x1MM = 1/4
x0MM = 3/4
unrelated
x0MM = 1
x1MM = 0
Genotypes
Joint Genotypic Probabilities for X-markers and two
males
General Maternal
Uncle – Nephew Unrelated
Ai, Ai x1MMpi + x0
MMpi2 1/4pi + 3/4pi
2 pi2
Ai, Aj x0MMpipj 1/4pipj
pipj
Joint X Chromosomal Genotypic Probabilities (Male-Male pair)
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Other examples for the use of X-Chromosomal markers
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
“Are two females related as paternal grandmother granddaughter?”
1. Paternal Grandmaternity
“Have two females the same father?”
2. Paternal Sisterhood
Examples for the use of X-Chromosomal markers
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Examples for the use of X-Chromosomal markers
X Chromosomal markers – Alleged father unavailable for testing
P(F1 & F2 sharing at least one IBD X-allele) = 1
Mendelian incompatibilities can be found
F2 1 F1 1
X X
F1
F2
X X
X
X
1/2
1
X
F1 F2
X X X
X X X X
1/2 1/2
1 1 X
X X
Power of exclusion: Probability of finding, in randomly chosen individuals, inconsistencies with Mendelian rules of transmission.
Autosomes X Chromosome Markers
Duos
=
<
Trios
=
<
A
B
A
B
A
B B
A
B A B
A
C
A B B A
C
B
A
C
A B
C
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Example (Paternal Grandmaternity - Motherless case):
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
The profiles correspond to a pair of genetically unrelated females :2H
The profiles correspond to a pair of females genetically related as paternal grandmother-granddaughter.
:1H
B
A
vs. A & B unrelated
Hypotheses:
1. The putative paternal grandmother has no monozygotic (‘identical’) twin(s).
2. The putative father has no monozygotic (‘identical’) twin(s).
3. The putative father and the real father are genetically unrelated with the mother
of the child.
4. The putative father is either the true father or genetically unrelated with him.
5. The tested individuals are assumed to belong to the population sampled for the
estimation of gene frequencies (reference and/or description of the population
sample used, including sampling criteria).
6. No gametic association (linkage disequilibrium) exists between the analyzed set
of markers.
Example (Paternal Grandmaternity - Motherless case):
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Assumptions:
Conclusions
Assuming the conditions described in Annex XXX, the results obtained show that the genetic profile configuration is YYYYY times more likely assuming the hypothesis that So-and-so is the biological paternal grandmother of Child than under the hypothesis of the individuals being genetically unrelated (results per set of markers presented in Table ZZZZZ).
Example (Paternal Grandmaternity - Motherless case):
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
After an abortion female foetal material is collected for analysis. The woman has a mental disease and there is the possibility of incest. Some suspicions were raised that the mother was abused by her own father and brother. For the investigation genetic material was collected from the woman and female foetus, and three hypotheses of kinship were considered: (a) the father is unrelated with the mother, (b) the father is also the father of the woman, and (c) the father is also the brother of the woman.
Examples for the use of X-Chromosomal markers: Incest case
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
How X Chromosomal markers can be useful?
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Examples for the use of X-Chromosomal markers: Incest case
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Examples for the use of X-Chromosomal markers: Incest case
Undistinguishable through unlinked autosomal markers.
=
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Examples for the use of X-Chromosomal markers: Incest case
=
Undistinguishable through unlinked autosomal markers.
M:
D:
M:
D:
M:
D:
1/4 1/4 1/2
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Examples for the use of X-Chromosomal markers: Incest case
≠ ≠
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Examples for the use of X-Chromosomal markers: Incest case
≠ ≠
Probability of the foetal being X-autozygous (homozygous for IBD X-alleles) for one locus:
M:
D:
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Examples for the use of X-Chromosomal markers: Incest case
≠ ≠
0
Probability of the foetal being X-autozygous (homozygous for IBD X-alleles) for one locus:
1/4 1/2
M:
D:
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Examples for the use of X-Chromosomal markers: Incest case
≠ ≠
Probability of the foetal sharing two pairs of IBD X-alleles with the mother for one locus:
M:
D:
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Examples for the use of X-Chromosomal markers: Incest case
≠ ≠
0
Probability of the foetal sharing two pairs of IBD X-alleles with the mother for one locus:
1/4 1/2
M:
D:
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Examples for the use of X-Chromosomal markers: Incest case
≠ ≠
Probability of the foetal sharing exactly one pair of IBD X-alleles with the mother for one locus:
M:
D:
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Examples for the use of X-Chromosomal markers: Incest case
≠ ≠
1
Probability of the foetal sharing exactly one pair of IBD X-alleles with the mother for one locus:
1/2 0
M:
D:
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Examples for the use of X-Chromosomal markers: DVI cases
Case I:
Missing cousins
Relative available for comparision
One part of a body is recovered.
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Examples for the use of X-Chromosomal markers: DVI cases
Case I:
Missing cousins
Relative available for comparision
One part of a body is recovered. Autosomal markers are useless.
P(A&B sharing a pair of IBD X-alleles at one locus) = 3/4
P(A&C sharing a pair of IBD X-alleles at one locus) = 0
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Examples for the use of X-Chromosomal markers: DVI cases
Case II:
F
M F
M
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Examples for the use of X-Chromosomal markers: DVI cases
Case II:
F
M F
M
0
P(F&M sharing one pair of IBD X-alleles):
1/2
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Examples for the use of X-Chromosomal markers: DVI cases
Case III:
F
M F
M
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Examples for the use of X-Chromosomal markers: DVI cases
Case III:
F
M F
M
3/4
P(F&M sharing one pair of IBD X-alleles):
1/4
Muchas Gracias!
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Workshop program: Familial testing, X-files, FamLinkX
XXI Jornadas del GHEP-ISFG, 06-09-2016, Bayahíbe, República Dominicana
Referencias: Jacquard, A. The Genetic Structure of Populations, Biomathematics. vol. 5. Springer-
Verlag, Berlin-Heidelberg-New York; 1974 (pp. 102–107). Weir, B.S., Anderson, A.D., Hepler, A.B. Genetic relatedness analysis: modern data and new
challenges. Nat. Rev. Genet. 2006;7:771–780. Egeland, T., Sheehan, N. On identification problems requiring linked autosomal markers. Forensic
Sci. Int. Genet. 2008;2:219–225 Pinto N, Gusmão L, Amorim A, Likelihood ratios in kinship analysis: Contrasting kinship classes,
not genealogies, Forensic Science International: Genetics (2010) 4(3): 218-219 Pinto N, Gusmão L, Amorim A, X-chromosome markers in kinship testing: A generalisation of the
IBD approach identifying situations where their contribution is crucial, Forensic Science International: Genetics (2011) 5(1):27-32.
Pinto N, Gusmão L, Egeland T, Amorim A, Paternity exclusion power: comparative behaviour of autosomal and X-chromosomal markers in standard and deficient cases with inbreeding, Forensic Science International: Genetics (2013) 7: 290-295
Referencias adicionais: Pinto N, Silva PV, Amorim A, General Derivation of the Sets of Pedigrees with the Same Kinship
Coefficients, Human Heredity (2010) 70(3): 194-204 Pinto N, Silva PV, Amorim A, A general method to assess the utility of the X chromosomal
markers in kinship testing, Forensic Science International: Genetics (2012) 6:198-207