1. Genetic linkage analysis
Gene Hunting: find genes responsible for a given disease Main idea: If a disease is statistically linked with a marker on a chromosome, then tentatively infer that a gene causing the disease is located near that marker.
Some slides were prepared by Ma’ayan Fishelson, some by Nir, and most are mine. I have slightly edited all slides. .

2. Human Genome Most human cells contain 46 chromosomes:
2 sex chromosomes (X,Y):
XY – in males.
XX – in females.
22 pairs of chromosomes named autosomes.
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3. Sexual Reproduction egg sperm zygote gametes ביצית תא זרע ביצית מופרית
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תא זרע
ביצית מופרית
תאי מין

4. Chromosome Logical Structure
Locus – the location of genes or other markers on the chromosome.
Allele – one variant form (or state) of a gene/marker at a particular locus.
Locus1
Possible Alleles: A1,A2
Locus2
Possible Alleles: B1,B2,B3

5. Genotypes versus Phenotypes
At each locus (except for sex chromosomes) there are 2 genes. These constitute the individual’s genotype at the locus.
The expression of a genotype is termed a phenotype. For example, hair color, weight, or the presence or absence of a disease.

6. Recombination Phenomenon
A recombination between
2 genes occurred if the
haplotype of the individual
contains 2 alleles that resided in different haplotypes in the
individual's parent.
(Haplotype – the alleles at different loci that are received by an individual from one parent).

7. An example - the ABO locus.
The ABO locus determines detectable antigens on the surface of red blood cells.
The 3 major alleles (A,B,O) interact to determine the various ABO blood types.
O is recessive to A and B. Alleles A and B are codominant.
Genotype
Phenotype
A/A, A/O A
B/B, B/O B
A/B AB
O/O O
Note that the listed genotypes are unordered
(we don’t know which allele is from the father
and which one is from the mother).

8. Example: ABO near AK1 on Chromosome 92 4 5 1 3 A
A1/A1 O
A2/A2
A1/A2
O O
A1 A2
A O
A2 | A2
A2 A2
Recombinant

9. Example for Finding Disease Genes2 4 5 1 3 H
A1/A1 A
A2/A2
A1/A2
A A
A1 A2
H A
H | A
A2 | A2
A2 A2
Recombinant
We use a marker with codominant alleles A1/A2.
We speculate a locus with alleles H (Healthy) / A (affected)
If the expected number of recombinats is low (close to zero), then the speculated locus and the marker are tentatively physically closed.

10. The method just described is called genetic linkage analysis
The method just described is called genetic linkage analysis. It uses the phenomena of recombination in families of affected individuals to locate the vicinity of a disease gene.

11. Comments about the example
Often:
Pedigrees are larger and more complex.
Not every individual is typed.
There are more markers and they have more than two alleles.
Recombinants cannot always be determined.

12. Usually recombination can not be simply counted2 4 5 1 3 A
A1/A1
A2/A2
A1/A2
? ?
A1 A2
A O
A2 | A2
A2 A2
Recombinant ?
Sometimes !
One can compute the likelihood of data given every location and choose the most likely location.

13. A Bayesian Network Model
L11m
L11f
Selector of maternal allele at locus 1 of person 3
X11
S13m
P(s13m) = ½
L13m
Maternal allele at locus 1 of person 3 (offspring)
Selector variables Sijm are 0 or 1 depending on whose allele is transmitted to offspring i at maternal locus j.
P(l13m | l11m, l11f,,S13m=0) = 1 if l13m = l11m
P(l13m | l11m, l11f,,S13m=1) = 1 if l13m = l11f
P(l13m | l11m, l11f,,s13m) = 0 otherwise

14. Probabilistic model for two loci
S13m
L11f
L11m
L13m
X11
S13f
L12f
L12m
L13f
X12
X13
Model for locus 1
S23m
L21f
L21m
L23m
X21
S23f
L22f
L22m
L23f
X22
X23
Model for locus 2

15. Probabilistic model for Recombination
S13m
L11f
L11m
L13m
X11
S13f
L12f
L12m
L13f
X12
X13
S23m
L21f
L21m
L23m
X21
S23f
L22f
L22m
L23f
X22
X23
θ2 is called the recombination fraction between loci 2 & 1.

16. Modeling Phenotypes I
L11m
L11f
X11
S13m
Y11
L13m
Phenotype variables Yij are 0 or 1 depending on whether a phenotypic trait associated with locus i of person j is observed. E.g., sick versus healthy. For example model of perfect recessive disease yields the penetrance probabilities:
P(y11 = sick | X11= (a,a)) = 1
P(y11 = sick | X11= (A,a)) = 0
P(y11 = sick | X11= (A,A)) = 0

17. Introducing a tentative disease Locus
S13m
L11f
L11m
L13m
X11
S13f
L12f
L12m
L13f
X12
X13
Marker locus
Disease locus: assume
sick means xij=(a,a)
S23m
L21f
L21m
L23m
X21
S23f
L22f
L22m
L23f
X22
X23
The recombination fraction θ 2 is unknown. Finding it can help determine whether a gene causing the disease lies in the vicinity of the marker locus.

18. SUPERLINK
Stage 1: each pedigree is translated into a Bayesian network. 
Stage 2: value elimination is performed on each pedigree (i.e., some of the impossible values of the variables of the network are eliminated).
Stage 3: an elimination order for the variables is determined, according to some heuristic.
Stage 4: the likelihood of the pedigrees given the θ values is calculated. This is done by by performing variable elimination according to the elimination order determined in stage 3.