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The Ising Model
in
Physics and Statistical Genetics
Introduction
ASP (affcted-sib-pair) analysis
 Definitions: Any two identical copies of an allele l are said to be identical by
state (IBS). If these alleles are inherited from the same individual then they are
also identical by descent (IBD). Clearly, IBD implies IBS but not vice versa.

 Main idea: if affected siblings share more IBD alleles at some marker locus
than randomly expected among siblings, then that locus might be near a
locus of a predisposing gene.
The idea is that any two siblings are expected to have one allele IBD by chance. When a
deviation of this pattern is detected, by examining many sib-pairs, linkage is established
between a disease gene and the marker location.
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1/1
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No allele is IBD.
One allele is IBS.
Exactly one allele IBD.
1/2
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At least one allele IBD.
Expected 1.5 alleles IBD.
Introduction
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Analog
Magnetism
ASP
Spin up/down
Shared/unshared
Interaction between adjacent dipoles
Linkage between adjacent genetic markers
External field
disease
Advantage
Multipoint analyses have the advantage of extracting
maximum IBD-sharing information and a lower overall
genomewide type I error.
It can be easily adapted to the analysis of complex
genetic models with several genetic effects and with
interaction, or epistasis, between genes.
Methods

The Ising model in Physics
Methods
Adaptation to Genetic Data
Data: n*m matrix
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1
-1
1
0
1
-1
1
1
1
-1
-1
1
-1
-1
-1
-1
-1
-1
-1
-1
0
-1
-1
-1
-1
-1
-1
-1
1
-1
1
-1
1
-1
0
0
Distribution:
j(t): if a marker is shared IBD the neighboring markers have an increased chance
to be also shared
h(t): a genetic effect causing an increase in IBD shagring at the t locus (there will
be an apparent strong field close to the disease gene.)
There are 2m-1 parameters.

1
-1
1
-1
Methods
Parameter Estimation
 Maximum likelihood-Powell’s Method
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
Z-recursive calculation
Methods

Significance Testing