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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. 1/2 1/3 1/2 1/3 1/2 1/1 1/2 1/3 No allele is IBD. One allele is IBS. Exactly one allele IBD. 1/2 1/1 1/1 1/1 At least one allele IBD. Expected 1.5 alleles IBD. Introduction 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 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 Z-recursive calculation Methods Significance Testing