The Ising model in physics and statistical genetics

Interdisciplinary communication is becoming a crucial component of the pres ent scientific environment. Theoretical models developed in diverse discipl ines often may be successfully employed in solving seemingly unrelated prob lems that can be reduced to similar mathematical formulation. The Ising mod el has been proposed in statistical physics as a simplified model for analy sis of magnetic interactions and structures of ferromagnetic substances. He re, we present an application of the one-dimensional, linear Ising model to affected-sib-pair (ASP) analysis in genetics. By analyzing simulated genet ics data, we show that the simplified Ising model with only nearest-neighbo r interactions between genetic markers has statistical properties comparabl e to much more complex algorithms from genetics analysis, such as those imp lemented in the Allegro and Mapmaker-Sibs programs. We also adapt the model to include epistatic interactions and to demonstrate its usefulness in det ecting modifier loci with weak individual genetic contributions. A reanalys is of data on type 1 diabetes detects several susceptibility loci not previ ously found by other methods of analysis.