Linkage disequilibrium and gene mapping: an empirical least-squares approach

This paper proposes a novel approach for fine-scale mapping of disease genes that is based on the well-known linkage-disequilibrium parameter delta. Using a very simple, very general model, I show how delta can be interpreted in terms of identity-by-descent probabilities. The value of delta follows a piecewise curve along the chromosome, with the maximum occurring at the disease locus where the two pieces intersect. A semiparametric, multilocus approach is used to fit this nonlinear regression curve in order to estimate the gene location. Using the bootstrap to empirically estimate much of the probability model from the data avoids the need for many detailed population assumptions. One advantage of the approach is its use of the observed covariance structure of the data, which can be highly informative as to the gene location. I illustrate the method on the cystic fibrosis data of Kerem et al.