Rate of decay in admixture linkage disequilibrium and its implication in gene mapping

Modeling linkage disequilibria (LD) between genes usually observed in admixed natural populations has been shown an effective approach in high-resolution mapping of disease genes in humans. A prerequisite to obtain accurate estimation of recombination fraction between genes at a marker locus and the disease locus using the approach is a reliable prediction of the proportion of the admixture populations. The present study suggested the use of gene frequencies to predict the estimate of the admixture proportion based on the observation that the gene frequencies are much more stable quantities than the haplotype frequencies over evolution of the population. In this paper, we advanced the theory and methods by which the decay rate of nonlinear term of LD in admired population may be used to estimate the recombination fraction between the genes. Theoretical analysis and simulation study indicate that, the larger the difference of gene frequencies between parental populations and the more closely the admixture proportion approaches 0.5, the more important the nonlinear term of the LD in the admixed population, and hence the more informative such admixed populations in the high-resolution gene mapping practice.