A novel method to express SNP-based genetic heterogeneity, Psi, and its use to measure linkage disequilibrium for multiple SNPs, D(g), and to estimate absolute maximum of haplotype frequency

Single nucleotide polymorphisms (SNPs) are important markers to investigate genetic heterogeneity of population and to perform linkage disequilibrium (LD) mapping. We propose a new method, Psi, to express frequency of 2(N(s)) haplotypes for N(s) di-allelic SNPs. Using the new expression of haplotype frequency, we propose a novel measure of LD, D(g), not only for SNP pairs but also for multiple markers. The values of D(g) for SNP pairs were revealed to be similar to values of conventional pairwise LD indices, D' and r(2), and it was revealed that D(g) quantitated components of LD that were not measured by conventional LD indices for SNP pairs. Also we propose a distinct method, D(g)-based absolute estimation, to infer the absolute maximum estimates of haplotype frequency. The result of the D(g)-based absolute estimation of haplotype frequency for SNP pairs were compared with the conventional expectation-maximization (EM) algorithm and reported that the new method gave better inference than the EM algorithm which converged infrequently to a local extreme.