An Exponential Dispersion Model for the Distribution of Human Single Nucleotide Polymorphisms

An analysis of 1.42 million human single nucleotide polymorphisms (SNPs), mapped by the International SNP Map Working Group, revealed an apparent power function relationship between the estimated variance and mean number of SNPs per sample bin. This relationship could be explained by the assumption that a scale invariant Poisson gamma (PG) exponential dispersion model could describe the distribution of SNPs within the bins. In this model the sample bins would contain random (Poisson distributed) numbers of identical by descent genomic segments, each with independently distributed and gamma distributed numbers of SNPs. This model was both qualitatively and quantitatively consistent with the conventional coalescent model. It agreed with the empirical cumulative distribution functions derived from the SNP maps as well as with simulated data. The model was used to estimate the heterozygosity pi, and the mean number and size of haplotype blocks for each chromosome. These estimates were consistent with measurements from conventional studies. This PG model thus provides an alternative to Monte Carlo simulation for description of the distribution of SNPs.