Computational Problems in Perfect Phylogeny Haplotyping: Xor-Genotypes and Tag SNPs

The perfect phylogeny model for haplotype evolution has been successfully applied to haplotype resolution from genotype data. In this study we explore the application of the perfect phylogeny model to other problems in the design and analysis of genetic studies. We consider a novel type of data, xor-genotypes, which distinguish heterozygote from homozygote sites but do not identify the homozygote alleles. We show how to resolve xor-genotypes under perfect phylogeny model, and study the degrees of freedom in such resolutions. Interestingly, given xor-genotypes that produce a single possible resolution, we show that the full genotype of at most three individuals suffice in order to determine all haplotypes across the phylogeny. Our experiments with xor-genotyping data indicate that the approach requires a number of individuals only slightly larger than full genotyping, at a potentially reduced typing cost. We also consider selection of minimum-cost sets of tag SNPs, i.e., polymorphisms whose alleles suffice to recover the haplotype diversity. We show that this problem lends itself to divide-and-conquer linear-time solution. Finally, we study genotype tags, i.e., genotype calls that suffice to recover the alleles of all other SNPs. Since most genetic studies are genotype-based, such tags are more relevant in such studies than the haplotype tags. We show that under the perfect phylogeny model a SNP subset of haplotype tags, as it is usually defined, tags the haplotypes by genotype calls as well.