A genotype likelihood function for DNA mixtures

The recent advent of genetic genealogy has brought about a renewed interest in genome-scale forensic analyses, of which kinship estimation is a critical component. Most genomic kinship estimators consider SNPs (single nucleotide polymorphisms), often leveraging the co-inheritance of shared alleles to inform their analyses. While current estimators cannot directly evaluate mixed samples, there exist well-established SNP-based kinship estimators tailored to considering challenged samples, including low-pass whole genome sequencing. As an example, several studies have shown remarkable success in imputing genotype posterior probabilities in low template samples when linked sites are considered. Critical to these approaches is the ability to account for genotype uncertainty; the lack of an expression for a genotype likelihood in imbalanced mixtures has prevented direct application. This work develops such an expression. The formulation is fully compatible with genotype imputation software, suggesting a genomic pipeline that estimates genotype likelihoods, performs imputation, and then estimates kinship when the sample is a mixture. Further, when framed as an imbalanced mixture, the problem of mixture deconvolution is reducible to the problem of genotyping mixed samples. Herein, the ability to genotype two-person mixtures is assessed through example and in silico settings. While certain mixture scenarios and classes of sites are inherently inseparable, simulations of read depths between 60 and 190 appear to produce likelihoods of sufficient magnitude to deconvolve two-person mixtures whenever the mixture fraction is moderately imbalanced. The described approach and results suggest a path forward for estimating the kinship coefficient (and similar inferences on relatedness) when the sample is a mixture.