SNP Based Parentage Verification via Constraint Non-Linear Optimisation

Abstract

Since the introduction of parentage verification by molecular markers this technique is based mainly on short tandem repeat markers (STR). With the advent of single nucleotide polymorphism (SNP), advances in genotyping technologies and decreasing costs, SNPs have become the marker of choice for genotyping projects. This is because the genotypes have a wide range of applications and imputation technologies provide well a developed compatibility layer between different types of SNP genotypes. Thus, the subsequent step is to use SNP genotypes for parentage verification as well. However, algorithms for parentage verification mostly date back to the STR era, and recent developments of SNP based algorithms such as evaluating opposing homozygosity have drawbacks, for example the inability of rejecting all animals of a sample of potential parents. This paper describes an algorithm for parentage verification via non-linear optimisation which overcomes the latter limitations and proofs to be very fast and highly accurate even with number of SNPs as low as 100. The algorithm was tested on a sample of 90 animals with 100, 500 and 40k SNP genotypes. These animals were evaluated against a pool of 12 putative parents containing random animals only, random animals and the true dam, and random animals, the true dam and the true sire. Assignment quality of the algorithm was evaluated by the power of assignment (Pa , probability of picking the true parent when true parent was among the putative parents) and the power of exclusion (Pe, probability of rejecting all parents if the true parent was not among the putative parents). When used with 40k genotypes, the algorithm assigned parentage correctly for all 90 test animals. That is, if one or both parents were among the putative parents they were correctly identified. If both were absent parentage was ruled out for the whole set of putative parents. A similar result was achieved when shrinking the genotypes to 500 randomly selected SNP, with Pe = 0.99 and Pa = 1. When only 100 SNP, randomly selected but the sample space narrowed by the minor allele frequency >0.3, were used, Pe and Pa were still 0.99 and 0.96, respectively. The described method is an easy to implement, fast and accurate algorithm to assign parentage using genomic marker data of size as low as 100 SNP. It overcomes limitation of methods such as evaluation of opposing homozygosity by not relying on the presence of a true parent in the pool of putative parents.