Integer programming for selecting set of informative markers in paternity inference

Background Parentage information is fundamental to various life sciences. Recent advances in sequencing technologies have made it possible to accurately infer parentage even in non-model species. The optimization of sets of genome-wide markers is valuable for cost-effective applications but requires extremely large amounts of computation, which presses for the development of new efficient algorithms. Results Here, for a closed half-sib population, we generalized the process of marker loci selection as a binary integer programming problem. The proposed systematic formulation considered marker localization and the family structure of the potential parental population, resulting in an accurate assignment with a small set of markers. We also proposed an efficient heuristic approach, which effectively improved the number of markers, localization, and tolerance to missing data of the set. Applying this method to the actual genotypes of apple ( Malus × domestica ) germplasm, we identified a set of 34 SNP markers that distinguished 300 potential parents crossed to a particular cultivar with a greater than 99% accuracy. Conclusions We present a novel approach for selecting informative markers based on binary integer programming. Since the data generated by high-throughput sequencing technology far exceeds the requirement for parentage assignment, a combination of the systematic marker selection with targeted SNP genotyping, such as KASP, allows flexibly enlarging the analysis up to a scale that has been unrealistic in various species. The method developed in this study can be directly applied to unsolved large-scale problems in breeding, reproduction, and ecological research, and is expected to lead to novel knowledge in various biological fields. The implementation is available at https://github.com/SoNishiyama/IP-SIMPAT .