A new method to reconstruct the direction of parent-offspring duo relationships using SNP array data and its demonstration on ancient and modern cultivars in the outcrossing species Malus × domestica

Unordered parent-offspring (PO) relationships are an outstanding issue in pedigree reconstruction studies. Resolution of the order of these relationships would expand the results, conclusions, and usefulness of such studies; however, no such PO order resolution (POR) tests currently exist. This study describes two such tests, demonstrated using SNP array data in the outcrossing species apple (Malus × domestica) on a PO relationship of known order ('Keepsake' as a parent of 'Honeycrisp') and two PO relationships previously ordered only via provenance information. The first test, POR-1, tests whether some of the extended haplotypes deduced from homozygous SNP calls from one individual in an unordered PO duo are composed of recombinant haplotypes from accurately phased SNP genotypes from the second individual. If so, the first individual would be the offspring of the second individual, otherwise the opposite relationship would be present. The second test, POR-2, does not require phased SNP genotypes and uses similar logic as the POR-1 test, albeit in a different approach. The POR-1 and POR-2 tests determined the correct relationship between 'Keepsake' and 'Honeycrisp'. The POR-2 test confirmed 'Reinette Franche' as a parent of 'Nonpareil' and 'Brabant Bellefleur' as a parent of 'Court Pendu Plat'. The latter finding conflicted with the recorded provenance information, demonstrating the need for these tests. The successful demonstration of these tests suggests they can add insights to future pedigree reconstruction studies, though caveats, like extreme inbreeding or selfing, would need to be considered where relevant.