Set covering approach for reconstruction of sibling relationships

A new combinatorial approach for modeling and reconstructing sibling relationships in a single generation of individuals without parental information is proposed in this paper. Simple genetic constraints on the full-sibling groups, imposed by the Mendelian inheritance rules, are employed to investigate data from codominant DNA markers. To extract the minimum number of biologically consistent sibling groups, the proposed combinatorial approach is employed to formulate this minimization problem as a set covering problem, which is a well-known NP-hard combinatorial optimization problem. We conducted a simulation study of a relaxed version of the proposed algorithm to demonstrate that our combinatorial approach is reasonably accurate and the exact version of the sibling relationship construction algorithm should be pursued. In addition, the results of this study suggest that the proposed algorithm will pave our way to a new approach in computational population genetics as it does not require any a priori knowledge about allele frequency, population size, mating system, or family size distributions to reconstruct sibling relationships.