Combinatorial Reconstruction of Sibling Groups

Knowledge about sibling relationships is used in genetic epidemiology, conservation biology, and animal management. For example, knowledge of the genetic relationships among individuals is critical for estimating heritabilities of quantitative characters, for characterizing mating systems and fitness, and for managing populations of endangered species. When parental data are available, sibling groups can be established through parentage assignments (e.g., [3]). Assignment of individuals to full or half sibling groups in the absence of parental data is more challenging, however, it is often more practical. In recent years, there has been an explosion of methods that reconstruct sibling relationships without the parental data [1]. We propose the first fully combinatorial optimization approach to reconstructing sibling groups based on single generation genetic data with no parental information. We use the Mendelian inheritance rules to impose constraints on the genetic content possibilities of a sibling group. We formulate the inferred combinatorial constraints and use a provably correct algorithm to construct the smallest number of groups of individuals that satisfy these constraints. Our algorithm allows half-sibling relationships to exist in the population. The algorithm requires no prior knowledge about the allele frequency, number of loci sampled, mating system, or the size of the family groups. It can be easily extended to incorporate null-allele type errors. To assess the accuracy of our approach, we use a weaker (but computationally cheaper) version of our algorithm on simulated data that has known parents and, therefore, sibling groups.