Column-Generation Framework of Nonlinear Similarity Model for Reconstructing Sibling Groups

Establishing family relationships, such as parentage and sibling relationships, can be extremely important in biological research, especially in wild species, as they are often key to understanding evolutionary, ecological, and behavioral processes. Because it is often not possible to determine familial relationships from field observations alone, the reconstruction of sibling relationships often depends on informative genetic markers coupled with accurate sibling reconstruction algorithms. Most studies in the literature reconstruct sibling relationships using methods that are based on either statistical analyses (i.e., likelihood estimation) or combinatorial concepts (i.e., Mendelian inheritance laws) of genetic data. In this paper we present a novel computational framework that integrates both combinatorial concepts and statistical analyses into one sibling reconstruction optimization model. To solve this integrated optimization model, we propose a column generation approach with a branch-and-price method. Under the assumption of parsimonious reconstruction, the master problem is to find the minimum set of sibling groups to cover the tested population. Pricing subproblems, which include both statistical similarity and combinatorial concepts of genetic data, are iteratively solved to generate high-quality sibling group candidates. Tested on real biological datasets, our approach is shown to efficiently provide reconstruction results that are more accurate than the ones provided by other state-of-the-art reconstruction algorithms in the literature.