Constructing founder sets under allelic and non-allelic homologous recombination

Homologous recombination between the maternal and paternal copies of a chromosome is a key mechanism for human inheritance and shapes population genetic properties of our species. However, a similar mechanism can also act between different copies of the same sequence, then called non-allelic homologous recombination (NAHR). This process can result in genomic rearrangements-including deletion, duplication, and inversion-and is underlying many genomic disorders. Despite its importance for genome evolution and disease, there is a lack of computational models to study genomic loci prone to NAHR. In this work, we propose such a computational model, providing a unified framework for both (allelic) homologous recombination and NAHR. Our model represents a set of genomes as a graph, where haplotypes correspond to walks through this graph. We formulate two founder set problems under our recombination model, provide flow-based algorithms for their solution, describe exact methods to characterize the number of recombinations, and demonstrate scalability to problem instances arising in practice.