Quantifying the Rearrangement Complexity of Pangenomes

The study of evolution between species (phylogenetics) and the study of evolution within a species (population genetics) are highly related, as the same biological mechanisms are fundamental to both fields. Although both have been studied for a long time, their joint study in a unified setting has been prevented by the different time scales they consider and the different data types they employ. A similar discrepancy holds for their whole-genome specializations, comparative genomics and pangenomics. Two active areas in these fields are genome rearrangement studies and graphical pangenomics, respectively. Since the emergence of graphical pangenomics, these have existed as separate fields, despite observations that central data structures representing genomic variants in both fields are highly similar. While there exists a wealth of theoretical results for various rearrangement models in comparative genomics, the application to pangenomic data is hampered by the limitations of rearrangement problem formulations. On the practical side, pangenomes typically contain too many individual genomes for classical problems, such as the often NP-hard parsimony problems, to be solved, or for all-vs-all comparisons using rearrangement distances to be performed. On the theoretical side, some assumptions in the formulation of rearrangement problems, such as the assumption of an underlying tree, are inadequate for many pangenomes. In this work, we propose the Complete Ancestral Reconstruction for Pangenomes (CARP) problem, which overcomes these limitations while retaining intuitive relationships to both classical rearrangement problems and pangenome graphs.