Duplication and inversion history of a tandemly repeated genes family

Given a phylogenetic tree for a family of tandemly repeated genes and their signed order on the chromosome, we aim to find the minimum number of inversions compatible with an evolutionary history of this family. This is the first attempt to account for inversions in an evolutionary model of tandemly repeated genes. We present a branch-and-bound algorithm that finds the exact solution, and a polynomial-time heuristic based on the breakpoint distance. We show, on simulated data, that those algorithms can be used to improve phylogenetic inference of tandemly repeated gene families. An application on a published phylogeny of KRAB zinc finger genes is presented.