Motivation: Autopolyploidization and allopolyploidization events multiply the number of chromosomes and genomic content. Genome rearrangement phylogenetics requires that all genomes analyzed have the same set of orthologs, so that it is not possible to include diploid and polyploid genomes in the same phylogeny.
Results: We propose a framework for solving this difficulty by integrating the rearrangement median and genome halving algorithms. Though the framework is general, some problems remain open. We implement a heuristic solution to the prototypical case of a tree with one tetraploid and two diploid genomes, and apply it to study the evolution of cereals and of yeast.