An algebraic model for inversion and deletion in bacterial genome rearrangement

Chad Clark*, Julius Jonušas, James D. Mitchell, Andrew Francis

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Inversions, also sometimes called reversals, are a major contributor to variation among bacterial genomes, with studies suggesting that those involving small numbers of regions are more likely than larger inversions. Deletions may arise in bacterial genomes through the same biological mechanism as inversions, and hence a model that incorporates both is desirable. However, while inversion distances between genomes have been well studied, there has yet to be a model which accounts for the combination of both deletions and inversions. To account for both of these operations, we introduce an algebraic model that utilises partial permutations. This leads to an algorithm for calculating the minimum distance to the most recent common ancestor of two bacterial genomes evolving by inversions (of adjacent regions) and deletions. The algebraic model makes the existing short inversion models more complete and realistic by including deletions, and also introduces new algebraic tools into evolutionary distance problems.
Original languageEnglish
Article number34
Number of pages23
JournalJournal of Mathematical Biology
Issue number2
Early online date30 Jul 2023
Publication statusPublished - 1 Aug 2023


  • Inversion
  • Distance
  • Bacterial genomics
  • Partial permutation
  • Phylogenetics
  • Deletion


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