Fig. 1

Application of TDRL ({4,5},{1,2,3},1) to the circular permutation [(1 4 2 5 3)]_∼. The resulting circular permutation is [(4 5 1 2 3)]_∼. The circular permutation [(1 4 2 5 3)]_∼ (respectively [(4 5 1 2 3)]_∼) is represented in (a) by a circular illustrations on the top (respectively bottom) which gives the corresponding representatives when read in clockwise direction. Whereas (a) shows the application of the TDRL by using circular illustrations, (b) illustrates the same application by applying a tandem duplication to the representative π ₁∈[(1 4 2 5 3)]_∼ followed by the subsequent loss of one copy of every duplicated gene. In particular, the elements of F={4,5} are kept in the first copy (illustrated by a bright gray) and the elements of S={1,2,3} are kept in the second copy (illustrated by a dark gray) of the duplicated intermediate. Elements that are lost during this process are crossed out. Permutation τ∘π ₁=(4 5 1 2 3) is a representative of the resulting circular permutation, namely [τ∘π ₁]_∼=[(4 5 1 2 3)]_∼