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Popular methods for exploring the space of rooted phylogenetic trees userearrangement moves such as rNNI (rooted Nearest Neighbour Interchange) andrSPR (rooted Subtree Prune and Regraft). Recently, these moves were generalizedto rooted phylogenetic networks, which are a more suitable representation ofreticulate evolutionary histories, and it was shown that any two rootedphylogenetic networks of the same complexity are connected by a sequence ofeither rSPR or rNNI moves. Here, we show that this is possible using only tailmoves, which are a restricted version of rSPR moves on networks that are moreclosely related to rSPR moves on trees. The connectedness still holds even whenwe restrict to distance-1 tail moves (a localized version of tail-moves).Moreover, we give bounds on the number of (distance-1) tail moves necessary toturn one network into another, which in turn yield new bounds for rSPR, rNNIand SPR (i.e. the equivalent of rSPR on unrooted networks). The upper boundsare constructive, meaning that we can actually find a sequence with at mostthis length for any pair of networks. Finally, we show that finding a shortestsequence of tail or rSPR moves is NP-hard.

Exploring the tiers of rooted phylogenetic network space using tail moves