HGTs are not SPRs: In the presence of ghost lineages, series of Horizontal Gene Transfers do not result in series of Subtree Pruning and Regrafting

When a gene is horizontally transferred (HGT), under the "replacement" model where the transferred gene replaces its homolog in the recipient genome, the corresponding gene phylogeny departs from the species phylogeny by a Subtree Prune and Regraft (SPR) operation: the "recipient branch" is moved from its initial position to attach to the "donor branch". Based on this observation, various methods have used SPRs to infer HGTs. We examine this apparent equivalence in the light of ghost lineages, i.e. related species absent from the phylogeny because they are extinct, unknown or have not been sampled. In this case an SPR is not directly interpretable by an HGT from the donor branch, because HGTs can have ghost lineages as donors. A possible and frequent interpretation - that we call "induced HGT" - is that the transferred gene leaves the sampled phylogeny for a ghost lineage at the donor branch, and is transferred back from a ghost lineage at the recipient branch. We show by simulations that this interpretation is misleading in a significant number of cases. For instance if the studied phylogeny represents 1% of all the species susceptible to exchange genetic material with the 100 sampled species, and 11 transfers occurred, then SPRs do not correspond to induced HGTs in around 50% of the cases. This leaves the question of a coherent interpretation of SPR in the presence of ghosts open, and applies to a certain extent to other phylogenetic simulation or inference methods of HGT, like reconciliation, or phylogenetic networks.