should be replaced by Alyssum gmelinii,
see AlyBase https://alysseae.sav.sk/checklists/detail/335 It will help to avoid confusion with A. montanum (different geographic distribution and morphology), see e.g. https://doi.org/10.12705/633.18 and https://doi.org/10.1093/botlinnean/box039

I have contacted POWO. Alyssum gmelinii is now listed as an accepted name in POWO (with Alyssum montanum subsp. gmelinii as a synonym). Please swap the names.

Thank you. But is it possible to move all the observations listed under Alyssum montanum subsp. gmelinii to Alyssum gmelinii in one go (and include Alyssum montanum gmelinii as a synonym of Alyssum gmelinii)? Because both taxa are now treated as accepted in iNat.

Yes, Alyssum montanum montanum should be swaped into Alyssum montanum sensu stricto. Thank you.

I am not familiar with the technical procedure, but I think that moving the name Alyssum montanum subsp. gmelinii into Alyssum gmelinii is sufficient (so that the name is automatically replaced in all observations identified as subsp. gmelinii). As for the split, I propose to split Alyssum montanum in accordance with the current identifications. This means: observations identified as A. montanum subsp. gmelinii will be moved to A. gmelinii, all other observations will remain with Alyssum montanum (the name Alyssum montanum subsp. montanum is no longer necessary). People will continue to make errors in identification, I will continue to revise the identifications according to current knowledge.

Thank you for your assistence. The name Alyssum montanum has been used with different meanings in different parts of Europe, Asia and North Africa. I think that all the necessary changes to Alyssum montanum (some merges and some splits) in iNaturalist (and in POWO) cannot be done in one step, as the patterns of geographical distribution are quite complicated. Some important (but not all) findings: Alyssum montanum sensu stricto occurs only in France, Switzerland and southwestern Germany. A. gmelinii occurs in the rest of Germany, major part of Central Europe and in E Europe, see. The Iberian populations are A. fastigiatum (but not all, see the maps in http://dx.doi.org/10.12705/633.18 and https://doi.org/10.1093/evolut/qpad035 ). In the Balkans there are several different taxa instead of Alyssum montanum, see the maps in https://doi.org/10.1007/s00606-017-1468-x and https://doi.org/10.1007/s00606-017-1470-3. The populations in the Apennine Peninsula and SW Alps include A. diffusum, A. orophilum and A. cognense, see https://doi.org/10.3732/ajb.1100147 and https://doi.org/10.1093/botlinnean/boac041. Therefore, the first step (one of many) that I have proposed in this iNat flag is the complete removal of subsp. gmelinii from A. montanum. Further steps will follow and will be discussed with iNat and POWO on an ongoing basis.

I do not think this is a good idea. It would take us back to 20 years ago when everything was called Alyssum montanum (complex, aggregate or simply A. montanum). If you think it is necessary, then I would strongly recommend to use the term "Alyssum montanum–A. repens complex" instead of "Alyssum montanum complex" if that is an option. It is more universal and is used in all of our published articles. Otherwise, I fear that people will refrain from distinguishing between Alyssum montanum s.str. and other genetically distinct taxa (which admittedly are sometimes morphologically very similar, but many times clearly different and geographically limited). I think it is important to establish the use of all these other names in different regions for biodiversity conservation efforts.