Impossible to create a new subspecies if the homonym variety is already in use

I would say that they are the same nomenclaturally (because of the shared type), but not taxonomically if other infraspecific taxa are recognized. In that case the species rank includes more than one type, while the autonym is based only on one type.

Continuing with my Yucca brevifolia example, one needs a way to say, this plant belongs to the taxon that includes the type of Yucca brevifolia, but excludes the type of Y. brevifolia var. jaegeriana. Having Y. brevifolia var. brevifolia as an option is the only way to say that.

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Hang on, I don’t believe that’s entirely correct. Art 4.2 (Shenzhen Code) gives ranks “in descending sequence”: species, subspecies, variety, subvariety, form, subform (when “sub-” is used to extend the primary ranks species, variety, form), and Art 5.1 states that " The relative order of the ranks specified in Art. 3 and 4 must not be altered".

Art 24.1 provides that the names of infraspecific taxa are no more than trinomial, even if a deeper hierarchy exists (e.g., a variety of a subspecies that does not contain the type of the species).

Since each name is fixed to a type specimen, the question of whether a variety belongs to a particular subspecies, and so on, depends on how one chooses to circumscribe the higher taxon.

I agree that the inability to simultaneously support trinomials of different ranks is technically a bug, but probably not one that’s worth the effort to fix; in my experience, those elaborate infraspecific subdivisions have gone out of fashion, the use of subspecies versus variety being largely a matter of taste within the community.

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I would prefer to strictly follow the nomenclature codes but I wonder if, for the aims and the nature of iNaturalist, it would be preferable to chose to slightly deviate from those rules. Just in order to make the site easier to be used by both users and curators.
In the end, there are notable examples in which it is claimed that quadrinomials are accepted:
http://data.canadensys.net/ipt/resource.do?r=vascan

Oh, you can write a quadrinomial (or deeper), it just isn’t the official “name” as defined in the ICN. (See the example in Art. 24.1.)

If we were sticking purely to code-driven terminology then we wouldn’t have ‘Complex’ as a pseduo-rank. That is a very useful addition so I wouldn’t push for code-adherance. I just like to see clarity when nomenclature enters the discussion.

To clarify the difference with quadrinomials, which has been said earlier, but perhaps easier to grasp with a detailed explanation. Quadrinomials are expressions of classification but they are not names in the formal sense. The taxonomy page on iNat lists the classification … species with a parent genus, with a parent family, and so on up the hierarchy. You don’t write out this string of parent linkages as the ‘name’ of the taxon - it is a statement of classification. Varieties under sub-species are the same kind of classification statement. It can be written as a quadrinomial but nevertheless it is simply a statement of parentage. The same with ‘forma’, and in fungi ‘forma specialis’.