Requested feature overview description.
Okay so I have no idea how things run behind the scenes, and as such, if this is possible.
The species tags are one of the best things here, but can provide so much information that it's hard to sift through. So for example, a post with three characters might have the following species tags

capreoline
cervid
domestic_rabbit
gastropoda
lagomorph
leporid
mammal
mollusk
oryctolagus
rabbit
reindeer
snail

But if there were a way to nest tags under tags that imply them, it could look like this

mammal
^cervid
 ^capreoline
  ^reindeer
^lagomorph
 ^leporid
  ^rabbit
   ^oryctolagus
    ^domestic_rabbit
mollusk
^gastropod
 ^snail

I will say, I do recognize that this could get ugly for species with very well-defined tag hierarchies, like golden_retriever siting under eight other tags.
Why would it be useful?
It would make the identification of individual species much easier, especially in images containing multiple different species. It would also make browsing by species more convenient by making the hierarchy clear, e.g. making it easier to identify the next step up to browse related species. Also, a bit of added consistency as the species wiki pages already list the tags this way.

What part(s) of the site page(s) are affected?
The species tags section on individual posts

This might be possible on the client side, but it might be a herculean task too.

Here's the post you're referencing: post #3092272

I feel like a hierarchy could be useful for browsing tags in general, especially for posts that have a lot of implicated tags. e.g. tag_panic, absolutely_everyone, a bunch of different coloured body parts, etc.
It will declutter the listing, which might also help bring more unique search tags to the users' attention, since tags that don't get nested should be separate alongside the many parents.
On the other hand, it'd make figuring out what tags are missing a bit harder, since it obfuscates the children. Minor inconvenience; fixed by an ability to switch between a hierarchy and the classic list.

As for implementation, it's probably achievable using the existing tag implications, at least to a certain degree: Just force a tag which is deemed (by mods) a "parent" to pull all implied tags into a viewing tree.
Another issue might be how to handle when a single tags is implied by multiple parents. Does it get nested multiple times? Not nested at all? Or do mods have precise control over which parent gets it?

All that sad, I don't believe ’tis high on their front-end priority list. It's a (really) good and interesting feature, but not essential.

I also think it would be a helpful feature for cleaning up tags, that imply lots of others.
e.g.:
gynomorph_penetrating_gynomorph
├ gynomorph_penetrated
│.├ gynomorph
│.│.└ intersex
│.└ intersex_penetrated
│...├ intersex
│...└ penetration
├ gynomorph_penetrating
│.├ gynomorph
│.│└ intersex
│.└ intersex_penetrating
│...├ intersex
│...└ penetration
├ gynomorph/gynomorph
│.├ gynomorph
│.│└ intersex
│.└ intersex/intersex
│...└ intersex
└ intersex_penetrating_intersex
...├ intersex/intersex
...│└ intersex
...├ intersex_penetrating
...│├ intersex
...│└ penetration
...└ intersex_penetrated
.....├ intersex
.....└ penetration

^{_{(Sorry for the stupid dots. Without them, it collapsed for some reason)}}

And if it was collapsible, it wouldn't overfill the tag section, but look completely normal.

I really like the idea of this in general, honestly, especially if it's collapsible. It alleviates the "tag bloat" issue without outright getting rid of more specific tags. Sorry to bump this thread a year later, I just really like this suggestion.

personally I think the tree idea is strictly speaking correct, but you can see from Dubs post that displaying it that way would in some cases be more verbose (or else you would need to use some kind of backreference system like footnotes)

Another idea which could be less verbose is to divide tags into leaf, branch, and disconnected. That is, 1. those which do not imply other tag(s), 2. those which do, and 3. those which neither imply nor are implicated by any other tag. I make no particular claim about the usefulness of this, but IMO it would be easier to hack together something client-side for this than for a full on tree.

Yeah as a client-side userscript I think would be better than trying to make it into the site, and in case of worry towards visual clutter, there could just be a button or shortcut to collapse trees