[throwaway4585]

>Hierarchies [...] are often found in [natural] systems

Nah they aren't. The 'tree' of life is more of a full-fledged graph and the whole kingdom-order-genus-species thing is muddy and ill-defined. Most of the 'hierarchy' we find in natural systems is just our own projected deformation of much more complex relationships.

[throwaway_pdp09]

Once you get complexity past the ability to do horizontal transission, and past the point where divergent species can no longer interbreed, it pretty much becomes a tree I think. If not, please show me where 2 branches rejoin where there's no H transmission nor mutual fertility.

> the whole kingdom-order-genus-species thing is muddy and ill-defined

Well yes, it's somewhat an arbitrary construct for human convenience, but isn't much of the muddiness down to our limited understanding of the true relationships?

Regarding "cadherin/catenin or how epithelia are formed to see how a tissue is much more than a bundle of cells." could you give a link cos this is so far outside my area I really don't know what to look for (wiki article on Catenin wasn't very revealing of your point, sorry if I missed it)

[Someone]

”past the point where divergent species can no longer interbreed”

Species S may no longer interbreed with species T, but that does not imply they’ve separated completely. There may exist intermediate species U...Z that link them together (https://en.wikipedia.org/wiki/Ring_species)

[klyrs]

> If not, please show me where 2 branches rejoin where there's no H transmission nor mutual fertility.

Viral infections modify host DNA, and can also incorporate host DNA -- this is a mechanism by which lateral gene transfer can occur between macroscopic organisms. The platypus has mammal, reptile and avian DNA, and they seem to have come about long after those branches diverged -- evidence that lateral gene transfers occur between macroscopic organisms.

[contravariant]

To the best of my knowledge the tree of life actually is a tree though. Or are there known cases where two species have merged to create a new species?

Okay I suppose that it becomes a DAG if you zoom into the actual ancestral relations between individual organisms (which is where things become muddy). And I guess the concept of 'species' kind of forces a tree structure upon this DAG (although not exactly, but then the biologists didn't think to use a definition that provably produces a tree, in fact being of the same species isn't even an equivalence relation).

[charlysl]

But how about cells organized into tissues, into organs, into systems? Particles, atoms, molecules?

[throwaway4585]

Again, there's a lot more nuance to this. Look into the rabbit hole of cadherin/catenin or how epithelia are formed to see how a tissue is much more than a bundle of cells.

This hierarchical way of thinking is only designed for humans - because it helps us think more clearly. It's a crutch when you're attempting to learn, but at some point it becomes a hindrance when you want to run.