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I get the impression that no single method (genetics, morphology, ecology, geography, etc.) trumps the others in taxonomy. For example, Homo sapiens and Homo neanderthalensis interbred successfully and yet are separate species.

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There is no clear definition of "species".

Cladistics can be thought of as k-means clustering in a Hamming space of individual organisms attributes and genetics, I think. A species is a tight cluster, and as you go up towards phyla the clustering becomes more diffuse.

That's more phenetics (clustering by shared similarities) than cladistics. Cladistics needs a hypothesis of shared ancestry.

https://en.wikipedia.org/wiki/Phenetics https://en.wikipedia.org/wiki/Cladistics

That's a definition.

I'm not convinced it's "clear" :)

it's not even a definition, it's a heuristic approximation.

Likely the concept of species can't really be truly defined, but works best as a loose concept for organizing thinking about evolution.

I think some consider it a subspecies Homo sapiens neanderthalensis

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