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Indeed they are. I'm saying it may not be the right context in this case.

At least what they seem to be doing has little to do with metrics, and a lot more to do with probability distributions.

It's not clear what you're seeking. Probabilities appear because the magnitude of a space is a way of 'measuring' it -- and thus magnitude is closely related to entropy. Of course, you can follow your nose and find your way beyond mere spaces, and this may lead you to the notion of 'magnitude homology' [1]. But it's not clear that this generalization is the best way to introduce the idea of magnitude to ecology.

[1] https://arxiv.org/abs/1711.00802

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