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Why isn’t the mule regarded as a species?

In biology, a species is the basic unit of classification and a taxonomic rank of an organism, as well as a unit of biodiversity. A species is often defined as the largest group of organisms in which any two individuals of the appropriate sexes or mating types can produce fertile offspring, typically by sexual reproduction.

Wikipedia – Species

“I would my horse had the speed of your tongue…”

The mule (the offspring of a male horse and a female donkey) is regarded as a hybrid rather than a species because in most cases they can’t reproduce. It’s the same (in reverse) for hinnies.

They’re not species because the definition of species excludes them. But why is this the definition?

The penny dropped for me yesterday, so please forgive me for pointing out my newly-arrived-at-and-earthshattering-but-probably-obvious revelation: the mule is not a species because their DNA dies with them.

…and so good a continuer.”

The fundamental principle of a species is that, all else being equal*, it can carry on.

*The “all else being equal” clause holds a lot here – like, more or less the entire chain of being.

Other (hybrid) kicks:

Choose What You Want (on the ‘authentic’ watermelon, hybridity and selective breeding)
Cultural Hybridity, Fast and Slow
Whose Dhansak? Food and Authenticity
David Hume on combinatorial innovation and hybridity
Zen Hae on cross-pollination, imitation and innovation in Indonesian Peranakan literature
Hybrids (1) (John Stuart Mill on diversity)
Hybrids (2): combinations and connections (Tim O’Reilly on Combinatorial Innovation)
Hybrids (3): when ideas breed (Kevin Kelly on Combinatorial Innovation)
Technology (16): Clustering Technologies, Clustering People (v2)

I'd love to hear your thoughts and recommended resources...