Speciation is defined as the origin of a new species, and the generally accepted definition of a species is defined as a set of individuals who can produce viable, fertile offspring with and only with one another. Donkeys and horses are closely related enough to be able to produce mules, which are unfertile but viable.

Apparently, Humans, Klingons, and Vulcans are at least as closely related as donkeys and horses, because there are instances in Star Trek of viable crosses between both a Human and a Klingon (B'Elanna Torres) and between a Vulcan and a Human (the ever-joyful Mr. Spock). Torres has had a daughter with Tom Paris, a human; I am unsure whether Spock (or other hybrid characters) has ever produced offspring, but the very fact that he is viable suggests a very close genetic relationship between these species, even though they're from different planets and all.

Any one know how the hell this works?

Update, a few minutes later: Apparently, Oslo knows. Here's what he says:
Oslo says re Speciation in Star Trek: I believe a two-part episode in TNG explains this uncanny convergence between species of different planetary origin; A single, super-evolved, highly-intelligent species evolved millions of years in advance of TNG. This species, finding itself alone in the universe, spread its genetic material among several planets, in pieces which could be discovered, combined, and decoded, revealing a message from them to the species who collected the pieces. The message, as I recall, was one of peace, which was ironic since the Klingons thought it was a secret weapon, the Romulans some other kind of secret, etc.
Thanks, Oslo.

Other notes on speciation in Star Trek (thanks m_turner):
The Romulans and the Vulcans split "recently", i.e. after the Vulcans got warp technology. Whether or not this can be called a speciation I don't know, since they can not only produce fertile, viable offspring, but there hasn't been enough time in evolutionary terms to cause any genetic shift. If eventually there is speciation, it will be a classic example of cladogenesis, however. Also, there is, somewhere in the canon, a Klingon-Romulan with whom Worf fell in love, another inter-species hybrid.

Well let's see now.

Examples of cross-species breeding in Star Trek.

First, the quintessential example: Spock. Spock was the son of Ambassador Sarek of Vulcan and Amanda Grayson, a teacher from Earth. As Zaphikel reported, Amanda and Sarek underwent medical procedures in order to conceive. Spock seemed mostly Vulcan, and was raised that way, although he never was able to give up his emotions completely.

Next example is Deanna Troi, the daughter of Ian Andrew Troi, a human, and Lwaxana Troi, a Betazoid. The two had another daughter, Kestra Troi. It's unknown if any special measures were needed for the conceptions to take place, but Betazoids and humans seem similar physiologically. Unlike a full Betazoid, Deanna had only empathic abilities instead of telepathy.

Example three: K'Ehleyr, a half-Klingon, half-human diplomat. Her parentage is unknown, except that her mother was human and her father Klingon.

Example four: Alexander Rozhenko, the son of K'Ehleyr and Worf, and thus a three-quarters Klingon. This doesn't prove much except that K'Ehleyr was fertile without the use of any special medical procedures (since Alexander's conception was accidental).

Worf once met and fell in love with a half-Romulan/half-Klingon, who was conceived and born in a facility where the two species lived in peace. It's unknown whether there was any medical assistance involved.

For my sixth example, when Tasha Yar travelled back in time on the Enterprise-C, she was captured by Romulans and forced to become a Romulan officer's mistress. The relationship produced a daughter, Sela. It seems unlikely the Romulan would have put Tasha through any medical procedures intended to produce a child, so the two were likely compatible genetically. Whether Sela was fertile or not is unknown.

Seventh: Jadzia Dax (a Trill) and Worf attempted to conceive a child but were having difficulty, even with the help of Dr. Julian Bashir. It seems likely that this is due to genetic incompatibility between the two species, since any normal infertility problems should be solvable with 24th-century medicine.

Eighth: B'Elanna Torres is another example of a half-human/half-Klingon who was apparently fertile and able to conceive a child with Thomas Eugene Paris. It's possible that the EMH intervened, but given Torres' personality, I'd consider that unlikely. She barely even wanted the EMH there during the birth; I'm sure she wouldn't have wanted him there for the conception.

Ninth: In an alternate future aboard Voyager, Kes remained aboard and married Paris; their half-Ocampa/half-human daughter Linnis Paris then married Harry Kim; their son Andrew Kim was thus one-quarter Ocampa. As with the Torres-Paris relationship, it's possible the EMH had a role in facilitating these cross-species births, but it's not known for sure.

Last example I have is Charles "Trip" Tucker, who was somehow impregnated by an alien female. However, since it turns out that the baby held none of Trip's genetic material, this is not actually a case of interspecies conception.

What does all this mean? It basically means the writers are not consistent on how cross-species relationships work. Amanda/Sarek and Dax/Worf needed help to produce children; none of the others apparently did, although that is not impossible for any of the pairings (but highly unlikely in the cases of Tasha Yar and Worf/K'Ehleyr).

So, like most things in Star Trek, take it all with a grain of salt.

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