A while ago I wanted a one word alternative to 'only child' and my friend Hannah discovered monogene for me. The word isn't in my dictionary and doesn't seem to have one clear definition, but being the only begotten child is one alternative. It can also mean unique, special and one of a kind.
Much as I love my brother now, there were times whilst growing up when I'd have preferred to be a monogene. (I can't give examples as he's got as much on me as I have on him!)
Monogenesis is in my dictionary. It refers to the theory that all living things developed from a single cell. Apparently it was a bacteria like thingamy*. Monogeny is an alternative term as is monogenetics.
*sorry for the technical jargon!