I'm not the most experienced genetics person here, but with the aid of my trusty Storey's Guide, I think I can help. The short answer is this: The parents could be any of your ducks with the exception that they can't *both* be white.
The long answer:
The black gene is always present in blue and chocolate, and can be present in white. Thus:
* Blue is two black genes (E/E) plus one blue dilution (Bl/bl).
* Chocolate is two black genes (E/E) plus the sex-linked brown dilution (d/
d).
* White can be absolutely anything plus two white genes (c/c): The white completely covers everything, including black. Because it is recessive, it must be present in a double dose in order to express itself--therefore, a duck can carry a single white gene but show no physical evidence of white.
* The bibbed gene is more or less independent of color and just prevents pigmentation in the chest feathers, resulting in a white "bib." It is dominant and therefore will "express" itself regardless of whether one or two bibbed genes are present.
Okay, so... that means that ANY of your drakes could potentially carry a black gene (E) to pass on to offspring, and that your chocolate bibbed drake almost *definitely* carries two black genes (E/E) of which one would certainly be passed to its offspring. It also means that ANY of your hens could carry a black gene to pass to offspring, and that your chocolate bibbed and blue bibbed hens all almost definitely carry two black genes (E/E), of which one would go to the offspring. AND, any of your ducks regardless of their actual bibbed status, could in fact carry bibbed genes.
The upshot of which is, any breeding from your group in which two black genes were passed to the offspring along with either one or two bibbed genes would form the basis for a black duck with a white bib.
Okay, but in order for the black to fully express without chocolate or blue dilution, the baby has to have managed NOT to inherit any dilution genes. This is actually not difficult at all, because any of your white ducks could carry the black without dilution, plus the blue bibbed carries only one blue dilution and therefore could potentially NOT pass it to the offspring. The only difficulty is with your chocolates, who carry the sex-linked brown dilution, which was not inherited by your black duck. However, if your black duck is a female and the father was NOT chocolate, then she couldn't have inherited the brown dilution (because it's sex-linked--has to do with which chromosome it's on, and means a female can only inherit it from her father). But if it *were* the chocolate drake, then the offspring will have inherited it... UNLESS, the chocolate bibbed drake only carries one brown dilution gene, which is not typical in a true chocolate, but considering the addition of the bib there's a fair chance it's picked up "rogue" genes along the way and may carry only a single brown dilution... SOOO...
That was fun. And the upshot: Any of your drakes and any of your hens could produce black offspring, except that they can't BOTH have been white.
My best guess? Blue bibbed hen (because she will carry only one blue dilution gene, even if she's pure blue, and therefore would pass blue dilution on to offspring only half the time) with chocolate bibbed drake (because I'm guessing he's not pure chocolate and carries only one brown dilution, which I personally think is more likely than that your white drake is carrying black under the white).
But really--it's impossible to know without doing extensive breeding to test out the genetic backgrounds of each bird.
So. TMI?
I really love mixing up colors and finding out what will pop out next. I love when you get to second and third generations, not knowing what might lie under the colors, and seeing what pops out--sometimes fun surprises!
Congrats, by the way, on the babies.
