Wow, all of this is really fascinating. I read/skimmed over all the references you posted, Phillip. I'll just sort of rewrite all this in my own words both for my understanding and hopefully for yours as well. As always, someone please correct me if I say something incorrect. Van was posting as I was typing, so I apologize if this ends up being a retread of what he said.
So first, a brief review of what normally happens in European honey bees. All hymenopterans (that's bees, wasps, and ants) are haplodiploid, meaning the way that gender is determined is by how many sets of chromosomes (the actual strands of DNA) the individual's cells have. Drones are haploid; they have one set of 16 chromosomes. Workers and queens are diploid; they have 2 sets of 16 chromosomes, or 32 total.
In the queen's reproductive system, cells undergo a special type of division called meiosis to produce eggs. The eggs, you see, need to be haploid, so that when combined with a haploid sperm, the resulting bee will be diploid, and therefore female. However, if the queen does not fertilize an egg, the resulting bee is haploid, and therefore a drone. Here's a flow chart, if you are a visual learner.
The worker bees have ovaries just like queens, but they are kept from functioning by the queen pheromone, which suppresses their development. If a worker bee isn't getting enough queen pheromone, either because the hive is queenless or by happenstance, her ovaries will develop and she will begin producing eggs. However she has of course never mated, so she can only produce haploid eggs, which will be drones, since she doesn't have any sperm to combine with the eggs to make them diploid.
However, once in a very great while, something strange will happen. When a laying worker's reproductive cells are undergoing meiosis to produce eggs, sometimes the haploid proto-eggs (if you will) combine to form diploid eggs. Since this "accident" creates a diploid egg, it will develop into a female, since in honey bees, being diploid means you are a female. If the workers feed the larva only royal jelly, she will of course turn into a queen, just like any other female egg/larva would. The process of an unfertilized egg creating a female is called thelytoky, and this type of thelytoky is called automixis. Again, here is a flow chart.
The Cape honey bees are an interesting case study here, because for Cape honey bees, this isn't a once-in-a-great-while occurance; it happens all the time. Cape honey bees regularly produce queens from laying workers when the hive goes queenless, and this has led them to become parasites of sorts of the African honey bees where their ranges overlap. The Cape honey bee laying workers will enter nests of African honey bees, and lay eggs which can develop into Cape honey bees queens, thus turning the hive from an African honey bee nest into a Cape honey bee nest.
