Some help for all beekeepers.
When a colony swarms it will build a number of queen cells over a period of perhaps 6-7 days. Different colonies will build different numbers, varying normally from around 6-30, although it can be very many more. I once helped someone cut 119 queen cells out of a colony that had swarmed. Within a reasonable amount this number will stay the same i.e. if they build 8-10 they will build a similar number next time and the same if it is 25-30. This is a number the colony seems to be comfortable building and is taken at the point of swarming, not several days earlier when not all the queen cells are built. This is known as the Peak Queencell Number or PQN. The only place I have seen it described is in "The Honeybees of the British Isles" by Beowulf Cooper, with a brief reference in "Raise Your Own Queens by the Punched Cell Method" by Richard Smailes.
In my experience the above is usually the case and I don't understand why it is not more widely known. It does have significance in other areas of beekeeping as indicated below.
Swarminess of a colony
I believe the swarminess of a colony is in direct relation to the PQN. The more queen cells a colony will build the more swarmy it is, the less they build the less swarmy it is. I use this knowledge when I'm selecting queen cells or worker larvae when raising queens. I am happy to use queen cells from a colony with a PQN of 10-12, over that and I will only use them if I have nothing else available.
When a queen is removed from a colony the bees will build emergency cells, starting them over a period of several days. The total number built is usually similar to the PQN of a colony. If more than a few queen cells are cut out the colony will usually build more emergency cells, back up to the PQN, if there are worker larvae young enough.
When raising queen cells artificially e.g.grafting or cell punch, the colony is usually reluctant to raise any more queens than their PQN, but this is not always understood by many queen raisers, especially amateurs. In my own case I only put a bar of 10 larvae in a colony. I have tried to put two bars, totalling 20, but the bees don't seem to accept more than about 10-12 larvae. I have no problem with this, but if you are trying to reduce swarming, you won't be able to raise the large numbers of queen cells that you often read about, or see pictures of in books. Numbers of around 60 are often shown, but these are probably in other countries and I suspect the colonies used for cell building are very swarmy.