"the minimum size of operation (ie number of hives) one should have before they even begin rearing queens... "

There is a huge difference between rearing queens and breeding.  If you want to rear queens all you need is one hive.  If you want to breed queens the number depends greatly on what you are selecting for in your breeding program.  There is great historical data that says 30 or 40 hives is more than enough to breed for better honey production.  In fact I suspect ten is enough.  If you are selecting for or against swarming five or ten is plenty.  If you are going after mite resistance something like 500 or 1000 is likely the minimum unless you are using a DNA driven selection in which case you might get away with 100.  Anyone who thinks there is a single number of hives that answers this question knows nothing about genetics.  But, in skilled hands more is always better and progress will be faster with more.  In my pigeon genetics studies there have been times I raised 50 or more young before I saw the one I needed to see.  And in some cases I got far enough to realize that by simple breeding experiments, without also having DNA sequencing data, it would take thousands of young to stand any chance of answering  some questions.  None the less, back yard pigeon breeders who knew nothing about genetics managed to perform marvels by as a group raising a few hundred thousand young a year.  A fine example is the recently created breed named the racing homer.  Racing homers were created in the last 150 years starting with various breed crosses that would come home from no farther than 25 miles as young birds and 50 miles as yearlings or older.  By the 1950s good old birds would come home from 500 miles in a day.  Today young birds routinely come home from 500 miles in a  day.  Even today a few million homers are lost every single year that fail to come home.  That is where the feral pigeons in the US came from.

Definition: Rearing means simply propagating what you already have.  Breeding means you are propagating with the aim of improving what you already have.

Dick

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